Treatise on the Biblical Calendar by Herb Solinsky
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February 7, 2007
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Treatise on the Biblical Calendar, first edition (abbreviated TBC1)
by Herb Solinsky
February 7, 2007
[1] Preface
[2] Goals of this Study and the applied Philosophy to attain these Goals
[3] Cognate Words in Ancient Semitic Languages to aide Hebrew
[4] Disguised Confusing Footnote in the Brown-Driver-Briggs Lexicon
[5] Introduction to Ancient Calendars and Ancient Astronomy
[6] Ellipses and Orbits of Heavenly Bodies
[7] Astronomical New Moon (Conjunction) and Full Moon
[8] Variation from Astronomical New Moon to Full Moon; Variation from
New Crescent to Full Moon
[9] Ancient Meaning of the Full Moon
[10] When in History did Prediction of the Astronomical New Moon Begin?
[11] Transmission of Babylonian Astrology-Astronomy to other Peoples
[12] Egyptian Astronomical Science before Alexander the Great
[13] Did Ancient Israel Excel in Advanced Mathematical Astronomy?
[14] Did Abraham teach Mathematical Astronomy to the Egyptians?
[15] Appointed-times and Years are known from Lights in the Sky
[16] A Month is a Cycle of the Moon
[17] Full Moon occurs about the 14th and 15th Days of the Biblical Month
[18] A Biblical Month is a Whole Number of Days
[19] A Biblical Month has a Maximum of 30 Days
[20] The Sun and Moon are the Primary Lights in Gen 1:14
[21] Blowing two Silver Trumpets on the Day that Begins each Month
[22] Hebrew chodesh refers to the Day that Begins each Month
[23] The Biblical New Moon relates to the Sighting of the New Crescent
[24] Philo of Alexandria and the Jewish New Moon in the First Century
[25] Did the Jews use Calculation for their Calendar in the First Century?
[26] The Biblical Year is a Whole number of Biblical Months
[27] The Beginning of the Month and I Samuel 20
[28] Applying I Sam 20 to II Kings 4:23 and Amos 8:5
[29] Rapid Communication to inform the Nation about the New Moon
[30] Summary about the New Moon Celebration and the Role of the
Daytime
[31] Today’s Ambiguity in the Phrase New Moon
[32] Biblical View of the Sun's Yearly Motion is South - North
[33] The South - North Yearly Cycle indicated in Eccl 1:6A
[34] Equinox and Solstice is in the Bible
[35] Equal Daytime and Nighttime is Not the Biblical Equinox
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[36] The Vernal Equinox and Ex 12:2
[37] Karl Schoch’s Curve for Predicting Visibility of the New Crescent
[38] Ezra and Nehemiah in Relation to the Vernal Equinox and the
Babylonian Calendar
[39] Nisan and the Jews at Elephantine, Egypt
[40] Gen 1:14; Ezra 6:15; Neh 6:15 Show the Vernal Equinox Starts the
Year
[41] Philo explains when the First Month of the Biblical Year begins
[42] Declaration of the Vernal Equinox in Ancient Israel
[43] The International Date Line, the Sabbath, and the New Moon
[44] How the MCJC achieves Spiritual Unity using the IDL
[45] Avoiding Confusion (I Cor 14:33)
[46] Dwelling in Spiritual Unity Through the Declaration of the Priesthood
[47] Does Deut 16:1 Command Everyone to Look for the New-Moon?
[48] Ancient Israel did not Practice Local Visibility
[49] Confusion of a Difference of a Whole Month in the Calendar
[50] The Role of the Land of Israel
[51] The Boundary of Israel
[52] The law will go forth from Zion - Isaiah 2:3 and Micah 4:2
[53] Two Days for the Start of the Seventh Month
[54] What if the Whole Earth may Sight the Crescent to start the Month?
[55] The Ancient Situation Outside of Israel
[56] Modern Technology makes a difference
[57] Num 10:10 Avoids Confusion
[58] Differences between the Sabbath and the New Moon
[59] Does the priesthood of all saints (I Pet 2:9) change the calendar?
[60] Historical Evidence for Sighting the New Crescent
[61] Should only Jerusalem be used to Sight the New Crescent?
[62] Starting the Month when it comes to you
[63] Actual Sighting from Israel Today
[64] The Process of Declaring the New Moon
[65] Two Web Sites with New Crescent Reports from Israel
[66] Appendix A: Nisanu 1 in the Babylonian Calendar Compared to the
Vernal Equinox during the Century of Ezra and Nehemiah
[67] Bibliography
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[1] Preface
This is the first edition of this new treatise on the biblical calendar. It does
not presuppose that the reader is already familiar with various aspects of the
biblical calendar. It begins with the most basic matters and gradually fills in
the details in an orderly fashion, never requiring the reader to know
something that will be explained later. The main companion to this is a
literal Bible translation and a concordance with Strong’s numbers.
It is anticipated that eventually other related topics will be added in
subsequent editions. In recent months I have been gathering my varied notes
into this unified whole for the occasion of the unusual event toward the end
of March 20, 2007, namely, the expected appearance of the new crescent
over Israel, and subsequently, several hours later, the astronomer’s
calculated moment of the vernal equinox. The immediate purpose of this
treatise is to cover sufficient details of the biblical calendar, so that this
unusual event may be judged by the reader according to the evidence
presented. The evidence presented will show that March 21 is both the new
moon day and the day of the vernal equinox, so that March 21 is the first day
of the first month.
For those readers who already have significant knowledge of the biblical
calendar and desire a summary of how the conclusion is attained, I will now
refer to the chapter numbers. Chapters [10] through [14] are important for
some conclusions that have a bearing on the whole matter. Here the key is
the lack of mathematical astronomy by ancient Israel. Chapters [21], [25],
and [27] through [30] relates to the observational process and the
communication process that pertains to the day of the new moon and its
practical dissemination in ancient Israel. Next see chapters [35] and [36] for
the biblical understanding of the vernal equinox. Chapters [38] and appendix
A go together, and these are very critical in the whole effort to understand
the relationship between the day of the vernal equinox and the first day of
the first month in the Babylonian calendar. Chapter [41] is very important to
see the corroboration of chapter [38] from a first century witness. Finally,
chapter [42] ties together all the parts and gives separate evidence
independent of the detailed computer calculations in the appendix. People
who distrust computers should easily see the simple logic here. If the very
knowledgeable reader desires to see the final summary in a nutshell, just go
to chapter [42] and also to appendix A.
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I grew up in New York City and was the son of Jewish parents, who sent me
to a Hebrew school after public school hours for six years. The highlight of
this training was learning elementary biblical Hebrew. In adulthood I earned
an M.S. degree in Mathematics from the University of Arizona. My
profession is software engineering. This background served me well in later
biblical, astronomical, and calendaric studies.
The order of presenting the subject is critical to aide in logical reasoning and
especially to avoid circular reasoning. I avoid writing anything that uses a
result that is claimed to be proved later, because that approach can lead to
circular reasoning. An appendix that is focused on a single self-contained
technical topic may be read at the time it is first mentioned in the body of the
text, and is therefore not considered to violate the concept of proceeding in a
logical order without resorting to conclusions based upon what is written
later.
The meanings of certain Hebrew words in the Bible are especially
significant for an understanding of the biblical calendar. Archaeological
discoveries concerning ancient Semitic languages were achieved in the 19th
and 20th centuries, which are important toward recovering the meanings of
certain Hebrew words. One chapter is devoted to this in order to explain the
reason for the importance of ancient Semitic languages.
[2] Goals of this Study and the applied Philosophy to attain these Goals
There are two broad and primary goals of this study. The first is to discover
the nature of the calendar that was used by ancient Israel, i.e., the biblical
calendar. The second is to expound a procedure that may be applied in
today’s society by which this calendar (or one especially “close” to it) may
be used.
The modern calculated Jewish calendar will be abbreviated MCJC. If one
considers it worthwhile to replace the MCJC with another calendar, that
would only make sense if the proposed replacement was based upon the
same principles as the calendar used by ancient Israel, i.e., the biblical
calendar. The second requirement for replacing the MCJC is to expound a
procedure that may be applied in today's society by which this calendar may
be used.
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It is important to have a clear stated philosophy of the guiding principles that
are to be used to develop a procedure to apply the calendar that was used by
ancient Israel. The philosophy used in this study is now presented in the
order of the priority of the philosophical principles.
(A) The Biblical Model. If the same illustrative astronomical positions and
other conditions that occur today were also to have prevailed in ancient
times, the decision or conclusion to be determined today should agree as
much as possible with the ancient decision in Israel relating to the calendar.
The MCJC is weak in this respect, especially because the principles in its
calculation do not closely approximate the consistent reality of astronomy. If
this biblical model is not given the highest priority in the calendaric
procedure, then the procedure will be open to the same criticism as the
MCJC and will have no advantage over the MCJC.
(B) Avoiding Arbitrary Rules. The proposed procedure should embody a
minimum number of subjective rules with an arbitrary decision. The MCJC
is weak in this respect because there are many arbitrary rules related to the
calculation as well as to the final decision. If this point is violated, then the
proposed procedure is justly open to the criticism that it is a relatively
fictitious calendar, i.e., it is has modern invented rules, and is therefore
inherently no better than the MCJC. The criticism of adopting a fictional
calendar having subjective and arbitrary rules is a serious one.
(C) Spiritual Unity. The proposed procedure should resolve disputes over
the date for the festivals in any area of the world, so that if people desire to
attend a festival together, then they should arrive at the same date for the
holy convocations. This does not require or imply organizational unity of
those in attendance; instead, it implies spiritual unity that crosses
organizational boundaries. Spiritual unity does not imply doctrinal unity on
nearly all subjects, but it does imply a spirit of tolerance and peace. While it
is possible for people to meet together for a festival of tabernacles for which
all of their dates only agree upon six of the eight days, that is far from ideal
because there is a loss of 25 percent of the feast in full togetherness. Even if
some people plan to stay extra days beyond those that they personally
consider to be holy convocations, they are likely to avoid certain group
activities that conflict with their dates of holy convocation.
There is much in Scripture to support spiritual unity, and at the appropriate
place this will be discussed in some detail.
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[3] Cognate Words in Ancient Semitic Languages to aide Hebrew
The Bible is the ancient texts of Scripture in its original languages. But
unless we can know the ancient meanings of all the words and expressions
found in these ancient texts of Scripture, our understanding of the Bible will
have limitations. Let us consider how the Hebrew language came to be the
language of the Hebrew Scriptures.
About 1900 BCE Abraham left Ur of the Chaldeans to go to the land of
Canaan (Gen 11:31; 15:7). This area was about 450 miles northeast of
Jerusalem. Gary Rendsburg wrote on page 116 “… Abraham’s Ur should be
identified with modern Urfa in southern Turkey (near Harran), which not
only accords with local Jewish and Muslim tradition, but truly is ‘beyond the
River,’ to use the biblical expression [Josh 24:2].” Maps in most Bibles do
not show Ur near Harran where is ought to be. Ur is in a region for which
Akkadian was the ancient Semitic language. Abraham, Lot, and their
servants with their families brought this primary language of the Middle East
with them, but Isaac, Jacob, and his sons’ families lived in Canaan where
they were a tiny minority in the midst of the Canaanites who did not speak
Akkadian. In order to converse with their more numerous neighbors, these
descendants of the original group with Abraham had to learn the local
language of the Canaanites, and over time it should be expected that their
use of Akkadian gradually died out because it was impractical in that
environment. Roughly 500 years after Abraham's time, Joshua led the
Israelites back into the land of Canaan after their captivity in Egypt. It is not
known how much of the language of Canaan they retained during their
generations in Egypt, but once they entered the Promised Land, their
continuing contact with the native peoples led to further merging of the
language of the Israelites with that of the Canaanites. In the review by Galia
Hatav, on page 131 we read, “Saenz-Badillos provides a full survey of the
history of the Hebrew language, tracing its origins in the Canaanite period,
through a span of 3,000 years, including its modern use in Israel.” Saenz-
Badillos wrote, on page 53, “From the moment of its appearance in a
documented written form, Hebrew offers, as we saw in the previous chapter,
clear evidence that it belongs to the Canaanite group of languages, with
certain peculiarities of its own.”
On page 12 of the book by Cyrus Gordon there is a discussion about the
ancient city of Ugarit on the eastern coast of the Mediterranean Sea to the
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north of ancient Israel. This was the capital of the small Ugaritic Kingdom,
which flourished from about 1400 to 1200 BCE during the time period of the
Judges in Israel. This page states, “Ugarit itself was located near the
northwest corner of what we may call Canaan, the land that nurtured a
number of linguistically related groups including the Phoenicians and the
Hebrews.”
The discovery of the first texts in the Ugaritic language in 1929 is described
on page 14 of the book by Mark Smith. On page 15 he mentions that in 1930
a few scholars had assigned certain shaped letters in these texts to equivalent
letters in ancient Hebrew. These letter assignments were made based upon
the initial assumption that the Ugaritic language was very similar to ancient
Hebrew. Once this decipherment was made, the Ugaritic language was
easily understood by scholars who knew Hebrew.
While there are some differences in grammar between Ugaritic and ancient
Hebrew, these Semitic languages are very closely related. In 1930 a
significant library of Ugaritic texts was discovered in the Ugaritic Kingdom.
The northern boundary of the ancient Canaanites is unknown, so that leading
scholars of Ugaritic studies at the end of the twentieth century are no longer
willing to state that the Canaanites spoke the language that is called Ugaritic,
but it was surely very close to it, as was biblical Hebrew. On page 1 of the
Ugaritic grammar book by Daniel Sivan, he mentions that over 1300 texts
have been unearthed from this greater region. He wrote, “At the present
time, these clay tablets represent the only substantial second millennium B.
C. E. source wholly written in the language of the inhabitants of the greater
Syria-Israel region.” On pages 2-3 he wrote that a few scholars hold the
view that Ugaritic is a Canaanite dialect, but others maintain that it is an
independent language quite distinct from Canaanite. On page 4 Sivan wrote,
“Ever since the discovery of the Ugaritic writings many studies have been
written concerning the expressions of style and of form that are common to
Ugaritic and Biblical Hebrew literature both in larger literary units and
isolated refrains.” Later, on the same page we note, “The profound
connection between the two literatures serves to elucidate many difficult
passages in the Bible on [the] one hand and points to a common stylistic
stock on the other.”
On pages 224-225 of the book by Mark Smith, he wrote, “In retrospect, the
Ugaritic texts have fulfilled their promise for biblical studies. No other
corpus from Syria to Mesopotamia, no roughly contemporary corpus such as
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the Mari texts, the El-Amarna letters, or the Emar texts (though these still
hold considerable promise!), or even later texts such as the Dead Sea Scrolls,
have made the same impact on the understanding of Israel's languages and
culture.”
Certain words found in biblical Hebrew have a meaning that is not clearly
determined from the biblical contexts. Some of these words have a cognate
in the Ugaritic language or in another Semitic language. By a cognate, I
mean a word that sounds almost the same in the other language, is spelled
almost the same using equivalent letters, is used in similar contexts, and
which seems to have a common linguistic ancestry. Additional contexts of
the cognate in the other Semitic language often provide clarifications or
more precise meanings of some Hebrew words.
In his discussion of Hebrew lexicons, on page 201, Michael O'Conner wrote,
“The most important change between them [both the first edition of the
Koehler-Baumgartner Hebrew lexicon in 1953 and Zorell's Hebrew lexicon
of 1954] and Buhl [his revision of Gesenius' Hebrew lexicon in 1915] was
the discovery of Ugaritic [in 1929]: this is well represented in Koehler-
Baumgartner 1 and almost not at all in Zorell.” If grammatical care and most
especially contextual matching is not followed, then the use of allegedly
cognate words to transfer meanings can lead to wild speculations, and some
irresponsible scholars have thereby given a foul taste to the use of Ugaritic
in biblical studies; see pages 159-166 of the book by Mark Smith who
especially points to the abuses of Mitchell Dahood in damaging the
reputation of the use of Semitic cognates. Michael O'Conner comments on
this negativity as follows on page 203, “It may be that the [irresponsible]
excesses of G. R. Driver and Mitchell Dahood are to be blamed for the
negative view often taken nowadays of comparative [Semitic]
argumentation, but the neglect of such argumentation has had a deleterious
effect.” In other words, abuses of the use of Semitic cognates has led some
scholars to want to abandon its use altogether, and this abandonment has
been harmful, especially if grammatical care and good contextual matching
is achieved.
Another ancient nation on the eastern coast of the Mediterranean Sea and
north of Israel is Phoenicia whose language is called Phoenician. As
mentioned above in the quotation from the book by Cyrus Gordon,
Phoenician was also similar to ancient Hebrew. On pages 58 and 60 of the
book by Edward Lipinski, he wrote, “Phoenician is the Canaanite form of
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speech used in the first millennium B.C. in the coastal cities of Byblos,
Sidon, Tyre, in the neighboring towns, and in the various settlements and
colonies established in Anatolia, along the Mediterranean shores, and on the
Atlantic coast of Spain and of Morocco.”
The language of the Phoenician colonies is called the Punic language, which
is also very similar to Hebrew. Later, Aramaic became the language of the
Mesopotamian region, but Aramaic was originally an eastern Mesopotamian
Semitic language that also has many affinities to Hebrew. Syriac is a later
offshoot of Aramaic. The common ancient Semitic languages that are closest
to biblical Hebrew in order of closeness are the group of Ugaritic,
Phoenician, and Punic, followed by Aramaic, Syraic, and Akkadian. Arabic
is another Semitic language that is less close to biblical Hebrew.
The Israelites began their use of Hebrew in the land of Canaan where they
derived their language. It was directly north of this area that Ugaritic and
Phoenician were spoken. The deities of the Canaanites as mentioned in the
Bible, namely Baal and Dagon, are also discussed in Ugaritic along with
pagan practices associated with those deities, so the religion of the Ugaritic
Kingdom and the religion of the Canaanites must have been very similar.
Cognate words in these languages that are embedded in similar contexts and
are not used in an idiomatic expression should have virtually the same
meanings. The ancient Israelites adopted the vocabulary of this region in
their language.
Comments concerning whether etymology is useful are now addressed
because I have seen some individuals come to unwarranted conclusions from
the application of etymology. The supposed first or early use of a word is its
etymology. On page 148 of his linguistic discussion, Peter Cotterell wrote,
“The myth of point meaning. The first is the myth of point meaning - the
supposition that even if a word has a range of possible meanings attested in
the dictionary, there lies behind them all a single ‘basic’ meaning.” Then on
page 149 he wrote, “The etymological fallacy. The myth of point meaning is
closely related to the etymological fallacy. Words represent dynamic
phenomena, their possible range of associated referents constantly changing,
and changing unpredictably.” On page 150 he wrote, “Thus, the meaning of
a word will not be revealed by consideration of its etymology but by a
consideration of all possible meanings of that word known to have been
available at the time the word was used (thus avoiding the diachronic fallacy
[the meaning may change over time]), and of the text, cotext, and context
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within which it appears. Even then it is necessary to be aware that an
individual source may make use of any available symbol in any arbitrary
manner provided only that the meaning would be reasonably transparent to
the intended receivers.” Later on this page the author continues, “The fact is
that the etymology of a word may help to suggest a possible meaning in a
particular text. But it is the context that is determinative and not the
etymology.” Even comparative Semitic cognates are useless if the contexts
of the cognates are not the same.
The KJV was published in England in 1611 at a time after that nation had
rejected the authority of the Roman Catholic Church and replaced it with its
national church, the Anglican Church. However, there was some religious
tolerance in England, especially for the Jews. Gesenius wrote his famous
Hebrew lexicon before the middle of the nineteenth century, and he often
used the meanings of ancient Arabic, Aramaic, and Syriac words to explain
some Hebrew words. Thus Gesenius employed Semitic cognates to help
understand biblical Hebrew, yet he did so in a responsible manner of
matching the context. But after his death newer archaeological discoveries
written in ancient Akkadian, Ugaritic, Phoenician, and Punic have been
made, and thus many useful papers, lexicons, and commentaries have been
written since the middle of the twentieth century that help explain certain
Hebrew words and phrases. This is called the use of comparative Semitic
languages applied to biblical Hebrew.
The Hebrew Scriptures were written over a period of hundreds of years in an
ancient culture. The reader who wishes to study the Scriptures in solitary
confinement with nothing but an English translation of the Bible will be
disappointed because some of the Hebrew words are only now being capable
of comprehension in its original context through archaeology, history,
comparative Semitic languages, etc. There is no single source to acquire that
will provide all data that one needs to fully understand the latest attainable
knowledge about ancient Hebrew. Strong's concordance is outdated in the
scholarship of its lexicons, which were prepared by volunteer students.
Many of its etymologies are conjectural and misleading. Etymology itself,
even if correct, is often not a reasonable guide to discover the meaning of a
Hebrew word. In general, etymology, especially when it is often a guess, is
not a good method to use to arrive at the meaning of a Hebrew word that is
not easily attained from its biblical contexts.
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When journal articles discuss the meaning of a Hebrew word, they never
refer to the Hebrew lexicon at the back of Strong's concordance because its
lack of authority and care is well recognized in scholarly circles. The claims
in Strong's concordance that word xxxx was etymologically derived from
word yyyy are generally mere conjecture and should not be repeated. The
only time I ever look at the lexicons at the back of Strong's concordance is to
check that another writer has correctly quoted from it. But the word numbers
in Strong's concordance are a very useful method for identifying the words
for English speaking people for whom this is being written. Most Hebrew
words do have stems, which are from two to four letters within the word.
I will provide literal translations of many Scriptures. For some significant
words I will supply the Strong's number and often provide a transliteration
of the Hebrew word in its standard singular form (for non-verbs) or its
infinitive form (for verbs). Sometimes I will put the Strong's number and the
transliteration in square brackets. Authors, editors, and other sources that are
used are cited in full in the bibliography at the end. The English letter
spellings that are used within Strong's concordance to transliterate the
Hebrew words are most often contrary to all of the three Jewish schools of
pronunciation (Ashkenazic, Sephardic, and Yemenite). Hence I will not use
the spellings in Strong's concordance.
[4] Disguised Confusing Footnote in the Brown-Driver-Briggs Lexicon
The original BDB Hebrew lexicon was first published in 1907 by Oxford
University Press. In 1979 this was reprinted by Hendrickson Publishers, who
added Strong’s numbers to the Hebrew words, but kept the text and the page
numbers the same. The 1979 edition also added a useful appendix with
Strong’s numbers at the end. Long after this lexicon was completed in 1907,
some important discoveries about some biblical Hebrew words have been
made utilizing comparative Semitic languages, especially derived from
excavations of Ugaritic writings north of Israel and the Dead Sea Scrolls
south of Jerusalem. These discoveries affect the meanings of some Hebrew
words. Nevertheless, for most words BDB remains an especially complete
and useful reference work.
Sometime after the original 1907 edition was printed, the original publisher
added a final chapter on pages 1119-1127 titled, “Addenda et Corrigenda”,
which is a list of further notes and corrections. When Hendrickson
Publishers decided to reprint BDB in 1979, instead of leaving this final
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chapter at the end, they took each entry and attempted to place it as a
footnote on the same page as the word to which it adds or corrects.
Unfortunately, in some rare instances, the added note from the final chapter
was too long to fully fit as a footnote on the same page as the original word,
so that it was continued onto the next page without a clear warning near the
bottom of the continuation page. This has deceived some sincere people on
the continuation page for a critical Hebrew word concerning the calendar.
The Hebrew word chodesh, having Strong’s number 2320, is discussed on
pages 294-295 of BDB, and is given the translation “new moon” or
“month”. At the bottom of page 294 there is a difference between all
printings from Oxford University Press compared to the 1979 edition. The
1979 edition has four extra lines at the bottom of the page, and some people
have been led astray by not realizing that these four lines are the
continuation of a footnote from the bottom of page 293 for the Hebrew verb
chadar, having Strong’s number 2314. Therefore, these four lines have
nothing to do with chodesh, and they appear as a disguised confusing
footnote. Part of this footnote says, “conceal behind curtain, conceal,
confine”, and this gives the false impression that chodesh refers to the
condition of the moon when it cannot be seen. In the chapter of “Addenda et
Corrigenda” in the later reprints by Oxford University Press, this long note
for chadar appears in the middle of column 1 on page 1123 where it
specifies that it refers to the Hebrew word chadar from page 293. BDB
makes no implication at all concerning the appearance of the moon at the
“new moon”. The new moon will be discussed below where it seems most
appropriate.
[5] Introduction to Ancient Calendars and Ancient Astronomy
In modern times much has been discovered about ancient calendars
generally, especially with the help of applying the computer and astronomy
software to ancient records in order to sift out conjecture from fact. During
the 20th century many volumes of ancient astronomical records were
translated and published. These have been studied in detail, and an improved
history of ancient mathematical astronomy has been erected, especially since
the Akkadian language of Assyria and of the priests of Babylonia was first
deciphered in the late 1800's and archaeological discoveries were translated.
It is unfortunate that such information is not readily available in every small-
town library or on the Internet without cost. Recent research is copyrighted
and may not be legally reproduced on the Internet for free or without
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permission. Thus the person who desires to study such matters today is very
greatly handicapped by either living far away from research libraries, or
even when only 50 miles away, a major effort must be made to fight one's
way through congested traffic many times over a period of years to become
familiar with the available literature. Sometimes the innocent unsuspecting
blind person comes to premature conclusions about the biblical calendar and
then writes with conviction, thus leading other innocent blind ones into
conclusions that would not stand up among learned people. Other people are
not so innocent because they have a bias against all ideas contrary to the
modern calculated Jewish calendar. Such bias often leads those to throw dust
and smoke into the air and attempt to cause confusion among others who
really seek genuine biblical understanding.
Since the calendar is linked to the astronomy of the sun, earth, and moon, it
is important to discuss this early to define certain technical terms and to
ensure that irrational and erroneous thoughts about astronomy are avoided.
[6] Ellipses and Orbits of Heavenly Bodies
The path that one heavenly body takes as it goes around another heavenly
body is called its orbit. Ancient peoples did not know that the planets orbited
the sun. Instead they thought that all the heavenly bodies circled around the
earth. There was only one ancient Greek astronomer who went against his
contemporaries by espousing his theory that the "wandering stars and the
earth" (the planets) circled the sun, namely Aristarchus of Samos c. 280
BCE (see pages 74-75 of Toomer 1996). The only other ancient astronomer
who is known to have accepted this sun-centered viewpoint is Seleucus of
Babylon c. 150 BCE (see page 391 of Pedersen and page 247 of Stahl).
When discussing history, it is always best to quote from the original
historical sources or translations of them (these are called primary sources),
and then arrive at conclusions. Unfortunately, when the history of ancient
astronomy is the topic, problems are encountered that prohibit quoting from
original sources before Ptolemy (c. 150 CE). One insurmountable problem is
that the important ancient astronomical texts are not written for the purpose
of teaching others their methods; there are no ancient textbooks. Instead we
find columns or tables of numbers with some occasional notes, and there are
records of observations with some notes. The ingenuity of modern historians
of mathematics and astronomy has enabled them to determine the meanings
of the various columns and the meanings of the scientific terms used.
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Modern science has reverse engineered the ancient texts to learn what must
have been their ancient methods in order for the columns of numbers and the
occasional notes to make sense. While English translations of ancient
astronomical texts certainly exist, there would be no benefit to quote from
any one text for an understanding of the underlying methods unless one were
writing a detailed textbook which required some significant knowledge of
mathematics and astronomy. This difficulty in not being able to quote from
the primary sources pertaining to ancient astronomy for the layman makes it
necessary to quote and cite modern secondary sources.
For the history of astronomy the original ancient sources are so obscure that
a correct interpretation requires great care by specialists in this field, so that
scholars who are only historians or only modern astronomers may easily go
astray in their conclusions. A generic example of the obscurity is a writing
tablet with orderly columns of numbers having some symbol at the top of
each column and some miscellaneous remarks. First, one translates the
numbers into today's numbers, and also translates the miscellaneous
remarks. Second, one determines patterns to the numbers and relates these
patterns to known values relating to astronomical time periods of heavenly
bodies. Some columns become reasonably easy to interpret or explain, while
other columns may remain a matter of modern scholarly debate for 100
years or more because the tablets themselves do not define the meaning of
the columns. Simply publishing a literal translation of the tablet does not do
the layman any good at all.
Because of this, when some scholar publishes a paper about the history of
ancient astronomy, it may require some years of scholarly debate in order
that a clear mutual understanding of the correctness of that paper will
emerge. During the twentieth century some papers were published in this
subject that were subsequently proven false by the best scholars in this field.
But less knowledgeable writers on the history of science thought that some
of these papers were correct before they were proven false, and thus popular
published articles, Internet website articles, and books on the history of
ancient astronomy are available with information that modern specialists in
this field know to be false. Unless a person devotes some years of study to
the literature on this subject and keeps up with the latest journals and
advanced books related to the history of ancient astronomy, it is easy to be
led astray. I have performed Internet searches and have been greatly
dismayed at the widespread misinformation available. I have taken great
care to learn who the best authorities are in this field, and I have only used
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internationally respected specialists for my quotations and sources. I have
kept up with the latest literature for the specific details that are especially
significant for this study.
Educated people of today know that the earth rotates on its axis once each
24-hour day, but we still speak of the sun rising up in the morning rather
than the earth rotating to enable us to see the sun. Thus the sun does not
really move fast around the earth so as to truly rise in the morning, but the
expressions in our language, which have been handed down to us since
ancient times have remained. The NKJV states in Eccl 1:5, “The sun also
rises, and the sun goes down, And hastens to the place where it arose”.
Nothing is improper here by saying what appears to happen from the
perspective of an observer on earth. Gen 1:14 mentions the dividing of the
daytime from the night, and it says that the lights in the heavens have this
purpose. We must not be critical of the Bible here on the grounds that the
rotation of the earth on its axis would be explained as the cause today.
Regardless of the physics, the Bible was written in terms of human
perception from the surface of the earth and must be accepted this way.
The Bible gives no hint of advanced mathematical or astronomical
knowledge from the days of Moses. Ancient people thought that the sun
went around the earth in an orbit having the shape of a circle, and that the
moon went around the earth in an orbit having the shape of a circle. Ancient
Greek astronomers used the mathematics of circles to approximate the
predictions of eclipses and other astronomical events, but they had to add
some complexity to their mathematical schemes because they eventually
discovered that the speed of the moon around the earth was not constant.
They modified their mathematics in an attempt to make their predictions
agree with what they observed later, yet they continued to accept circular
motion of the heavenly bodies.
The German astronomer Johannes Kepler (1571-1630) discovered that the
orbit of Mars around the sun had the shape of an ellipse. Sir Isaac Newton
(1642-1727) proved that all planets of our solar system had an orbit around
the sun shaped as an ellipse. Ancient predictions could never become
extremely accurate compared to what was achieved by Newton because
ancient astronomers did not truly understand the laws of motion, the shape
of orbits, the physical reality of what was primarily moving, and the higher
mathematics needed to prove the more precise physical relationships through
time. Kepler was innovative and brilliant in using geometry to derive his
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results about Mars, but without having the calculus that Newton was the first
to apply to astronomy, Kepler was greatly handicapped to go beyond his
great achievements. But Kepler had at his disposal the very carefully
documented results of many years of fine observations by Tycho Brahe, who
used accurate carefully constructed mechanical astronomical instruments,
and Brahe was funded by willing donors who were not concerned that the
effort was not useful to people at that time. Kepler stood upon the shoulders
of Brahe. Newton said that his achievements were only possible because he
stood upon the shoulders of giants. The inventions of the telescope and the
pendulum clock were a great help to astronomers who gave accurate data to
Newton. The invention of the printing press helped to spread scientific
achievements far and wide so that brilliant minds in diverse places could
rapidly feed upon each other's results. The funding of European universities
and the exchange of knowledge among people in a variety of scientific
disciplines that was characteristic of the renaissance helped to make this
achievement possible. The ancient world lacked such a critical mass of
diverse inventions and published scientific papers that teamed together to
enable such magnificent results. A key word of this paragraph is ellipse. A
few remarks about the nature of an ellipse may be useful in order for the
reader to appreciate certain later comments concerning the moon's orbit
around the earth. If the reader does not understand some of the discussion in
the next few paragraphs, it is of no great consequence.
Picture a circular white pancake resting on a dark tabletop and consider
looking at it from directly above. Its boundary looks like a circle. Then
picture yourself standing upright on the floor a short distance from the table
while looking at the pancake. If the height of the table is only the size of
your big toe, the boundary of the pancake will look very much like a circle,
but if the height of the table is only a little below the height of your eyes, the
boundary will look like a very squashed circle. At some in between height,
the boundary will look somewhat like an egg. Each boundary shape of the
circular pancake viewed from a very low height to one near the height of
your eyes is technically called an ellipse in mathematical terminology.
The orbit of the earth around the sun is nearly a perfect ellipse that is
somewhat close to being a circle. The orbit of the moon around the earth is
nearly a perfect ellipse that is a little less circular. If the moon and the
planets did not attract the earth, then the earth's orbit would be as perfect an
ellipse as one could expect for a physical object. If the sun and the planets
away from the earth did not attract the moon, then the moon's orbit around
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the earth would be a nearly perfect ellipse. However, in a technical sense the
last sentence is not quite true because if the sun continues to pull at the earth
and would no longer pull on the moon, the moon would fly off away from
the earth because the annual orbit of the moon around the sun is based on the
sun's pull on the moon, not the earth's pull on the moon.
The position of the sun within the earth's orbital ellipse and the position of
the earth within the moon's orbital ellipse are not at the center where one
might expect. The following will explain where they are. Picture a straight
stick nailed to the center of an ellipse, and picture the length of the stick to
only extend from one edge of the ellipse to the other. Now imagine hitting
the stick so that it spins around the ellipse, but imagine the length of the
stick stretching and shrinking as it turns, so that it always only extends from
one edge of the ellipse to the other. The major axis of the ellipse is the stick's
line segment when it is longest in its spin, and the minor axis of the ellipse is
the stick's line segment when it is shortest in its spin. These axes are
perpendicular to one another and cross at the center of the ellipse.
Picture a stick in the position of the major axis, but imagine it to be broken
at the center of the ellipse with its two halves loosely glued together so that
it may change angle where the glue holds them. Now imagine putting the
palm of each of your hands at the ends of the stick and slowly pushing them
together as when beginning to clap hands. The clapping movement should
be toward the center of the ellipse so that as both hands move at the same
speed, the stick rests in the plane of the ellipse, and the glued spot moves up
the minor axis. Stop the movement when the glue touches one end of the
minor axis. The two ends of the stick at your palms lie along the major axis,
and the two halves of the stick are joined at one end of the minor axis. Now
each end at a palm is at a point called a focus of the ellipse. Each ellipse has
two foci, both of which are on the major axis and off the minor axis. The
procedure described shows that the distance from each focus to an end of the
minor axis equals half the length of the major axis. There is only one point
on an ellipse closest to a focus; that is the nearer of the two points at the ends
of the major axis. Similarly, there is only one point on an ellipse furthest
from a focus; that is the further of the two points at the ends of the major
axis.
The sun is at a focus of the earth's orbital ellipse. The earth is at a focus of
the moon's orbital ellipse. Thus the sun is never at the center of the earth's
orbit and the earth is never at the center of the moon's orbit.
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[7] Astronomical New Moon (Conjunction) and Full Moon
From the viewpoint of an observer on the earth far away from the north and
south poles, the moon has periodically changing appearances. Typical
appearances of the moon's cycle may be described as (1) the widening
crescent, (2) the moon increasing toward full circle, (3) the full circle, (4) the
moon decreasing away from full circle, (5) the narrowing crescent, and (6)
invisibility. The astronomical new moon (as recognized by modern
astronomers) is the moment in time (or the moon's position) in each cycle of
the moon around the earth at which the center of the moon is closest to the
straight line between the sun and the earth. The astronomical new moon is
also called the conjunction of the sun and the moon as observed from a
person on the surface of the earth.
A solar eclipse is the covering of the sun by the moon as seen by an
observer on the earth when the moon comes between the sun and the earth.
Such an eclipse is called total eclipse when the circle of the moon lies inside
the circle of the sun. A solar eclipse can only occur during the time of the
conjunction. How dark is it during a solar eclipse, and how long does a solar
eclipse last? On pages 198-199 of Zirker we read, “During a total eclipse,
however, the corona [the sun's disk] is only as bright as the full moon.” On
page 30 we read, “The maximum diameter difference is 2'38" and the
maximum duration of totality is 7 minutes and 40 seconds for an observer
near the equator. The 1973 eclipse in West Africa came very close to this
maximum theoretical totality. On the average, a total eclipse only lasts for
two or three minutes and seems much shorter.”
Chapter 12 of Zirker's book is titled “The Great Hawaiian Eclipse” where
Zirker describes the famous total eclipse over the Hawaiian Islands on July
11, 1991, which is significant because of the world famous observatory on
Mauna Kea at 13,700 feet above sea level, which provided superb scientific
facilities for observation. This total eclipse lasted 4 minutes 11 seconds
(page 197). Page 197 states, “Schoolchildren [on Hawaii] were equipped
with dark slides to view the eclipse and preparations were made to bus them
to favorable locations.” The reason that they look through special dark slides
is so that their eyes are not damaged due to the harmful rays of the sun.
During the 4 minutes 11 seconds of totality of the solar eclipse, one's eyes
should not be damaged because the brightness is near that of the full moon,
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but outside that narrow window of time, one's eyes surely will be damaged
when the moon only partially blocks the sun.
The following definitions are relative to a place on the earth significantly
away from the north and south poles. The crescent period of the moon's
cycle is the time after the three-quarter-size moon and before the following
one-quarter-size moon excluding the time during which the moon is
invisible and the time at which there may be a solar eclipse. The moon is
called a crescent during the crescent period. The old crescent is the moon
during the time that it is visible, assuming the atmosphere is clear, on the last
day that it is visible prior to the astronomical new moon. The old crescent is
seen looking east in the morning. The new crescent is the moon during the
time that it is visible, assuming the atmosphere is clear, on the first day that
it is visible after the astronomical new moon. The new crescent is seen
looking west in the evening. The new crescent is sometimes called a young
crescent.
Bartel Leendert van der Waerden (1903-1996) was an internationally
prominent scholar in the fields of mathematics and the history of ancient
astronomy. On page 169 of van der Waerden, he wrote: “The difference
between the first days of an exact month [month starting with and ending
with the conjunction] and an observed lunar month [month starting with and
ending with the new crescent] is one or two days, or in exceptional cases
three days.”
On page 66 of Beaulieu we find, “In ancient Babylonia the day was
reckoned from one sunset to the next. The monthly count was based on lunar
phases, with the month beginning after sunset when the new crescent of the
moon was seen again in the western horizon. This happened at the earliest
one day, and at the latest three days after conjunction.”
At the end of the above sentence is “2” (footnote) which states the following
(same page, square bracket comments are in the journal, not from me), “That
the moon never disappeared for more than three days following conjunction
was evidently known to Assyrian and Babylonian astronomers, as shown in
H. Hunger, Astrological Reports to Assyrian Kings (SAA 8, 1992), text 346,
a report sent by the scholar Asaredu the younger: ‘On this 30th day [the
moon became visible]. The lord of kings will say: “Is [the sign?] not
affected?” The moon disappeared on the 27th; the 28th and the 29th it stayed
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inside the sky, and was seen on the 30th; when else should it have been
seen? It should stay in the sky less than 4 days, it never stayed 4 days.’”
On page 87 Beaulieu wrote: “Even after the 6th century B.C., when
Babylonian astronomers developed the mathematical schemes which
enabled them to calculate month-lengths in advance, it is probable that
observation remained the sole authoritative way of fixing the beginning of
the month.” Page 244 of Britton 1999 indicates that the Babylonian method
for predicting the sighting of the new crescent is likely to have originated
within the years 457-419 BCE. The Babylonian calculation for the sighting
of the new crescent is based upon approximate repeating sequences of data
over long periods of time. Existing records of some of the data that are used
in these patterns go back to 568 BCE, which is 18 years after Solomon's
temple was destroyed in 586 BCE, and the earliest archaeological source
that has all astronomical parameters that are needed for the prediction of the
sighting of the new crescent is dated 373 BCE (see page 197 of Hunger and
Pingree). Thus the time at which the Babylonians developed methods to
approximately determine the day of the new crescent is about 450 BCE.
Perhaps about 400 BCE their method was actively being used. I have not
seen any published papers that attempt to quantify how accurately the
Babylonian methods predicted the new crescent.
Based upon data showing that one factor of considerable significance to the
Babylonians is predicting the time from when the sun sets below the western
horizon to the time when the moon sets below the western horizon during
the crescent phase (although other time based factors were also sought by
the Babylonians), and knowing that this method has some degree of
reliability toward predicting the visibility of the new crescent (but is far from
a perfect method), my estimated guess is that their predictions for the new
crescent were correct between 80 and 85 percent of the time when the
weather was clear.
Today we speak of the conjunction and we define it in terms of the three
dimensional geometry of the sun-earth-moon system and the language of
orbits. But ancient people did not have our modern concept of a sun centered
solar system (except for two known ancient astronomers who were
ridiculed), and to the best of our knowledge today, ancient people did not
have our three dimensional model of the sun-earth-moon system. We must
realize that the ancient concept of the conjunction and our modern concept
are different. They could see a solar eclipse, and whenever there was a solar
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eclipse, there was necessarily a conjunction also. But that was the only kind
of conjunction they could see. What concept could they have for the
conjunction generally if they could not see it? Page 110 of Koch-Westenholz
states, “The Babylonians seem never to have given an astronomical
explanation of eclipses.” Page 101 of Koch-Westenholz states, “I know of
no Babylonian astronomical explanation of the phases of the moon, ...” The
Babylonians did notice the obvious fact that when the full moon occurs the
moon and sun are at opposite ends of the sky, and during the symmetrically
opposite time of the lunar cycle the moon and sun are traveling along side by
side. A translation of an ancient Babylonian text that discusses the moon's
cycle of disappearance is on page 101 of Koch-Westenholz, where “you”
refers to the moon: “On the day of disappearance, approach the path of the
sun so that [on the thirtieth day (?)], you shall be in conjunction, you shall be
the sun's companion.” Here the author's translation “conjunction” does not
require that it refer to an instant in time. It is merely the time that the sun and
moon are companions, traveling together.
With clear weather the Babylonians knew there could be one, two, or three
nights of invisibility of the moon (as mentioned above from van der
Waerden and from Beaulieu). At the moment of true conjunction the moon
and sun can be at most 5.2 degrees apart from a point on the earth's surface.
At this narrow an angle if the sun is in view or very near the horizon, the
light from the sun will be too brilliant for the moon to be seen directly or
even indirectly (the latter is called earthshine). Earthshine is the light from
the sun to the earth, which then reflects back to the moon and then reflects to
the observer on earth. Thus earthshine is the light seen from a double
reflection. It is usually easy to see earthshine as the completion of the
moon's circle as a faint grayish blue with the crescent at one edge on the
second day old crescent. Often earthshine may be seen on the day of the new
crescent if it is not a very narrow crescent. Neither modern nor ancient
people could see earthshine at the time of conjunction because the sun's
brilliance is too close to the moon, and this has nothing to do with air
pollution.
When the conjunction occurs, the moon is invisible except during a rare
solar eclipse when the moon covers the sun from view from observers in a
certain region on the earth for at most 7 minutes and 40 seconds (see the
quote from Zirker above). Without knowledgeable calculations, it is not
possible to accurately determine the time of the conjunction. Because the
conjunction is not visible except during a rare solar eclipse, ancient people
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who did manage to arrive at some mental concept of the conjunction (such
as the time period when the sun and moon are traveling together) and who
also desired to achieve a mathematical computation to predict the time of the
conjunction, would only be able to check the accuracy of their mathematical
prediction during the rare occasion of a solar eclipse where they were
located. The strong desire of certain ancient peoples, specifically the
Chinese, the Babylonians, and the Greeks, to be able to predict solar
eclipses, along with a knowledge of the mathematics that enabled then to
make this approximation led to their interest in the conjunction as the
approximate time when the sun and moon were traveling together.
Historical records of eclipses over a long period of time will suggest cycles
of repetition of eclipses, and this may be simply described as a
“bookkeeping” method to predict eclipses. In the book on ancient eclipse
predictions by John Steele 2000, he discusses Chinese eclipse predictions on
pages 175-215. On page 177 in the context of China, Steele wrote,
“Although there are many steps in this process – and many potential places
for mistakes – it has the advantage that eclipse prediction is reduced merely
to bookkeeping, and yet the method still predicts most visible eclipses over
the course of a hundred years or so. Furthermore, the calendar tends to
predict too many, rather than too few, eclipses.” Later on this page we find,
“The first mathematical treatment of eclipse calculation [in China] without
reference to an eclipse cycle is found in the Ch’ing-ch’u-li from the third
century AD.” Steele’s description of these methods reveals a computation to
repeat an eclipse rather than a mathematical geometrical model of where the
heavenly bodies will be in the future. The purpose of including this piece of
history is to remove some of the exotic imagined ideas that some laymen
possess concerning the abilities of ancient peoples.
The full moon is the moment in time (or the moon's position) in each cycle
of the moon around the earth in which the center of the earth is closest to the
straight line between the sun and moon. The full moon is also called the
opposition. When the full moon occurs, it looks like a full circle. However,
the time of the moon's appearance as a full circle lasts at least two nights and
it looks quite circular for several nights, so without knowledgeable
calculations, it is not possible to accurately determine the time of the full
moon by observing the circularity of the moon. On the other hand, it is
possible to use a different observational method to make a judgment of the
day after the moment of full moon as follows. During the several days near
the time of the full moon the following two statements are true. Before the
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moment of the full moon, the moon rises in the east before the sun sets in the
west. After the moment of the full moon, the moon rises in the east after the
sun sets in the west. Using these principles one can use the rule that the first
evening in which the moon rises in the east after the sun sets in the west
begins the day after the moment of the full moon. One drawback of using
this observational method is that it requires a straight horizontal
unobstructed view of both the eastern horizon and the western horizon, and
both of these horizons must be at the same altitude above sea level. Hills and
trees will hinder accuracy. Besides this, if two observers perform this
activity from different locations that have opposing horizons, which differ in
their altitude above sea level, it is possible that their conclusions will differ
in a near borderline case.
[8] Variation from Astronomical New Moon to Full Moon; Variation from
New Crescent to Full Moon
Someone may imagine that since the day immediately following the moment
of the full moon could be known by the method described above, perhaps
the day of the conjunction could be known from the day of the full moon.
This conjecture is now discussed.
On the bottom of page 6 of Parker 1950, he wrote, “The necessary time for
full moon varies from 13.73 to 15.80 days after conjunction.” This is a
swing of 2.07 days, which is about 49 hours 41 minutes. This shows that the
conjunction (i.e., astronomical new moon) does not have to be exactly
opposite the full moon.
By examining a few cases near these extremes in the 20th century we may
compare the day of the lunar month based upon whether one considers the
first day of the lunar month to be the day on which the conjunction occurs or
the day on which the new crescent is seen. Let us consider three cases in
which the computation for visibility of the new crescent is made from
Jerusalem, and the boundary for a new day is computed as sunset. For those
who wish to check with other software, I am considering the latitude of
Jerusalem to be 31.80 N and the longitude of Jerusalem to be 35.22 E, which
are the coordinates I have seen for an official weather station of Jerusalem.
The abbreviation UT stands for “universal time”, and is intended to refer to
the time zone based upon Greenwich, England.
Case 1: Conjunction on July 7, 1967 at 17:01 UT and sunset 16:48 UT
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The full moon occurred on July 21, 1967 at 14:39 UT. The time from
conjunction to full moon is 13.90 days (a little over the minimum of 13.73).
Note that the conjunction occurred shortly after sunset, close to the
beginning of a new day. For a month that is considered to begin on the day
of the conjunction, the full moon occurs on the 14th day of the month in this
example.
On the evening that ends July 9, 1967 the new crescent will be theoretically
visible. For a month that is considered to begin on the day beginning with
the new crescent, the full moon occurs on the 12th day of the month.
Case 2: Conjunction on December 12, 1966 at 3:15 UT and sunset 14:35 UT
The full moon occurred on December 27, 1966 at 17:45 UT. The time from
conjunction to full moon is 15.60 days (a little under the maximum of 15.80
days). For a month that is considered to begin on the day of the conjunction,
the full moon occurs on the 15th day of the month in this example.
On the evening that ends December 13, 1966 the new crescent will be
theoretically visible. For a month that is considered to begin on the day
beginning with the new crescent, the full moon occurs on the 13th day of the
month.
Case 3: Conjunction on September 26, 1973 at 13:54 UT and sunset 15:32
UT
The full moon occurred on October 12, 1973 at 3:11 UT. Note that the
conjunction occurred shortly before sunset, close to the end of a new day.
The time from conjunction to full moon is 15.55 days (a little under the
maximum of 15.80 days). For a month that is considered to begin on the day
of the conjunction, the full moon occurs on the 17th day of the month in this
example!!
On the evening that ends September 28, 1973 the new crescent will be
theoretically visible. For a month that is considered to begin on the day
beginning with the new crescent, the full moon occurs on the 14th day of the
month.
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Conclusion from these Examples
In these examples, for a conjunction month, the full moon occurs from the
14th to the 17th day of the month. The 17th is very rare.
In these examples, for a new crescent month, the full moon occurs from the
12th to the 14th day of the month. In the most extreme case for a new
crescent month, the full moon can occur on the 16th day of the month, but
this is very rare. Typically the full moon occurs on the 13th, 14th, and 15th
for the new crescent month.
[9] Ancient Meaning of the Full Moon
What did the full moon mean to the ordinary person in ancient times? We
have one example of what it meant to the Jewish philosopher Philo who
lived in Alexandria, Egypt and who wrote in the early first century. On page
17 of Philo_QE (section 9), in a context concerning Passover, Philo wrote,
“For when it [the moon] has become full on the fourteenth (day), it becomes
full of light in the perception of the people.” On page 401 of Philo_7
(Special Laws 2:155), in a context concerning the seventh month, Philo
wrote, “The feast begins at the middle of the month, on the fifteenth day,
when the moon is full, a day purposely chosen because then there is no
darkness, but everything is continuously lighted up as the sun shines from
morning to evening and the moon from evening to morning and while the
stars give place to each other no shadow is cast upon their brightness.” We
see here that Philo considers both the 14th and the 15th days of the month to
be days of the full moon. Hence he does not consider the full moon to be an
instant in time or only one day of the month, but a general period when the
moon is quite circular. As an ordinary person he did not adopt the meaning
for the full moon of advanced Greek astronomers as a mathematically
predicted moment when a lunar eclipse would sometimes occur. Due to the
elliptical orbit of the moon, this mathematical moment will vary by a few
days in relation to the conjunction, and it will also vary by a few days in
relation to the new crescent. The precision of mathematics was not Philo's
approach to the meaning of the full moon.
Although Philo, a Jew who lived in Alexandria, Egypt, is a historical first
century witness that the moon is full on the 14th and 15th days of the Jewish
months, this is not a biblical argument that a biblical month is full on the
14th and 15th days of the month.
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In the early first century Vitruvius wrote the views of the Greek astronomer
and mathematician Aristarchus of Samos (c. 280 BCE) concerning the full
moon. On page 264 Vitruvius wrote, “On the fourteenth day, being
diametrically across the whole extent of the firmament from the sun, she is
at her full and rises when the sun is setting.” This is approximately the rule
given above, namely the first evening in which the moon rises in the east
after the sun sets in the west begins the day after the moment of the full
moon. However, Philo of Alexandria took a looser concept of the full moon
allowing both the 14th and 15th days of the month to be days of the full
moon.
[10] When in History did Prediction of the Astronomical New Moon Begin?
The history of ancient astronomy shows that it was not until near the time of
the birth of Alexander the Great that ancient astronomers were first able to
estimate the time of the conjunction of the moon by a calculation.
On page 169 of van der Waerden, he wrote:
“In Babylonia, the month began on the evening on which the crescent was
visible for the first time after [the astronomical] New Moon. More precisely:
If on the [ending] evening of the 29th day of any month the crescent was
visible, the month has 29 days; if not, the month has 30 days. The same rule
still holds in Muslim countries.”
“I shall call these months ‘observed lunar months’. The words of Geminos
indicate that the Greek months originally were just observed lunar months.”
“The months beginning with the conjunction will be called ‘exact lunar
months’ or ‘conjunction months’. These months are a theoretical
construction; they could not be used in practice in classical times, because
before Kallippos [Callippos] (330 B.C.) astronomers were not able to predict
the true conjunction.”
Thus van der Waerden points to 330 BCE as the time before which ancient
mathematical astronomical knowledge was not able to predict the time of the
astronomical new moon.
The orbit of the moon around the earth is an ellipse. The earth is not at the
center of this ellipse, but at one of the two foci of the ellipse. The moon
moves faster around the earth when it is closer to the earth than when it is
farther from the earth. Due to the sun's gravitational attraction to the earth
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and moon, the distance from the earth to the sun affects the distance from the
moon to the earth, which in turn affects the time from conjunction to
conjunction! The exact time from conjunction to conjunction does vary
through the year! Knowing the average time from conjunction to
conjunction does not help to know any current lunar month's time from
conjunction to conjunction.
The minimum time from one conjunction to the next conjunction is 13 hours
40 minutes less than the maximum time from one conjunction to the next
conjunction (see pages 21-22 in Stephenson and Baolin). A mathematical
mastery of this variation is needed in order to accurately predict the time of
an astronomical new moon.
A high level of confidence of the accurate prediction of solar eclipses by
ancient peoples was certainly impossible because this requires a knowledge
of where the moon's shadow will reach the earth, and that requires a
knowledge of the distance from the moon to the earth (which requires a
knowledge of the elliptical orbit of the moon), the size of the earth, and the
shape of the earth (which is somewhat pear-shaped rather than perfectly
spherical). Since they could not predict the shadow path of the moon upon
the earth, the best they could achieve is a statement that a solar eclipse was a
reasonable possibility. But in order to do that, they would need to have a
good ability to predict the astronomical new moon as well as how to rule out
most astronomical new moons as being capable of providing a solar eclipse.
This simply shows that we can judge the ability of ancient astronomers to
approximately predict the astronomical new moon by their attempts to
predict a possible solar eclipse.
Of specific interest is the paper by John M. Steele 1997 where, on page 134
he lists the oldest Babylonian solar eclipse prediction for which we have full
data in 358 BCE, exactly 100 years after Ezra first brought a group from the
House of Judah back to Jerusalem after the Babylonian captivity. This solar
eclipse prediction was 181 years after King Cyrus the Great of Persia
conquered Babylon on October 12, 539 BCE (see page 14 of Parker and
Dubberstein). Since the empire was now the Persian Empire rather than the
Babylonian Empire, the learned astronomers who continued their work
should be called Persians, but the general practice is to continue referring to
them as Babylonian or “late Babylonian”. The same pagan priests continued
to improve their work in mathematical astronomy. John Steele 1997
analyzes the 61 preserved solar eclipse predictions of the Babylonians for
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which full data is available including the time at which the eclipse is hoped
to be seen, and these fall within the years 358 BCE - 37 CE. The
terminology used by the Babylonians shows that a solar eclipse was to be
“watched for”, showing an uncertainty that it would be seen. Less than half
(28 of 61) were either seen or would have been seen if the precise time of
the eclipse would have occurred during daytime in the region of Babylon. In
other words, in these 28 cases the latitude of the moon's shadow did fall
within some part of greater Babylon, but in the other 33 cases the moon's
shadow was outside this region. These ancient astronomers used water
clocks, which divided the day into 360 equal parts, each being four minutes.
The average error of these water clocks is eight minutes from true time. The
predictions included the calculated time for the eclipse to occur. The worst
two predictions among these 28 cases were 8.08 hours in error and 4.76
hours in error (page 135). The average error was 1.96 hours (page 136). For
the other 33 cases of predictions the average error in the time of conjunction
(here the word “conjunction” relates to a hoped for solar eclipse) is 3.67
hours, nearly twice as great (page 137)! Their predictions of solar eclipses
did not get more accurate in the later period of their recordings (pages 138-
139).
The mathematical methods that were used by the Babylonians were very
different from the methods used by the Greeks. The former used nearly
repeating sequences based on prior historical records (not a formula based
on a general physical mathematical model), while the latter developed a
geometrical mathematical model based on circles after 400 BCE. The
Greeks were aware of the methods used by the Babylonians (see page 118 of
Jones, the chapter by Toomer 1988, and page 61 of Fatoohi and others), but
the most advanced Greek astronomers preferred their own methods. The
methods of the Greeks were more advanced in the sense that they were
based on mathematical methods for approximate geometrical models, and
the geometry itself led to the concept of the conjunction. In contrast to this,
the Babylonians were interested in predicting solar eclipses, which by
definition only occur at the time of a conjunction; they did not show a
general interest in predicting the time of all conjunctions, and this was likely
the cause for van der Waerden's limiting of the year for calculating the
approximate astronomical new moon (conjunction) to 330 BCE. On page 41
of Aaboe we read, “Babylonian mathematical astronomy has two features
that seem strange to modern eyes, and it may thus be in order to mention
them here. First, it is entirely arithmetical in character or, in negative terms,
there is no trace of geometrical models like the ones we have become
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accustomed to since the time of Eudoxos [Greek astronomer of Cnidos, c.
408 to 355 BCE (see pages 63-66, 335 of Pedersen)]. Second, the cuneiform
literature [clay tablets bearing the Akkadian language of the Assyrians and a
remnant of the Babylonians] nowhere attempts to justify the precepts of the
procedure texts; thus it has rested with modern scholars to uncover the
underlying theoretical structures.” In other words, the Babylonians have left
us their many tablets showing columns of numbers, and it remained for
modern scholars to decode the meaning of these columns and how they were
computed. In some cases there are narratives that accompany these numbers
that mention certain sighted phenomena in the heavens or some indications
of the meanings of one or more columns, but there are no geometrical
diagrams showing a mathematical model of anything in the heavens among
the Babylonians.
The conclusion is that there are unusual aspects of the variation of the
moon's cycle around the earth that prevented ancient people from predicting
the approximate conjunction until about 330 BCE by the advanced methods
of the Greeks, or instead, until about 360 BCE for the non-geometrical
methods of the Babylonians whose average error was about three hours.
Moreover, the Babylonians were focused on solar eclipses rather than
conjunctions in general, while the Greeks showed an interest in
conjunctions. Another very significant factor that contributed to the
difficulty of predicting the conjunction is the lack of visual confirmation of a
conjunction unless there was a rare solar eclipse to confirm it. The water
clocks used by the ancient Babylonian astronomers had an average error of
eight minutes and their smallest unit of measuring time was four minutes.
Their predictions were long term, i.e., there is nothing to indicate that they
attempted a revised prediction within days of a solar eclipse. When
conditions were not right for a solar eclipse they never predicted a
“conjunction” because it would have been foolish to predict a phenomenon
that was not potentially verifiable with an observation.
A lunar eclipse is the covering of the sun's light to the moon by the earth as
seen by an observer on the earth when the earth comes between the sun and
the moon. In sharp contrast to the special difficulties of predicting solar
eclipses, there are no comparable problems in predicting lunar eclipses.
Lunar eclipses must occur during the full moon, may be seen by nearly half
of the people on the earth where the weather is not nasty (the side of the
earth where it is night), are visible more frequently than solar eclipses from
any one location, have calculations that may be tested from monthly
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approximate sightings of the full moon, and do not require predicting the
path of a shadow (in this case, the shadow of the earth upon the moon).
Hence there is a vast difference between the difficulty in predicting solar
eclipses (some conjunctions) and the ease in predicting lunar eclipses (some
full moons) by ancient astronomers. Page 3 of Britton 1989 states, “For a
given location, therefore, lunar eclipses are seen nearly 4 times as frequently
as solar eclipses.” But even when there is no lunar eclipse, the full moon is
still visible. When there is no solar eclipse, the moon is not visible.
Ancient Babylonian astronomers were significantly more successful in their
accuracy at predicting lunar eclipses than they were at predicting solar
eclipses. Of specific interest is the paper by John M. Steele and F. Richard
Stephenson. The oldest Babylonian lunar eclipse prediction for which we
have full data is in 731 BCE (see page 125), which is 373 years before the
first known reasonably accurate solar eclipse “hoped for” prediction by the
Babylonians for which we have complete data! They were successful in their
prediction for 731 BCE. Page 125 lists 35 Babylonian predictions of lunar
eclipses for which we have complete data including the time of prediction to
be observed. Also listed is the duration of time for which the eclipse was
observed by the Babylonians, when it was successfully seen. These are dated
from 731 to 77 BCE. Their average error for predicting the time of lunar
eclipses was about one hour (page 130). In 90 percent of the predictions they
were either successful or there was a near miss as defined by the authors
(pages 123, 130). Their average error for lunar eclipse predictions was about
one hour compared to about three hours for solar eclipses. It took about 400
years more for the Babylonian astronomers to be able to predict reasonably
accurate possible solar eclipses (associated with the conjunction) than for
them to be able to predict lunar eclipses (associated with the full moon).
There are numerous other dates of predictions of both lunar and possible
solar eclipses by the Babylonians, but the time of day of their expected or
hoped for sighting is not provided in the ancient sources. Without having the
time of day of a predicted lunar eclipse or a possible solar eclipse it is
impossible to judge the accuracy of the method of prediction, so it is not
reliable to include such records in a discussion of known results. On the
other hand, where columns of data are provided in a Babylonian text, it is
possible for a modern specialist in this area of ancient science to judge
whether the method is quite different from the more accurate later methods.
In Britton 1989, John Britton evaluates the method used by the Babylonians
for their earliest known attempt to predict possible solar eclipses. This text,
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which he called Text S, describes 38 solar eclipse possibilities from 475 to
457 BCE (see page 1 of Britton 1989). On page 44 Britton states, “We find
in Text S an unusual mixture of disparate elements not known from other
texts.” After discussing the method used by these Babylonians, he wrote on
page 46, “Indeed, with one exception the entire theory [for predicting
possible solar eclipses] can be derived from counts of phenomena (lunar
eclipses, eclipse possibilities, and months), and there is no evidence that
measurements of times, angles or magnitudes played any role in its
creation.” From the data in Text S, Britton discusses its primary
computation, which he calls “psi-star-of-S”. His conclusion on page 46 is,
“We see this best in the fact that psi-star-of-S, a function clearly derived
from lunar eclipses and measuring the proximity to the node of the earth's
shadow at conjunction (or the moon at mid-eclipse), is correctly applied to
solar eclipse possibilities by simply moving the entire function forward half
a month.” A simplified way of saying this is that these Babylonians
estimated the time of the conjunction to be the midpoint between two
successive computed full moons, and then judged the confidence for a solar
eclipse based on the history of repeating eclipses. But we have seen above
that it is very crude to estimate the conjunction to be the midpoint between
two successive computed full moons, so this method for predicting solar
eclipses by the Babylonians is indeed very crude compared to their later
method which has an average error of about three hours. Hence we must
dismiss this first Babylonian attempt at predicting solar eclipses (special
conjunctions) as inferior and not to be included in the chronology with their
later methods.
The conclusions are that the Babylonians were able to predict lunar eclipses
by about 750 BCE with a time error of about one hour, and the Babylonians
were able to predict possible solar eclipses about 360 BCE with a time error
of about three hours. The Babylonians started the practice of predicting the
sighting of the new crescent about 450 BCE.
[11] Transmission of Babylonian Astrology-Astronomy to other Peoples
For some decades of the 20h century Erica Reiner was the primary editor of
the multi-volume Akkadian dictionary project during its development at the
University of Chicago. One of her students in the study of Akkadian is
Francesca Rochberg, who is one of the world’s leading scholars of this
ancient language. On page 11 of Rochberg’s book in 2004 about the ancient
Akkadian authors and their writings that span the period from ancient
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Assyria to the first century, she wrote, “In the ancient Near East, our sources
do indeed indicate an indisputable progressiveness in astronomy.
Nonetheless, the realms of ‘astronomy’ and ‘astrology’ were not separate in
Mesopotamian intellectual culture, and so a self-conscious distinction
between them such as we make in using these terms does not emerge in the
cuneiform corpus.” On page 10 we find, “In the horoscopes in particular, an
interdependent relationship between astrology and predictive astronomy is
demonstrable by the identification of connections among a variety of
astronomical text genres and the content of horoscopes. Celestial divination,
which carries through from the middle of the second practically to the end of
the first millennium B.C., and the Babylonian astronomy of the post-500
B.C. period provide the intellectual context for the Babylonian horoscopes,
which bear relation to both of these distinct traditions. Because of these
relationships, the horoscopes afford a unique view into Late Babylonian
astronomical science.” On page 41 we find, “… from a social point of view,
Late Babylonian astronomy was supported by the institution of the temple.”
Also on page 41 we find, “It is clear that the individuals who computed
astronomical phenomena were the same as those who copied omen texts and
constructed horoscopes.” On page 165 we find, “The following discussion is
limited to those ideas that can be extracted from and supported by the
literature of the Babylonian scholar-scribe who specialized in divination and
took part in its related activities, such as prayer, incantation, or, indeed, the
mathematical prediction of lunar eclipses.”
At the time of the captivity and exile of the House of Judah to Babylon from
604 to 586 BCE, the common language of Babylon was Aramaic, but the
written language of the Babylonian priests, who produced mathematical
astronomy with its base 60 positional numbering system, continued to be the
Akkadian language of the previous Assyrian Empire. Because of their
positional numbering system and their motivation to use predictive
astronomy for astrological purposes that gave them prestige and income,
these Babylonian priests developed generalized methods for multiplication
and long division of fractional numbers. Thus the scientific language of the
Babylonian priests who were the mathematical astronomers was hidden from
the general population that had ceased using the Akkadian language. Except
for the private use by these priests, the Akkadian language ceased being a
living language.
The prophet Daniel was given great authority in the secular government
during the period c. 600 to c. 540 BCE, and based upon the biblical account
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in Daniel 2, he and his three friends were highest in the government. The
Babylonian pagan temple priests were simultaneously reduced in authority.
On page 209 Francesca Rochberg wrote, “One determinable change in the
environment of later Babylonian scholarship was the shift of the locus of
astronomical activity from the palace [i.e., support by secular government]
to the temple [pagan support]. When exactly this occurred, however, is not
well documented.” On this same page we find, “By the fourth century B.C.,
however, evidence for the intense involvement of the king with the [pagan
priestly] scholars appears to diminish.” Rochberg neglected to see the
excellent documentation in the Bible! When Daniel gained authority under
King Nebuchadnezzar, he reduced the influence of the pagan priests who
practiced their mixture of astrology with astronomy. Eventually they were
ousted from the palace and took refuge in the pagan temple where they
continued their practices. Both Ezra and Nehemiah, c. 450, were given favor
by King Artaxerxes, and undoubtedly the pagan priests remained in disfavor
with the king. On page 235 Rochberg wrote, “Regardless of the way
astronomy functioned within the temple institution, association with the
temple was without doubt the key to the survival of Babylonian astronomy
for so many centuries after it had become seemingly defunct in the political
sphere.”
There is no historical evidence to indicate any cooperative sharing between
the Levitical priesthood and the pagan Babylonian astrologers-astronomers
who continued writing their documents in the Akkadian language, which the
general population did not understand. The Akkadian cuneiform script was
vastly different from the 22-letter alphabet of both Hebrew and Aramaic.
Akkadian script consisted of hundreds of wedge-shaped signs (see page 1 of
Dalley). Since Scripture is opposed to the use of horoscopes (Isa 47:13), and
these were intimately associated with activities of the pagan temples where
astronomy was pursued and preserved, zealous Levitical priests should have
been motivated to stay away from such places and activities.
Pages 237-244 of Rochberg discuss the transmission of Babylonian
astrology with astronomy to the Greeks after Alexander the Great conquered
the Persian Empire in 331 BCE, and afterward to India. Astrology and
astronomy were sent together as a package.
[12] Egyptian Astronomical Science before Alexander the Great
On pages 128-129 of Clagett, he wrote the following:
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“It should be clear from my summary account that the ancient Egyptian
documents do not employ any kinematic models, whether treated
geometrically or arithmetically. However they did use tabulated lists of star
risings and transits (as is revealed clearly in Documents III.11, III.12, and
III.14), all tied to their efforts to measure time by means of the apparent
motions of celestial bodies.”
“On more than one occasion in this chapter, I have remarked on the absence
in early Egyptian astronomy of the use of degrees, minutes, and seconds to
quantify angles or arcs, though slopes were copiously used in the
construction of buildings, water clocks and shadow clocks, such slopes were
measured by linear ratios.”
Otto Neugebauer (1899-1990) is unquestionably considered to be the
greatest historian of ancient mathematical astronomy in the 20th century. He
studied the ancient Egyptian language as well as the ancient Assyrian
language known as Akkadian, and his pioneering studies were based on his
own readings of the original texts. Before he began his studies on ancient
Egyptian and Babylonian astronomy, he made a detailed study of their
mathematics. His doctoral dissertation was on ancient Egyptian
mathematics. It took his repeated efforts to convince Richard Anthony
Parker, the most acclaimed expert on ancient Egyptian science and
calendation, to join him as a professor at Brown University. Neugebauer and
Parker published three volumes of ancient Egyptian astronomical texts from
before the time of Alexander the Great (see Neugebauer and Parker). These
many texts from ancient Egypt show that we have an understanding of their
ancient knowledge of astronomy. These texts show no indication of the
abilities later achieved by the Babylonians and Greeks in predictive
astronomy, as Clagett pointed out.
On page 559 of HAMA, Neugebauer wrote, “Egypt has no place in a work
on the history of mathematical astronomy. Nevertheless I devote a separate
‘Book’ on this subject [10 pages] in order to draw the reader's attention to its
insignificance which cannot be too strongly emphasized in comparison with
the Babylonian and the Greek contribution to the development of scientific
astronomy.”
Concerning the extremely high accuracy of aligning the largest ancient
Egyptian pyramids with the east-west direction, and hence a precise
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knowledge of the time of the equinoxes by the ancient Egyptians,
Neugebauer wrote (1980) on pages 1-2, “It is therefore perhaps permissible
to suggest as a possible method a procedure which combines greatest
simplicity with high accuracy, without astronomical theory whatsoever
beyond the primitive experience of symmetry of shadows in the course of
one day.” A diagram and further discussion by Neugebauer explain how the
Egyptians could have achieved the accurate alignments without any
mathematically sophisticated theory.
Ronald Wells wrote a chapter titled “Astronomy in Egypt”, which concerns
the time before Alexander the Great and his command to build the most
modern city of ancient civilization, Alexandria. On page 40 of the book
edited by Wells, he provides the following summary: “Historians of science
concede only two items of [astronomical] scientific significance bequeathed
to us by the ancient Egyptians: the civil calendar of 365 days used by
astronomers even as late as Copernicus in the Middle Ages, and the division
of the day and night into 12 hours each. These fundamental contributions
may seem meager to many; engineering of the pyramids and surviving
temples notwithstanding.”
Otto Neugebauer wrote (1945) on page 11, “It will be clear from this
discussion that the level reached by Babylonian mathematics was decisive
for the development of such methods [for the numerical study of
astronomy]. The determination of characteristic constants (e.g., period,
amplitude, and phase in periodic motions) not only requires highly
developed methods of computation but inevitably leads to the problem of
solving systems of equations corresponding to the outside conditions
imposed upon the problem by the observational data. In other words, without
a good stock of mathematical tools, devices of the type which we find
everywhere in the Babylonian lunar and planetary theory could not be
designed. Egyptian mathematics would have rendered hopeless any attempt
to solve problems of the type needed constantly in Babylonian astronomy.”
On page 8 he wrote, “It is a serious mistake to try to invest Egyptian
mathematical or astronomical documents with the false glory of scientific
achievements or to assume a still unknown science, secret or lost, not found
in the extant texts.”
Neugebauer wrote (1969) on page 78, “The handling of fractions always
remained a special art in Egyptian arithmetic. Though experience teaches
one very soon to operate quite rapidly within this framework, one will
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readily agree that the methods exclude any extensive astronomical
computations comparable to the enormous numerical work which one finds
incorporated in Greek and late Babylonian astronomy. No wonder that
Egyptian astronomy played no role whatsoever in the development of this
field.”
From the many ancient texts of the Egyptians we conclude that they did not
apply mathematics to astronomy before the time of Alexander the Great.
After that time, the city of Alexandria was founded and the leading Greek
mathematicians and astronomers settled in that city of Egypt, so that it
became the world's leading center of Greek astronomy. But this was not part
of ancient Egyptian culture; instead, it was the transplanting of Greek
science into Egypt by foreigners due to the newly constructed city of
Alexandria with its modern marble streets and its grand marble museum and
library. This combination museum and library with its many lecture halls
became the best ancient equivalent to a modern university, and its library
became the greatest one in ancient times.
[13] Did Abraham teach Mathematical Astronomy to the Egyptians?
The Jewish historian Josephus (37 – c. 100) wrote a history of the Jews that
has many details that are not found in Scripture, and the question arises
concerning whether these details are true. One of these details concerns the
abilities of Abraham and the Babylonian knowledge of mathematical
astronomy at the time of Abraham.
On page 83 of Josephus_4 we find at Antiquities 1:166-168, “For, seeing
that the Egyptians were addicted to a variety of different customs and
disparaged one another’s practices and were consequently at enmity with
one another, Abraham conferred with each party and, exposing the
arguments which they adduced in favour of their particular views,
demonstrated that they were idle and contained nothing true. Thus gaining
their admiration at these meetings as a man of extreme sagacity, gifted not
only with high intelligence but with power to convince his hearers on any
subject which he undertook to teach, he introduced them to arithmetic and
transmitted to them the laws of astronomy. For before the coming of
Abraham the Egyptians were ignorant of these sciences, which thus traveled
from the Chaldaeans into Egypt, whence they passed to the Greeks.”
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The previous conclusions that were attained from archaeology with the help
of computers and the modern knowledge of mathematical astronomy are
now restated. The Babylonians were able to predict lunar eclipses by about
750 BCE with a time error of about one hour, and the Babylonians were able
to predict possible solar eclipses about 360 BCE with a time error of about
three hours. The Babylonians started the practice of predicting the sighting
of the new crescent about 450 BCE. But Abraham lived c. 2000 BCE, before
the great achievements of Babylonian mathematical astronomy occurred.
Furthermore, ancient Egypt did not possess mathematical astronomy until
the Greeks emigrated there and brought it with them after the death of
Alexander the Great in 323 BCE. We therefore conclude that Josephus did
not know the history of the acquisition of mathematical astronomy by the
Egyptians, and it does not make sense to believe that Abraham knew any
significant mathematical astronomy himself.
About a century before Josephus, other Jews bragged about Abraham’s
achievements, even in astrology! The interested reader may consult pages
146-151 of Gruen.
[14] Did Ancient Israel Excel in Advanced Mathematical Astronomy?
A good deal of effort has been put into the history of ancient astronomy in
previous chapters in order to evaluate what could have been known by
ancient Israel at the time of Moses and afterward. Ancient Israel used single
letters of their Hebrew alphabet that represented large numbers in a manner
similar to the Roman numeral system. They did not use a positional number
system with a zero as we do today. This is a great handicap that prevents
performing generalized multiplication and long division, which is essential
for mathematical astronomy.
The ancient Israelites from the time of Moses in Egypt could not have
borrowed mathematical astronomy from Egypt because Egypt did not
possess mathematical astronomical knowledge until it was brought there by
Greek astronomers more than 1000 years after Moses died. From biblical
chronology I estimate that the Israelite exodus from Egypt occurred c.1480
BCE.
Jewish scholars do not claim that the ancient Israelites had abilities in
mathematical astronomy that surpassed that of their ancient neighbors. There
is no historical evidence for it. On pages 555-556 of Langermann we find,
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“Although the sun, moon, and stars are mentioned in the Hebrew Bible, that
ancient and sacred text does not display any sustained exposition which can
be called an astronomical text. The earliest sources for a Hebrew tradition
are found in a few passages in the Talmud and Midrash [c. 200-600 CE].”
The Babylonian Talmud, specifically the section designated Rosh Hashanah
25a (RH 25a), which is on page 110 of BT-RH, quotes Rabban Gamaliel II
of Yavneh as having said, “I have it on the authority of the house of my
father's father [Gamaliel the Elder from the early first century] that the
renewal of the moon takes place after not less than twenty-nine days and a
half [day] and two-thirds of an hour and seventy-three halakin.” Since there
are 1080 halakin in one hour, this is 29.5 days 44 minutes 3 1/3 seconds.
Thus RH 25a claims that from one new moon to the next new moon is at
least this length of time. On page 308 of Swerdlow this is shown to exactly
equal the value used by the Greek astronomer Hipparchus (c. 190 - c. 120
BCE) for the average length of the month, which he wrote in the base
60 as 29;31,50,8,20 days, which equals 29 + 31/60 + 50/(60x60) + 8/
(60x60x60) + 20/ (60x60x60x60) days. But did Hipparchus derive this value
himself? No! The paper by Toomer 1980 discusses this value for the average
lunar synodic month in more detail. On page 108 footnotes 6 and 11 he
clearly points out (as he implied on pages 98-99) that the Babylonians had
already derived this value at an earlier time, and thus he shows that this
value was not first computed by Hipparchus, but accepted as true by
Hipparchus and taken by him from the Babylonians. Toomer also gives
credit to Asger Aaboe for a paper he wrote in 1955 indicating that Aaboe
realized that this number came from the Babylonians rather than Hipparchus.
On page 98 Toomer credits F. X. Kugler as apparently recognizing this in a
book he wrote dated 1900. On pages 168, 240-241 of Hunger and Pingree it
is stated that this length of an average synodic month comes exactly and
directly from column G in the Babylonian lunar System B, and on page 236
this book states that the earliest tablet containing System B material from
Babylon is dated 258 BCE. Hence this number was derived by the
Babylonians some time before 258 BCE. On page 54 of Britton 2002, John
Britton estimates the origin of the mean synodic month to c. 300 BCE.
How might ancient people determine the length of a lunar month? By taking
two widely separated eclipses of the same kind and when the moon is
traveling at about the same point in its cycle of varying velocity, and then
dividing the time length between them by the number of lunar months, one
may estimate the average length of a synodic month. Hipparchus was trying
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to compute eclipse periods, and for this purpose he used two old records of
eclipse observations from Babylon that he possessed as well as two eclipse
observations from his own lifetime. From these two pairs of eclipses
Toomer's paper explains that a computation of the average lunar synodic
month would in fact disagree with the number that he received from
Babylon, but Hipparchus accepted their number anyway. The last of the base
60 numbers above is 20, but the computation from Hipparachus' eclipse
records would instead round off this last number to a 9. While the long
division computation gives a different number, the difference between these
values is less than a tenth of a second! How accurate are these numbers (20
and 9 for the last place) compared to the true value of the average lunar
synodic month near the time of Hipparchus and the earlier Babylonians?
On page 87 of Depuydt 2002, Leo Depuydt provides the following estimated
modern computations for the mean synodic month in the years 2000 BCE,
1000 BCE, and 1 CE, and I have converted these to the Babylonian base 60
system. The computed estimated time is based upon eclipse records going
back to 747 BCE and the assumption that the trend continued in a similar
way prior to that date.
2000 BCE 29d 12h 44m 2.08s = 29; 31, 50, 5, 12
1000 BCE 29d 12h 44m 2.29s = 29; 31, 50, 5, 43.5
1 CE 29d 12h 44m 2.49s = 29; 31, 50, 6, 13.5
Compare the above modern computed lengths of the mean synodic month
through time with that of the Babylonians and the Greek astronomer
Hipparchus below.
Babylonians c. 300 BCE = 29; 31, 50, 8, 20 (also the Talmud)
Hipparchus' data c. 150 BCE = 29; 31, 50, 8, 9
We have seen that the Babylonian Talmud, which was released by Jewish
scholars c. 600 CE, uses the exact time length of a mean synodic month that
originates from ancient Babylonian astronomers at roughly 300 BCE, yet the
Talmud refers back to the house of Gamaliel in the first century for this
figure. Is it reasonable to think that some Israelites derived this time for the
average length of a lunar month independently on their own? No it is not,
because this number is slightly under one second too large based upon the
above data. The use of different eclipse records for a computation ought to
give a different result. The paper by Toomer points out that the Greek
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astronomer Ptolemy of Alexandria c. 150 CE wrote about the achievements
of Hipparchus 300 years earlier, and both of them realized that picking a
different pair of eclipses from which to compute the average length of a
lunar month would provide a different result. Ptolemy discussed the specific
nature of which eclipse records would likely produce a more reliable result,
and he based this on the earlier work of Hipparchus. The reason for the use
of different eclipses producing a different result is that the apparent speed of
the moon as observed from the earth varies at different times of the month,
at different times of the year, and at different times of the eclipse cycle
known as the Saros, which is 223 mean synodic months (18.03 years). Thus
any computation based upon a specific pair of eclipse observations will
result in a unique value for the average length of a lunar month, although
properly chosen records will provide close results.
The Babylonians began predicting the visibility of the new crescent at
roughly the year 400 BCE, and this prediction is based upon an accurate
understanding of the moon's cycle for repeating its speed variation, or lunar
anomaly, within the Babylonian System A (see the paper by Britton 1999,
especially page 244). The cycle of lunar anomaly is the Saros cycle. From
roughly this time onward they would be in a good position to be able to
judge which pair of eclipse records should produce an accurate figure for the
average lunar synodic month. As stated above, the oldest existing
Babylonian System B material is dated 258 BCE, and this system includes
the fundamental parameter that Hipparchus used for the mean synodic
month, which was championed by Ptolemy c. 150, and was later
incorporated into the Babylonian Talmud c. 600. We have no explicit
knowledge of exactly when or exactly how this length of the mean synodic
month was determined within System B by the Babylonians, although it is a
very reasonable conjecture that some pair of eclipse records from the same
part of a Saros cycle was a key. On page 45 of Britton 2002, John Britton
estimates the origin of System B to be as early as c. 330 BCE, but on page
54 his estimate for the origin of the mean synodic month is c. 300.
Pages 13 and 22 of Spier show that the modern calculated Jewish calendar
uses the approximation for the average length of a month from RH 25a in
the Babylonian Talmud, yet we now know that this came from ancient
Babylonian astronomers c. 300 BCE. The Babylonian Talmud is called
“Babylonian” because its Jewish authors lived in Babylon at the time of its
production c. 600 CE, not about 900 years earlier when the Babylonian
astronomers derived this figure. But other factors are also used for the
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modern calculated Jewish calendar, which are not due to either ancient
Babylon or Hipparchus, and are not found in the Talmud. Num 10:10 shows
a responsibility of the Levitical priesthood in declaring the “beginning of the
months”, and thus control of the calendar and its knowledge could be
expected to have been passed down from generation to generation via the
hereditary priesthood. However, after the Temple was destroyed in 70 CE
the Levitical priesthood vanished from Jewish history along with its
influence over the calendar. No writings from this priesthood have survived
from before the destruction of the Temple, except for the fact that Josephus
was a priest who was born in 37 CE and died c. 100. While his writings
exist, none of them were written before the destruction of the Temple, and
he does not discuss when a month begins in any direct way. He never
mentions any astronomical calculations being done by the ancient Jews, and
neither does Philo of Alexandria (c. 20 BCE - c. 50 CE).
In order to perform the mathematical computations for general long division
of fractional numbers that would be necessary for predictive astronomy, it
would be necessary to utilize a number system with a base, which would
therefore enable a positional notation and the use of a symbol for zero. For
computational uses without a computer, modern society uses the base 10 for
ordinary purposes, although modern computers use the base 2, and for the
sake of human ease of readability, the base 2 is typically converted to base
16 (hexadecimal) for computer professionals. The Babylonians and Greeks
used the base 60 number system for their capable calculations. After the
achievements of the Babylonians and Greeks in the Eastern Hemisphere, the
Mayan Indians in the Western Hemisphere used the base 20 number system.
The way that the Hebrew text of the Bible expresses numerical values
indicates that the ancient Israelites did not use a positional number system
with a base and a symbol for zero.
Hence, from a mathematical viewpoint along with the lack of any
archaeological evidence to the contrary (although there are archaeological
discoveries in the site of ancient Israel), it is safe to conclude that ancient
Israel, before the destruction of Solomon’s Temple by Nebuchadnezzar in
586 BCE and the three waves of Israelite exile to Babylon from 604–586
BCE, did not possess the type of mathematical abilities that would have
enabled them to perform the mathematical computations needed for success
at predictive astronomy.
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The ancient pagan Babylonian priests were interested in astrology. They
predicted the future of kings and kingdoms. They gained wealth and political
prestige through this practice until Daniel told both the dream and its
interpretation to the king (Daniel 2). They then lost political prestige, but
their pagan practices continued as they developed horoscopy. Some of these
pagan priests were the predictive astronomers. Their desire for wealth and
prestige led to their efforts at computational and predictive astronomy. The
Greeks had a greater interest in science for the sake of knowledge, although
they too were interested in astrology and its use to gain wealth. The leisure
time to devote to astronomy came from the wealth gained by astrology.
The historical evidence indicates that neither the ancient Israelites before the
destruction of Solomon's Temple in 586 BCE nor the Jews after this until the
destruction of the Second Temple in 70 CE sought to develop their own
mathematical astronomy. Ancient Egypt before Alexander the Great did not
possess any predictive mathematical astronomical knowledge, so ancient
Israel could not have inherited such knowledge from them. Neither the
Bible, nor archaeology, nor Jewish history give any indication that Israelites
before the destruction of the Second Temple in 70 CE had advanced abilities
in mathematical astronomical knowledge. It was not until the time of
Alexander the Great, that ancient astronomers were able to approximately
predict the time of the true conjunction.
The difference in time between the computed average time of the
conjunction (based on repeated additions of the average synodic lunar
month, which is employed in the modern calculated Jewish calendar) and the
true conjunction is about 14 hours according to page 45 of Wissenberg. Thus
the modern calculated Jewish calendar (MCJC) is not based upon predicting
the true conjunction. The Jews at the time of Moses were not using the
MCJC with its adoption of the Babylonian length of the average month, and
they were not able to calculate the time of the conjunction.
[15] Appointed-times and Years are known from Lights in the Sky
I will examine Gen 1:14-15 to show that appointed-times and years are
determined from lights in the sky.
Gen 1:14, “And the Almighty said: Let there be lights [3974 mahohr] in the
expanse of the heavens to separate between the daytime and between the
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night, and let them be for signs, and for appointed-times [4150 moed], and
for days and years.”
Gen 1:15, “And let them be for lights [3974 mahohr] in the expanse of the
heavens to give light on the earth, and it was so.”
In verse 15 the word “them” refers back to the subject in verse 14, namely
the lights. Thus verse 15 is saying in essence, “let the lights be for lights ...
to give light on the earth”. Even the names of the heavenly bodies are absent
to put emphasis on the “light bringing” purpose and mission of these
heavenly bodies to fulfill the need to determine “signs, appointed-times,
days, and years”. The triply emphasized mission of light from the heavenly
bodies to supply light to determine appointed-times and years must be given
its appropriate place in thought and use.
The word “signs” [226 oht] in Gen 1:14 is used for the rainbow in Gen 9:12-
13, for the ten plagues in Egypt, for the Sabbath in Ex 31:13, 17, for a
miracle in Judg 6:17, for the prediction of two deaths in I Sam 2:34, and in
other ways. Gen 1:14 is saying that the lights in the heavens are examples of
signs. Carefully reread Gen 1:14 to note that it is not saying that signs [226
oht] are to determine the appointed-times and years. The subject of the
sentence is the lights in the sky, not the signs. The lights in the sky
determine signs. The lights in the sky determine appointed-times. The lights
in the sky determine days. The lights in the sky determine years. Verse 15
shows that it is some aspect of the light from these lights in the sky that
cause the determination.
For the sake of completeness and to continue to show the use of the light
from these heavenly lights, I now literally translate Gen 1:16-18.
Gen 1:16, “And the Almighty made the two great lights [3974 mahohr], the
greater light [3974 mahohr] to rule the daytime and the lesser light [3974
mahohr] to rule the night, and [He made] the stars [to rule the night].”
Gen 1:17, “And the Almighty set them in the expanse of the heavens to give
light upon the earth”
Gen 1:18 “and to rule by daytime and by night, and to separate between the
light and between the darkness.”
The nature of the rulership of the heavenly lights mentioned in verses 16-18
is the dominance of their light, which again puts emphasis on the light from
these lights. At the end of verse 16, concerning the stars, I added in brackets
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“to rule the night” because that is exactly what is mentioned about the
heavenly lights, including the stars, in verse 18.
There are people who teach that the biblical month begins at the sundown of
a day when the moon cannot be seen at all. Some people will use the time of
the conjunction (astronomical new moon). I will call this theory the invisible
moon theory or the conjunction theory. This is contrary to the biblical
emphasis and stress on the use of light to determine the appointed times.
On various occasions I have heard advocates of the conjunction theory claim
that before the Babylonian captivity under Nebuchadnezzar, ancient Israel
(specifically the House of Judah) determined the start of a month with the
sundown that began a day, but the moon was invisible near that sundown.
These people go on to claim that after the return from captivity under Ezra
and Nehemiah, Israel, under the influence of the Babylonian calendar and
Persian political dominance, no longer continued the alleged original
practice since the time of Moses. To judge the rationality of this view, let us
read a couple of verses from Neh 8.
Neh 8:2, “And Ezra the priest brought the law before the assembly of men
and women and all who could hear with understanding on the first day of the
seventh month.”
Neh 8:9, “And Nehemiah who [was] the governor, and Ezra the priest the
scribe, and the Levites who taught the people, said to all the people: Today
is holy to YHWH your Almighty.”
Since the day that is stated to be the first day of the seventh month is
definitely declared to be holy, it must have been determined correctly, and
this was after the return from the captivity under Ezra and Nehemiah. Hence
they could not have adopted a pagan practice contrary to what was correct
under the law as taught by Moses. The Levitical priesthood had the proper
pattern to determine the start of a month set in motion from this day onward
down through the later centuries until the Temple was destroyed in 70 CE,
and there is no known time during which the priesthood is thought to have
had any significant doctrinal upheaval in its own ranks during this period.
[16] A Month is a Cycle of the Moon
No discussion has yet been given concerning the meaning of appointed-
times in Gen 1:14.
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Ps 104:19, "He made the moon [3394 yahrayach] for appointed-times [4150
moed], the sun knows its going-away."
This use of appointed-times establishes that the moon is one of the heavenly
bodies specifically indicated in Gen 1:14.
I Ki 6:38, "And in the eleventh year in the month [3391 yerach] Bul, it [is]
the eighth month [2320 chodesh], the house was finished for all its parts and
for all its plans, thus he built it seven years."
I Ki 8:2, "And all the men of Israel were assembled toward King Solomon at
the feast in the month [3391 yerach] Ethanim, which [is] the seventh month
[2320 chodesh]."
Strong's number 3394 for moon (yahrayach) and Strong's number 3391 for
month (yerach) have the same three Hebrew consonants and look the same
when the vowels points are removed. (In the Hebrew language the 22 letters
shown in the sections of Ps 119 are called consonants even though some of
them act as vowels. The original Hebrew text of the Scriptures only had
these 22 consonants. The vowels points (and some such marks are more than
points, but that is the term by which they are called in Hebrew school) were
added to aid pronunciation by the Masoretes about the year 650. This
identical original appearance in the Hebrew word for moon (3394) and the
Hebrew word for month (3391) shows that a biblical month is a cycle of the
moon. These verses, I Ki 6:38; 8:2, also have another word for month [2320
chodesh], and it shows that the two different words, yerach and chodesh,
indicate the same thing, a month.
[17] Full Moon occurs about the 14th and 15th Days of the Biblical Month
Ancient Semitic writings in Ugaritic that are discovered through
archaeological excavations do not show the vowel signs that have been
common to biblical Hebrew since c. 650 when the Masoretes added these
marks to help the reader to pronounce the words. Scholars who transliterate
the Ugaritic words into English letters do not add the vowels because they
are not in the original writings. Scholars often write the Hebrew letter chet
as h instead of ch as I have done. If the vowels are omitted and only one
English letter is written for one Hebrew letter, the two Hebrew words for
month could be written yrh and hds, instead of yerach and chodesh. In words
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that are cognate between Ugaritic and Hebrew, the sound for t in Ugaritic
often replaces the sound for the letter shin (written sh or merely s) in
Hebrew. The Ugaritic language has the cognate words for both of the
Hebrew words for month, and scholars write them yrh and hdt!!!
The Hebrew word for “day” is yom, and without the vowel marks, it is ym,
The Ugaritic cognate word for “day” is also written ym!!!
On page 270 of the book by Pardee where he discusses the pagan context in
the Ugaritic Kingdom, we find the following about the Ugaritic word yrh,
“yrh, cognate with Hebrew yareh; ‘new moon’ is expressed by the word hdt
alone, literally ‘newness,’ in the phrase ym hdt, ‘day of the new moon’; the
plural hdtm in text 58 (RS 19.015.13) designates a series of ‘royal sacrificial
feasts’ extending over an unknown number of months; ‘full moon’ is
expressed by mlat, literally ‘fullness,’ also with the word for ‘day’ (ym mlat,
‘day of the full moon’); in terms of sacrifices offered, the new moon festival
was less important than that of the full moon.”
On pages 271-272 of the book by Gregorio del Olmo Lete, we find the
following, “According to its heading, the Ugaritic text KTU 1.109 can be
defined as ‘a sacrificial new-moon ritual,’ either on a particular month or,
more probably, during each month of the year. In any case, this is the only
indication of time for the ritual act: the 14th-15th day of the month, ym mlat
(lit.: ‘day of fullness’). The translation of the Ugaritic text is given as
follows on page 273, “On the fourteenth day the king washes (remaining)
purified. On the day of the full moon two month-old head of cattle are felled
as a banquet offering to Balu of Sapanu, (plus) two ewes and one ‘domestic’
dove; …”
As was discussed near the beginning of this study, the Hebrew language of
ancient Israel developed using the basic vocabulary of the language of
Canaan and the nearby peoples, so that the cognate words of the same
context should have the same meaning. From the Hebrew words in the
Scriptures relating to the cognate words in Ugaritic, this shows that the full
moon occurs near the 14th or 15th day of the biblical month.
[18] A Biblical Month is a Whole Number of Days
A cycle of the moon around the earth is about 44 minutes more than 29.5
days, but in this chapter we shall see from some verses using both of the
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Hebrew words for month, namely chodesh and yerach, that biblically
speaking, a month is a whole number of days, with no fraction remaining. In
Judea in the first century the Jewish culture did use a common term for hour,
but earlier in ancient Israel’s history, there is no small subdivision of time
such as hours or minutes. However, by some unknown means, the night was
apparently split into three “watches” (Ex 13:34; Judg 7:19; Ps 63:6; 90:4;
119:148; Lam 2:19).
If there is always clear weather for good visibility, and the sighting of the
new crescent is made from Israel, then every month should have 29 or 30,
days. This is not true for all places on the earth. For example, with good
visibility from southern Australia, on rare occasions there can be a 31-day
month.
The literal expression a month of days as seen in several verses below, is
idiomatically translated a full month in almost all translations. These
examples show that a biblical month is a whole number of days.
Gen 29:14, “And he dwelt with him a month [2320 chodesh] of days.”
Num 11:19, “You shall not eat one day, or two days, or five days, or 10
days, or 20 days,”
Num 11:20, “[but] until a month [2320 chodesh] of days, until it comes out
from your nostrils, and it will be loathsome to you because you have rejected
YHWH who is among you, and you have wept before Him saying, Why did
we go out of Egypt?”
Num 11:21, “And Moses said, the people [are] 600,000 on foot among
whom I am, and You said, I will give them flesh that they may eat a month
[2320 chodesh] of days.”
Deut 21:13, “and she shall put off her captive's clothing and remain in your
house, and grieve for her father and mother a month [3391 yerach] of days.
And after that you may go in to her and be her husband and she will be your
wife.”
II Ki 15:13, “Shallum the son of Jabesh reigned in the 39th year of Uzziah,
king of Judah, and he reigned a month [3391 yerach] of days in Samaria.”
[19] A Biblical Month has a Maximum of 30 Days
We have seen that a biblical month is a cycle of the moon around the earth,
and it is a whole number of days. A cycle of the moon averages a little more
than 29.5 days. Suppose the moon cannot be seen at all for some number of
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days when the month would normally be expected to end? How many days
can a biblical month continue if the moon is not seen at all? There is a
prophetic time when the moon will not give its light.
Isa 13:9-10, “Behold the day of YHWH comes, cruel with both wrath and
fierce anger, to lay the land desolate. And He will destroy its sinners from it.
For the stars of heaven and their constellations will not give their light. The
sun will be darkened in its going forth, and the moon will not cause its light
to shine.”
Note the similarity to Joel 2:1-2; Ezek 32:7-8. The time length of the lack of
light from the moon is not clear from this. All of the “day of YHWH” may
be included, and the use of the word “day” here may refer to a lengthy time.
To students of biblical prophecy the context of Dan 7:21-27 fits that of the
day of YHWH. The following begins to explain an important prophetic time
period called a “time and times and half a time”.
Dan 7:25, “He shall speak pompous words against the Most High, shall
persecute the saints of the Most High, and shall intend to change times and
law. Then the saints shall be given into his hand for a time and times and
half a time.”
This identical expression is also mentioned in Dan 12:7 and Rev 12:14. The
context of Rev 12:14 fits perfectly with Rev 12:6, and the latter is explicitly
stated to be 1260 days.
The beast of Rev 13:6 fits perfectly with the beast of Dan 7:25, which is the
fourth beast in Dan 7:7-8, 19-27. The “time and times and half a time” in
Dan 7:25 was already shown to refer to 1260 days. Therefore, the 42 months
that are mentioned in Rev 13:4-6 is the same time period of 1260 days,
which is a “time and times and half a time”.
Now “42 x 30 = 1260” and here “42 months is 1260 days. In this
circumstance a month divides out to be 30 days. This may be explained by
recognizing that the moon will not give its light, as shown above in Isa 13:9-
10 and Ezek 32:7-8.
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The result of this examination is the conclusion that a month is not permitted
to have more than 30 days if the moon does not give its light or is not
visible.
While some people may conjecture that astronomy will be altered to
miraculously force a month to have 30 days at this future time, it seems
more rational that the miracle of the lack of light from the moon will prevent
a month from exceeding 30 days.
There is another miracle associated with “the shadow of the sun dial of Ahaz
going back 10 degrees” in II Ki 20:11 and Isa 38:8. But the context
associates this with the time of Sennacherib, king of Assyria, in II Ki 19:35-
37; 20:6; Isa 38:6. The 14th year of Sennacherib is mentioned in both II Ki
18:13 and Isa 36:1, and secular history along with biblical reference works
date this to 701 BCE. However, archaeological evidence from Babylonian
cuneiform inscriptions of astronomical eclipses and other events perfectly
agree with computer calculations going backwards to 747 BCE, which verify
the unchanging continuation of the orbits of the heavenly bodies back to that
time. This proves that the miraculous event associated with “the shadow of
the sun dial of Ahaz going back 10 degrees” was a miracle as perceived by
people concerning the miraculous placement of light and shadow. Although
a literal translation of Isa 38:8 appears to say that the sun itself moved back
10 degrees, the context is discussing the shadow of the sun moving 10
degrees rather than the sun itself. Hence “the shadow of” should be added in
italics in order to read, “So the shadow of the sun returned 10 degrees” in
verse 8.
People have conjectured that astronomy became altered during “Joshua’s
long day” (see Josh 10:12-13). The earth rotates on its axis to produce the
visual effect of the sun moving around the earth. But the sun does not
actually move around the earth. When Joshua requested that the sun stand
still, this was according to Joshua’s perception that the sun actually moved
rather than the earth rotating. In this miracle, according to the literal Hebrew
wording, both the sun and the moon appeared to stop moving according to
human perception, so that light would be provided for the battle. The Bible
is not clear how this miracle came to pass. This may have been a miracle of
light perception or light movement rather than a temporary cessation of the
rotation of the earth and a temporary cessation of the movement of the moon
around the earth, or some other alteration of orbits involving the sun, earth,
and moon. An astronomical alteration would have required a combination of
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many miracles including the prevention of massive ocean floods upon many
shores as well as the falling of buildings and the imbalance in standing living
creatures during the massive change in bodily momentum as the earth’s
rotation would have been affected. It is far more plausible that the miracle
involved human perception of light rather than an alteration in the relative
position of the heavenly bodies. In any case, Joshua’s request does not take
into account the reality of what happens astronomically, namely, that the
earth rotates instead of the sun moving around the earth. There is too little
information about this in the Bible to conclude that orbits were altered.
During the time of the flood there is another unusual association with the
length of a month. Gen 7:11 mentions that the flood began on the 17th day
of the second month. In Gen 8:3-4 the wording seems to imply that 150 days
passed until the 17th day of the seventh month. Here five months seem to
total 150 days, which divides out to 30 days per month. This may be
explained by realizing that with so much water covering the earth, there
would be thick clouds (with much rain at the beginning), so that when the
month would normally begin, no moon could be seen to mark its beginning.
Therefore, the maximum length of the month, namely 30 days, would be
permitted.
The extent of a month is from one sundown to some later sundown, with a
total of 29 or 30 days, at least in theory. In practice, if there is a succession
of months for which the sky is cloudy or rainy over all of Israel where
people reside on days near the start of each of those months, then each of
those months will have the maximum number of days per month, namely 30
days. Then, when the weather first becomes clear at the start of a month, that
month may have less than 29 days to make up for the artificial prolongation
of some months to 30 days.
[20] The Sun and Moon are the Primary Lights in Gen 1:14
To explain the significance of the translation “appointed-times” in Gen 1:14,
let us now consider the following.
Lev 23:2, “The appointed-times [4150 moed] of YHWH which you shall
proclaim [to be] holy convocations, My appointed-times [4150 moed] are
these:”
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Lev 23:3, “Six days work may be done, but on the seventh day is a Sabbath
of rest, a holy convocation, you shall not do any work, it is a Sabbath to
YHWH in all your dwellings.”
Lev 23:4, “These [are the] appointed-times [4150 moed] of YHWH, holy
convocations which you shall proclaim in their appointed-times [4150
moed]:”.
These verses show that the appointed-times discussed in this chapter are
days upon which there is to be a holy convocation. In Lev 23:3 note that the
appointed-times include the Sabbath that repeats every seventh day. But this
Sabbath example of an appointed-time [4150 moed] is not determined by the
moon; instead it is determined by counting days, and days are determined by
the alternation of darkness during the night followed by light during the day.
This alternation of darkness and light is a result of the alternation of the
absence and presence of the light from the sun, so that the sun is involved in
determining this appointed-time, the Sabbath, but the moon is not involved
for the following reason. Each month (or specific cycle of the moon) there
are from one to three nights during which the moon cannot be seen at all,
even with clear weather. During this period of invisibility of the moon, the
days that are counted to arrive at the Sabbath have no contribution in
counting light by the moon because the moon cannot be seen at that time.
Notice the following description of rulership or dominance by the light of
the heavenly bodies.
Ps 136:7, “To Him who made the great lights ...”
Ps 136:8, “The sun to rule in [the] daytime ...”
Ps 136:9, “The moon and the stars to rule in [the] night ...”
These verses show that the sun and moon are called the great lights, but the
stars are also said to rule in the night. If it is not cloudy or rainy all night
(and sometimes it is), it is possible to count the days by counting the nights
during which one sees the stars as well as the daytimes during which one
sees light given by the sun. However it is not possible to count days by
counting the light from the moon due to its varying period of invisibility
each month.
The use of the sun rather than the moon to determine the count to the
Sabbath as an appointed-time, as well as calling the sun and the moon “the
great lights” in Ps 136:7-9 and declaring the moon to be for appointed-times
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in Ps 104:19, show that the sun and moon are the major contributors as
lights to determine the appointed-times.
When one considers all the lights in the sky (sun, moon, stars, planets, and
comets), the stars, planets, and comets do not have a cyclical period that
matches the cycle of the year on the earth. Due to precession of the
equinoxes, every 1000 years the stars shift 14.1 days further away from the
vernal equinox. Therefore, by eliminating the other choices from
consideration, the last word in Gen 1:14, “years” must involve the sun in
some way.
[21] Blowing two Silver Trumpets on the Day that Begins each Month
Num 10:1-2, “And YHWH spoke to Moses saying, Make yourself two
trumpets of silver. You shall make them of a hammered piece. And they
shall be for summoning the assembly and for the breaking of the camps [to
prepare to travel].”
The Hebrew noun (used as a gerund) that I translated “summoning” is
meekra and has Strong's number 4744 (see BDB page 896, column 2). The
Hebrew noun that I translated “assembly” is adah and has Strong's number
5712 (see BDB page 417, column 1).
Num 10:8, “And Aaron's sons, the priests, shall blow with [the two silver]
trumpets.”
Num 10:10, “And on [the] day of your gladness, and on your appointed-
times [4150 moed], and on the beginnings of your months [2320 chodesh],
you shall blow with [the two silver] trumpets over your burnt offerings and
over [the] sacrifices of your peace offerings, and they shall be to you for a
memorial before your Almighty; I am YHWH your Almighty.”
Two general purposes are mentioned for these two silver trumpets in verse
2: (1) summoning the assembly, and (2) for the breaking of the camps. The
latter purpose is relevant during the 40 years of wandering in the wilderness
when they journeyed from place to place, and they also journeyed when
going to war. Whenever the relevant people were called together for the
purposes mentioned in this section, the trumpets were blown in specific
ways to signal the nature of the event.
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This shows that the Levitical priests were to blow two silver trumpets on all
the important occasions, which included the first day of each month as well
as on the appointed-times, and the latter include each seventh day recurring
Sabbath as shown in Lev 23:2-3.
[22] Hebrew chodesh refers to the Day that Begins each Month
Now compare Num 10:10 with I Chr 23:30-31.
I Chr 23:30, “and [the sons of Aaron are] to stand every morning to thank
and to praise YHWH, and likewise at evening,” I Chr 23:31, “and for all the
burnt offerings to YHWH for the Sabbaths, for the new-moons [2320
chodesh], and for the appointed-times [4150 moed] in the count [of animals],
[according to the] ordinance concerning them continually before YHWH.”
In I Chr 23:31 above we notice that the burnt offerings on the new moons
[2320 chodesh] are mentioned, and in Num 10:10 above we notice that the
burnt offerings on the beginnings of your months [2320 chodesh] are
mentioned. The whole phrase “beginnings of your months” appears in verse
10 compared to “new-moons” in verse 31, showing that a month begins with
a new moon. Verse 31 translated this word chodesh as “new-moons”, while
verse 10 translated the same word as “months”. Other examples also show a
double meaning for this word. Some examples where chodesh means
“month” are Gen 29:14; Num 10:11; I Ki 5:14. Some examples where
chodesh means “new-moon” are II Ki 4:23; Ezek 46:3; Hos 2:11; Amos 8:5.
The last verse indicates that in ancient Israel the new moon day was treated
as a public holiday where businesses were closed, although refraining from
work on a new moon is not stated as a commandment in the law of Moses.
It has already been shown that a cycle of the heavenly body called the moon
determines a month. The translation “new-moon”, but without the hyphen, is
the common translation for chodesh when it refers to the beginning of a
month. Nevertheless, one may question whether “new-moon” is the best way
to translate chodesh. Based upon Num 10:10 one may translate this single
Hebrew word as “month-start” or “new-month” since it is definitely the
beginning of a month. As already seen above, the word for moon is
yahrayach [3394], which has no resemblance to chodesh. No Hebrew word
for the physical body called the moon has a resemblance to the Hebrew word
chodesh.
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It is only through the other Hebrew word for month, yerach [3391], that we
have the connection to the physical body known as the moon. On this basis it
would be more literal to translate the Hebrew word chodesh as “month-start”
or “new-month”. The Hebrew noun chodesh [2320] has the same consonants
as the Hebrew adjective chadash [2319] (almost always translated “new”)
and the Hebrew verb chadash [2318] (about half the time translated “renew”
and half the time “repair”). The month following any month is not a renewal
of the previous month or a repair of the previous month; instead it is indeed
a new month. While the translation of chodesh as “new-month” seems more
literal and precise than “new-moon”, the latter is so firmly accepted that this
will be used in the present study.
What about the suggestion to translate chodesh as “renewed-moon”? The
moon itself is older than it was the previous month and the physical body
itself is not renewed. If one wishes to make a case for translating the word
chodesh as “renewed-moon” based upon the light from the moon, this is
quite subjective because chodesh has the primary affinity with month, and
the month is “new”, not “renewed”.
If we apply Num 10:1-2, 8, 10 to the beginnings of the months as specified
in verse 10 along with “summoning the assembly” in verse 2, the following
conclusion is drawn. Two priests were to blow two silver trumpets to
summon the assembly and thereby announce that a new month had begun.
Deut 16:16 shows that only three times during the year all men are
commanded to appear at one central place, not at the start of all the months.
Therefore, the summoning of the assembly at the beginning of their months
pertained to those people that were near the one place where the two silver
trumpets were blown and the sacrifices were performed, not all people
throughout the nation.
Num 10:10 shows the authority of the priesthood in declaring the start of
each month through the blowing of the two silver trumpets. Num 28:11 also
has the same phrase “and on the beginnings of your months”. The passage in
Num 28:11-15 describes the burnt offerings, the grain offering, and the drink
offering that is specific for the priests to perform on the beginnings of their
months. At this time when the people heard the specific sound of the two
silver trumpets blown by the two priests, they then knew that the ceremony
of the offerings for the beginning of the month were to begin soon. This
sound would summon the people who were within a reasonable distance to
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come and witness the priestly ceremonies associated with the beginning of
the month. This would be an occasion for prayers, singing, and playing
musical instruments when the priesthood fully developed the service for the
beginning of the month.
[23] The Biblical New Moon relates to the Sighting of the New Crescent
We have seen that a month is a cycle of the moon, and the full moon
typically occurs on the 14th or 15th day of the biblical month. We have also
seen from Gen 1:14-18 that a month begins using the light from the moon as
a visual indicator. The only visual discernable candidates for the biblical
new moon that are available from this information are the old crescent and
the new crescent.
Ancient Egypt had a civil calendar that ignored the cycle of the moon. But
according to page 140 of Depuydt 1997, ancient Egypt also had a religious
calendar that began its month with the morning one day after the old
crescent was seen in the morning. The reason they waited until the morning
after the morning on which the old crescent was seen, is that they could not
know that the old crescent was actually the old crescent until one morning
later when nothing was seen. When a narrowing crescent is not especially
thin, maybe it will not be the old crescent or maybe it will. This can only be
known one morning later because the old crescent is, by its definition, the
last of the narrowing crescents during the moon’s cycle. This requirement to
wait until one morning after the old crescent is one significant difference
between the determination of the old crescent and the determination of the
new crescent. When the new crescent is seen, it is immediately known
because it had not been seen the night before.
In the previous chapter it was mentioned that Hebrew noun chodesh [2320]
(meaning month as well as new-month or new-moon) has the same
consonants as the Hebrew adjective chadash [2319] (almost always
translated “new”, and having the meaning “new”) and the Hebrew verb
chadash [2318] (about half the time translated “renew” and half the time
“repair”). Hence the collective association of new, renew, and repair is
associated with the Hebrew word chodesh, rather than the concept of old,
dwindling, or thinning, which is associated with the old crescent. Therefore,
from the choice of the Hebrew word chodesh for the new-moon, it must
refer to the new crescent rather than the old crescent.
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An astronomical reason for a biblical month consisting of a whole number of
days is that each new crescent first becomes visible close to sundown when
the Sabbath begins and when a numbered day of the month begins. We thus
see that from the biblical viewpoint, the average synodic month as a precise
fraction of days, hours, and minutes is never hinted at in Scripture and is
foreign to biblical thought.
Ezra 6:15 mentions the month Adar and Neh 6:15 mentions the month Elul.
These are Hebrew transliterations of month names in the Babylonian
calendar, but these verses are in the context of Jerusalem. Scripture is a
witness here that ancient Israel adopted the month names of the Babylonian
calendar at the time of Ezra and Nehemiah. This would cause severe
confusion unless a biblical month began by the method of the Babylonian
calendar. Indeed, a month in the Babylonian calendar began with the day
whose beginning evening was close to the time that the new crescent was
seen in the western sky. But no month was permitted to have more than 30
days in the Babylonian calendar. This corroborates what was already
determined from other biblical and archaeological evidence.
[24] Philo of Alexandria and the Jewish New Moon in the First Century
As a Jew living in Alexandria, Egypt in the early first century, Philo
discusses the new moon from his Jewish perspective. On page 333 of
Philo_7 (Special Laws 2:41) Philo wrote, “The third [feast recorded in the
law] is the new moon which follows the conjunction of the moon with the
sun.” Since this follows the conjunction, it must refer to the (visible) new
crescent. On pages 391 and 393 of Philo_7 (Special Laws 2:141-142) Philo
wrote, “Following the order stated above, we record the third type of feast
which we proceed to explain. This is the New Moon, or the beginning of the
lunar month, namely the period between one conjunction and the next, the
length of which has been accurately calculated in the astronomical schools.
The new moon holds its place among the feasts for many reasons. First,
because it is the beginning of the month, and the beginning, both in number
and in time, deserves honour. Secondly, because when it [the new moon]
arrives, nothing in heaven is left without light, for while at the conjunction,
when the moon is lost to sight under the sun, the side which faces earth is
darkened, when the new month begins it resumes its natural brightness. The
third reason is, that the stronger or more powerful element [the sun] at that
time [the new moon] supplies the help [light] which is needed to the smaller
and weaker [the moon]. For it is just then [at the new moon] that the sun
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begins to illumine the moon with the light which we perceive and the moon
reveals its own beauty to the eye.”
In Alexandria, the leading center of Greek mathematical astronomy at that
time, the conjunction is a well known concept to Philo, and he mentions the
conjunction as a contrasting time to the new moon. It is clear that to Philo
the Jew in the early first century in Alexandria, the new moon is the new
crescent, and this begins the first day of the Jewish month. Evidently the
Greek geometrical abstract concept of the conjunction had filtered down to
the educated non-astronomer, Philo. He used this concept in writing to his
audience without defining it, so he understood that his audience would also
understand this term.
[25] Did the Jews use Calculation for their Calendar in the First Century?
On page 302 of The Mishnah the section Rosh Hashannah 2:8 appears,
which Neusner subdivided into parts “A” through “I” as follows, and
Neusner wrote what is in square brackets below. This is quoted word for
word.
A. A picture of the shapes of the moon did Rabban Gamaliel have on a tablet
and on the wall of his upper room, which he would show ordinary folk,
saying, “Did you see it like this or like that?”
B. M'SH S: Two witnesses came and said, “We saw it at dawn [on the
morning of the twenty-ninth] in the east and at eve in the west.”
C. Said R. Yohanan Nuri, “They are false witnesses.”
D. Now when they came to Yabneh, Rabban Gamaliel accepted their
testimony [assuming they erred at dawn].
E. And furthermore two came along and said, “We saw it at its proper time,
but on the night of the added day it did not appear [to the court].”
F. Then Rabban Gamaliel accepted their testimony.
G. Said R. Dosa b. Harkinas, “They are false witnesses.”
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H. “How can they testify that a woman has given birth, when, on the very
next day, her stomach is still up there between her teeth [for there was no
new moon!]”
I. Said to him R. Joshua, “I can see your position.”
Now I have some comments on the above.
(A) Due to the other names, this is considered to be the grandson of the
Gamaliel in the NT, and this is considered by Orthodox Jews to be in the
second century, perhaps about 110.
(B) The story may be invented to illustrate the stature and greatness of
Gamaliel II. One cannot accept the historical truthfulness of everything in
the Mishnah.
(C) Part A above is taken by Orthodox Jewish commentators including
Maimonides to imply that Gamaliel II was able to calculate what the new
moon should look like and whether it could be seen, and through his
questioning of the witnesses and his calculations he could judge whether the
witnesses were lying. But this is reading far too much into what is said.
Assuming that this is historically true, Gamaliel may simply be trying to
rattle the witnesses, so that they would not try to falsely testify. In other
words, he wanted to see how confident they would be in their claim. Each
year at about the same season, the angle of the new crescent would be
generally the same, but not exactly the same. Thus an ignorant person would
not know approximately what it ought to look like, but a knowledgeable
person would know its approximate angle, although a knowledgeable person
at that time in history would not know in advance whether it would be seen.
On the other hand, in the majority of cases months did alternate with 29 and
30 days.
(D) This is the entire evidence that exists of the claim that in ancient times
learned Jews could calculate whether the new crescent could be seen.
(E) The claim in B is false because it is not possible to see the old crescent
and the new crescent so close together in time.
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(F) The statement at the end of E indicates that on the next night the court
was not able to see the new crescent, and this is the reason for the analogy
given in part H.
(G) Parts G and I indicate that some people doubted that the alleged
witnesses saw the new crescent, despite the fact that Gamaliel II accepted
their testimony.
(H) The whole procedure and interest in obtaining witnesses for having seen
the new moon should make it obvious that if its visibility was declared at the
end of the 29th day, then the ending month had only 29 days. Hence they
were not using a calculation to determine the start of a month.
From the above, does it seem rational to accept the opinion and
interpretation that in the early second century Jewish leaders could calculate
whether the new crescent could be seen? Certainly not.
[26] The Biblical Year is a Whole number of Biblical Months
A tropical year is the average time from one vernal equinox to the next
vernal equinox, or equivalently, from one autumnal equinox to the next
autumnal equinox. In ordinary speech this is also called the solar year, and it
approximates the agricultural year without drifting away.
Since a biblical month averages about 29.5 days, a 12-month period will
contain about 354 days and a 13-month period will contain about 384 days.
But a tropical year contains about 365.2422 days, which is about 11 days
more than 12 biblical months.
Leviticus 23 is the most concentrated single area of the Hebrew Bible
dealing with calendaric aspects of the festival days. Upon reading through
Lev 23 it should be noted that months are never mentioned by name in this
chapter, but always by numbered occurrence through the year. Thus once the
first month is determined, all the other months are determined because they
follow sequentially by number. The first month maintains a fixed
relationship to the festivals. But now it will be shown that the festivals
maintain a fixed relationship to the agricultural year in Palestine. Ex 34:22
shows that the Feast of Weeks approximates the wheat harvest. Ex 23:16
shows that the Feast of Ingathering approximates a harvest time of the year.
Deut 16:13 shows that the Feast of Booths approximates a harvest time of
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the year, but a comparison of Ex 23:14-17 and Deut 16:16 shows that the
Feast of Ingathering is the same as the Feast of Booths. Since there is no
harvest in Palestine during late autumn and winter, the festivals must
maintain an approximately fixed relationship to the agricultural year.
Therefore, the first month must maintain an approximately fixed relationship
to the agricultural year and hence the tropical year. Technically this is
expressed by saying that the biblical calendar is lunar-solar in nature.
The Bible has an example of a year with 13 months, showing that the
biblical year was not an exact tropical year. Here is the example. The time
difference between Ezek 1:1-2 and Ezek 8:1 is the difference between month
4 day 5 in the 5th year of King Jehoiachin's exile and month 6 day 5 in the
6th year of his exile. This is 14 or 15 months depending on whether the 5th
year of his exile had 12 or 13 months. If the difference is 14 months, this is
about 29.5 times 14 (= 413) days with an overestimate of 30 times 14 (=
420) days. The overestimate of 420 days is 17 days short of the known
events because Ezek 3:15 accounts for 7 days and Ezek 4:4-6 accounts for
390 plus 40 days, the total being 437 days. Thus the difference must have
been 15 months, which is about 29.5 times 15 (= 442.5) days, just five or six
days more than the known events of that time period.
If one should claim that the 5th year of the king's exile was a tropical year,
and an overestimate of 366 days (“leap” year) plus 60 days (two extra
months) is allowed, the total is 426 days, which is still far short of the 437
days for the known events.
Thus, although the biblical year maintains an approximately fixed
relationship to the agricultural year, the example with 13 months shows that
the biblical year is not an exact tropical year.
It will now be shown that a biblical year consists of a whole number of
biblical months rather than a smaller subdivision such as days. A biblical
reason for this is that Num 28:14 has the Hebrew expression chodesh bh
chadshoh lh chadshay ha shanah, meaning “month by month for months of
the year”, but idiomatically “each month throughout the year”. Also, I Chr
27:1 has the Hebrew expression chodesh bh chodesh lh col chadshay ha
shanah, meaning “month by month for all months of the year”, but
idiomatically “each month throughout the whole year”. The above example
of a year with 13 months is further biblical evidence that a year consists of a
whole number of months.
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A biblical year cannot contain fewer than 12 months because Est 9:20-23, 26
maintains that each year on the 14th and 15th days of the month Adar the
Jews are to celebrate the festival called Purim. Est 8:12 states that Adar is
the 12th month. If a year could only have 11 months, then the Jews would be
unable to celebrate Purim that year. Further evidence of a requirement of at
least 12 months in the year comes from I Ki 4:7 and I Chr 27:1-15.
Hence a biblical year contains 12 months or 13 months, or approximately
354 days or 384 days. This is an illustration of the fact that the modern
cultural concept of a year always having 365 or 366 days need not
necessarily be practiced in some ancient societies.
In ancient Egypt, from some time onward, their civil calendar always had
365 days, which was divided up into 12 months of 30 days each plus five
extra days (see page 28 of the reference by Ronald Wells). The time of the
establishment of the 365-day Egyptian civil calendar has not been
convincingly proved. However, from writings that have survived from
Elephantine, Egypt during Persian rulership over Egypt, the double dating
scheme that equates certain dates in the Egyptian calendar with dates in the
Babylonian calendar unquestionably demonstrates that from 471 BCE
onward into the Middle Ages this Egyptian calendar was used (see Horn and
Wood 1954 and Parker 1955). Since this calendar loses about 1/4 of a day
each tropical year, in 120 years it would lose about 30 days. The Egyptians
certainly realized that this calendar would continuously lose time in
comparison to the agricultural year, but it did not stop them from using it
anyway. Furthermore, this Egyptian calendar became the preferred calendar
by which the best Greek astronomers in Alexandria recorded their
astronomical observations, although they knew it fell short of the tropical
year, which they measured quite accurately.
The main point in all this is to emphasize that any practical ancient calendar
may have a concept of a year associated with that calendar, so that such a
calendar year need not equal the tropical year. As long as a society considers
a calendar year sufficiently practical for its use, it may use such a year for
centuries regardless of its lack of accuracy compared to the tropical year. For
ease of computation in whole numbers and payment for months worked, it is
convenient to use 12 months of 30 days each and thus use a civil calendar of
360 days. The existence of such a calendar year does not provide evidence
that a tropical year ever actually contained 360 days. The only way that such
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a claim could be proved is if there was historical evidence that the
agricultural year actually averaged 360 days over many years, or if surviving
archaeological statements associated with astronomical cycles claimed or
directly implied that a tropical year equaled 360 days. This question of
whether there is any known evidence in man’s history for a 360 day tropical
year has come up twice on the web site for discussions on the history of
astronomy, HASTRO-L, since I became a member in 2000, and thereby
received all its emails since then. HASTRO-L is the only on-line discussion
group exclusively devoted to the history of astronomy on the Internet.
HASTRO-L has many active contributors who are professors of history and
professors of astronomy. There is no historical evidence that a tropical year
ever equaled 360 days, although there is evidence for an ancient calendar
having 360 days in certain areas of the ancient Middle East.
Some people have conjectured that during the time of the biblical flood in
the days of Noah, a tropical year or a biblical year had 360 days. This
remains unproved speculation. Chapters 7 and 8 of Genesis do not claim that
each of the periods of time mentioned are non-overlapping, and do not claim
that the sum of these time periods fully cover one exact year. The belief that
a tropical year at the time of Noah had exactly 360 days is mere speculation.
[27] The Beginning of the Month and I Samuel 20
I Samuel 20 is very instructive to show how the biblical month began during
the time of Samuel the prophet when King Saul reigned. It will be shown
from the wording of this chapter that no calculated calendar could have been
used at this time in Israel's history.
At this time of David's young adulthood, he has already experienced
attempts by King Saul to kill him (I Sam 18:10-11; 19:9-10), but his very
close friend Jonathan, the king's son, has great difficulty believing that his
father wants to kill David. In order to convince Jonathan that Saul wants to
kill David, David devises a plan to cause Saul to reveal his attitude toward
David in the presence of Jonathan. Notice that this plan involves a day count
of three from the following literal parts of verses.
I Sam 20:5, “until the third evening”.
I Sam 20:12, “about [this] time the third morrow”.
I Sam 20:19, “and [on the] third [day]”.
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This shows their advance confidence that it would probably take two
successive days for Saul’s actions to bring to light his attitude toward David.
They expected that Jonathan would witness two consecutive days of Saul's
behavior. The context assumes that the reader will automatically understand
this without any explanation. We need to carefully examine the context to
note what the writer of the text expected the reader to know.
I Sam 20:5, “And David said to Jonathan, Behold, tomorrow [is a] new-
moon, and I should sit with the king to eat ...”.
I Sam 20:18, “And Jonathan said to him, Tomorrow [is a] new-moon, and
you will be missed because your seat will be empty”.
These two verses show that it was considered important for David to be
present at a banquet hosted by the king due to a “new moon”, and there was
a seat reserved for David. There is nothing in the context to suggest that this
was the beginning of the seventh month and that a holy convocation was to
take place. Indeed, if this had been the beginning of the seventh month,
verses 5 and 18 would have more to say about why David would be missed!
The reason given is the new moon, nothing more.
The Hebrew syntax in verses 27 and 34 is the same for one phrase that is not
like any place in the Hebrew Scriptures where a numbered day of the month
is mentioned. The Hebrew word order is “the chodesh the second”, which
occurs that way four times in the Hebrew Bible: I Sam 20:27, 34; I Ki 6:1; I
Chr 27:4. In the latter two places it means “the second month”. This
expression “the chodesh the second” does not have the Hebrew word yom
for “day”, does not have a preposition attached to the beginning of the
number, and has the number after the word chodesh. These three factors do
not occur in any place where a numbered day of the month is mentioned in
the Hebrew Bible. A Hebrew expression for a numbered day of the month
occurs 98 times in the Bible. In 92 of these cases the Hebrew preposition bh
(meaning “in” or “on”) precedes the number. In two of these cases the
Hebrew preposition ad (meaning “until”) precedes the number. In 39 of
these cases the Hebrew word yom (meaning “day”) occurs at the number.
While there are a total of four cases (Ezra 3:6; 10:17; Est 9:19, 21) in the
Hebrew Bible where a numbered day of the month is mentioned and no
preposition is prefixed to the number, all of these cases do have the Hebrew
word yom, and none of these four cases have the number after the word
chodesh. There is no example in Scripture with the syntax as in I Sam
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20:27, 34 to indicate that is could mean a numbered day of the month.
The Hebrew word chodesh sometimes means “new-moon” and sometimes
means “month”, but because the syntax of this phrase in these two verses is
never used for a day of the month, and because its meaning as “new moon”
here gives a satisfying explanation to the context including the planned
meeting of Jonathan and David on the third day from their initial meeting,
chodesh will be translated “new-moon” below.
I Sam 20:27 literally states, “And it happened on the morrow of the new-
moon the second, [the] place of David was empty. Then Saul said to
Jonathan his son, Why didn't the son of Jesse come either yesterday or today
to the meal?”
When the NASB is used, items in square brackets will show where the
NASB has italics, indicating that no Hebrew word occurs for the italics. It
may sometimes be useful to consider omitting the words in square brackets
in the NASB because they are not based on words in the Hebrew text.
I Sam 20:27 [NASB], “And it came about the next day, the second [day of]
the new moon that David's place was empty ...”
Thus there was something special about that meal on two successive days
that made David's presence expected at both meals.
In verses 28 through 33 Saul and Jonathan dialogue with one another so that
Jonathan becomes convinced that Saul wants to kill David.
I Sam 20:34 literally states, “And Jonathan arose from the table in fierce
anger, and did not eat food on [the] day of the new-moon the second because
he was grieved for David, for his father had dishonored him.”
I Sam 20:34 [NASB], “Then Jonathan arose from the table in fierce anger,
and did not eat food on the second day of the new moon, for he was grieved
over David because his father had dishonored him.”
I Sam 20:35 literally states, “And it happened in [the] morning that Jonathan
went out [into] the field at [the] time appointed [with] David, and a little boy
[was] with him.”
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The morning in verse 35 is within the third day that David and Jonathan had
planned to meet.
The special meal at the king's table on two successive days during which the
presence of David, a national hero, was expected, shows that both meals
were to commemorate the start of the month. The need existed to have two
days of commemorative meals because they did not know in advance which
of the two days would in fact begin the new month. From I Sam 20:27 we
can say that David and Jonathan did not know in advance which of two
successive days would officially be declared the new moon day, because
otherwise there would not have been a need for two successive days of a
festive meal during which David was expected to appear. The phrase in I
Sam 20:5, 18 that “tomorrow is a new-moon” is literally misleading because
it can be expected to cause the reader to think that they knew in advance that
tomorrow would in fact actually be the first day of the new month. It should
be translated “tomorrow is the new moon [festivity]”.
I Sam 20:5, 18 was applied to the first day to come, and the designation of
“new-moon the second” was given to the second day to come. The need to
have a second day of commemoration indicates that on the first of the two
days, the new moon was not officially declared by the Levitical priesthood
to be the start of a new month by the blowing of two silver trumpets in
accordance with Num 10:10.
The average length of a month is close to 29.5 days, and most of the time
there is an alternation of 29 and 30-day months, although there certainly are
exceptions. At the time that David and Jonathan first met, one would
surmise that the previous month had 29 days, so that it was most likely that
the current month that was nearly over would have 30 days. Thus, when
David and Jonathan first met, they planned for the current month to be a 30-
day month so that their next meeting would be on the third day rather than
on the second day. They believed it was most likely that a second festive
meal day would be needed due to an expected 30-day month. Therefore,
when I Sam 20:5 and 18 speak of “tomorrow [is the] new-moon”, that refers
to the festive national holiday (not holy day) on the first of two successive
days during which the new month might begin. The author of I Samuel 20
expected the reader to understand that there was to be at least one, and
possibly two, successive days of festive meals at the king's table at the start
of each month.
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The start of a month is used to determine festivals, so by Gen 1:14, the light
of a heavenly body must determine the start of a month. The first light of the
moon would not anciently be known until it was seen. I Sam 20 is evidence
that the day of the new moon was not pre-calculated, because otherwise
there would not have been a need to plan for two successive days of festive
meals. A pre-calculation would have been calculated to precisely one day
rather than a choice of two days.
I Sam 20:5 and 18 should be understood to mean “tomorrow [is the] new-
moon [festivity]” rather than the officially declared new moon. In other
words, David and Jonathan did not really know that “tomorrow” would
actually be the first day of the new month. In fact they expected that
“tomorrow” would not be the first day of the new month!
When reading Josephus, one must be on guard for any reason that Josephus
might have for distortion in his account of an event. In his description of I
Sam 20 it is difficult to see any reason why he might deliberately distort any
technicalities of the story. This chapter should not have been a controversy
among Jews in the time of Josephus. He was certainly living at a time when
Hebrew was still spoken among the upper class in Jerusalem where he was
reared in the first century. Josephus was born in the year 37, so he was 32 or
33 years old when the Temple was destroyed in 70.
Josephus corroborates the translation of second new-moon in his paraphrase
of I Sam 20:27. On pages 283 and 285 of Josephus_5, Ant 6:236, we read,
“But when, on the second day of the feast of the new moon, David again did
not appear, he asked his son Jonathan why, both on the past day and on this,
the son of Jesse had been absent from the festive meal.”
The Greek word that Josephus uses for “new moon” in the above translation
is noumeenia (Strong's number 3561), not the Greek word meen (Strong’s
number 3376), which means “month”. Thus the NASB, taking the Hebrew
syntax as it is, translates it so as to agree with Josephus who chose the Greek
word for “new moon” rather than the Greek word for “month”. The William
Whiston translation is very poor here because he translates it as though
Josephus used the other Greek word (meen).
Page 861 of the chapter by Moshe David Herr translates I Sam 20:27 “But
on the morrow of the second new moon ...”, and translates I Sam 20:34 “...
and he ate no food the second new moon day”. According to pages 84-85 of
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the book by Cahn, the Karaite Benjamin Nahawendi c. 825 CE understood I
Sam 20:27, 34 similarly. The German interlinear translation by Rita Steurer
also translated these verses using the German translation equivalent to
“second new moon” rather than “second day of the month”. The German
word for new moon is different from the German word for month.
On page 36 of the book by Solomon Gandz he wrote, “There can be no
doubt that ‘on the morrow of the second new moon’ [in verse 27] has the
same meaning as ‘on day of the second new moon’ [in verse 34] and that
both phrases refer to the second day of the new moon festival, on which a
festive meal was given at the King’s table and in which David was supposed
to take part.” The very title of the chapter by Gandz is “The Origin of the
Two New Moon Days”, and his analysis is consistent with the analysis given
here, although his arrangement of the explanation is different and he does
not use all of the logic presented here.
Within the above quote from Gandz, I have added the items in square
brackets, and the two expressions enclosed within apostrophes have, in
Gandz' work, the Hebrew words rather than the literal translation that I have
substituted. Gandz discusses this chapter and Jewish commentaries upon it
during the past 1700 years.
Horace was a Roman poet and satirist who wrote in Latin and lived from 65
BCE to 8 BCE. On page 20 of the book by Horace, Satire 1.9.67-70 states:
“’Surely you wanted to tell me something, something confidential?’ ‘Oh,
yes, but I'll choose a better time. Today is the thirtieth Sabbath. Why offend
the circumcised Jews?’ ‘I don't care about religion’, I moan”.
Here the expression “thirtieth Sabbath” is a literal translation of Horace's
Latin expression tricesima Sabbata. On page 375 of the book by Louis
Feldman we find the following comment on this expression as found in the
satire, “In summary, Horace's allusion in tricesima Sabbata is more effective
if it refers not to some meaningless nonsense but rather to the thirtieth, a
Sabbath, that is, the New Moon, so prominently celebrated in Horace's
time.” Here it must be understood that the Jews desired to have a holiday
(not holy day) on the new moon days. The Romans understood that the word
Sabbath to a Jew meant a day on which he did not work at his ordinary job.
It was easier for the Jews to tell the Romans that the new moon day that was
the thirtieth of each month was always a Sabbath (called the thirtieth
Sabbath) than to use other more accurate words from the biblical viewpoint.
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Biblically the new moon was not a Sabbath, but the Jews called it a Sabbath
to simplify the implications of not working to the Romans.
The first of the two possible days of sighting the new crescent would place
the first day of the month on the 30th day of the old month. Hence in
Jewish practice of that time the 30th would be a holiday or a vacation day,
and by loose extension (not technically correct), called a Sabbath. Since
Horace expected his readers to understand him, this new moon holiday,
called the “thirtieth Sabbath” was well known in Rome in the late second
century BCE.
It was common knowledge in the Roman Empire during Horace's adulthood
that Jews refrained from work on the first of the two possible days on which
the new month might begin. This harmonizes perfectly with the implications
from the Hebrew in I Sam 20:27, 34 and the whole chapter. The paraphrase
by Josephus also agrees with this.
If Israelite society at the time of King Saul, when the prophet Samuel was
still alive, was using a calculation to determine the start of the next month,
there would have been no point in having two successive days of festive
meals associated with the new moon, which shows an uncertainty of which
day among two successive days that would start the month. Thus no
calculated calendar could have been used at this time of Israel's history.
Ancient Israel did not employ predictive astronomy for their calendar.
[28] Applying I Sam 20 to II Kings 4:23 and Amos 8:5
In II Ki 4:8-11 we see that a woman in Shunem made a room available for
Elisha to lodge at whenever he was in that neighborhood. According to maps
that are commonly available in some Bibles, and according to Josh 19:18,
which shows Shunem within the boundary for the tribe of Issachar, Shunem
was about 10 miles to the southwest of the Sea of Galilee (named differently
in Elisha's day). This is in the southern part of Galilee, about 60 miles north
of Jerusalem, certainly not local to Jerusalem to be able to hear two silver
trumpets blowing, and then soon going to witness a priestly ceremony for
the beginning of the month. In II Ki 4:22 she asked her husband to prepare a
donkey for her to ride upon to visit Elisha. In verse 23 her husband
responded, “Why are you going to him today? It is neither the new-moon
nor the Sabbath.” This shows that under normal circumstances this wealthy
woman rode a donkey to visit Elisha on the new moon and on the Sabbath.
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However, in I Sam 20, the day for a new moon festivity was simply called
the new moon, and it occurred immediately after the 29th day of the month.
The same is true in the days of the Roman poet Horace before the first
century. Based upon this, we should understand the question in I Ki 4:23 to
mean, "It is neither the new-moon [festivity] nor the Sabbath." This new
moon festivity may be the first of two successive days of festivity.
Recognizing now, that the context with the Hebrew word chodesh for “new-
moon” may mean "new moon [festival]", the reader should not be surprised
if this translation is proposed for appropriate contexts. The prophet Amos
criticizes many people in the land who complain as follows in Amos 8:5,
“When will the new-moon [festival] be past that we may sell grain and the
Sabbath [be over] that we may trade wheat?” This indicates that there were
restrictions by the national government against some activities on the new
moon festival, but it does not indicate that there was some law within the
law of Moses that prevented certain work on such days; there is no such law.
There is no sin where there is no law. Nevertheless, Amos 8:5 along with II
Ki 4:23 does indicate that the population beyond Jerusalem did involve
themselves to some degree with the new moon festivity.
Since the new moon festivity had significance throughout Israel, it would
especially have significance where the High Priest, the ark, the Temple, and
the ceremonial sacrifices took place. Although ceremonial details are not
specified in Scripture, this implies that people near the Temple would
witness the priestly ceremonies associated with the beginning of the month.
However, there is no commandment in the law of Moses that ordinary work
was forbidden or that attendance at this priestly ceremony was required for
the beginning of the months.
[29] Rapid Communication to inform the Nation about the New Moon
Lev 23:24-25, “Speak to the children of Israel saying, ‘In the seventh month,
on [the] first [day] of the month, you shall have a rest, a memorial of
soundings, a holy convocation. You shall not do any servile work and you
shall offer a fire offering to YHWH.’”
This first day of the seventh month was a festival day in which no ordinary
work was done, and there was a commanded meeting with a festival service
for this day. Deut 16:16 specifies the three times of the year when the adult
male population was commanded to gather in one location within Israel, and
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the first day of the seventh month was not one of those three times.
Therefore, this festival at the beginning of the seventh month was kept at
various local places throughout the nation. About half the months had 29
days and half the months had 30 days. These did not always alternate. The
weather might be cloudy. Thus there would often be uncertainty whether the
first of the two possible days for the new moon festivity would be the actual
beginning of the seventh new month. With such uncertainty, the people
would have no choice but to avoid normal work and have a holy convocation
on the 30th day. If that first day would not be declared the actual beginning
of the seventh month, they would then celebrate two consecutive days for
the first day of the seventh month. A method of rapid communication would
be needed to inform the local gatherings around the country that the first day
of the new moon festivity was declared to be the actual start of the seventh
month, if this had happened. Once the priesthood declared the first day to be
holy, the next day was not holy. Rapid communication would make it
unnecessary to celebrate a second day as a holy day in the local areas after
the priesthood declared the first day to be holy.
How would rapid communication throughout all Israel be possible in ancient
times?
When the new crescent is seen, shortly afterward the moon falls below the
horizon and then there is no moonlight at all and it is very dark all night.
This makes it dangerous to travel at night, whether to go to the top of some
local hills or to return after arriving. A lantern could make travel possible,
but it would be slow and still dangerous in total darkness. Consequently,
regardless of the method of primitive communication (certainly no
telephones, Morse code, or radio), it would have to wait until daylight.
During some circumstances of difficulty in sighting the new crescent near
Jerusalem, the priesthood might even have to wait until some time during the
middle of the following daytime to know whether to declare that first day as
the true start of the new month.
Any big task is performed more quickly if multiple people are able to divide
the task into smaller pieces, each one doing a small piece. For this to be
effective in reducing the total time from start to finish, the time of their
activity must overlap. Light travels much faster than people, horses, camels,
or birds. Consider the following proposal. On the morning of the 30th day of
the month certain people are appointed to travel to the top of designated hills
throughout the country with materials that are able to start a controlled fire.
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The separated hills throughout the country would have to be close enough
that they could see the fire from hills in the various directions. When the two
silver trumpets were blown to announce the declaration of the start of the
new month, the designated people who heard the trumpets would light their
fires, and then this would rapidly spread throughout the country. The biggest
time lag factor would be the time required to light the fire. It is even possible
that a very small fire that could not be seen from far away was started first,
and then this fire that was already kindled could speedily be used to start a
larger fire that could be seen from other hills. Such a system could enable all
of Israel to know about the declaration of the new month within a few hours
during the afternoon of the 30th day. While it is perhaps possible to imagine
this happening at night, it does not seem very likely because of the possible
danger when visibility is impossible without a fire. Another problem with
suggestions that the procedure occur at night is the likelihood that some of
the watchers might fall asleep at night while waiting to see a fire at another
hill. During the daytime it would be more interesting to be looking because
there would at least be visible scenery.
There is documentation of such a fire system for rapid communication in the
Mishnah, which was published c. 200 by Judah the Prince. This document
cannot generally be trusted for historical accuracy concerning the early first
century or 1000 years earlier for at least the following four reasons: (1)
Possible doctrinal bias and genealogical bias by Judah the Prince or any
written sources available to him; (2) Doubt that comprehensive written
sources ever existed for religious practices that were supposedly copied from
generation to generation by the priesthood; (3) Sometimes the statements of
the laws are so detailed that one easily doubts that this was handed down in
writing; and (4) Some of the practices seem to be politically motivated
against the priesthood which vanished from history soon after the Temple
was destroyed in 70. I reject the theory of the Oral Law, which asserts that
there was a body of law handed down without error in oral form (not to be
written) from Moses onward until Judah the Prince was permitted to cast it
into written form.
Despite these reasons for the lack of confidence in the infallibility of both
doctrine and history within the Mishnah, such a fire system for rapid
communication does make common sense and it is difficult to imagine why
there ought to be doctrinal bias associated with the general concept even if
some of the details are embellished and not trustworthy.
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On page 301 of the Mishnah at RH 2:3 we find (square brackets are by Jacob
Neusner),
“A. How did they kindle flares?
B. They bring long cedar wood sticks, reeds, oleaster wood and flax tow.
C. One binds them together with a rope.
D. And he goes up to the top of a hill and lights them.
E. Then he waves them to and fro and up and down, until he sees his fellow,
doing the same on the next hilltop, and so on the third [and beyond].”
On the same page at RH 2:5 we find,
“A. There is a large courtyard in Jerusalem, called Bet Yazeq, to which all
the witnesses gather.
B. And there the court examines them.
C. Now they prepare big meals for them, so that they should make it a habit
of coming.”
On page 302 at RH 2:6 we find,
“A. How do they examine the witnesses?
B. The pair which makes its appearance first do they examine first.
C. They bring the elder of them and say to him, ‘Tell us, How did you see
the moon? Was it facing the sun or turned away from it? Was it to the north
or to the south? How high was it, and in which direction was it leaning? And
how broad was it?’
D. If he said, ‘It was facing the sun,’ he has said nothing at all.
E. Then they would bring in the second party and examine him.
F. If their testimony coincided, their testimony was confirmed.
G. And in the case of all the other pairs of witnesses, they ask the main
points,
H. not because they need their [evidence], but so that they should not go out
disappointed,
I. so that they would make it a habit of coming along in the future.”
[30] Summary about the New Moon Celebration and the Role of the
Daytime
In summary, the 30th day of each month was a national holiday, not a
commanded holy day, except for the seventh month. Two successive days
may be celebrated for the beginning of the seventh month, and indeed for the
beginning of every month. The priesthood had certain commanded duties to
perform at the beginning of each month, but this was only commanded in
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one location where two priests blew two silver trumpets to summon the
assembly, thus announcing the beginning of the new month and alerting the
local people that the time had arrived for them to come and celebrate the
proceedings associated with the new moon ceremonies. Some of the
population in various parts of Israel was involved in feasting on the 30th day
of each month. Based on the example of I Sam 20, such feasting would also
occur on the next day if the new moon was not declared on the 30th day.
The following are some practical factors that are associated with the 30th
day:
(1) There was a need to enable the whole of Israel to know whether the 30th
day began the new month.
(2) There was a need to wait for possible witnesses to arrive at the site where
the two silver trumpets were waiting with the priests, and this might not
happen until sometime during the following daytime.
(3) Rapid communication would require the daytime to enable the whole
nation to be informed of the day that began the month.
The daytime of the 30th day was an important part of the celebration, and
not merely for a festive meal. While it is certainly possible that witnesses
could arrive during the night, only during the daytime was it possible for
significant numbers of local people to witness the ceremonies associated
with the new moon, provided that the declaration was made. For that reason,
even if witnesses arrived during the early part of the night, common sense
would dictate that the priesthood would always want to begin the ceremonies
at a time of the daytime when a maximum number of people could be
present. Therefore, the daytime of the first day of each month was
significant for the ceremonies and the people. The daytime was also
significant for communication on the 30th day to the rest of Israel.
The sundown that began the 30th day was primarily significant in watching
for the new crescent, not for the celebrations of that day if the new moon
was declared.
[31] Today’s Ambiguity in the Phrase New Moon
One source of possible confusion is the failure to realize that present day
astronomers and almanacs define a new moon in a way that usually precedes
the biblical new moon by one or two days. In order to avoid confusion, I will
call the modern astronomer’s new moon the astronomical new moon, not
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the new moon. Another modern equivalent expression for the astronomical
new moon is the conjunction of the moon with the sun, or more briefly and
simply, the conjunction. At the time of the conjunction no one can see the
new moon.
[32] Biblical View of the Sun's Yearly Motion is South - North
Ecclesiastes mentions the sun (shemesh in Hebrew) more than any other
book of the Bible - 35 times! One pair of verses gets specific about its
motion, but this is only noticed if care is taken to preserve the Hebrew word
order and if courage is exercised to allow the Hebrew to make sense! A
literal translation of Eccl 1:5-6 with special attention to keeping the word
order the same as it is in the Hebrew text is:
Eccl 1:5, "And rises the sun and goes [away] the sun and to its place it pants,
rising it there [again].
Eccl 1:6A, It [the sun] goes toward south and turns around toward north.
Eccl 1:6B, Turns around [and] turns around goes the wind, and on its circuits
returns the wind."
Page 55 of Zlotowitz translates Eccl 1:5-6, “And the sun rises and the sun
sets - then to its place it rushes; there is rises again. It goes toward the south
and veers toward the north; the wind goes round and round, and on its
rounds the wind returns.” On the next page appears the comment, “Midrash
Leckach Tov [by Toviah ben Eliezer, 11th century] interprets this verse
[verse 6A] as referring to the course of the sun as manifested by the winter
and summer seasons, but it adds that on a deeper level the verses [5-6] refer
to the Jews [they have moved from place to place due to persecution].”
About the year 400 CE Jerome translated the Tanak from Hebrew to Latin,
which, except for the Psalms, became the Latin Vulgate. Page 307 of Japhet
gives the following careful translation from Jerome's Vulgate for Eccl 1:5-6,
(additions in square brackets are made by Japhet), “The sun rises and [the
sun] sets and returns to its place. It rises there, goes to the south and turns
about to the north. As it circles the world around goes the spirit, and upon its
circuit returns [the spirit].” Jerome made this rhyme in the Latin.
In general I never use the Septuagint translation (abbreviated LXX) as a
means of understanding some seldom used Hebrew words or difficult
passages of the Tanak because it often shows mere guesses for the Greek
translation, so it is not reliable as an ancient indicator of the meaning of the
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Hebrew Bible. Among all of the books of the LXX, Ecclesiastes stands apart
in a special way. Page 7 of Seow reveals, “The translation technique of LXX
Ecclesiastes is unique among the books in the Bible, so that one may say
with a reasonable amount of certainty that the translator is not the same as
for any other books. The translation shows a number of features that are
typical of the works of Aquila of Pontus, a second-century (C.E.) gentile
convert to Judaism. Aquila, a pupil of the famous Rabbi Aqiba is best known
for his translation of the Hebrew Bible into literalistic Greek [about 135 CE],
among other reasons, to provide Jews who spoke Greek but did not read
Hebrew or Aramaic with a translation that would reflect the Hebrew as
much as possible. Thus, the Hebrew word order is rigidly adhered to and all
details in Hebrew are represented, even when they seem awkward or even
nonsensical in Greek.” While scholars debate whether Aquila was the
translator, we do know that the LXX for Ecclesiastes is literal and sticks
very closely to the Hebrew. The commonly available translation of the LXX
by Brenton translates Eccl 1:5-6, “And the sun arises, and the sun goes down
and draws toward its place; arising there it proceeds southward, and goes
round toward the north. The wind goes round and round, and the wind
returns to its circuits.” This translation reflects the fact that the word for
“wind” does not occur in the Greek until after the word for “north”. In fact,
the Greek word order after “north” is “round round courses the wind”, so
Brenton's translation does put “wind” earlier in the verse than the Greek
indicates. The Greek word pneuma, Strong's number 4151, is used for wind,
which is the translation of the Hebrew word ruach, Strong's number 7307.
Page 300 of Japhet translates the LXX more literally, “And the sun rises and
the sun sets and draws to its place. It rises there, goes to the south and turns
about to the north. Turns about, turning goes the ruach (pneuma), and upon
its circuit returns the ruach (pneuma).” In footnote 31 on page 301 Japhet
remarks, “This faithfulness to the MT [Massoretic Text of the Hebrew] is
particularly striking when it creates forms which are awkward in the Greek.”
Pages 298-299 of Japhet point out that Rashi, the well known Jewish
commentator of the late middle ages, also treats the sun as the subject in
Eccl 1:6.
The Syriac language is an offshoot of first century Aramaic and is thus a
Semitic language that has affinities to Hebrew. The Syriac Peshitta is a
translation from the Hebrew Bible that was made about 200 CE. The
Peshitta in its literal word order, is in agreement with the Hebrew text of
Eccl 1:5-6 in continuing with the sun as the subject of Eccl 1:6A; however,
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George M. Lamsa's translation from the Syriac Peshitta departs from the
literal view and translates it as if the wind were the subject at the beginning
of verse 6. Lamsa often departs from the Syriac to agree with the KJV.
Page xi of Sternberg translates Eccl 1:5-6A, “The sun rises and the sun sets
and hastens to its place and rises there. It walks to the south and returns to
the north.”
In Sternberg's above translation the word “walks” comes from the Hebrew
word halach, Strong's number 1980, which is typically used in reference to
people walking, yet it is used in other ways for the movement of inanimate
objects. However, from the viewpoint of an observer on earth, the position
of the sun at sunset from day to day does change in distinct increments as a
“walk”, and the position of the shadow cast by a narrow object at noontime
from day to day also changes in distinct increments as a “walk”. These
changes do form a south-north yearly cycle as will now be explained.
[33] The South - North Yearly Cycle indicated in Eccl 1:6A
A person who views sunsets daily from a place at which there is a clear view
of the horizon might notice that the sun does not set at the same part of the
horizon each day. He might think of performing the following experiment to
determine the daily change in the position of the sun at sunset.
Permanently place a straight board and an object with a sighting point so that
the middle of the board is about the length of a person west of the sighting
point, and when looking approximately west with one's eye at the sighting
point, the long top edge of the board is even with the horizon. Each day near
sunset make a mark on the board where the board crosses the line of sight
from the sighting point to the middle of the sun. For accuracy this should be
done when the center of the sun is at the horizon.
If this is done from anywhere in the north temperate zone, for example
Jerusalem (latitude 31.8 degrees north), during the coldest part of the year,
the daily marks on the board keep going north (to the right). During the
hottest part of the year the daily marks on the board keep going south. For
several days while the temperature is getting quite hot, the marks will be at
about the spot that is the furthest north of the marks; the middle day of this
group is the day of the summer solstice. For several days while the
temperature is getting quite cold, the marks will be at about the spot that is
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the furthest south of the marks; the middle day of this group is the day of the
winter solstice. The word “solstice” means “stopping of the sun” which
describes the state of the marks at the solstices. At all other times of the year
the marks are separated from one another while heading north, or separated
from one another while heading south.
The marks on the board are furthest from one another at the midpoint
between the solstice marks because the south-north motion of the sun is
fastest at these points. The mark closest to the midpoint while the marks are
heading north is the mark at the vernal equinox. The mark closest to the
midpoint while the marks are heading south is the mark at the autumnal
equinox. Although this method determines the equinoxes quite precisely by
first knowing the solstices, it is not necessary to know the day of the
solstices precisely because the marks barely change for several days about a
solstice. Page xii of Sternberg is one of several sources that discusses this.
[34] Equinox and Solstice is in the Bible
The Hebrew word tkufah, Strong's number 8622, occurs four times in the
Bible, Ex 34:22; I Sam 1:20; II Chr 24:23; Ps 19:7. In 1907 when the BDB
lexicon was published (see page 880 for tkufah), the Dead Sea Scrolls were
not yet discovered and clarifying insightful meanings into some ancient
Hebrew words were not yet available. The Dead Sea Scrolls use the Hebrew
word tkufah in contexts before the first century, and this is now discussed.
The paper by Hoenig discusses a scroll labeled I QH among the Dead Sea
Scrolls. On pages 312-313 he explains two expressions found there: one is
“tkufah of the day” and the other is “at the appointed time of the night at
tkufah”. Hoenig explains that the former means “zenith of the day” meaning
“noon” and the latter means “at the appointed time of the night at zenith”
meaning “midnight”. It is particularly interesting that in the expression “at
the appointed time of the night at tkufah” the Hebrew word for “appointed
time” is moed, the same word used for the holy days in Lev 23 and for
seasons in Gen 1:14. Thus it is not foreign to ancient Hebrew to use or
associate tkufah with moed. This use of tkufah shows two heavenly bodies,
the earth and sun, interacting on a daily basis so that at astronomically
distinctive points in time tkufah refers to those points in time.
In the book chapter by Johann Maier one of the Dead Sea Scrolls is
discussed that contains the Hebrew word tkufah. On page 146 Maier writes,
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“The Songs themselves are attached to the thirteen Sabbaths of one quarter
or season (tqufah) of a year, according to the editor the first quarter (the
Nisan season) only.” Here we see the Hebrew word tkufah used for the
season of spring, which begins with the vernal equinox and ends with the
summer solstice. Here also astronomically distinctive points in time
involving the earth and sun define a time period called tkufah.
The intertestamental apocryphal Book of Sirach (also known as
Ecclesiaticus) contains the Hebrew word tkufah. This book was written in
Hebrew about 190 BCE, but today only incomplete sections of it have
survived, having been discovered with thousands of other Hebrew texts in
the attic of a synagogue in Cairo, Egypt toward the end of the nineteenth
century. The treasure of texts in that attic, which survived for many
hundreds of years, is known as the Cairo Geniza. There are many copies of
Sirach in Greek translation, and most of the Hebrew words in Sirach 43:7
are preserved, one of them being tkufah. The Greek translation for tkufah is
suntelia (Strong's Greek number 4930), which means completion,
fulfillment, or destruction. These words indicate a point in time at which
some event occurred. In harmony with this idea, the Jerusalem Bible
translates Sirach 43:7, “the moon it is that signals the feasts, a luminary that
wanes after her full”. Here “her full” refers to the full moon and is translated
from tkufah or suntelia. Here tkufah refers to a natural distinctive time of the
moon in its movement about the earth.
These contexts from the Dead Sea Scrolls and from Sirach from before 70
CE show that the Hebrew word tkufah is used to refer to natural distinctive
points or time intervals associated with the heavenly bodies of the earth, sun,
and moon.
On page 394 of the lexicon by Holladay the word tkufah is defined. The
parentheses and square brackets are part of the text of that book by Holladay
where he writes about tkufah “turning (of sun at solstice) Ps 19:7; (of the
year, i.e. end of year, at autumnal equinox) Ex 34:22; (of the days [i.e. of the
year] = end of year I Sam 1:20”.
In Ex 34:22 Moses was told, in literal translation, “And you shall celebrate
... the Feast of Ingathering tkufah the year”. There is no Hebrew preposition
attached to tkufah here so that the relationship between this feast and tkufah
is very indefinite although translations attempt to make it definite by adding
some preposition that is not in the Hebrew. This verse does not define an
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explicit relationship between these events, but merely indicates that there is
some vague closeness in terms of the general year. In harmony with the
astronomical uses shown above, this refers to the autumnal equinox.
Certainly Moses was aware of the equinoxes from the knowledge he gained
in his upbringing in Egypt (Acts 7:22), and the fact that the greatest
pyramids had one wall aligned exactly east-west. Only on the days of the
equinoxes does the shadow of a vertical object fall exactly east-west all day
long. The ancients were easily able to determine an east-west line. Therefore
the equinoxes are visible signs of the sun in relation to the earth and do fall
within the purview of signs in Gen 1:14 “lights in the expanse of the heavens
... for signs and for festivals and for days and years”.
The main points are:
(1) The Hebrew word tkufah found in Scripture does have use outside the
Bible before Herod's Temple in Jerusalem was destroyed in 70 CE.
(2) Contexts with tkufah show it to mean distinctive points in time in
relation to movements of the heavenly bodies as observed from people on
earth. Also, it is used for the time period between the distinctive points, e.g.,
the Nisan tkufah or spring season. The word tkufah has multiple uses, as the
examples showed.
(3) Moses used this word. While he did not specifically use it to refer to the
vernal equinox, Ex 34:22 refers to the autumnal equinox, at least showing
that Moses had a word in Hebrew that refers to an equinox.
Does Ex 34:22 refer to the end of the harvest when it uses the word tkufah?
There is no ancient context that forces tkufah to mean a “point” of time
defined by a harvest in contrast to ancient contexts that show it to relate to
heavenly bodies. This is simply a matter of finding contexts that bring out
meaning that is clear. Incidentally, the three main crops harvested at that
general time of the year are figs, olives, and grapes. Figs are a summer fruit,
whose harvest hardly ever extends into fall. The olive harvest occurs in
September and October, and is over in most parts of Israel by about the third
quarter of October. The grape harvest begins with sour grapes in July but
with ripe grapes in some areas of Israel from the beginning of August. The
grape harvest continues through about the first third of November in the area
of Jerusalem. The uses of tkufah in the Dead Sea Scrolls show the meaning
of a point in time.
[35] Equal Daytime and Nighttime is Not the Biblical Equinox
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The word “equinox” comes from the Latin language and means “equal
night” in that language, which implies that daytime and nighttime are equal
at the time of an equinox. But did the ancient people that used this Latin
name equinox use the meaning of this word in practice, or was it a mere
guess that daytime and nighttime are equal on the days of the equinox? It
will be shown that this was a mere guess.
Near the dates of the equinoxes the difference in time from sunrise to sunset
from one day to the next is about two minutes. In order to determine the date
upon which daytime and nighttime are equal at a certain latitude, it is
required that a clock exist that can measure time during a 12 hour period to
an accuracy that is better than two minutes per day. When ancient
Babylonian astronomers recorded an eclipse or the disappearance of a planet
behind the moon, they wrote down the time it occurred as well as the month,
day of the month, and year of a king's reign. The paper of Stephenson
explains that the smallest Babylonian unit of time was called an us and
equaled 1/360 of a day, which is four minutes. Moreover, the Babylonians
never expressed time as a fraction of an us. This shows that they made no
attempt to express time more accurately than to the nearest four minutes
with their water clocks. The paper of Steele showed a summary of a
computer study of Babylonian astronomical phenomena from 562 BCE to 41
BCE, all recorded with a time of day. The conclusion was that the average
accuracy of the recorded time was two us's which represents eight minutes
from the true time. Moreover, accuracy remained the same during this 500-
year period; their water clocks used for this purpose did not improve. One
reason that water clocks were not accurate is that as temperature changed,
the dripping rate changed. Another reason is that the construction of the
mechanism and the recording method were not accurate. Page 609 of Ward
shows a graph of how the accuracy of time mechanisms improved through
history, based on historical improvements. This chart shows a sudden leap to
about two minutes per day in the year 1656 when Christiaan Huygens
perfected the pendulum clock. Ancient peoples did not have the ability to
determine the day at which daytime and nighttime were equal because their
clocks were not accurate enough. The day upon which daytime and
nighttime are equal depends on the latitude of the observation because
refraction of light increases as one gets closer to the north and south poles.
As already explained from Eccl 1:5-6, the Bible indicates that the sun's
annual position was noted on the basis of its south-north movement which
was not a matter of measuring the time of day.
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The Hebrew noun tkufah has an inner stem in common with the Hebrew
verb nahkahf, which occurs 19 times in the Hebrew Bible. The latter means
“to surround” 11 times - I Ki 7:24; II Ki 6:14; 11:8; II Chr 4:3; 23:7; Job
19:6; Ps 17:9; 22:16; 88:17; Isa 15:8; Lam 3:5. It means “to go around” four
times - Josh 6:3, 11; Ps 48:12; Isa 29:1 (“add year to year, let feasts ‘go
around’”). It means “to destroy” twice - Job 19:26; Isa 10:34. It means “to
curve” once - Lev 19:27. It means “to finish” once - Job 1:5. The overall
flavor of this word indicates the idea of encirclement, which does not have
any implication about accurate clock time measurement. The relationship
between tkufah and nahkahf indicates that encirclement of heavenly bodies
provides the basis of the meaning rather than the Latin meaning of equinox
(equal night with day). When the word equinox is used, its original Latin
meaning is discarded, and instead, the time of its practical determination
anciently is meant. This time agrees with the modern astronomer's time for
the equinox although the modern astronomer uses a technical definition that
ancient peoples could not have used.
Page 124 of Pannekoek states, “Another instrument they [the Greek
astronomers living in Egypt after the time of Alexander the Great] used was
an equatorial ring, placed before the temples in Alexandria, in Rhodes, and
perhaps in other towns, for calendar purposes. It consisted of a cylindrical
belt, with its upper and lower borders exactly in the direction of the
equatorial plane; the shadow of the southern half upon the inner side of the
northern half left a narrow line of light at the upper or at the lower side of
the equator. Thus the exact moment of the equinoxes could be fixed.” This
modern description of this ancient instrument uses the term “equatorial
plane” which the ancient Greeks did not use; they bisected shadow angles at
the solstices in order to construct this instrument, which is today called the
equatorial ring. A discussion of the equatorial ring in use by the Greek
astronomers and its inaccuracy due to refraction of the light from the sun is
discussed on pages 15-17, 24-37 of the book by John Britton 1992. This
problem of refraction could cause an error of one day if an equatorial ring
were used.
Pages 73-74 of Pannekoek state, “The Babylonians, according to Greek
testimony, used a vertical pole for measuring shadow length; thus they could
determine the moments of solstice and, as medium points between the
solstices, the moments of vernal and autumnal equinoxes.”
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The paper by Neugebauer 1980 proposes a simple geometric method by
which the Great Pyramid could have been constructed so that it could have
achieved its great accuracy in cardinal directions (precise east-west and
north-south). Only on the days of the true equinoxes (not when daytime and
nighttime are equal) does the shadow of a vertical object fall exactly east-
west all of the daytime. This will be discussed further in the next chapter.
Pliny the Elder, writing about the middle of the first century, defines the
equinox in two ways that are somewhat contradictory on page 309 of
Pliny_1. He writes that “at the season of the equinox sunrise and sunset are
seen on the same line”, and this is the east-west line; this definition is
practical and accurate, and while stated in a way that is very different from a
modern astronomy book, it is nevertheless the same in the time. Pliny also
writes “the equal hours of day and night at the equinox”. When rounding off
to hours this is correct, but not when rounding off to minutes in the latitude
of the Mediterranean Sea where Pliny lived.
On page 81 of Pasachoff we find, “These points are called equinoxes
because the daytime and the nighttime are supposedly equal 12-hour lengths
on these days. Actually, because the refraction by the earth's atmosphere
makes the sun appear to rise ahead of the middle of the sun, at U.S. latitudes
the daytime exceeds the nighttime by about 10 minutes on the days of the
equinoxes. The days of equal daytime and nighttime precede the vernal
equinox and follow the autumnal equinox by a few days.” This is about four
or five days for the U.S.
[36] The Vernal Equinox and Ex 12:2
Gen 1:14 mentions the lights in the heavens, and these are the sun, the moon,
the stars, the planets, and comets. The cycles of the planets and comets are
much too irregular in comparison to repeatable phenomena on the earth to
consider in relation to a biblical calendar when considering the lights in the
heavens. The stars must be excluded because during every 1000 tropical
years the time of the appearance of the stars slowly shifts about 14.1 days
further into the tropical year thus losing touch with the earth's seasons; this
is called precession of the equinoxes in books on astronomy. Only the sun
and moon remain to be considered. The moon determines the months but not
which month is the first. Only the sun remains to be considered. The only
repeatable time points involving the sun are the two equinoxes and the two
solstices. Considering that the barley and wheat in Israel are harvested in the
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spring, the vernal equinox is the only logical candidate to consider that
involves the lights in the heavens on the direct basis on Gen 1:14.
We must seek to know what Moses knew. Acts 7:22 reads [NKJV], “And
Moses was learned in all the wisdom of the Egyptians, and was mighty in
words and deeds.” Pages 333, 336-337 of Lockyer show that most of the
Egyptian pyramids are oriented east-west, and the two largest pyramids at
Gizeh built by Cheops and Chephren are oriented east-west, having one wall
aligned exactly east-west. Pages 63-64 of Lockyer explain that the sun's
shadow on a vertical object from sunrise to sunset fall exactly east-west only
on the days of the equinoxes. So it is clear that Moses knew how to
determine the days of the equinoxes. When one considers that Gen 1:14
points to the lights in the heavens to determine the festivals and knowing
that only the vernal equinox is related to the time of the year under
consideration, Moses would naturally think of the vernal equinox in relation
to Ex 12:2. That would be Egyptian training, Egyptian thinking, Egyptian
context, and in harmony with Gen 1:14, the only explicit Scripture that
directly addresses the determination of the festivals. Would Moses think of
the vernal equinox if it had not yet occurred by that day? No, it would be
premature for him to think of it. The natural thinking from Ex 12:2 in the
context of Egypt and what Moses knew would point to the vernal equinox as
having occurred.
Would Moses think it was necessary for him to explicitly mention the vernal
equinox in the context of Gen 1:14? If this is the only choice there was, he
need not think it was necessary. But the real biblical evidence will come
when we get to Ezra and Nehemiah..
[37] Karl Schoch’s Curve for Predicting Visibility of the New Crescent
During the years 1907-1927 the German astronomer Karl Schoch (1873-
1929) developed astronomical tables to predict the visibility of the new
crescent. This was first published in German in 1927 and then in English in
1928. Before his death in 1929, he revised his tables downward into one
simpler table. When the points are connected in this simpler table, it
becomes a curve, which I call Schoch’s curve. The revised table is found on
page 162 of the paper by Fotheringham. This is the table that I personally
use. It is only useful in the approximate latitudes of Israel and Babylon and
below 4000 feet above sea level. (Schoch’s revised table is very close to the
table that was independently created by Paul Victor Neugebauer.) Although
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the original theoretical basis of Schoch’s curve was eventually rightly
criticized because it was partially based upon Babylonian records that were
predictions rather than observations, further study based upon his table has
verified its usefulness despite the fact that there is a borderline region during
which it cannot accurately predict the visibility of the new crescent.
The paper by Fatoohi 1999 examines 209 examples of records of actual
sightings of the new crescent by the ancient Babylonians. This involves the
correct latitude for applying Schoch’s curve, and the altitude is below 4000
feet. On page 66 of this study all 209 examples are plotted on a graph. This
graph shows the original first curve of Schoch in 1927 compared with the
curve of Paul Victor Neugebauer (this is close to Schoch’s revised curve,
which I use). It should be noted that the ancient Babylonians did not have
the air pollution that prevails in modern society and even c. 1900 in Europe
with its factories and smokestacks. The effect of today’s general air
pollution on visibility of the new crescent is not known. In the graph of the
209 cases, 8 of them fall below both the original Schoch curve and the curve
of P. V. Neugebauer, the lowest two cases by about 0.9 degrees. I presume
that today’s air pollution would prevent those two cases. The fraction 8/209
is 3.8 percent of error below the curve. In this test there was no opportunity
to know the number of cases in which people looked for the crescent above
these curves and no one saw it. This graph also shows 8 examples above the
lower curve, but not more than half a degree above the lower curve. Thus
there are 16 examples out of 209 (which is 7.7 percent) that were borderline
cases based upon plus or minus half a degree yet counting the two very low
exceptions. If we exclude those two very low cases thinking that they would
not be seen with today’s air pollution, we have 14/209, which is 6.7 percent.
We may tentatively conclude that about 7 percent of the cases are in the
borderline region of plus or minus half a degree. This implies that Schoch’s
curve should be reliable about 93 percent of the time.
Schoch’s curve is based upon certain angles of the sun, earth, and moon with
respect to one another at the time of sunset, assuming clear weather, no air
pollution, a reasonably low altitude above sea level (from today’s knowledge
we can say, under 4000 feet, which is higher than Mt. Zion), and the
observation region is approximately in the latitudes of Israel and Babylon.
Schoch observed both with and without binoculars, and correlated data with
the results of others. His curve assumes naked eye observations (no
binoculars, except perhaps for initial location to examine without
binoculars). Above that curve one can expect visibility of the crescent;
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below that curve, no visibility. In live practice, there is a narrow band near
Karl Schoch’s curve where it is near borderline and uncertain, so that some
people with sharp vision looking at the right spot do see it, and others do not.
Before Internet reports of crescent visibility were available, I used a
computer program that utilized Karl Schoch's curve. I still use it and can tell
whether it is near borderline, which generally should not exceed plus or
minus 1/2 of a degree on Schoch’s curve. If the humidity is very low or
during the autumn when a low crescent looks like a flattened backwards C in
the northern hemisphere, it may be seen as much as 1/2 of a degree below
Schoch’s curve, or possibly slightly lower. At the moment of the sighting of
the crescent, if it is above 4 degrees in altitude above the horizon, then the
distortion due to refraction is perhaps tolerable enough to consider that it
might truly be recognized as the crescent. Below 4 degrees it is very
doubtful that it could be recognized.
The principles of Karl Schoch’s curve are explained next, without involving
ourselves with mathematics. It is simply that the contrast between reflected
light of the moon and the background sky must be different enough to
perceive the arc of light.
For example, why don't people see the stars during the day? The stars are
most certainly there during the day, but we do not see them because the
contrast between the light of the stars (not their size which is much smaller
than the center width of arc of the moon!) and the background sky is not
enough. In other words, the sun’s light is too brilliant to see the stars’ light.
The most important word here is contrast or difference. That is why a
nighttime bicycle rider is told to wear reflective or brilliant colored clothes.
It does not matter whether the rider is fat or thin, but what matters is the
contrast between his clothing and the blackness of night.
The same is true in seeing the light of the moon. Some computer programs
(like Yallop’s criterion) are based upon the apparent width across the center
of the moon (or the percent reflection of the light of the moon, for example
full moon 100 percent reflection).
When the sun sets, and you look at the background sky to the west, the
brilliance of the sky is not the same everywhere. The further you look from
where the sun sets, the less brilliant the background sky at that point. Also,
it is more brilliant directly above where the sun sets, than the same distance
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above, but also some distance to the right or left. It is these angles away
from where the sun set that is an accurate measure of the brilliance of the
background sky. If the moon is at a place where the background sky is not
very brilliant, then and only then, can you see it. Thus the key is knowing
the angles (the curve based on the graph coordinates of two angles) of where
the sun is compared to where the moon is. This gives a measure of the
contrast between the background sky and light from the moon.
Summary: Use the appropriate angles to determine the contrast, which was
used to determine Schoch’s curve.
If you take some width of the crescent and put it where the contrast is great,
you see it. But if you take the same width of the crescent and put it where
the contrast is small, you do not see it. Hence the width is not the main
factor, but instead the contrast. This concept is very simple, but the
mathematics and astronomy are complex.
I do not use a program that predicts visibility of the crescent! Instead I use a
program that gives me the accurate angles I want. Then I use the printed
table that Karl Schoch determined (which really makes a curve by
connecting the dots) to see if the moon is above the curve or below the
curve. Above means visible. Below means not visible. But borderline is
about 1/2 a degree above or below the curve (under 4000 feet) based upon
extremes of humidity. As was mentioned above concerning the paper by
Fatoohi and others, in ancient Babylon there were two cases among 209 in
which people had reported seeing the new crescent at 0.9 degrees below
Schoch’s curve, but the air is more polluted today.
The key for borderline cases is humidity. The further you go below Schoch’s
curve, the lower the humidity must be to see it. For the areas with extremely
low humidity one can go 1/2 a degree below Schoch's curve and still just
barely see it.
Before modern high-speed communication and astronomical theory, one
would have been reduced to local visibility, although I do not know how to
define this and have never seen a definition of this that may be applied in a
uniform manner considering the case of overlapping geographical areas for
individual congregations. The first goal for a proponent of “local visibility”
should be to define it so that the definition covers the issues of distance,
height above sea level, bad weather, the use of modern communications, et
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cetera. Perhaps one may give a definition of local visibility in terms of
technology that was available about 1800 before the telephone and
telegraph, but even the issue of using race horses for separated groups of
people to communicate would begin to complicate matters. Can one apply a
definition that might have made sense in 1800 to today's society, thus
forbidding telephone calls and driving automobiles to learn what others have
seen? While some people might say “yes” and want to pretend that we are
locally primitive, even that is an arbitrary rule, and many people would want
to communicate with others to determine what they individually should do.
[38] Ezra and Nehemiah in Relation to the Vernal Equinox and the
Babylonian Calendar
Ezra 6:15 mentions the month Adar and Neh 6:15 mentions the month Elul.
These are Hebrew transliterations of month names in the Babylonian
calendar, but these verses are in the context of Jerusalem with the stamp of
approval from Scripture. This chapter provides historical evidence that the
Jews adopted the month names of the Babylonian calendar into their own
calendar, apparently from the time of Ezra and Nehemiah onward. This
would cause an obvious confusion unless it was true that nearly all of the
time the months in Jerusalem would agree with the months in Babylon
during the century of Ezra and Nehemiah. The goal is to learn when the first
month of the biblical calendar begins by determining when the first month of
the Babylonian calendar began during the century of Ezra and Nehemiah.
Later, other corroborating evidence will be presented.
Appendix A provides the details that show the first month of the Babylonian
calendar in the years from 499 BCE to 400 BCE, and it includes a discussion
of the 19-year cycle. This appendix shows that near the middle of this
century Ezra and Nehemiah journeyed from Babylon to Jerusalem.
The results from appendix A yield the following rule to determine the day of
the vernal equinox in the Babylonian calendar during this century. Find the
date containing the noontime that is closest to the time of the vernal equinox.
That date is counted as the date of the vernal equinox. The appendix also
provides the details showing that the first day of the first month of the
Babylonian calendar during this century followed the pattern that the new
crescent of Nisan was the new crescent that fell on or soonest after the day
of the vernal equinox. This implies that first the new crescent was sighted,
and later that same day the vernal equinox was determined to have occurred.
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The Jews were apparently willing to replace the use of the name Abib with
the name Nisan in the context of Jerusalem because they accepted the
Babylonian month names. Neh 8:2, 9 show that Ezra kept the holy day of the
first day of the seventh month at the correct time. From this time onward
Israel used the Babylonian month names for their calendar, which would
have led to confusion unless the Israelite calendar and the Babylonian
calendar began Nisan at the same time, almost always, during the century in
which Ezra and Nehemiah lived.
The claim has been made that the Persian Empire forced the Jewish
leadership in Israel to accept the Babylonian month names into their
religious calendar and discontinue all of the original month names. Ezra 7
gives the text of a letter from the Persian King Artaxerxes to Ezra the priest,
and in verse 16 the king writes that the religious laws are in the hand
(power) of Ezra, showing that the king is respecting the independence of the
priest in carrying out the laws of the Bible. Neh 5:14 shows that Nehemiah
was appointed governor by the king, and in Neh 13:30 Nehemiah writes,
“Thus I cleansed them [the Israelites] of everything pagan.” Israel had
religious autonomy and self-determination. If the Babylonian Nisan was
oftentimes not the Jewish first month, then the Jews would have kept both
sets of names to avoid confusion with their numbering of religious months.
Or instead, the Jews could have merely used numbers of the months without
names for the religious calendar. Another response to this is that the Persian
Empire had no control over Scripture, and through inspiration of the Holy
Spirit, Ezra 6:15 and Neh 6:15 could have used the month number rather
than the month name in the context of Jerusalem. These verses give approval
to the use of Babylonian month names and provide a calendaric witness to
us.
The book of I Maccabees covers the history of Israel from about 175 BCE to
130 BCE and was originally written in Hebrew. It shows the military
struggle of the Jews to gain independence from Seleucid domination. The
Jews had some degree of success, but it was a continual struggle. In this
context of greater Jerusalem the Jews use Babylonian month names for their
calendar in I Macc 4:52, 59; 7:43, 49; 14:27; 16:14 when the Babylonian
Empire and the subsequent Persian Empire no longer existed. Josephus also
uses these month names and calls them Jewish, and these names have been
kept by the Jews until today. The existing biblical and historical evidence is
that the Babylonian month names were not merely a secondary secular
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alternate method to designate dates apart from the biblical month numbers
(as we today use January to December apart from the biblical month
numbers), but that the Babylonian month names and the biblical month
numbers were synonymous in designating months. For example, I Macc
4:52 reads, “Early in the morning on the 25th day of the ninth month, which
is the month of Chislev, ...” This does not say that in this particular year the
ninth month happened to be Chislev, but that the ninth month is Chislev. To
emphasize this point even more vigorously, verse 59 states, “Then Judas and
his brothers and all the assembly of Israel determined that every year at that
season the days of dedication of the alter should be observed with joy and
gladness for eight days, beginning with the 25th day of the month of
Chislev”. Thus this festival of Hanukkah (Feast of Dedication in John 10:22)
was always to begin on Chislev 25, thus requiring Chislev to always be the
ninth month.
The book of Esther discusses the origin of the Feast of Purim, which has
been kept by Jews from that time in 473 BCE in Babylon until today. For the
year 473 BCE see the note to Est 8:12 in NIV. The date of the writing of the
book of Esther is less certain. On page 718 of NIV we find, “Several
scholars have dated the book in the Hellenistic period; the absence of Greek
words and the style of the author's Hebrew dialect, however, suggest that the
book must have been written before the Persian Empire fell to Greece
[Alexander the Great] in 331”. In Est 9:19-23 it is clear that the Jews had
decided that every year on the 14th and 15th days of the 12th month Adar
they would celebrate Purim. Note the specific wording in Est 9:20-21, “And
Mordecai wrote these things and sent letters to all the Jews, near and far,
who were in all the provinces of king Ahasuerus, to establish among them
that they should celebrate yearly the 14th and 15th days of the month of
Adar,” and verse 23 concludes, “So the Jews accepted the custom which
they had begun, as Mordecai had written to them”.
Thus Scripture teaches that the Jews accepted that the month named Adar
would always be the month in which the Feast of Purim would fall. Adar is
the name of the 12th month in the Jewish calendar as well as in the
Babylonian calendar. The month names and month numbers were locked
together; they did not slide around with respect to one another.
[39] Nisan and the Jews at Elephantine, Egypt
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About 600 BCE a group of Jewish mercenaries were first employed on the
island of Elephantine along the Nile River in southern Egypt about 500
miles south of the Mediterranean Sea close to the border of Ethiopia (see
pages 7 and 34 of Bickerman 1962). The purpose of this military base was to
protect the southern border of Egypt from invasion from the south. When
Persia defeated Egypt in 525 BCE under the leadership of Cambyses, this
military base became funded by the Persian Empire instead of Egypt because
its need still existed.
A number of letters written in Aramaic have been discovered on this island
of Elephantine during the late 19th and early 20th centuries. These letters
date from the fifth century BCE when the Jewish mercenaries were there.
Page 35 of the book by Bickerman states, “The ‘Jewish force’ (as the
regiment is officially styled) was divided into companies, the captains of
which bear Babylonian or Persian names; a Persian was ‘the chief of the
force’.” Since it was called a Jewish force, the bulk of the mercenaries were
obviously Jewish, but it was under the command of Persians, so it was not
autonomously controlled by Jews. This is a significant difference between
Elephantine compared Judea under the governorship of Nehemiah. Judea
was autonomous, while Elephantine was totally funded by Persia, under
Persian military command, and was not autonomous. This implies that the
calendar in use at Elephantine was the Babylonian calendar rather than the
Jewish calendar, although it is quite likely that most of the time there was no
difference between these calendars at that time. In the paper concerning
Elephantine by Richard Parker 1955, on page 274 he wrote, “A Persian
military garrison in a Persian satrapy would most probably use the Persian-
Babylonian calendar”.
One of the Aramaic letters found at Elephantine is known in scholarly
circles today as the Passover Papyrus. The Hebrew-Aramaic alphabetic
characters in this letter along with an English translation are found on pages
56-57 of Lindenberger. In the following quotations from the letter, the
square brackets and the contents within them appear on page 57 of
Lindenberger. The letter contains “This year, year five of King Darius”,
which dates the letter in 419/418 BCE. There are gaps in the letter because it
is poorly preserved. The addressing of the letter says “[To] my brothers
Yedanyah and his colleagues, the Jewish garrison, from your brother
Hananyah”. It was written from one Jew in friendship to the Jews on the
island with whom the author had familiarity. Part of the preserved text of the
letter says, “Be scrupulously pure. Do not [do] any work [...]. Do not drink
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any [...] nor [eat] anything leavened [... at] sunset until the twenty-first day
of Nisan [...]”. Another translation of this same segment of this letter is on
page 283 of Whitters where he adds in square brackets some guesses in gaps
in the text as follows, “be pure and take heed. [Do n]o work [on the 15th and
the 21st day, no]r drink [fermented drink, nor eat] anything [in] which
the[re] is leaven [from the 14th at] sundown until the 21st of Nis”. Note that
the final letter of Nisan is missing in the poorly preserved papyrus so only
“Nis” is shown. This provides historical evidence that after the return from
exile under Ezra and Nehemiah, Jews named the first month Nisan as a
substitute for Abib. On page 283 Whitters comments, “The letter came from
one Hananiah, who apparently wanted the Jews in Egypt to celebrate
Passover and Unleavened Bread appropriately. The address and greeting rule
out a local Egyptian official or Persian overlord.” If the name Nisan was not
significant for the first month, the letter could simply have said the first
month or Abib.
[40] Gen 1:14; Ezra 6:15; Neh 6:15 Show the Vernal Equinox Starts the
Year
Ezra 6:15 and Neh 6:15 tie in with Gen 1:14 to give the biblical and
archaeological evidence that together show explicit evidence that Gen 1:14
involves the vernal equinox. The Babylonian cuneiform inscriptions are
archaeological clay records that are now mostly in the British Museum.
These tablets have eclipse data as well as new moon sighting data that
correlate with computerized astronomy to prove the dating of their calendar.
From the knowledge of the Babylonian calendar with the use of these month
names in Israel we can say that Nisan 1 is the new moon on or the soonest
new moon after the day of the vernal equinox (see appendix A). In
discussions above it was pointed out that by the process of logical
elimination of choices, about the time of Ex 12:2 and within the parameters
of Gen 1:14 involving the lights in the heavens, the vernal equinox is the
only candidate for starting the year.
Some people have proposed that merely the 16th day of the first month need
be on or after the equinox, and not the first day of the first month. Aside
from the fact that this is not a natural thing for Moses to imagine, there is the
practical problem of having to predict at the beginning of the month whether
the 16th day of the month will be on or after the equinox. From one equinox
to the next is 365 or 366 days, and it is not an easy matter to predict between
the two because there is no repetitive pattern. However, it is only in unusual
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cases when the first day of the month will be within a day of the vernal
equinox.
If it had originally been true that merely the 16th day of the first month need
be on or after the equinox to determine the first month, then about half the
time the Israelite first month named Nisan would have been one month
earlier than the Babylonian Nisan, and consider what confusion there would
be in that case. The confusion would be unacceptable.
[41] Philo explains when the First Month of the Biblical Year begins
There is a Jewish witness whose writings date from the early first century
who discusses the meaning of Gen 1:14 and Ex 12:2. This witness is Philo
of Alexandria. This witness would be of no consequence and irrelevant if the
applied calendar of Judaism at the Temple in the early first century was not
correct. It is necessary to establish some relationship between the calendar of
Judaism at the Temple and Philo's thinking in order for Philo's comments on
Gen 1:14 and Ex 12:2 to be relevant.
In Gen 1:14 where the Hebrew text has the plural of moed, which is typically
translated seasons, or festivals, or appointed times, the Greek translation of
the Hebrew Bible known as the Septuagint has the Greek word kairos
(Strong's number 2540). The various versions of the Jewish Aramaic
paraphrased translations of the Hebrew Bible known as the Aramaic
Targums all interpret moed to include the meaning festivals. The Jewish
commentaries of the middle ages also agree with this understanding of
moed. In Lev 23 the Hebrew moed occurs six times: Lev 23:2, 2, 4, 4, 37,
44. The association of moed with festivals is clear from its use in Lev 23 as
well as in Ps 104:19 and elsewhere. In contrast to this, kairos occurs in Lev
23:4, but nowhere else in the Septuagint of Lev 23. In Greek, kairos is a
very general word for time, and it is not noted for being associated with the
festivals or any other regular repetitive time. Thus one would not
particularly expect Philo to interpret kairos as festivals, and indeed Philo
does not interpret it that way. But he does use the word kairos in discussing
this portion of Gen 1:14, indicating that his version of the Septuagint Gen
1:14 is similar to the one that is commonly available to us.
Philo discusses Gen 1:14-16 on pages 34-47 of Philo_1 (On the Creation 45-
61). On pages 44-45 (paragraph 59) Philo wrote, “By ‘appointed times’
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[kairos] Moses understood the four seasons of the year, and surely with good
reason.”
It is a little humorous that he puts this interpretation in Moses’ mind as if to
say this is what Moses knew it to mean rather than this is Philo's
interpretation. Since the four seasons are bounded by the equinoxes and the
solstices, he certainly believes that Gen 1:14 includes these astronomical
events. On pages 46-47 (paragraph 60) Philo continues, “The heavenly
bodies were created also to furnish measures of time: for it is by regular
revolutions of sun, moon, and the other bodies that days, and months, and
years were constituted.” Since the calendar is based on these units and he
declares these units to be based on measures of time of the heavenly bodies,
he leaves no place for the barley to be the determining factor for the first
month. The reader might be curious about why Philo wrote here “and the
other bodies”. While we know that the Greek astronomer Hipparchus proved
that the stars drift very slowly from the equinoxes, and he discovered this
about 100 years before Philo was born, this knowledge had not been
popularized and accepted, so that Philo does not know this. Thus Philo
implies the thought that the cycle of the appearance of stars agrees with the
sun’s signs of the equinoxes and solstices that make the seasons.
Philo wrote on page 151 of Philo_7 (Special Laws I.90), “Who else could
have shewn us nights and days and months and years and time in general
except the revolutions, harmonious and grand beyond all description, of the
sun and the moon and the other stars?” Notice that the way Philo asks this
question emphatically shows that agriculture is not the way to determine
years and the first month. Again Philo leaves no place for the use of barley
in calendaric determinations. If, on an annual basis, the Jews in Alexandria
had to wait for a report on the state of the barley from the priests in Judea in
order to know when to leave for a journey to keep the feast of unleavened
bread at the Temple in Jerusalem, Philo would not neglect such an important
annual event in its role to determine the time of the first month. In this
matter the Septuagint has no distortion that would give Philo a reason to
have a prejudice against the use of barley, but he surely knows nothing of
the role of barley in the early first century to determine the first month.
Having examined Gen 1:14 in Philo's writings, the next step is to consider
his comments on Ex 12:2. In order to properly evaluate this, certain
terminology of Philo and his age needs to be discussed first. One concern is
the meaning of “the Ram” (also called Aries which is the Latin word for
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Ram) in the sense of the first of the twelve annual signs of the zodiac.
According to pages 594-595 of HAMA (volume 1) secular writers of the
first century wrote that the eighth day of the Ram is when the vernal equinox
occurred. However, the elite group of Greek astronomers who employed
mathematics considered the first day of the Ram as the day of the vernal
equinox (page 600); it took a few centuries for Roman society to gradually
accept the astronomer’s definition.
Philo was not studied in the area of astronomy and would have used the
secular meaning. Hence Philo speaks of the vernal equinox as being in the
Ram instead of occurring at the start of the Ram. Secular society also
considered the autumnal equinox to occur on the eighth day of the sign of
the zodiac called the Scales.
With the help of a little sloppiness in the existing translations it is easy for
readers to become confused about what Philo means. To help explain one
confusing part of Philo's writings I made a word for word translation from
the Greek. Here is my literal translation of Philo's On the Creation,
paragraph 116 (in chapter 39) on pages 92-95 of Philo_1: “The sun, too, the
great master of the day, bringing about two equinoxes each year, spring and
autumn, the spring in [the] Ram and the autumn in [the] Scales, supplies
very clear evidence of the sacred dignity of the seventh [number], for each
of the equinoxes occurs [near a] seventh month, and during them [these
seventh months] there is enjoined by the law the keeping of the greatest
national festivals, since [during] both of them [these seventh months] fruits
of the earth ripen, [in the] spring indeed grain produce and all else that is
sown, and [in] autumn the [fruit] of the vine and most of the other fruit
trees.”
One peculiar thing to notice here is that Philo uses the word “spring” twice
as though it meant “spring equinox” and the word “autumn” twice as though
it meant “autumn equinox”. Elsewhere he seems to use the word “equinox”
to mean the season that it begins; for example, he writes separately of the
feast of trumpets at/in the autumn equinox and the feast of tabernacles at/in
the autumn equinox. Philo enjoys analogies, symmetry, and approximation
in his writings.
Philo discusses Ex 12:2 on pages 2-5 of Philo_QE (Exodus, Book 1.1). On
page 2 he wrote, “’This month (shall be) for you the beginning of months; it
is the first in the months of the year.’ (Scripture) thinks it proper to reckon
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the cycle of months from the vernal equinox. Moreover, (this month) is said
to be the ‘first’ and the ‘beginning’ by synonymy, since these (terms) are
explained by each other, for it is said to be the first in order and in power;
similarly that time which proceeds from the vernal equinox also appears (as)
the beginning both in order and in power, in the same way as the head (is the
beginning) of a living creature. And thus those who are learned in astronomy
have given this name to the before-mentioned time. For they call the Ram
the head of the zodiac since in it the sun appears to produce the vernal
equinox.” Then on page 3 he writes, “And that (Scripture) presupposes the
vernal equinox to be the beginning of the cycle of months is clear from the
notions of time held in the ordinances and traditions of various nations.”
As a commentary to this last sentence, page 391 of Samuel states, “In the
areas of Syria and the East controlled by the Seleucid kings, the Macedonian
calendar was adjusted to make its months coincide with the months of the
Babylonian calendar, which was in turn regulated locally by a nineteen-year
cycle. The system was in general use in the East, and persisted in an adjusted
form in cities all over the eastern regions well into the period of Roman
domination.” The first day of Nisan in the Babylonian calendar since 499
BCE fell on or after the vernal equinox. Although Parker and Dubberstein
show an exception to this in the year 384 (page 34), this alleged exception
should be corrected because it is now regarded to be a faulty examination of
a cuneiform text; see pp. 14 and 16 in Aaboe and others 1991.
When Philo speaks of the “traditions of various nations”, from Samuel’s
statement he is referring to the continuation of the Babylonian calendar
whose first month did not begin before the day of the vernal equinox. This is
the only place where Philo makes a statement about the first month that is
capable of some explicit comparison with the vernal equinox.
In none of this is there any use of barley to determine the first month, and
the Septuagint does not force Philo to take his position. There is never a hint
that the Jews in Alexandria waited with anticipation to hear the news of
barley reports so they could begin their plans for the Passover.
[42] Declaration of the Vernal Equinox in Ancient Israel
Based upon Num 10 as discussed above, it should be accepted that the
Levitical priesthood had the authority to declare the new moon days and thus
regulate the calendar for ancient Israel. This priesthood performed specific
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animal sacrifices on the new moon days (Num 28:11-15; 10:10), so the
priesthood had an essential role. This role was highly visible and
authoritative before all the people as long as the Temple stood, but after it
was destroyed in the year 70, the priesthood’s visibility ceased. There is
some scholarly controversy over who controlled the calendar from the
Temple in the early first century and much could be said about it, but this is
not our concern now. As already shown above, the vernal equinox was
significant to determine the first month, Nisan or Abib.
The first question is whether the vernal equinox was determined by
observation or by a calculation in ancient Israel. To answer this question, a
summary of several points from above along with a few related matters are
now brought together.
(A) There is no word in biblical Hebrew for “astronomer”, although there is
a Hebrew word for “astrologer”, havar, Strong’s number 1895. This word
only occurs once, in Isa 47:13, a negative statement against a practice in
Babylon.
(B) Neither the Dead Sea Scrolls, nor archaeology from Israel, nor the Bible,
nor Philo of Alexandria, nor Josephus indicates any native development of
mathematical astronomy in Israel.
(C) Biblical Hebrew for the expression of numbers along with the Dead Sea
Scrolls and archaeology indicate that ancient Israel had no positional
numbering system with a zero, so that general multiplication and long
division, especially of fractions, would have been prohibitive. This is a
heavy strike against any suspicion that ancient Israel could have had a native
mathematical astronomy.
(D) Ancient Egypt did not possess mathematical astronomy until the Greek
astronomers moved to Alexandria after 330 BCE. Thus Israel could not have
inherited such knowledge when Moses led them out of Egypt.
(E) Mathematical astronomy began in Babylon roughly 500 BCE. On pp.
51-52 of Britton and Walker we note, “Around 500 BC Babylonian
astronomy began a process of transformation which led to the development
of radically new techniques for predicting celestial phenomena. These
techniques were mathematical in nature, rational in approach, and entailed
separating complex phenomena into components which could be described
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by mathematical functions which could then be combined to predict the
phenomena in question.” This mathematical astronomy was developed and
recorded by the pagan priests of Babylon only in the Akkadian language,
with its hundreds of symbols, at a time when this language was no longer in
general use, having been supplanted by the Aramaic language. It was only
after Alexander the Great defeated the Persian Empire in 331 BCE that
Alexander apparently commanded that the Babylonians make their
astrology-astronomy available to the Greeks for study. Not long after this,
the Greeks were using Babylonian period relationships of the heavenly
bodies, and also Babylonian horoscope techniques.
(F) Both Philo of Alexandria and Josephus were Jews from the first century
who wrote extensively and were well educated. Neither of them implied any
significant abilities in themselves or other Jews concerning mathematics or
astronomy. Josephus likes to exaggerate the achievements of the Jews, and
he only does this in science through bragging about Abraham’s knowledge
of arithmetic and astronomy, and that Abraham taught this to the Egyptians.
This claim must be historically false because at the time of Abraham neither
the Egyptians nor the Assyrians (later Babylonians) possessed mathematical
astronomy, although the ancient Babylonians did record observed eclipses
and other heavenly phenomena, and the ancient Egyptians did record the
approximate time of certain appearances of heavenly bodies. Such recorded
observations are not mathematical astronomy.
(G) The Rabbinical writings do not claim any advanced mathematical
knowledge in their history. In the Talmud, Gamaliel II is claimed to give
credit to his grandfather Gamaliel I for handing down the length of a month,
yet this was derived by the Babylonian astrologer-astronomers as part of
their astronomical System B in Babylon c. 300 BCE.
(H) Conclusion: It would be folly to think that ancient Israel had a calendar
that was based on mathematical astronomy. The same conclusion should
apply to the determination of the vernal equinox.
The vernal equinox is only known from the light of the sun or shadows from
the sun. This can only occur during the daytime. Thus, while the new
crescent is sighted near the time of sunset and most often during the middle
of twilight, the vernal equinox must be determined during the daytime, based
upon some commonly known definition.
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The biblical months do not have an alternation of 29 and 30-day months, so
that the pattern is not predictable. About half of the biblical months have 30
days, so that when the new crescent is sought in the hope of its sighting at
the end of the 29th day of each month, no one can generally know whether
the new crescent will be seen anywhere in ancient Israel. Since there will be
full darkness that night, no one expects witnesses from far off to walk to
some authority in Jerusalem during that night of darkness. Also, no one
would expect people to be at the top of hills at night to signal a declaration
of the new moon by the Levitical priesthood. All the questioning of
witnesses, the subsequent declaration of the new moon through the blowing
of the two silver trumpets, the fire signals to spread the news, and the
commanded sacrifices associated with the arrival of the new moon, along
with singing praises at the Temple where all the nearby people could travel
to witness and participate in the festivities through singing, would have to
wait until the daytime.
It would be during that same daytime of questioning witnesses concerning
the new crescent that the Levitical priesthood would also examine the sign
of the sun for the vernal equinox.
The obvious correlation of Nisanu 1 with the vernal equinox acknowledges
this day in the Babylonian calendar, and Philo is a historical witness that
corroborates the same thing. Gen 1:14 also points to this through the process
of elimination of other possibilities.
Previously, Pliny the Elder from the mid-first century was quoted to show
that he regards the day on which “sunrise and sunset are seen on the same
line”, which means that the sun’s shadow makes a straight line, as the day of
the vernal equinox. This is the true east-west line and it shows the vernal
equinox. The alignment of one wall along the east-west line for each of the
most prestigious pyramids of Egypt shows that ancient Egypt knew how to
determine the vernal equinox. Moses was trained in the knowledge of Egypt
(Acts 7:22) and would be expected to know this. This only requires
observation, no calculation, and no mathematical astronomy.
On page 158 of the book by Robert Newton there is a chart of 20 equinox
observations by Hipparchus. These are dated from 162 to 128 BCE. He is
considered to be the greatest of the ancient Greek mathematical astronomers.
Even with his gifted application of trigonometry to attempt to use
observation to calculate the time of the equinox, he is nevertheless off by an
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average of several hours. But ancient Israel did not use a calculation. By
observation alone it is impossible to judge the hour of an equinox.
Now consider the borderline situation of both the new crescent starting
the day and the vernal equinox later on the same day in ancient Israel.
Suppose witnesses saw the new crescent at the beginning of the day, and on
the next daytime they appear to testify as would be typical. Further suppose
that the typical investigation of the sun’s shadow line compared to an exact
east-west line by the priesthood that next morning showed that the vernal
equinox had arrived. Such an observation cannot be so precise that one can
judge the hour of the equinox. Only its day is known. On the previous
daytime there was no vernal equinox yet, but this next morning the vernal
equinox is seen true. At the same time they also examine witnesses of the
new crescent and this is determined true. They know that both occurred.
This should be the first month because both arrived. The priests declare both
simultaneously.
There is another example to consider as a precedent for accepting this
reasoning. For 40 years in the wilderness, manna arrived in the morning
each day except on the Sabbath. The arrival of manna was a morning
activity just as the examination for the vernal equinox would be sometime in
the morning. That the morning is the arrival time for the manna is seen in Ex
16:8, 12, 21. Now note the literal translation of Ex 16:23, “And he [Moses]
said to them, ‘That is what YHWH said, tomorrow is a rest, a holy Sabbath
to YHWH. Bake what you will bake and boil what you will boil. And all that
remains lay up for yourselves to be kept until the morning.’”
On the ordinary six days, the manna would spoil and have worms in the
morning, and there would be a new supply of manna on the ground in the
morning. In Ex 16:23 note the word “tomorrow”, which is translated from
the Hebrew word machar, Strong’s number 4279. This word refers the next
daytime. The next daytime includes the morning, which is normally the time
that any manna from the previous day would be seen spoiled and manna
would be seen on the ground. Tomorrow would be an exception due to the
Sabbath. Ex 16:23 states that “tomorrow is a rest, a holy Sabbath”. Although
the Sabbath is from sundown to sundown, in order to emphasize that
tomorrow is when they would see the exception of no spoilage in the manna
and no manna on the ground, Moses said, “tomorrow is a rest, a holy
Sabbath”. By what they would notice tomorrow, they would be able to
verify that the whole day was the Sabbath. Similarly, by what the priests
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would notice on the morning of the day of the vernal equinox, they would be
able to verify that the whole day was the day of the vernal equinox. The time
of the equinox would have to be identified with one sundown-to-sundown
day. The most obvious way to identify this is to take the day whose
noontime is the closest to the time of the vernal equinox. That daytime
would most be identified with the vernal equinox by visual inspection. This
does agree with the conclusion from appendix A.
[43] The International Date Line, the Sabbath, and the New Moon
Beginning with this chapter, the subject of how to determine the first day of
the month for the various parts of the world is treated. In order to avoid
forcing the curious reader to wander ahead to discover the conclusion, I will
give a brief summary of the next group of chapters here. Summary for the
next group of chapters: The sighting of the new crescent for the purpose of
defining the start of a new month should be from within the biblical
boundaries of Israel, and sundown at the International Date Line should
begin each first day of the month before anyone in Israel would be able to
see it. This implies that on some occasions people to the east of Israel would
begin a new month that later was determined to be one day prior to the new
month. This would primarily matter on the first day of the seventh month,
when they might keep two successive days as was sometimes done in
ancient Israel.
Many people do not realize that there is a need for an International Date
Line (IDL), and they need to be convinced that there is such a need. During
the 19th century the international community recognized the need for an
IDL, and they established it in the Pacific Ocean by agreement of some of
the most influential nations. Perhaps the most obvious need was seen in
simply recording the date and time of events in various parts of the world. If
it is noon on Saturday in England, what time and day is it in Australia? The
answer partially depends upon where the IDL is placed. If the IDL is placed
between Australia and Japan, you get one answer. If the IDL is placed
between Australia and Hawaii, you get another answer. The IDL also affects
the day for keeping the Sabbath in some parts of the world, as we shall
explore next.
If a group of people in Israel performed the following experiment, consider
the outcome. Let half of them travel east 1000 miles during the course of six
days and rest on the seventh, and the other half travel west 1000 miles
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during the course of six days and rest on the seventh. Since there are about
24,000 miles around the earth at the latitude of Israel, each 1000 miles
represents one hour of time. At the end of the six days in the experiment, the
group that traveled east will start their Sabbath two hours earlier than the
group that traveled west, because they are 2000 miles further east. If this is
continued for another week in the same direction, the group that traveled
east will be start their Sabbath four hours earlier. If this experiment is
continued for 12 weeks and boats are available for water travel, the two
groups will meet in the Pacific Ocean. The group that traveled east will start
their Sabbath 24 hours sooner than the group that traveled west, so that
while neither group lost track of the days and both groups had sincere
intentions, if they got together on the same boat there would be confusion on
which day to begin the Sabbath.
If ships had carried colonists from countries that had previously adopted the
seven day weekly cycle to North America, and if they had originally traveled
east across the Pacific Ocean instead of west across the Atlantic Ocean, then
they would have given the name Sunday in North America to the day we
now call Saturday, and their week would be shifted one day.
These examples show the absolute need for an IDL to officially start the day
for the purpose of keeping the Sabbath and avoiding confusion on the day it
begins. If an IDL were proposed that crossed land where people lived, then
neighbors on one side of the line would keep a different day as the Sabbath
compared to others across the line. This destroys spiritual unity and is a
source of confusion.
Jewish scholars since Talmudic times have recognized that a spherical earth
requires an IDL for the purpose of keeping the Sabbath. Pages xxiii-xxiv of
Sternberg give his translation of a passage in the Babylonian Talmud (RH
20b) that relates to the IDL. Page xxv gives the opinion of Chazon Ish that
this implies that the IDL occurs at the end of the Asian continental landmass.
On page 343 of the article by Jakobovitz, he states, “The international
dateline has also been endorsed by the rabbinate in Jerusalem in its reply of
1942 to the inquiry received from the refugees in Japan.” This means that
society's IDL has been accepted by Jewish authorities as the IDL for the
Sabbath, thus overruling the Babylonian Talmud, a very rare event. It is
interesting to note that modern Jews desired to have a ruling come from
Jewish authorities in Jerusalem, and this occurred in 1942, before Israel was
recognized as a nation in the geopolitical sense.
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Scientists today believe that the land surface of the earth was once together
as one mass of land with one very large ocean around it. This is evident from
examining the globe's landmasses and noticing how they fit together, such as
mentally pushing North America and South America into Europe and Africa.
This is also noted by matching geological rock formations and plant species
with corresponding parts of matching areas across the Atlantic Ocean. At the
time when the world only had one land mass it was only sensible that the
IDL run through the one ocean to avoid neighbors keeping the Sabbath on
two different dates, thus avoiding confusion. As the one land mass
separated, the IDL should not change. This would put the IDL in the middle
of the Pacific Ocean as men have decided to do in the nineteenth century.
But the creation shows the mind of the Creator in establishing the IDL at
that place to avoid confusion on when to start the Sabbath day. The biblical
principle is found in I Cor 14:33.
If it is confusing, annoying, or disruptive to run some line along a landmass
and imagine that people on one side of the line keep the Sabbath on one day
and people on the other side of the line keep the Sabbath on the next day,
why shouldn’t it also be equally confusing when the first day of a biblical
month is considered in the same way? In my mind it would be confusing to
begin a month with a disruptive line on a landmass that separated the month
start on one side of the line from the month start on the other side of the line.
This is especially true if the line were to change from month to month, and it
would even be more discomforting if the line was wide and fuzzy with
pockets of exception in various places due to humidity, height above sea
level, and bad weather. Considering the philosophical principle of avoiding
confusion, it is natural to extend this from the Sabbath to the start of a month
using the IDL.
The Sabbath cycle is much simpler than the monthly cycle because the
former is always a seven day cycle, while the latter is a cycle of 29 or 30
days, which does not necessarily alternate between 29 and 30 days. There
are some natural reasons for desiring to take simplifying concepts that apply
to the Sabbath, such as the IDL, and also transfer them to the start of each
month. Lev 23 discusses all of the days of holy convocation. Relating to all
the festivals as well as to the seventh day Sabbath, the words holy
convocation(s) occur in verses 2, 3, and 4 of Lev 23. Lumping the seventh
day Sabbath together with the festivals in the same chapter under the larger
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umbrella of holy convocations does seem to be a reason to transfer
simplifying concepts that apply to the Sabbath to the festivals as well.
It must be admitted that the confusion primarily stems from the fact that we
have modern methods of communication today. Not only do we have the
Internet and telephones, but we also have automobiles and jet planes, so that
we may travel for attendance on the Sabbath and on the festivals. If modern
technology was completely removed and each family was an island unto
itself without contemplation of travel, the confusion would disappear. But no
one expects society to give up modern technology for travel and
communication, so there is a need to face and solve the resulting issues.
[44] How the MCJC achieves Spiritual Unity using the IDL
From a strictly mathematical viewpoint, the IDL is not part of the
computation of the day of each month of each year that is performed
according to the rules of the MCJC. But in a practical sense the Jewish use
of the MCJC includes the Jewish adoption of the IDL, so that Jews in the
modern world would have a method to determine when to keep the festivals
in their area of the world. From this applied mainstream Jewish viewpoint,
the MCJC is used with the IDL. Since spiritual unity on the holy
convocations is a philosophical goal, let us consider for a moment how the
MCJC achieves spiritual unity. First it determines a specific date for the start
of each numbered month. Once the beginning of the month is established,
mainstream Judaism respects the IDL, so that the first place for the start of a
new day (including the Sabbath, a festival day, or a new moon day) is at this
IDL at sundown. Then sundown flows to the west on the earth, and each
place begins the new day as sundown comes to that place. This achieves a
simplicity and spiritual unity that is in harmony with Sabbath observance
around the world by multitudes of groups that are motivated to keep the
Sabbath. Moreover, this method extends to the festivals and the days of the
new moon. The big problem with the MCJC is that the computation of the
first day of each month is incorrect about 80 percent of the time within the
borders of Israel, and the determination of the month number is off by one
month in some years. One exceptional aspect was overlooked in this
explanation. When people on the earth are near the North Pole or the South
Pole, sundown as well as the ability to see the moon are greatly distorted,
especially during certain long periods of the year. In such cases, people
typically resort to choosing 6:00 pm on modern clocks as the time to begin
each day.
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The Jewish approved IDL-applied aspect with the MCJC has the advantages
of (1) Attaining spiritual unity; (2) Respecting the universal method for
observing the Sabbath; and (3) Being in agreement with the time that ancient
Israel kept the Sabbath. In a certain sense the IDL is not arbitrary because
some place for an International Date Line is a necessity and the Pacific
Ocean is where the one major body of water on the earth was originally
placed. The only aspect of the IDL that may be considered arbitrary is the
specific way that it wiggles around certain groups of islands in the Pacific
Ocean. If a correction would be made to the MCJC to arrive at the first day
of each numbered month that was much more in harmony with the calendar
of ancient Israel, then the philosophical goals originally expounded would be
met.
[45] Avoiding Confusion (I Cor 14:33)
If there is a significant density of people around the earth desiring to keep
the festivals, any boundary that began the new month that cut across a
landmass would cause confusion among the people. Even though people
may be organizationally independent, that should not hinder friendships and
occasional visits away from one's normal attendance site during biblical
festival days whose dates depend upon determining the first day of the
month. If there are different dates by different people who come together to
keep the festivals, there are likely to be date conflicts and disunity. All
biblical contexts that mention the festivals seem to take it for granted that
there are no conflicts and that there is just one day that is holy for each
specific commanded assembly. The only exception might be the start of the
seventh month where ancient Israel could occasionally keep two successive
days unless the first day of the two was confirmed to be the first day of the
month.
Organizational independence need not require confusion on the
determination of the start of the first and seventh months. In order to avoid
confusion, the first day of each month should respect the IDL rather than
cause it to change every month with a new curved line. Such a proposed
curved line of first visibility is in reality a fiction because it depends on the
observer's altitude above sea level, humidity (high humidity hinders
visibility and low humidity favors it), air pollution, rain, etc. The
approximate angle of such a curved line will change from month to month
because the moon's path changes somewhat with respect to the earth's axis
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(the orbit of the moon does not lie in the plane of the earth's orbit, and in fact
this approximately repeatable pattern follows the Saros eclipse cycle of
18.03 years). Any such curved line is not a sharp narrow line because it will
depend on the eyesight of individual people who are striving to see it. There
will be regions where some percentage of the people will see it and others
will not. Such a curved line will not be one neat pattern because humidity
variations will cause it to wiggle in significant ways, and oftentimes,
altitudes that are at least above 4000 feet above sea level will produce
geographical areas of visibility that are isolated from other larger regions of
visibility. Regions of high humidity will sometimes cause local regions of
non-visibility in the midst of much larger regions of visibility. When people
do not see the crescent at their dwelling place and others some distance off
do see it, the question remains concerning the conditions that would cause
the individual to accept the sighting of others. It may matter to some people
if others that attend the same congregation did see it, although such people
may have traveled quite a distance to get to the meeting place. If two
different organizations that had overlapping geographical areas of attendees
came to different conclusions based upon who saw the crescent within each
congregation, wouldn't that be a cause of confusion if they wanted to meet
together for a festival?
For the purpose of establishing the beginning of the month, using so called
local visibility of the new crescent from outside Israel leads to arbitrary
decisions and confusion. The first aspect of arbitrary decisions and
confusion is defining local visibility. Suppose the new crescent can be seen
from Fort Worth, but cannot be seen from Dallas, which is 30 miles to the
east. Should people in Dallas accept the testimony of people in Fort Worth
for visibility of the new crescent to start a month? What distance should be
the limit for accepting someone else's testimony? Suppose the only places in
the United States from which people can see the new crescent are over 8000
feet above sea level in the Rocky Mountains. Should people elsewhere in the
United States accept their testimony? If no one in the United States can see
the new crescent, but some people in Baja, Mexico can see it, should their
testimony be accepted in the United States? In order for local visibility of the
new crescent to be applied in today's world, it must first be defined so that
there is a principle to apply. In order to be practical it should be defined in
some manner so that any proposed definition may be applied in different
areas of the world, not merely on one small island.
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If someone proposes that the first place on the earth that any two witnesses
see the new crescent starts the new month for the whole world, there are still
problems. The most significant philosophical problem is that whenever this
place is to the west of Israel's time for sighting the new crescent and still
before the IDL, Israel would be made to keep any festivals of that month one
day sooner than Israel would keep it if the Levitical priesthood existed and
functioned exclusively within the boundaries to which they were anciently
confined among the original tribes. Another problem with this proposal is
that people on one side of the sundown line at that time will not be in the
same day as those on the other side of the sundown line. Thus people who
are geographically very close will potentially be keeping the festivals one
day apart, so that confusion will still exist by this method. Another potential
problem is that if some two people in one very remote area of the world post
a message on some web site that they saw the new crescent, how would
people know whether they were not pranksters? In Israel today, those who
are witnesses to the sighting of the new crescent are known by those who
post the sightings, so the problem of pranksters is virtually eliminated. To
some people, another problem with this proposal is that one segment of the
world that did not see the crescent would be deprived of seeing the new
crescent on the day that they would be expected to begin the month; this
latter reason is the cause for those specific people today to be zealous
supporters of their concept of "local" visibility, although there is a problem
in defining local visibility for various circumstances without inventing
arbitrary rules.
If someone proposes that some mathematical calculation substitute for the
actual sighting of the new crescent, there would be the objection that this
would not always agree with actual sighting of the new crescent from Israel,
which was anciently used. A mathematical calculation would only be
attractive if modern methods of communication broke down, and this was
attractive before timely web site postings of sightings of the new crescent
were available.
[46] Dwelling in Spiritual Unity Through the Declaration of the Priesthood
Ps 133:1, “A song of the upward-steps, by David, Behold how good and
how pleasant [is the] dwelling of brothers, yes-indeed in-unity.”
Ps 133:2, “[It is] like the good oil upon the head, descending upon the beard,
Aaron's beard, descending upon the edge of his garments.”
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Ps 133:3, “Like the dew of Hermon descending upon the mountains of Zion,
because there YHWH commanded the blessing of life forever.”
Verse 2 mentions Aaron, the first High Priest, who thus represents the
Levitical priesthood. It also mentions good oil, which represents the holy
spirit (Mat 25:3-4; Rom 8:11; John 8:12; I Cor 6:17; Mat 5:15-16; John
12:36). In flowery language this is saying that dwelling in spiritual unity is
like the holy spirit upon the Levitical priesthood, because spiritual unity can
only come if the priesthood properly teaches the law (Lev 10:8, 11; Mal
2:7), so that the people are motivated to keep it. Only then can there be
spiritual unity, and this will result in the blessing of eternal life (note verse
3). The priesthood was supposed to promote spiritual unity by proper
teaching. The appointed-times, the days of holy convocation, were
announced by this priesthood through the blowing of the two silver trumpets
(Num 10:1-2, 8-10), and this was a means of promoting unity in worship and
unity of the days of holy convocation.
I Cor 14:33, “The Almighty is not of confusion, but-oppositely of peace, as
in all the congregations of the saints.” If knowledge to achieve spiritual unity
is attained, it should produce uniformity in recognizing the days of holy
convocation, the appointed-times. Once the ability for widespread
communication exists to make spiritual unity possible, biblical principles
that promote unity in recognizing the days of holy convocation should be
promoted. If people in their own areas around the world attempt to
determine the start of a month by individually sighting the new crescent, it
will most certainly lead some people who are relatively close to one another
to have conflicting days for the appointed-times.
We do not have any Levitical priesthood today, but if we are given the same
information that they could have through postings on a web site, then we
could presumably arrive at the same decision they would.
[47] Does Deut 16:1 Command Everyone to Look for the New-Moon?
Deut 16:1 has been used by various peoples to promote highly specific
viewpoints regarding the calendar, each of these viewpoints conflicting with
the others, but all from the same verse. I have about a one inch thick folder
with photocopies from a wide variety of sources just on this verse, and I
have looked this up in about 40 different translations and many
commentaries.
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One basic principle of properly understanding the Bible is that a technical
expression should have the same meaning wherever it is used. This is
especially true if the writer is the same in all instances of its use. All of the
six places that chodesh ha aveev occurs were written by Moses, and two of
these places are in Deut 16:1. This technical expression chodesh ha aveev
should mean the same thing in both places of its use in Deut 16:1.
In the second instance of its use in Deut 16:1, chodesh ha aveev refers to the
time that the Israelites were freed from Egypt in the middle of the first
month, not at the start of the month. Consequently, although the word
chodesh in the general situation can mean either new-moon or month, in the
specific expression chodesh ha aveev it needs to have one fixed meaning,
and from its second use in Deut 16:1, its meaning must be “month”, not
“new-moon”.
From the above reasoning, Deut 16:1 should NOT mean approximately “Go
out looking [in the sky] for the new crescent of Abib”. Otherwise the second
half of this same verse would mean that in the new crescent of Abib the
Israelites were freed from Egypt, and this is not true according to Num 33:3.
Those who interpret Deut 16:1 in the sense of a commandment to watch for
the new crescent would use the examples of I Sam 19:11; Ps 59:1; 130:6;
Eccl 11:4 where the Hebrew word shamar, Strong's number 8104, could
mean to watch with one's eyes.
One conclusion is that Deut 16:1 is not a specific commandment for
everyone to go out looking for the new-moon that begins the first month.
[48] Ancient Israel did not Practice Local Visibility
Knowing that two priests in ancient Israel were commanded to blow two
silver trumpets on the first day of each month to officially declare the
beginning of the month (Num 10: 1-2, 8-10), when the time arrived at which
the Israelites were to keep the three annual festivals in one place (Deut 16:
5-6, 10-11, 13-16; 12:5-21), Israel did not practice "local" visibility to begin
the month and determine the festival dates since, when gathered together at
the festivals they were all together in one place with one High Priest. Thus
Israel was united in keeping the festivals on the same days and united on
beginning the months on the same days, which is against local visibility in
different parts of Israel.
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[49] Confusion of a Difference of a Whole Month in the Calendar
In some years local visibility (assuming this may be defined in a satisfactory
way) could make the difference between a month being considered as the
13th month for part of the earth and as the first month for the remainder of
the earth. This would cause the festivals to be kept one month apart for
different parts of the earth in such a year, resulting in greater confusion. The
year 2007 provides an example.
[50] The Role of the Land of Israel
The role of the land of Israel must be appreciated in the plan of Scripture.
This land is called the inheritance of Israel (Num 26:51-56; Deut 4:21; 31:7)
while the resurrection to eternal life is called the inheritance of the saints (I
Pet 1:3-6). Entering the land of Israel is called a rest (Deut 12:9; 25:19; Josh
22:4; Ps 95:11; Heb 3:11), which is a type of the rest of the resurrection to
eternal life (Heb 4:1, 8, 11). Among the adults in Israel who left Egypt, only
Joshua and Caleb were allowed to receive the inheritance by faith (Num
14:6-9, 24, 30, 38; Heb 4:2), which is a type of the faith of the saints that is
needed to receive eternal life. The land promise to Abraham, Isaac, and
Jacob (Gen 12:1; 15:7, 18; 17:8; 26:1-3; 28:10-15; 35:12; Deut 34:4) was a
theme for over 430 years (Ex 12:41; Gal 3:16-17) before the beginning of its
literal fulfillment. A stranger could become a full citizen in Israel through
fleshy circumcision, which made him become like a native of the land (Ex
12:48), which is a type of the circumcision of Christ (Col 2:11-12). The land
was to have a Sabbath rest (Lev 25) which is a type of the Sabbath rest of the
saints (Heb 4:4). Finally, according to Deut 11:11-12, the eyes of YHWH
are always upon this specific land. From time to time through the history of
Israel in this land, the priesthood moved from place to place. The first
Passover in the land was kept at Gilgal by all of Israel (Josh 5:10). Soon
Shiloh became the political center (Josh 18; I Sam 1:3, 24). At first King
David reigned from Hebron (II Sam 2:11), but afterward he reigned from
Jerusalem (II Sam 5:5). For approximately the first 400 years of Israel's
history in the land, the political headquarters was not Jerusalem, but the
calendar continued regardless of the political center.
There is a biblical principle that in the mouth of two or three witnesses a
matter shall be established (Deut 17:6; 19:15; Mat 18:16; II Cor 13:1; I Tim
5:19). Does it make sense that if the weather is rainy at wherever the
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political center of Israel happens to be, no citizens of Israel from elsewhere
in Israel may appear as witnesses before the priests for having observed the
new crescent? No.
[51] The Boundary of Israel
Since Israel is prominent in the eyes of YHWH according to Deut 11:11-12,
the subject of its boundaries is now discussed.
In a covenant with Abraham, the southwest border of Israel is stated in Gen
15:18. There, for the southwest, it states the River of Egypt. J. H. Hertz
comments on this verse that the River of Egypt is “the Wady-el-Arish, which
is the boundary between Egypt and Palestine”. A map on page 71 of the atlas
by J. Carl Laney shows the Wadi el-Arish at the place where other maps
show the Wadi of Egypt or Brook of Egypt that starts at the Mediterranean
Sea and goes toward Eilat (also spelled Elath or Eloth), but appears to stop
in the desert before reaching Eilat.
The Tanakh translation of I Ki 9:26 states, “King Solomon also built a fleet
of ships at Ezion-geber, which is near Eloth on the shore of the Sea of Reeds
[Red Sea which goes into the Gulf of Aqaba] in the land of Edom”. Ex 23:31
states, “I will set your borders from the Sea of Reeds [Red Sea at Elath] to
the Sea of Philistia [Mediterranean Sea], and ...”. Map 4 in the NIV shows
the region labeled Edom and continuing down through Elath (using a color
marking and an identifying legend) to be part of the Empire of David and
Solomon. Because the southern desert down toward Elath was not populated
due to lack of rain and opportunity for crops, most maps ignore it and even
cut off the map before it reaches Elath. The use of Beersheba in II Sam 24:2
in the expression “from Dan to Beersheba” indicates that Beersheba was the
most southern populated city, not that the territory of the kingdom ended
there.
Some years ago when Israel agreed to give back the Sinai region to Egypt
for a peace treaty, I was very surprised until I investigated and learned that
according to Jewish scholars (as summarized in Gen 15:18; Ex 23:31; I Ki
9:26, mentioned above), Israel was only giving Egypt what Israel considered
to be reaching up to the boundary specified in Scripture. The modern
southwest boundary of Israel is believed to be the boundary stated or directly
implied by the three verses.
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[52] The law will go forth from Zion - Isaiah 2:3 and Micah 4:2
Scripture does not give an explicit comprehensive discussion of the biblical
calendar as it applies to the entire world with modern technology, but those
who recognize the need to observe the festivals, desire to understand when
to keep the festivals. In an effort to understand the will of YHWH
concerning the biblical calendar, certain principles of application are sought.
Attention is now turned to one biblical principle that has been used by
various people who discuss the biblical calendar, including the Jerusalem
Talmud and the Babylonian Talmud.
Isa 2:3 and Micah 4:2 say, “... the law will go forth from Zion and the word
of YHWH from Jerusalem.” This is a prophecy of the future when the
Messiah will reign. It relates to the seat of government where decisions are
made.
John 4:21 says, “Woman, believe Me, the hour is coming when you will
neither on this mountain, nor in Jerusalem, worship the Father.” In a very
narrow sense the “you” in this verse refers to the woman, but the nature of
the statement in its context implies that it refers to people in general. More
specifically the context is worship, and this brings to mind such Scriptures as
Jer 7:1-2 and Zech 14:16-17, which relate to holy convocations on the
Sabbath and the festivals. John 4:21 is a prophecy (not a commandment) that
was fulfilled when Jerusalem was destroyed by the Romans in 70 CE, and
was more strictly fulfilled in 135 CE when the Jewish rebellion under Bar
Kochba was defeated by the Romans. Nevertheless, eventually Jews
returned to Jerusalem. Since Israel became an independent nation in 1948,
even some Sabbath keeping Christians have settled in Jerusalem and Israel.
Thus the period of the relevance of this prophecy has been fading.
Historically, when the prophecy of John 4:21 was in fulfillment, the law did
not go forth from Zion (Isa 2:3 and Micah 4:2), because Zion was not the
seat of priestly or theocratic government.
When seeking guidance from the Scriptures on any matter, there are
examples of biblical derivation and interpretation that provide a pattern.
Three examples are now presented.
Mat 22:40, “On these two commandments hang all the Law and the
Prophets.”
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In other words, all of the teaching of the Hebrew Scriptures contains laws
and principles that grow out from the two general commandments found in
Deut 6:5 and Lev 19:18. A narrow contextual view is not taken of these two
verses of the Hebrew Scriptures in Mat 22:40.
I Cor 9:9-10, “For it is written in the law of Moses [Deut 25:4], ‘You shall
not muzzle an ox while it treads out the grain.’ Is it oxen the Almighty is
concerned about? Or does He say it altogether for our sakes? For our sakes,
no doubt, this is written, that he who plows should plow in hope, and he who
threshes in hope should be partaker of this hope.”
In other words, Paul is not taking a narrow contextual view of Deut 25:4, but
is broadly applying it beyond the animal realm to those who devote full-time
energies to preaching and teaching.
Gal 3:8, “And the Scripture, foreseeing that the Almighty would justify the
nations by faith, preached the gospel to Abraham beforehand, saying, ‘In
you all the nations shall be blessed’”.
Gal 3:16, “Now to Abraham and his seed were the promises made. He does
not say, ‘And to seeds’, as of many, but as of one, ‘And to your seed’, who
is Christ.”
The above two verses extract quotations from the following.
Gen 22:17, “blessing I will bless you, and multiplying I will multiply your
seed as the stars of the heaven and as the sand which is on the seashore; and
your seed shall possess the gate of their enemies.”
Gen 22:18, “In your seed all the nations of the earth shall be blessed,
because you have obeyed My voice.”
Gen 26:4, “And I will make your seed multiply as the stars of heaven; I will
give to your seed all these lands; and in your seed all the nations of the earth
will be blessed;”
Gen 26:5, “because Abraham obeyed My voice and kept My charge, My
commandments, My statutes, and My laws.”
The Hebrew word zerah (Strong's number 2233), is the word translated
“seed” that occurs twice in verse 17, once in verse 18, and three times in
verse 4. In all these places the form of the word zerah is the same. Page 253
of volume 1 of TWOT makes the following comment, “Commencing with
Gen 3:15, the word ‘seed’ is regularly used as a collective noun in the
singular (never plural). This technical term is an important aspect of the
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promise doctrine, for Hebrew never uses the plural of this root to refer to
‘posterity’ or ‘offspring.’” Although Gen 22:17 and Gen 26:4 relate the
number of the stars to the number of “seed”, so that the context implies that
a plural number is intended, the Hebrew word occurs in the singular form
regardless of whether the intended number is singular or plural. The apostle
Paul was inspired to use this grammatical aspect of the Hebrew word in Gal
3:16 in order to attach the word “seed” to the singular “Christ”.
Nevertheless, the original context implies that the intended original use is
plural. Hence the New Testament interprets the literal context of the promise
to Abraham in a non-contextual way.
These three examples of the use of quotations of the Hebrew Scriptures in
the New Testament show that when using the Scriptures, one is not required
to use a narrow contextual interpretation if none is available. If there is no
Scripture that applies like a hand in a glove in its natural context, then one
has the liberty of generalizing and broadening the context of the Scripture in
order to find guidance in an attempt to avoid arbitrary subjective decisions.
The explanation above provides one reason that Isa 2:3 and Micah 4:2 may
be used with regard to the biblical calendar before the arrival of Messianic
rule from Jerusalem. However there is yet another reason that should be
given some thought. Both the Jerusalem Talmud (c. 400 CE) and the
Babylonian Talmud (c. 600 CE) give parallel yet slightly different accounts
of the same incident involving the Jewish sage Hananiah. Jacob Neusner
dates this event c. 145 CE (see page 120 within pages 113-121 of the
original 1965 discourse by Neusner, and page 129 within pages 122-130 of
the 1984 reprint). The account of this event in both Talmuds uses Isa 2:3 and
Micah 4:2 to settle this calendaric dispute c. 145. They use these verses as
the single greatest factor, as a general principle, as a biblical weapon to
decide the issue.
Since I will shortly discuss this incident involving Hananiah occurring in
both Talmuds, which quote from Isa 2:3 and Micah 4:2, the reader may well
ask for some justification for quoting from the Talmud. Understand that my
goal here is to explore a method of reasoning from these verses, not whether
the incident from the Talmud is historically accurate. The reader must decide
whether the method of reasoning is sensible. How do I view the Talmuds? I
will now briefly digress to answer this.
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When I first began to study the biblical calendar in depth, I realized that
Rabbinical writings from c. 200 CE to c. 600 contained many statements
about the calendar, and I began to collect this material along with all the rest
of the calendar information. The arduous and discouraging task of
attempting to evaluate the worth of the Rabbinical writings loomed massive
in my path to seek knowledge. I did not shy away from this decades-length
battle of evaluation, which waxed and waned in spurts. Jewish scholars
themselves often clashed on the issue of the value of these writings, which
compounded the effort of my task. It is beyond the scope of this present
study to attempt to adequately explain and document the fruit of my effort to
evaluate the Rabbinical writings, but it is my duty to at least say a few words
because of its relevance here.
The Mishnah is the first Rabbinical document. It is roughly the size of the
Bible, and it is primarily a Jewish legal document. It is not written in a
manner that is easy to grasp without a commentary. I am convinced that
when the Mishnah was first released to its scholarly audience (i.e.,
“published”, in the primitive sense) c. 200, that its contents reflected the
opinions of its primary author, Judah the Nasi, at that moment in time, and it
was not largely based upon extensive and detailed written records that were
carefully preserved from before the destruction of the Second Temple in 70
CE. The elite among the Jews were trapped in Jerusalem during the war
from 66 to 70 CE, and the relatively few that escaped did not have the
luxury to take extensive writings with them. Jerusalem and the Temple were
burned by the Romans, and according to Josephus, only a small number of
writings survived. The Jewish scholars who survived the destruction of the
Second Temple did not have reason to quickly imagine that there would be
no substitute for the Temple within a reasonable amount of time. After
Solomon's Temple was destroyed in 586 BCE, it took 70 years to initially
complete the Second Temple in 516 BCE (see Ezra 6:15 and commentary
notes there from various sources). Beginning in the second century BCE
Herod the Great magnificently enhanced the Second Temple. There was no
motivation for the immediate scholarly survivors of the destruction of
Jerusalem to rush to write down everything they could remember of the
details of how the priesthood and the Sanhedrin did everything. The years
132 to 135 saw the second great Jewish war with the Romans known as the
Bar Kochba revolt, and it is not known whether more Romans died in this
war or the war from 66 to 70. When Judah the Nasi published the Mishnah c.
200, he no doubt had sources that could give him reliable history since the
year 135, and there were probably some reasonably reliable legends from the
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years between 70 and 135. But it is doubtful that there were many legal
details that survived from before 70.
In the name “Judah the Nasi” as the primary author of the Mishnah, the title
Nasi is sometimes translated Prince, and it refers to the primary leadership
role among so-called mainstream Judaism, although there is debate among
Jewish scholars concerning whether there was truly a mainstream Judaism
throughout all of Judea and Galilee in the first century, and even during the
next few centuries. Jewish history suffers from a lack of documents that
represents a broad based history as well as a very credible history. Before
the destruction of the Temple in 70, the title Nasi was equivalent to the
President of the Sanhedrin, according to Rabbinical writings. Jewish
scholars debate the issue of whether there was any primary “Sanhedrin”
within Judaism after the Temple was destroyed.
According to Rabbinical writings, there continued to be one leader called the
Nasi after 70. Undoubtedly some legendary sketches of written material
were preserved by some scholars, but no one knows how much. Judah the
Nasi had control over the contents of the Mishnah, and his motivations were
varied concerning what to include and why to include it. There were many
Gamaliel's in a genealogical succession beginning with Gamaliel the Elder
(Gamaliel I), who taught the apostle Paul, and this line was descended from
King David according to the Rabbincal writings.
The line of Gamaliel was given a greatly exaggerated role in the Rabbinical
writings, especially for the first century, compared to what is justified in
historical reality. In Rabbinical writings Gamaliel I, a Pharisee according to
Acts 5:34, is given the role of the Nasi (President) of the Sanhedrin in
Jerusalem, contrary to the Gospels and Acts in the New Testament, which,
except for Acts 5:34-40 generally gives the greatest attention, in the sense of
spokesmanship, to whoever is serving as the High Priest in the context.
Many Jewish scholars have recognized this conflict and have postulated the
existence of at least two most prominent Sanhedrins having different roles
before 70, so that the apparent conflict between the New Testament and the
Rabbinical writings could be resolved with the latter retaining its credibility.
But the existence of such multiple primary Sanhedrins in the area of the
Temple has not withstood the test of scholarly debate, and the Rabbinical
writings have suffered a great credibility gap in the process. There are other
reasons for the credibility gap besides this. Of course the Orthodox Jewish
position is that all Rabbinical writings are inspired and fully true, and by
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“Orthodox”, I refer to its meaning as held by Jewish culture in the United
States, not Israel, where “Orthodox” has come to have a different meaning.
The male succession in the line of Gamaliel is Gamaliel I, Simon I, Gamaliel
II, Simon II, Judah the Nasi, etc. From this lineage is it obvious that Judah
the Nasi, the primary author of the Mishnah, might have some motivation to
exaggerate the importance of his own lineage in his account of the snippets
of supposed history of Judaism from the first century onward.
When the Rabbinical writings mention that a Gamaliel or a Simon made an
official proclamation that he was adding an extra month to the calendar for a
combination of reasons, I do not at all believe in the historical validity of
such a claim, nor do I believe that the combination of reasons stated were in
fact operative during the first century! Philo of Alexandria only mentions the
vernal equinox. The Mishnah claims that a select committee within the
Sanhedrin made such a decision, so this contradicts Talmudic claims that a
Gamaliel or a Simon made the decision. The Mishnah is the first part of the
Talmud; thus the Talmud is self-contradictory. Based upon the authority that
I see vested in the chief priests in the Temple area according to the New
Testament, it seems to me that the chief priests made such calendaric
decisions rather than a select committee that was heavily represented by
non-priests.
Rabbinical writings say absolutely nothing about any Jewish sage before 70
having any abilities in mathematical astronomy, and this even includes
Daniel and Abraham. When Gamaliel II is said to have mentioned the length
of a synodic month in the Babylonian Talmud, this exact time period
including the fraction of a second comes from Babylonian astronomer-
astrologers whose calculation originated c. 300 BCE. The Talmud does not
claim that Gamaliel II himself directly possessed such mathematical and
astronomical skills, although some later Orthodox Jewish commentators
interpret a text in the Mishnah so as to infer that Gamaliel II possessed such
skills. The Babylonian Talmud does ascribe much mathematical skill to Mar
Samuel (c. 250 CE), who is said to have had the ability to compute a
calendar for many years into the future. Commentators on this matter claim
that Mar Samuel's proposed calendar was not accepted.
I believe that the Talmuds contain some remnants of historical value from
the first century, but with some fabricated embellishments. Some of it
represents false tradition and some true tradition. In some cases Josephus
and the Talmud do agree on legal details not directly discussed in Scripture,
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but this may reflect only the Pharisaical position rather than practiced
reality. In general, I do not accept Talmudic teachings as binding.
My primary reasons for introducing the account of Hananiah (c. 145) are to
provide the reader with additional thoughts regarding the use of Isa 2:3 and
Micah 4:2, as well as to provide the Orthodox Jewish viewpoint on how
these verses may be applied to the calendar. With regard to the sighting of
the new crescent in order to establish the day of the new moon, the Karaites
in Israel today only accept witnesses who sight the new moon from within
Israel. There are significant matters concerning which I disagree with the
Karaites from Israel.
An interesting source and commentary on the Hananiah event is pages 106-
111 of the book by Gafni. Hananiah was a Jewish sage (scholar) who was a
native of Palestine and educated there. A rough guess of the year of his birth
is 100. Due to unfavorable conditions for the Jews after the Bar Kochba
revolt against the Romans began in 132, Hananiah emigrated to Babylonia
where he continued to gain respect as a sage. The setting of the event is with
Hananiah in Babylonia. On page 108 Gafni has a translation of the account
from the Jerusalem Talmud (Sanhedrin 1.19a), and he provides useful
comments of his own in ordinary parentheses as follows. “Hananiah the
nephew of R. Joshua intercalated (i.e. proclaimed leap-years) abroad. Rabbi
(here the term means the Patriarch, most probably Rabban Shimon b.
Gamaliel [Simon II], circa 150 CE) sent him three letters with R. Isaac and
R. Nathan. In one he wrote: ‘To his holiness Hananiah’, in one he wrote:
‘The lambs you left behind [in Palestine] have become rams [scholars]’, and
in one he wrote: ‘If you do not accept upon yourself (our authority), go out
to the desert of Atad and there be a slaughterer [no longer a sage], and
Nehunion a sprinkler.’ He [Hananiah] read the first [letter] and honored
them, the second and honored them, the third – and wished to dishonor
them. They told him: You cannot [dishonor us now], for you have already
honored us. R. Isaac stood up and read in the Torah: ‘These are the festivals
of Hananiah the nephew of R. Joshua!’ They [with Hananiah] said: ‘These
are the festivals of the Lord!’ (Lev. 23:4). He [R. Isaac] replied: By us! R.
Nathan arose and completed (read the haftarah from the prophets): ‘For out
of Babylonia shall come Torah and the word of God from Nehar Pekod.’
They [with Hananiah] said: ‘From out of Zion shall come Torah and the
word of God from Jerusalem’ (Isa. 2:3). He [R. Nathan] said to them: By us!
He (Hananiah) went and complained about them [R. Isaac and R. Nathan] to
R. Judah b. Bathyra at Nisibis [for advice]. He (Judah) said to him
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[Hananiah]: After them, after them ... He (Hananiah) rose up and rode on his
horse. Whither he reached he reached (and corrected the local calendar), and
whither he did not reach – they observe in error.”
One obvious important point here is that the Jerusalem Talmud (as well as
the Babylonian Talmud’s account of the same incident) accept the
application of Isa 2:3 and Micah 4:2 to the situation. In this context this
implies that some sage in Israel must make the decision rather than some
sage in Babylonia. To what extent this is a fully true account we do not
know, but it does portray the acceptance of the sages in Babylonia to the
reasoning based upon Isa 2:3 and Micah 4:2. Modern Jewish commentators
such as Gafni and Neusner (and others that I have seen) do not question the
reasoning based upon these prophetic Messianic contexts applied to a non-
Messianic age.
My conclusion to this discussion concerning Isa 2:3 and Micah 4:2 is that
because the New Testament does not require an exact contextual match in
order to apply a verse in the Hebrew Bible to some situation, and since Jews
generally have no problem applying the principle in these verses to give
weight to the testimony of those who have situated themselves in the land of
Israel, neither do I have any problem with applying this principle in limited
ways. Certainly if a clearly illogical ruling comes from someone in Israel, I
do not have any motivation to accept such a ruling.
In 1997 someone asked me whether I would accept the calendaric decisions
of a new Jewish Sanhedrin in Israel if it began to function and make rulings
on the calendar. My response was that if such a Sanhedrin made rulings that
were based upon the biblical calendar, I would accept those rulings. But, for
example, if arbitrary postponement rules were adopted by that Sanhedrin, I
would not accept it. Nevertheless, a reconstituted Levitical priesthood should
make the determination of the calendar based on Num 10, not a Sanhedrin. It
does bother me that Jews go to the Talmud to substantiate a Sanhedrin rather
than to the Bible. The Talmud views the choosing of the 70 elders in Num
11:16-17, 24-25 as the first Sanhedrin, and uses this to show that the ideal
body of elders for Israel is the Sanhedrin. This command for Moses to select
70 elders was a response to Moses’ complaint to have the burden of dealing
with all the problems of all the people lifted from him (Num 11:14-15).
These 70 were to be disbursed throughout the people to deal with individual
problems and disputes between parties, not to convene as one body as a
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substitute for Moses. You never see any example of this body of 70 meeting
together in one place.
[53] Two Days for the Start of the Seventh Month
Should there occasionally be times that the first day of the seventh month
will be celebrated for two successive days today? This is the subject of the
present chapter. This partially concerns the question of whether people to the
east of Israel up to the IDL should begin to observe the first day of the
seventh month before anyone in Israel has an opportunity to observe the new
crescent.
Isa 2:3; Micah 4:2 says, “the law will go forth from Zion”. I take this to
imply that when the Messianic kingdom is established, the declaration of the
first day of the numbered new moons will be made from Zion. I also take
this to imply that witnesses for the visibility of the new crescent from Israel
will be accepted by the governing authority in Zion, and that such witnesses
will have to testify that they saw the new crescent before the governing
authority in Zion. It might happen that some audiovisual technology may be
used so that witnesses may appear before some technology station away
from Zion and be questioned from Zion. Maybe some transportation device
will convey witnesses to Zion using automation so that they will not have to
ride a horse or a camel. Maybe a biometric device for identification along
with the Internet will be used, and no travel will be necessary.
In today’s society witnesses for having seen the new crescent communicate
to at least one of two web site hosts. Then the result is sent out via email to
individuals who have signed on to the emailings. In other words the Internet
is used as a modern technology tool to inform people concerning witnesses
for the sighting of the new crescent.
If the astronomical conditions for sighting the new crescent are borderline so
that no one can accurately predict whether the new crescent will be seen (if
the weather is clear), then all people who live to the east of Israel up to the
IDL should begin to celebrate the first day of the seventh month in advance
of receiving Internet reports. It may turn out that such people will indeed
celebrate two successive days for the first day of the seventh month, just as
would occasionally have happened to ancient Israel as indicated by I Sam
20:27, 34.
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In ancient times transportation methods were slow, so that if witnesses of the
new moon had to travel from far off in Israel, the priesthood might have to
wait several days for the witnesses to arrive. If no witnesses testify for the
first day and the second day, how long should the priesthood wait? Why not
wait up to the time of the ninth day of the month to accommodate the fast
day, the tenth day of the seventh month? Priests can accept the testimony of
witnesses retroactively before the tenth day of the seventh month and thus
avoid artificially limiting the location of witnesses within Israel. This is
sensible and workable in ancient times. Anciently camels could run at 40
miles per hour and walk for long periods at half that speed so that within a
couple of days it would be possible to travel from the southernmost part of
ancient Israel to Jerusalem.
Without predictive mathematical astronomy in ancient Israel, there was
often uncertainty of the first day of the new month during several days of
waiting for witnesses to testify for having seen the new crescent. In the case
of the first day of the seventh month, it is virtually certain that they often
kept two successive days for that festival because of no reports of visibility
on the first of the two possible days for sighting the crescent. Today, due to
computer calculations, there is uncertainty under rare circumstances,
assuming we accept visibility from desert regions of Israel where it almost
never rains. When actual witnesses from Israel are available, if we reject
their testimony and only use a computer calculation, it is certainly true that
we make matters easy for ourselves, but then we set ourselves up as an
authority that contradicts the ancient use of human instruments for sighting
as originally intended. In this modern age, people often want to be able to
plan everything precisely in advance. If we have uncertainty due to a
borderline case in a rare circumstance, we can still plan for two successive
days and have ourselves covered. People can plan an airplane trip one extra
day ahead of time so that either event will work out okay.
[54] What if the Whole Earth may Sight the Crescent to start the Month?
If the boundary for ending the sighting point for visibility of the new
crescent does not stop at the borders of the land of Israel, where does it stop?
The further to the west one goes, the easier it becomes to see the new
crescent, although higher than about 4000 feet above sea level it gradually
becomes ever easier to see the crescent, and low humidity favors seeing the
new crescent. How far to the west can one go? The natural answer based
upon its modern acceptance is the IDL in the Pacific Ocean. If one goes
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there, then everyone's attention would be focused on the IDL to give the
very last look to the most western line before deciding that that day will not
suffice for starting the new month. In other words, some islands in the
Pacific Ocean would get all the attention instead of the land of Israel or its
headquarters, Jerusalem. That would mean that local or worldwide visibility
to determine the new crescent would be redefined to visibility at some
islands in the Pacific Ocean. This makes no sense.
If one proposes that the IDL should be totally ignored and the exact moment
of the first sighted crescent should be used to determine the start of the new
crescent for the whole earth, this method will often cause some line along a
landmass to separate one day beginning at sundown from the next day on the
eastern side of the line. The reason for this is that a new day begins at
sundown rather than some random time within a day. Thus neighbors will
not be in harmony on the day that begins the new month and confusion will
result. Another problem is that this method will sometimes produce a one
day difference with the day that would have been selected for the new moon
day in Israel under ancient circumstances of the Levitical priesthood.
[55] The Ancient Situation Outside of Israel
Suppose some ancient Israelites went exploring on a ship to North America.
How would they begin a month? Without the Internet, without long distance
telephone service, et cetera, they could not contact (even through
intermediaries) the High Priest for a knowledge of when each month began.
They would have no choice but to use visibility of the crescent from
wherever they were. If such a ship gave rise to two colonies separated by
100 miles, and if these colonies remained isolated from one another, there
would no doubt be months in which they began a month one day apart. If
they kept in contact with one another, then it is reasonable to think that the
colony with rainy weather would accept the witness of the other colony, so
that both would be in harmony on the start of a month. As we add more
colonies it becomes ever more difficult to hypothesize how one could define
local visibility. Nevertheless, with primitive isolation of settlements outside
of ancient Israel, there is no confusion so that I Cor 14:33 would not apply.
It is only after significant communication is possible and the modern age
enters the scene that confusion enters.
[56] Modern Technology makes a difference
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Anciently, if appropriate technology were available, the ideal situation
implied by Num 10:10; Isa 2:3, Micah 4:2 would result in all people
everywhere accepting the word of the High Priest, whose responsibility
would include questioning witnesses who came from the Israel. Some people
imagine that it is “not fair” to use modern technology to report on such
visibility, and instead we must pretend we only have what people had in the
days of ancient Israel. Such pretending should also include pretending we
have no telephones, pretending we have no automobiles, pretending we do
not have modern computers, pretending there is no Internet, even pretending
we are in ancient Israel, i.e., in the Promised Land because that is where
people had access to Scripture. Certainly in Israel all were united on the day,
following the lead of the High Priest. Hence rainy areas accepted testimony
from clear weather areas in Israel.
[57] Num 10:10 Avoids Confusion
According to Num 10:1-2, 8-10 the Levitical priesthood is commanded to
blow two silver trumpets on the first day of each month. The Levites were
commanded to be disbursed in 48 cities throughout the 12 tribes (Num 35:2-
8), not all over the world. The priests must observe, or reliable witnesses
must inform them where they are, concerning the new crescent (Deut 17:6;
19:15; Mat 18:16; II Cor 13:1; I Tim 5:19). In concept, even though we do
not have the Levitical priesthood functioning today, one must still view
matters from the standpoint of the priesthood blowing trumpets on the first
day of the month using two silver trumpets, implying they were being blown
from one location. The biblical focus of attention for world government is on
Israel, and specifically Jerusalem (Deut 11: 11-12; Ps 132: 13-14; Isa 2:3;
Micah 4:2).
[58] Differences between the Sabbath and the New Moon
In ancient Israel there was certainly a difference between how each Sabbath
began throughout Israel and how each month began throughout Israel. Each
Sabbath began based on sundown for each person. While the time of
sundown might vary by a minute throughout Israel, the beginning of the
month did not begin this way. According to Num 10:10 the Levitical
priesthood was commanded to blow two silver trumpets to officially
announce the beginning of each new month. If someone and his neighbor
observed the new crescent together in a difficult to observe circumstance and
they neglected to appear as a witness before the appropriate priests, and if no
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one else appeared before the priests to testify for having seen the new
crescent, the priests would not have blown the trumpets and the new month
would start a day later. Thus those two witnesses who failed to appear before
the priests would not begin the new month when “it came to them”, but
would have to use the starting of the new month according to the
determination by the priests, when they blew the silver trumpets. In ancient
Israel when the holy days were kept in one central place (Jerusalem after the
first six years of King David's reign), those two witnesses could not argue
with the priests when they appeared for the festival at the middle of the
month. The priests would have no choice but to say to the two witnesses:
“Why didn't you come to us near the start of the month and testify at that
time? If you had done so, then we would be starting the feast one day
sooner. Now it is too late to testify.”
The point being made here is that merely because we keep the Sabbath when
it comes to us according to the IDL, that is not a deep enough or thorough
enough examination and explanation of the different issues involved with
the start of the month. The concepts for the month start and the Sabbath start
were different in ancient Israel, yet the need for avoiding confusion is the
same. Levitical priests did not have to blow the trumpets to officially notify
everyone in Israel that the Sabbath had begun. It is certainly true that the
Levitical priesthood does not exist today, but one must consider how one
might sensibly approach this matter today given what we do know and the
ever present need to avoid confusion among saints that are spread out in the
world, often in close proximity to one another (I Cor 14:33).
Since we cannot define "local visibility" to cover all circumstances away
from the north and south poles, and since our Creator who wants us to
worship Him on the festivals is not the author of confusion (I Cor 14:33), the
way to avoid it is to use the implication of Paul in Acts 18:21 in which he
showed respect for the determination of the calendar by the Levitical
priesthood by wanting to be there for the feast. Num 10:10 is there to
achieve unity in ancient Israel. The central declaration of the new moon by
the priesthood was not needed for the Sabbath even though the trumpets
were still blown on the Sabbath as well because they are also appointed
times according to Lev 23:1-4. The announcement for the new moon of the
seventh month had to reach all of Israel quickly if the ending month had
only 29 days, or else people would needlessly keep two days as the new
moon of the seventh month. Such an announcement all over Israel was not
needed for the Sabbath.
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When people live some distance outside the temperate zones, even with
clear weather there will occasionally be a 31 day month based upon the
concept of only personal eyeballs doing the looking (no phone calls, no
Internet, no automobiles, no carrier pigeon communication, no fire signals,
etc.). Thus the basic principle of a maximum 30-day month can no longer be
used from outside of Israel with only personal eyeballs doing the looking.
Then what does one do when it is raining or very cloudy and only depending
on personal eyeballs (do you sometimes have a 32 or 33 day month)?
[59] Does the priesthood of all saints (I Pet 2:9) change the calendar?
The Levitical priesthood is a genealogical priesthood with physical duties,
physical objects, and a physical service, although it was expected to teach
spiritual laws and principles. The priesthood of all saints is a spiritual
priesthood without the physical objects such as the silver trumpets to blow
and announce the new months. Just as the priesthood of all believers does
not have the authority to wave the sheaf during the Days of Unleavened
Bread, it does not have authority to blow the two silver trumpets and
announce the start of each month. If two different organizations of believers
were in the same geographical area outside of Israel and observers in both
organizations came to different conclusions of the day to start the month
based upon what they saw separately in each organization, and then
members within each organization separately blew their silver trumpets on
two different days, wouldn't that have to be regarded as confusion in the
same area?
Heb 7:12 points out that there is a change in the priesthood and a change in
the law relating to it for the saints. Yet Heb 9:7 points out that when this was
written, the High Priest still functioned and entered the holy of holies once
per year, showing that this was still a continuing practice of the Levitical
priesthood, which was not shown disrespect by the author of the letter to the
Hebrews. Heb 10:11 shows the continuation of the Levitical priesthood, yet
with its limitations of effectiveness.
If different members of the priesthood of all saints were to blow two silver
trumpets on the days that they thought the new moons were, but they
differed from one another, perhaps when even a few miles apart, is this not
confusion and is this what YHWH wants? Does He desire to sanctify
multiple pairs of days for the same festivals when people have modern
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communication? Num 10:10 was there to avoid this in ancient times. Since
we can know whether the new moon was sighted in Israel today by means of
mass communication, this is a unifying principle and taken out of the hands
of one human organization or authority.
It is true that there is no Levitical priesthood functioning today, yet the
principle in the law is that in the mouth of two or three witnesses a matter is
to is established (Deut 19:15), and this principle was applied in other
situations later (Mat 18:16). To avoid confusion the witnesses should be
drawn from where the Levitical priesthood was to reside, namely the
boundaries of ancient Israel.
[60] Historical Evidence for Sighting the New Crescent
In the early first century, Philo of Alexandria reported that the new month
for Jews began with the sighting of the new crescent after the conjunction
(see page 333 of Philo_7, Special Laws 2:41). Historical evidence
concerning testifying about having witnessed the new moon does not exist
before the Mishnah, which dates from about 200 CE. While I do not accept
the Mishnah as an inspired document or for an accurate valid statement
concerning Jewish history, by combining the written witness of Philo with
corroboration from the Mishnah, it is sensible that witnesses of the sighting
of the new crescent were expected to testify.
[61] Should only Jerusalem be used to Sight the New Crescent?
If we today were to propose that only the sighting of the crescent from
Jerusalem mattered (avoiding areas of Israel outside of Jerusalem), then
since there are people today who report on the sighting of the crescent on the
Internet, we would often be changing at the beginning of the first and
seventh months based on rain or heavy clouds over Jerusalem, even if other
areas of Israel were clear, it was not a borderline case, and humidity was not
an issue. This shows that Jerusalem sighting does not make matters easier,
but actually complicates matters because there would be more uncertainty on
more occasions than using visibility throughout Israel, which includes desert
regions so that computer predictions would only fail in some rare borderline
cases.
If we had no reports of actual sighting from Israel in the modern world, but
wanted to avoid confusion and utilize the concept of sighting the crescent
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based upon Gen 1:14-18, then a calculation of the high probability of
sighting the crescent is the only choice, and the vast majority of the time (no
borderline condition or slightly under borderline where low humidity is a
question) the calculation and actual sighting will agree. The calculated dates
will work over 90 percent of the time in the latitude of Israel under 4000 feet
above sea level.
[62] Starting the Month when it comes to you
Today the part of the world east of Israel always starts the Sabbath before
Israel, and the part of the world west of Israel always starts the Sabbath after
Israel. Thus India starts the Sabbath before Israel and the United States starts
the Sabbath after Israel. To be consistent with the way we keep the Sabbath,
we should also begin the start of the month according to the same principle:
the people in India begin the start of the month before the people in Israel
and the people in the United States begin the start of the month after the
people in Israel. This principle extends to the IDL and is what mainstream
Judaism uses.
[63] Actual Sighting from Israel Today
In September 2004 a new problem arose when the Karaites in Israel
introduced a new concept of what constituted a valid observation. They
allowed momentary sightings of something that would not even have been
recognizable anciently as a crescent to be validly considered a sighting of a
crescent. This was done on the basis of having observed the moon with
binoculars and a tripod for steady viewing for some time, so that they
“knew” it was the crescent, although no one in ancient times could have
known it was the crescent. If an alleged sighting from the Karaites is more
than half of one degree below Karl Schoch's curve, then I do not trust that
sighting as having been acceptable in ancient times, most especially if the
sighting is not done from a place of low humidity. Details must be provided
by those who issue reports in such unusual circumstances.
[64] The Process of Declaring the New Moon
(A) Israel as the Geographical Anchor
Num 10:10 shows that the Levitical priesthood was to blow two silver
trumpets to declare that a new month had begun. Through this brief
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statement we can at least say that the priesthood had the responsibility to
gather testimony concerning the sighting of the new moon and make a
decision of whether to declare it. Since the priesthood was commanded to
dwell within the boundaries of ancient Israel, that place is the region from
which testimony would have been taken as long as the Levitical priesthood
existed. Jumping to today's society in the modern world, if multiple peoples
around the world were to arrive at an independent determination based upon
individual arbitrary regional decisions of “locally” sighting the new crescent,
that implies that YHWH declares regional feast days that may overlap and
conflict in certain geographical areas, making two different days holy even
in the same place where two different organizations may overlap in
geography. This makes YHWH the author of confusion, contrary to I Cor
14:33. Different people may invent different concepts of how to determine a
new moon in their own area in terms of distance and height above sea level,
and there is no biblical guideline for such a definition. As long as people
elsewhere are able to communicate with people in Israel, the only way to
avoid making YHWH the author of confusion and also respect the concept
of Num 10:10 (even recognizing that the Levitical priesthood no longer
exists), is to use the boundaries of Israel as the geographical anchor for
visibility of the crescent.
(B) A minimum of Two Witnesses for sighting the New Crescent
Deut 17:6; 19:15 declares, “on the mouth of two witnesses or on the mouth
of three witnesses a matter shall be established”. This is quoted in Mat
18:16 and II Cor 13:1 as applying to other situations.
(C) Only a continuous Naked Eye sighting should be admitted as a Witness
As an avid student of the history of ancient astronomy I can say that the
invention of the telescope is not provable before 1608, but in that year
several Europeans constructed telescopes about the same time. Galileo first
constructed one in 1609 and made important improvements. See pages 326-
329 in the book by John North. Ancient peoples showed great interest in the
moon, yet there is no ancient drawing that shows details of the surface of the
moon that would require a telescope, nor is there any historical evidence that
ancient peoples invented a telescope.
When people discuss the sighting of the crescent today, it seems generally
agreed that evidence for the new crescent should not be accepted by methods
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that were not available in the days of the functioning of the Levitical
priesthood. This means that if an individual is in an airplane flying over
Israel, that altitude would prevent accepting such a testimony for having
seen the new crescent. In fact, it means that the observer should be standing
on the ground or sitting on some object that is on the ground, and certainly
using naked eye observation at the time of declaring having seen the new
crescent. Furthermore, the sighting should be a continuous one rather than
one that lasted only about a second, even if separately repeated later for
about a second. This prevents a vivid imagination from fooling a sincere
mind. The question of how much use of a telescope or binoculars may be
acceptable is treated next.
(D) Partial use of a Telescope or Binoculars
The principle that evidence for the new crescent should not be accepted by
methods that were not available in the days of the functioning of the
Levitical priesthood is generally accepted, although there are exceptions to
almost everything when human opinions are taken. But sometimes observers
go to great lengths to enhance the likelihood that they will see a new
crescent with the naked eye. For example, they will use a knowledge of
modern astronomy and mathematics to correctly predict where and when in
the sky the crescent should be seen, and then focus a telescope upon an
accurate mounting pointing to that location. When they finally see it at that
location through the telescope, they will then try to locate it with binoculars.
Then they will periodically remove the binoculars to try to see it with the
naked eye. Then upon seeing it continuously with the naked eye, they will
declare they have seen the new crescent. Obviously different people will
have different opinions about this process.
One aspect that relates to mathematics and binoculars deserves special
comment. This has to do with the refraction of light from an astronomical
body as it travels to the eye of an observer. Having watched some new
crescents as they lowered down to the horizon from my sighting location
that has been near the latitude of Israel (especially the area around Dallas,
Texas), I noted that they changed shape significantly during last part of the
descent. This change of shape is due to the increasing effect of refraction as
the light from that object neared the surface of the earth. The density of the
earth's atmosphere increases as one approaches sea level. As the density of
the atmosphere increases, refraction also increases. This increasing
refraction distorts the shape of what one sees. When it gets low enough, it
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ceases to have the characteristic appearance of the new crescent, and what
one sees can be confused with a cloud or a piece of a cloud. If one sees this
for the first time in its very low position in the sky, one will be very
uncertain that this is the new crescent, but if one has seen it that way all
along for the previous 15 minutes, there will be no reason to doubt that it is
the new crescent.
When the crescent is seen from the northern hemisphere, it looks different
near the time of the vernal equinox compared to near the time of the
autumnal equinox. Near the vernal equinox it looks somewhat like a bowl
whose bottom is horizontal and down. Near the autumnal equinox it looks
somewhat like a backwards letter “C”. In the spring when it gets near the
horizon, the bowl shaped crescent gets flattened to a very short horizontal
straight line, and anyone seeing this who had not already been watching it
before would not think this was a crescent since all the curvature would be
gone. In the autumn when it gets near the horizon, the backwards “C”
shaped crescent gets flattened to the outline of what appears to be an
extremely narrow squashed tip of a cigar, but not filled internally, and
anyone seeing this who had not already been watching it before could easily
mistake it for the outline of a cloud.
Armed with the above information, let us contemplate the following.
Consider two observers, observer “A” using the sophisticated modern
techniques of an aimed mounted telescope and binoculars, and observer “B”
who is nearby with only his eyes to see, but “B” is not in contact with “A”.
If this is a very difficult case in which to imagine seeing the new crescent
and both of them happen to first see it with their naked eye at the same time,
and moreover, the moon is very close to the horizon, the thoughts in their
minds are likely to be quite different. Observer “A” is likely to think as
follows. I have been watching this crescent all along for many minutes with
binoculars and now I finally see with my naked eyes what I have been
looking at all along, so I know it is the new crescent. Observer “B” is likely
to think as follows. I see something out there, but I'm not quite sure what I
am looking at, because it doesn’t have the typical characteristic appearance
of the new moon; it could be the latter stage of what a new moon looks like,
but it is so low that it's difficult to be sure if this is a crescent or perhaps a
piece of cloud.
If one accepts the principle that evidence for the new crescent should not be
accepted by methods that were not available in the days of the functioning of
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the Levitical priesthood, then one must consider the difference between the
thinking of observer “A” and the thinking of observer “B”. While I would
not object to an observer knowing where to look and even using a telescope
and binoculars to pinpoint the direction to look, upon seeing the object with
my naked eye, I would have to make a judgment of whether the appearance
of the object is sufficiently close to a crescent that if I were seeing this for
the first time, I would be convinced this is a crescent rather than a piece of
cloud. If the appearance alone is not convincing, even though I would in
reality know it is the new crescent because I had been observing it for a
number of minutes with binoculars, it should not be admitted as evidence for
seeing the new crescent because it would be unconvincing to an ancient
observer.
This means that when a report is given by observers of the new moon in a
difficult situation where binoculars or a telescope was used, the report
should include details of approximately how long it was seen continuously
with the naked eye, how its shape appeared to the naked eye, and a judgment
of whether it would have been convincing to an ancient observer who knew
approximately how it ought to appear at this time of the year. If it would not
have been convincing to an ancient observer, then it should not be accepted
as a witness to the new crescent.
Summary: The problems with using local visibility are:
(1) How is it defined in today's world?
(2) How is it consistent with Num 10:10 where the priests determine the new
month from Israel?
(3) How can it avoid confusion (I Cor 14:33)?
(4) Does it avoid arbitrary decisions of distance for accepting witnesses?
The advantages of using visibility of the new crescent within Israel are:
(1) The definition is simple.
(2) It is consistent with Num 10:10.
(3) It avoids confusion.
(4) Over 90 percent of the time it is not a borderline situation and it is
predictable.
(5) This, along with the IDL, best fulfills the philosophical principles stated
at the beginning of this study.
The use of the IDL for the 24-hour day, starting with sundown as it
gradually sweeps across the globe, has attained worldwide acceptance by
keepers of the Sabbath, and this principle for the start of a month has been
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accepted by mainstream Judaism (Orthodox, Conservative, and Reformed),
and the Karaites also accept it, but typically starting one or two days later
than the MCJC. This method does cause people to the east of Israel up to the
IDL to begin to observe the first day of the seventh month prematurely,
perhaps on some occasions causing two days of observance. In ancient times
Israel did the same thing as indicated in I Sam 20:27, 34. Hence this is not a
significant fault. The sighting of the new crescent from within the
boundaries of Israel should determine the day, and this day should be
accepted around the world based upon the IDL with sundown as it sweeps
across the globe.
[65] Two Web Sites with New Crescent Reports from Israel
There are two web sites hosted from Israel that report on new moon
sightings from Israel, and they do not consider reports from outside Israel to
be significant. One of them is hosted by Dr. Roy Hoffman, who works for
the Department of Organic Chemistry of The Hebrew University in
Jerusalem (see www.geocities.com/royh_il/). I have seen some emails
forwarded to me that make it clear that Dr. Hoffman favors the Rabbinic
writings and the commentaries by Orthodox Jewish sources. Some of his
reports of borderline sightings of the new crescent are more detailed than the
other web site. The other one is hosted by Nehemia Gordon, a spokesman
for the Karaites in Israel (see www.karaite-korner.org). These web sites
provide information of sightings, and then those that receive the emails are
free to decide whatever they want on the basis of these reports. Nehemia
Gorden tends to make statements that state what month this is on the basis of
his tenets, but no one is forced to agree with his conclusions.
[66] Appendix A: Nisanu 1 in the Babylonian Calendar Compared to the
Vernal Equinox during the Century of Ezra and Nehemiah
The use of Babylonian month names in Ezra 6:15 and Neh 6:15 in the
context of Jerusalem makes it relevant to examine the actual dates of the
vernal equinox compared to Nisanu 1 of the Babylonian calendar during the
100 years from 499 to 400 BCE, which is the century of Ezra and Nehemiah.
The month name Nisanu was transliterated to Nisan by the Jews in the
context of Jerusalem. The first chart shown in this appendix makes it clear
that the vernal equinox separated the first month Nisanu from the last month
of the old year. The adoption of the Babylonian month names in Scripture
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shows the acceptance of the rule of the vernal equinox in the calendar of
Jerusalem.
Before the year 499 BCE the Babylonian calendar year’s first month named
Nisanu did not follow any regular pattern with respect to the vernal equinox.
From that date onward a 19-year cycle was accepted for Nisanu by the
Babylonians. By this I mean that there were 235 lunar months in each
successive 19 years, and among these 235 months, the month numbers that
were called Nisanu were numerically repeated. Each 19 years in the cycle
had 12 years that contained 12 months and 7 years that contained 13 months.
The sequence of the years among the 19 that had 13 months was repeated in
each successive 19 years. In the years that had 13 months, the extra month is
called the intercalary month. This cycle was begun by the Babylonians.
The first day of Nisan in the Babylonian calendar since 499 BCE fell on or
after the vernal equinox. Although Parker and Dubberstein show an
exception to this in the year 384 (page 34), this alleged exception should be
corrected because it is now regarded to be a faulty examination of a
cuneiform text; see pp. 14 and 16 in Aaboe and others 1991
This appendix features a chart consisting of the 100 years from 499 to 400
BCE. For each year the date and time of the vernal equinox is stated and the
date of the first day of the first month, Nisanu 1, is stated. Both dates are
according to the Julian calendar. For each Julian date given, the Babylonian
day began on the evening that came before the Julian date (the latter is based
upon a midnight-to-midnight day). Determination of the vernal equinox for
these 100 years was made using the computer program BRESIM (see the
bibliography). This program is noted for its accuracy into ancient times for
the vernal equinox, but not for the position of the moon.
The book by Richard Parker and Waldo Dubberstein 1956 contains data that
has its origin in the writings on the cuneiform inscriptions on ancient clay
tablets from Babylon, most of which are in the British museum. The two
keys to the whole enterprise are: (1) The eclipse records on the clay tablets;
and (2) The number of years of the reign each of the of the kings who ruled
over the Mesopotamian region. The lengths of reign of these kings are in the
writings of Claudius Ptolemy (c. 150). The results of this book are based
upon modern astronomy and calculations that go backwards in time to verify
the accuracy in time of the data on the clay tablets. The Julian calendar dates
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that equate to Nisanu 1 during these 100 years are taken from pages 29 –33
of this book.
The book by Richard Parker and Waldo Dubberstein provides Julian
calendar dates for the ancient Babylonian calendar. Eclipse records from
ancient Babylon were used to determine those years that had 13 months
rather than 12 months. The underlying data that was used by Parker and
Dubberstein was examined by Fatoohi and others in a paper from 1999. The
conclusion on page 52 is that only 209 out of about 8670 new moons in this
book are provably based upon actual sighting by the Babylonians. All the
other new moons in this book are calculated based upon the methods of Karl
Schoch (see page 57 of Fatoohi and others). None of the 100 months that
began Nisanu in the chart below are among these 209 actual sightings of the
new crescent from Babylon. One day errors in Parker and Dubberstein may
be due to: (1) Any borderline case in Schoch’s curve at the end of the 29th
day where the true result is different (this might be true about 7 percent of
the time); (2) Poor weather that caused an otherwise visible crescent at the
end of the 29th day to not be seen; and (3) A mistake in calculation noting
that this book was prepared before the general availability of computers.
The chart does verify that the vernal equinox is indeed the borderline that
determines the beginning of Nisanu, the first month in the Babylonian
calendar. But additional care must be exercised in the small number of cases
where Nisanu 1 occurs on the vernal equinox or one day away from it. The
critical cases are examined separately in another chart afterward. For this
second purpose the time of the astronomical new moon that is published in
Goldstine is first used. This source takes into consideration the value of delta
T, which is the cumulative effect of the change of the length of the day,
which is the result of the slowing of the earth’s rate of rotation on its axis
due to tides, the wind against the land, the drag of the earth’s semi-liquid
core against its outer mantel, etc. According to page 60 of Fatoohi and
others, the estimate of delta T is 4.66 hours in 501 BCE. Most computer
programs do not have great accuracy that far back in time.
Then the number of hours from the astronomical new moon to sunset is
computed, and this is used to check the reasonableness of the date in Parker
and Dubberstein.
A friend of mine, Rob Anderson, wrote a computer program based upon the
Hewlett-Packard 3000 minicomputer and its unique operating system in
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1980-1982. This program was modeled after Schoch’s curve, and all the
months of the 20th century near the equinoxes were used in order to
determine the minimum required time from the astronomical new moon to
sunset in order to be able to see the new crescent, but only the latitude of
Jerusalem was used. This program determined that during the vernal equinox
the minimum required time varied from 16 to 24 hours, and during the
autumnal equinox the minimum required time varied from 18 to 48 hours.
This is corroborated by page 46 of Wiesenberg. This range of hours depends
on the angle between the ecliptic (the angle of the path of the sun) and the
western horizon. This means that for Nisanu 1 the benchmark for
comparison is the time interval between 16 and 24 hours. For the critical
years in our situation, it happens that this rule alone is sufficient to
determine the first day of visibility of the new crescent, provided the weather
was clear.
The journey of Ezra to Jerusalem mentioned in Ezra 7:7-9 is stated there to
have occurred in the seventh year of Artaxerxes. According to page 32 of
Parker and Dubberstein this was in the year 458 BCE, accepting that Ezra
entered Jerusalem before Nehemiah. The books by Horn and Wood, by Bo
Reicke, and by Kenneth Hoglund, accept or favor Ezra as settling in
Jerusalem before Nehemiah, and this is the traditional understanding.
Eventually Ezra and Nehemiah are in Jerusalem together (Neh 8:9; 12:26).
While opinions may be found that favor the opposite (Nehemiah preceding
Ezra), such opinions doubt the veracity of the stated accounts in Ezra and
Nehemiah. Discussion of this may be found on pages 89-93 of Horn and
Wood, pages 14-19 of Reicke, pages 40-44 of Hoglund, and pages 98-106 of
Grabbe 1991. Since Ezra 7:7 mentions the seventh year of King Artaxerxes
and Neh 2:1 mentions the 20th year of King Artaxerxes, it appears that
Nehemiah journeyed to Jerusalem about 13 years after Ezra. I accept Ezra’s
entry in 458 BCE and Nehemiah’s entry about 445 BCE, but only with the
understanding that if the method of numbering the year of reign was shifted
by half a year in Judah compared to Babylon, then these years might instead
be 457 BCE and 444 BCE. The commentaries differ on this and I do not
have a firm opinion.
In the table below the time is based on Greenwich, England as given in the
program BRESIM. Conversion to the time zone of Babylon could be
accomplished by adding three hours. The critical years for the vernal
equinox compared to the new moon in this table are 484, 465, 446, 427, and
408. These years are used for further analysis in the second table below.
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There are three times in the 100 years when the day prior to the vernal
equinox was a new moon day. All three times this new moon day began an
intercalary month (a month added beyond the 12 normal months) called the
second Adar, the 13th month. These dates are March 25, 454 BCE, March
25, 435 BCE, and March 25, 416 BCE.
Vernal Equinoxes compared to Nisanu 1in Babylonian Calendar
Date BCE Time V.E. Nisanu 1
Date BCE Time V.E.
Nisanu 1
3-27-499 00:29
4-11
3-26-449 03:07
3-29
3-27-498 06:22
3-31
3-26-448 08:50
4-16
3-26-497 12:10
4-18
3-26-447 14:36
4-06
3-26-496 18:04
4-08
3-26-446 20:30
3-26
3-26-495 23:43
3-28
3-26-445 02:26
4-13
3-27-494 05:36
4-16
3-26-444 08:14
4-03
3-26-493 11:35
4-04
3-26-443 14:02
4-22
3-26-492 17:13
4-23
3-26-442 20:00
4-11
3-26-491 23:06
4-12
3-26-441 01:50
3-31
3-27-490 04:56
4-02
3-26-440 07:37
4-18
3-26-489 10:40
4-19
3-26-439 13:27
4-07
3-26-488 16:30
4-09
3-26-438 19:17
3-28
3-26-487 22:08
3-30
3-26-437 01:06
4-14
3-27-486 03:57
4-18
3-26-436 06:48
4-04
3-26-485 09:52
4-06
3-26-435 12:33
4-23
3-26-484 15:27
3-26
3-26-434 18:28
4-13
3-26-483 21:17
4-14
3-26-433 00:20
4-01
3-27-482 03:15
4-03
3-26-432 06:04
4-20
3-26-481 09:05
4-21
3-26-431 11:50
4-09
3-26-480 15:03
4-11
3-26-430 17:39
3-29
3-26-479 20:50
3-31
3-25-429 23:26
4-16
3-27-478 02:40
4-19
3-26-428 05:09
4-05
3-26-477 08:38
4-08
3-26-427 10:56
3-26
3-26-476 14:16
3-28
3-26-426 16:50
4-14
3-26-475 20:04
4-15
3-25-425 22:42
4-03
3-27-474 01:59
4-05
3-26-424 04:27
4-22
3-26-473 07:42
4-22
3-26-423 10:18
4-11
3-26-472 13:30
4-12
3-26-422 16:18
3-31
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136
3-26-471 19:13
4-01
3-25-421 22:10
4-18
3-27-470 01:01
4-21
3-26-420 03:59
4-07
3-26-469 06:59
4-09
3-26-419 09:47
3-27
3-26-468 12:40
3-29
3-26-418 15:37
4-15
3-26-467 18:27
4-17
3-25-417 21:28
4-04
3-27-466 00:22
4-06
3-26-416 03:09
4-23
3-26-465 06:07
3:25
3-26-415 08:53
4-13
3-26-464 11:56
4-13
3-26-414 14:44
4-02
3-26-463 17:43
4-03
3-25-413 20:25
4-19
3-26-462 23:32
4-22
3-26-412 02:07
4-08
3-26-461 05:28
4-11
3-26-411 07:55
3-29
3-26-460 11:09
3-31
3-26-410 13:50
4-17
3-26-459 16:58
4-19
3-25-409 19:46
4-05
3-26-458 22:57
4-08
3-26-408 01:34
3-26
3-26-457 04:49
3-27
3-26-407 07:22
4-14
3-26-456 10:40
4-15
3-26-406 13:20
4-03
3-26-455 16:29
4-04
3-25-405 19:07
4-21
3-26-454 22:16
4-23
3-26-404 00:52
4-10
3-26-453 04:06
4-12
3-26-403 06:45
3-30
3-26-452 09:46
4-02
3-26-402 12:34
4-18
3-26-451 15:29
4-20
3-25-401 18:25
4-07
3-26-450 21:22
4-10
3-26-400 00:10
3-27
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The table below has the five critical years from the above table that the new
moon occurs in close proximity to the vernal equinox. The column headed
“Astronomical New Moon” has data that comes from the reference
Goldstine (its computation is based on the time zone from Babylon), but
three hours were subtracted to convert from the time zone of Nineveh to
Greenwich time. The column headed “Sunset” has data that comes from the
computer program “Loadstar Professional”; this has an adjustment for delta
T and it verifies the dates for Nisanu 1 according to Schoch’s curve for the
years below as given in Parker and Dubberstein. The ancient city of Nineveh
was used as the location in Babylon. It is located where Mosul, Iraq is today,
and its coordinates are longitude 43 degrees east, latitude 36 degrees 9
minutes north.
Vernal
Equinox
BCE
Astro-
nomical
New
Moon
Sunset
Nineveh
(Green-
wich
time)
Hours
from
conjunc-
tion to
sunset
Expected
New
Moon
(from
hours)
Parker
& Dub.
Prior
New
Moon
Number
of days
in the
prior
month
3-26-484
15:27
3-24-484
02:02
3-24
15:18
13:16
3-26
2-24
30
3-26-465
06:07
3-23-465
14:55
3-24
15:18
24:23
3-25
2-25
leap yr
29
3-26-446
20:30
3-24-446
11:35
3-25
15:19
24:44
3-26
2-25
29
3-26-427
10:56
3-24-427
12:09
3-25
15:19
27:10
3-26
2-25
29
3-26-408
01:34
3-24-408
11:07
3-25
15:19
28:12
3-26
2-25
29
In the above table the expected new moon always agrees with the computed
date from Schoch’s curve as given in Parker and Dubberstein. In all cases
except 465 BCE the expected new moon is the date of the vernal equinox. In
465 BCE it is possible that bad weather did not allow the new crescent to be
seen, so that the old month had 30 days instead of 29 days, and the actual
Nisanu 1 was March 26 instead of March 25. Three hours would have to be
added to attain the time zone of Nineveh. In all of these cases the following
rule would work out correctly. Find the date of the noontime which is closest
to the time of the vernal equinox. That date is counted as the date of the
vernal equinox.
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February 7, 2007
138
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