Treatise on the Biblical Calendar, second edition (abbreviated TBC2) by Herb Solinsky (c) April 3, 2009

[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 Abraham teach Mathematical Astronomy to the Egyptians?
[14] Did Ancient Israel Excel in Advanced Mathematical Astronomy?
[15] Authority of the Levitical Priesthood from the Tanak

(A) The Levitical Priesthood has a Role regarding the Calendar
(B) Anointing Oil is Symbolic of Authority upon Aaronic Priests
(C) The Origin and Exclusiveness of the Aaronic Priesthood
(D) Punishment by Death for Usurping the Domain of the Aaronic Priesthood
(E) The Teaching Authority Given to the Levitical Priesthood.
(F) Ps 133 shows Calendric Unity via the Authority of the Aaronic Priesthood
(G) People involved in Israel's Governance before the Babylonian Exile
(H) The Mishnah and the Great Sanhedrin
(I) History of Disruption and Restoration of the Levitical Priesthood
(J) Authority of the Levitical Priesthood Recognized in the New Testament

[16] Control of the Temple, and thus the Calendar, in the Early First Century

(A) Primary Sources of History in the early First Century
(B) Branches of Modern Judaism relate to evidence on this Issue
(C) The New Testament as a Primary Source
(D) Many of the Scribes were Sadducees. Mat 23:2 and Moses' Seat
(E) Sanhedrin in the New Testament
(F) The Parable of the Wicked Vinedressers
(G) How the High Priest Spoke to the Audience that included the Pharisees
(H) Pilate's Understanding of the Chief Priests’ Authority
(I) The Role of Gamaliel
(J) Legal Authority of the Chief Priests
(K) Conclusion from the New Testament
(L) The Roman Historian Tacitus
(M) The Roman Historian Pompeius Trogus

[17] Appointed-times and Years are known from Lights in the Sky
[18] A Month is a Cycle of the Moon
[19] Full Moon occurs about the 14th and 15th Days of the Biblical Month
[20] A Biblical Month is a Whole Number of Days
[21] A Biblical Month has a Maximum of 30 Days
[22] The Sun and Moon are the Primary Lights in Gen 1:14
[23] Blowing two Silver Trumpets on the Day that Begins each Month
[24] Hebrew chodesh refers to the Day that Begins each Month
[25] Isaiah 47:13, Astrologers, the Zodiac, and the meaning of chodesh
[26] The Biblical New Moon relates to the Sighting of the New Crescent
[27] Philo of Alexandria and the Jewish New Moon in the First Century
[28] Did the Jews use Calculation for their Calendar in the First Century?
[29] The Biblical Year is a Whole number of Biblical Months, 12 or 13
[30] The Beginning of the Month and I Samuel 20
[31] Applying I Sam 20 to II Kings 4:23 and Amos 8:5
[32] Rapid Communication to inform the Nation about the New Moon
[33] Summary about the New Moon Celebration and the Role of the Daytime
[34] Today’s Ambiguity in the Phrase New Moon
[35] Month Start Theories from Ps 81:3 and the double word b-keseh

(A) Three Translations of Ps 81:3
(B) Three Theories from Ps 81:3
(C) Discussion of Theory A (Full is Fifteenth)
(D) Discussion of Theory B (Full is New)
(E) Discussion of Theory C (New is Conjunction)
(F) Can keseh in Ps 81:3 be the verb kasah (3680)?

[36] The Noun keseh in Ps 81:3 means the Approximate Full Moon
[37] Biblical View of the Sun's Yearly Motion is South - North
[38] The South - North Yearly Cycle indicated in Eccl 1:6A
[39] Equinox and Solstice is in the Bible
[40] Equal Daytime and Nighttime is Not the Biblical Equinox
[41] The Vernal Equinox and Ex 12:2
[42] Karl Schoch’s Curve for Predicting Visibility of the New Crescent
[43] Ezra and Nehemiah in Relation to the Vernal Equinox and the Babylonian Calendar [44] Nisan and the Jews at Elephantine, Egypt
[45] Gen 1:14; Ezra 6:15; Neh 6:15 Show the Vernal Equinox Starts the Year
[46] The Zodiac and the Sign of Aries
[47] Philo explains when the First Month of the Biblical Year begins
[48] Declaration of the Vernal Equinox in Ancient Israel
[49] Saadia Gaon and the Origin of the Modern Jewish Calendar
[50] The International Date Line, the Sabbath, and the New Moon
[51] How the MCJC achieves Spiritual Unity using the IDL
[52] Avoiding Confusion and Disunity (Ps 133:1)
[53] Dwelling in Spiritual Unity Through the Declaration of the Priesthood
[54] Does Deut 16:1 Command Everyone to Look for the New-Moon?
[55] Ancient Israel did not Practice Local Visibility
[56] Confusion of a Difference of a Whole Month in the Calendar
[57] The Role of the Land of Israel
[58] The Boundary of Israel
[59] The law will go forth from Zion - Isaiah 2:3 and Micah 4:2
[60] Two Days for the Start of the Seventh Month
[61] What if the Whole Earth may Sight the Crescent to start the Month?
[62] The Ancient Situation Outside of Israel
[63] Modern Technology makes a difference
[64] Num 10:10 Avoids Confusion
[65] Differences between the Sabbath and the New Moon
[66] Does the spread of saints around the world change the calendar?
[67] Historical Evidence for Sighting the New Crescent
[68] Should only Jerusalem be used to Sight the New Crescent?
[69] Starting the Month when it comes to you
[70] Actual Sighting from Israel Today
[71] The Process of Declaring the New Moon
[72] Two Web Sites with New Crescent Reports from Israel
[73] Authority in Israel Distorted by Josephus

(A) Josephus on the Biblical Court System and the Biblical King
(B) Resolving Contradictions in Josephus over who had greater Authority
(C) General Conclusions about Josephus

[74] Josephus and his Aries Approximation
[75] Destruction of the Temple April 3, 2009 3
[76] The Easter Calendar Deception from Josephus
[77] Introduction to aviv and chodesh ha aviv
[78] Genetics of Barley
[79] Stages in the Development of an Ear of Barley
[80] Firstfruits and the Hebrew words bikurim and raysheet
[81] Meaning of Lev 2:14-16 which contains aviv
[82] Southern border of Ancient Egypt when the Israelites were Slaves [83] Introduction to the Plague of Hail and Ex 9:31-32
[84] Winter Grain, Agriculture, and Rainfall in Ancient Egypt
[85] Smith's Paper and Ears of Winter Barley in Egypt
[86] Lewis' Book and Ears of Winter Barley in Egypt
[87] Hartmann's Book and Ears of Winter Barley in Egypt
[88] Pliny the Elder and Ears of Winter Barley and Wheat in Egypt
[89] Ending of Ex 9:32
[90] Conclusions on the Time of the Hail and the Meaning of aviv
[91] Time of the Barley Harvest in Israel
[92] Comparison of Barley Harvest in Egypt and in Israel
[93] Lack of Applying aviv to Ex 12:2
[94] Gen 1:14 is a Cause and Effect Verse with Light, not Heat
[95] Septuagint’s Translation of aviv
[96] Meaning of aviv from the Mishnah
[97] Ambiguity of Identifying the Month of aviv from the word aviv
[98] Josh 5:10-12 and the Date of the Wave Sheaf Offering
[99] Meaning of omer for Sheaf and its State of Development
[100] Wave Sheaf Offering
[101] How the Wave Sheaf was Obtained
[102] More Comments on the Time of Early Ripe Barley in Israel
[103] Can the Barley Harvest begin before the Wave Sheaf Offering?
[104] The Meaning of Deut 16:1
[105] The First Month During the 40 Years of Wandering in the Wilderness
[106] Indirect Interpretation of Gen 1:14 and the Jews in Rome
[107] History of the Karaites
[108] Issues Against the Position that Barley Determines the First Month
[109] Epilogue

(A) Condensed Summary
(B) Summary of the Biblical Calendar from Scripture

[110] About the Author
[111] Appendix A: Yohanan ben Zakkai and the Sadducees
[112] Appendix B: Rabbinic Literature and History

(A) Conflict of Interest in the Lineage of the Author of the Mishnah
(B) Can the Talmudic Concept of the Oral Law be Historically True?
(C) Summary of some Reasons for Lack of Reliability in the Historical accuracy of the Mishnah
(D) Talmudic Decisions on the Calendar by the Gamaliel’s and Simon
(E) Modern Conservative Jewish Views concerning Rabbinic Literature

[113] Appendix C: Nisanu 1 in the Babylonian Calendar Compared to the Vernal Equinox during the Century of Ezra and Nehemiah
[114] Appendix D: Karl Schoch's Table for Visibility of the New Crescent
[115] Appendix E: Time from Sunrise to Sunset to compare with the Vernal Equinox
[116] Appendix F: Comparing the Sighting of the New Crescent with MCJC
[117] Appendix G: Smith's Paper
[118] Bibliography

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[1] Preface

This is the second edition of this general treatise on the biblical calendar, and a third edition is anticipated. It is written for English speaking readers who have an interest in the biblical calendar, and it does not require a knowledge of any other language. 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 except for some appendices. The main companion to this is a literal Bible
translation and a concordance with Strong’s numbers. This book is written for both Jews and non-Jews who have an interest in the biblical calendar.

Since reference works are primarily written for verse numbering as found in the KJV, the verse numbering used in this book follows that of the KJV rather than the alternate numbering found in Jewish translations. When I supply a literal translation that contains the Tetragrammaton (the sacred four-letter Hebrew name of the Almighty), I will use the four capital letters YHWH as a literal method to highlight this, and the reader will have the freedom to decide what to say if it is spoken.

The Hebrew Bible, with parts of Ezra and Daniel in Aramaic, is also called the Tanak. The name “Tanak”, with emphasis on the three consonants TNK, recognizes the division of this Bible into three distinct parts as preserved in Bibles printed by Jewish sources. The word “Tanak” will sometimes be used instead of the word “Scripture” or “Bible”.

Some readers will already have studied the calendar from a biblical
perspective and will want to know the conclusions immediately. They may turn to the chapter titled “Epilogue” near the end of this book. This epilogue is not intended to be self-explanatory as though it could stand on its own as a separate document. It assumes that the reader has already read this book and is a type of summary that emphasizes the biblical backbone for the conclusions.

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. This principle is violated in regard to the topic of Rabbinc literature, which is a topic of considerable controversy among the April 3, 2009 6
branches of modern Judaism. Rabbinic literature does discuss the calendar, but this book puts primary emphasis on the literal meaning of the Hebrew Scriptures rather than on Rabbinic literature. Yet at some occasions Rabbinic literature is of interest, and thus it is sometimes discussed with regard to its views on the calendar; this is always documented. An appendix discusses Rabbinic literature, and this is mentioned at various places in the body of this book. 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 without concern that it threatens circular reasoning. Thus a later appendix is not considered to violate the concept of proceeding in a logical order without resorting to conclusions based upon what is written later. Rabbinic literature is an exception because the appendix devoted to it draws upon certain material that is discussed in the body of this book. From the viewpoint of this book, Rabbinic literature is not the basis for understanding the biblical calendar.

When studying controversial aspects of history, one must first grasp proper methods of study. The most elementary and important matter in studying history is distinguishing between primary and secondary sources. A primary source is a record of the events that is dated close to the time of the events.

A secondary source is a rewriting of the available primary sources with personal reasoning, suppositions, interpretations, correlations, deletions, additions, modifications, conclusions, etc. A good secondary source will include documentation of the primary sources used so that the reader may go to those primary sources and check on the author's possible assumptions, additions, and biases. The primary sources must also be weighed for degrees of bias in them.

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.

Acknowledgements:

During the years 1980 through 1982 my friend Rob Anderson caught the biblical calendar interest as well, and he volunteered to write a computer program that ran on a Hewlett-Packard HP-3000 minicomputer that would approximate the visibility of the new crescent based upon Karl Schoch’s curve. The software that he wrote was partly based upon the bibliographic reference Van Flandern and Pulkkinen. His many and varied computer studies were a significant help to understand how the astronomical circumstances for the calendar changed for the first month and the seventh month, the minimum and maximum time from the astronomical new moon to the sighting of the new crescent, the time from sunset to moonset on days that the new crescent would be seen, the date that the biblical festivals would fall based upon a calendar of simulated visibility, the relationship between the time of the new crescent and the full moon, etc. He and I discussed many
aspects of the calendar in those years, and also the astronomy of the moon.

Rob also made some visits to various libraries for specialized related
subjects. In September 1982, using some of the tabulated results of the studies that Rob Anderson produced with his creative software, the book titled The Calendar God Gave to Moses became a reality. Although I wrote nearly all the words and determined the arrangement of the chapters, all of the statistical data concerning the calendar came from Rob Anderson’s efforts; thus its authorship was listed as “Herb Solinsky and Rob Anderson”.

The present treatise will occasionally make reference to Rob Anderson, and though his work stopped in 1982, that effort still lives on in this treatise.

Initially 400 copies were dispersed, but over the years several times that number were sent out. Jack Hines from Colorado Springs, Colorado and John Trescott from Anadarko, Oklahoma also sent out significant numbers of that 84-page book from 1982 over the years. Rob Anderson’s use of the HP-3000 computer was no longer available, and astronomy software needed to be pursued.
This present book is not merely a revision of the 1982 study, but a giant leap forward, addressing certain areas whose surface was only scratched at that time.

In early 1995 I began to explore astronomy software for use with the personal computer. I want to thank John Mosley, the Program Supervisor at Griffith Observatory in Los Angeles. He was very kind and patient with me as he answered my questions over several telephone calls about various astronomy software packages. He had tested and reviewed many software packages for Sky and Telescope magazine. He advised me that LoadStar Professional was the most accurate software available for the moon with an IBM PC compatible computer, including ease of use. It does use the JPL (Jet
Propulsion Laboratory) results for accuracy in the distant past. This is DOS based rather than Windows based, and it has never been upgraded, so that its graphics is primitive compared to what is currently available. Nevertheless, its accuracy still serves my needs very adequately.

On May 4, 1995 I was very thankful that I was able to spend 30 minutes over the phone speaking with Professor Bradley E. Schaefer, who, in my opinion is the most knowledgeable person alive on technical matters relating to the visibility of the new crescent. I learned much from that phone call, and some of his publications that were helpful are listed in the bibliography. He
was the first one to alert me about the need to consider humidity as a significant factor for the ability to see the new crescent.
In mid-September 1982 I had a desire to speak with Professor Otto
Neugebauer about the history of the Jewish calendar from before the destruction of the Temple in 70. I telephoned the History of Mathematics department at Brown University, and he himself answered the phone!!! My desire was satisfied and I acknowledge his assistance and willingness to speak with me.

In the summer of 1992 I noticed that there was an agricultural experimental station that was labeled as an extension of Texas A & M University, located in Plano, Texas. After contacting this facility by telephone, I was transferred to Professor David Marshall, who is a grain geneticist, specializing in wheat and barley. He invited me to visit him at his office, and I happily accepted for the purpose of learning more about barley, including how and when it ripens. I was mentally sky high as he loaned me a tall pile of his personal books about barley and grains. He told me that I should look into the
genetics of barley because different varieties ripen at different times. I followed his advice, and two months later I spent nearly three days at the library of Texas A & M University in College Station. I am grateful to David Marshall.

In November 1997 I received a telephone call from Jack Hines explaining the need to make computer projections of the dates of the biblical festivals through the year 2010. At his suggestion he and I agreed to independently use different software to apply Karl Schoch’s curve and then compare dates and reconcile differences in order to reach agreement. We did this, but in the process of reconciling differences and discussing the options in the software
that he was using, I learned more about the meanings of certain astronomical coordinate systems. I thank Jack Hines for his useful suggestions, his participation, and his encouragement.
Useful discussions transpired with Wayne Atchison, Phil Frankford, Ralph Lyman, Steve Rathkopf, and Jim Sorenson.

Herb Solinsky (c) April 3, 2009

[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.

It is important to have a clear stated philosophy with 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.

Herb Solinsky (c) April 3, 2009

(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 calendric 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 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 peace with the ability to accept people whose viewpoints do not always agree with yours. 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.

[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, the Tanak.

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 it 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 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 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 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 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.

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 immediately after the English word.

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 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 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 an innocent unsuspecting person may come to a premature conclusion about the biblical calendar and then writes with conviction, thus leading other innocent 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 1993 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.

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 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 arises, 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 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 have gravitational relationship with 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 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.

[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, 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 1960, 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 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 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 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 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 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.

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.

In the first century BCE Vitruvius wrote the views of the Greek astronomer and mathematician Aristarchus of Samos (c. 280 BCE) concerning the full moon. On page 264 Vitruvius (translated by Morgan) 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 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 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 accustomed to since the time of Eudoxos [Greek astronomer of Cnidos, c. 408 to 355 BCE. (see pages 63-66, 335 of Pedersen 1993)]. 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 umbers, 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 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, 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 20th 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 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.”

David Brown wrote on page 7 of his book, “The term ‘astrology-astronomy’ will be used to refer to the particular branch of Mesopotamian scholarship herein considered. It is to be differentiated from cosmological or cosmogonical speculation – theories concerning the universe as a whole, or concerning the creation of the universe as a whole. Astrology and astronomy mean different things today, but the two words were used interchangeably at least until the 6th century AD. That is not to imply that before this time no difference was ever appreciated between what we would term astrology and what we would term astronomy.”

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, through there were various dialects. David Brown wrote on page 31, “When reconstructing the background to the emergence of the accurate predicting of celestial astronomy, it is important to recall that the cuneiform languages, dialects and scripts were used only by an elite. The scientific developments that form the locus of this study appear only in these scholarly languages [not Aramaic].”

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 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 (see Isa 47:13 for the general tone, although it does not directly refer to horoscopes), 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 2004 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

Today a child learns to distinguish between 25, 205, and 2005 through the base ten position of the zeros. When performing the operations of addition, subtraction, multiplication, and division without a calculator, the vertical alignment of the digits into neat columns of units’ digits, tens’ digits, hundreds’ digits, etc., makes the general procedure for these basic operations seem exceptionally simple. In today's society we take this simplicity for granted. But archaeological remains of calculations by different ancient civilizations reveals that very few ancient cultures had a concept of a base value (such as 10) in which the same symbol (such as 2) in a different position would have a different value (such as 2, 20, 200, et cetera). The written biblical examples of numbers in the Hebrew language show no knowledge of a base ten positional number system with a symbol for zero to define the position and hence the value. Without this positional base concept using a zero, general long division becomes very cumbersome and time consuming.

For example, if the reader attempts to use the symbolism of the Roman number system (with “L” for 50, “XL” for 40, “C” for 100, “M” for 500, etc.), and then attempts to do general long division in this system, it will be a significant chore. Although ancient societies had a concept of a fraction and they knew how to divide by 10 (obtaining a tithe) because the language used words that were multiples of 10, this certainly does not imply that they had a simple general method for long division that could be done quickly. Dividing by 5 was twice a tithe, so that was easy. Dividing by 20 was half a tithe, so that was easy. But these are special examples rather than a general method for long division that would work for all numbers.

Try dividing the Roman equivalent of 237892.21 by the Roman equivalent of 542.37 using only the Roman number system and see how far you get without our modern symbolism for numbers with a zero. Without a positional base number system using a zero, the method for general long division that elementary school children are taught today would not even exist because that very method depends on position. The reference RMP (= Rhind mathematical papyrus) is an explanatory book concerning ancient Egyptian mathematics published by the British Museum. It provides a detailed analysis of a papyrus from ancient Egypt that gives examples of how to solve a wide variety of mathematical problems.

Page 16 of van der Waerden 1961 dates this papyrus after 1800 BCE, which is after the time of the building of the great pyramids at Giza. Page 12 of RMP states, “The hieroglyphic script had distinct signs for units, tens, hundreds, etc., the numbers of each being indicated by repetition of the sign. There was no sign for zero and no positional notation, so that the representation of large numbers became extremely cumbersome.” Page 5 of Gillings states that the ancient Egyptian method for writing the number 1967 required 23 characters while the method for writing 20,000 required only two characters. This ancient Egyptian method for the representation of numbers does not enable the simple methods of general long division used by modern elementary school children or the equivalent simple methods used by the ancient Babylonians. Pages 16-18 of RMP give examples of how long division was performed by the Egyptians, and page 19 of van der Waerden explains the Egyptian methods for long division in a slightly different way. The methods are laborious and cumbersome by today's standards, and if there were a need for many general long division computations, it would be discouraging to have to use the methods of the ancient Egyptians. Mathematical astronomy would require extensive use of general methods of long division where the divisor may be a whole number plus a fraction.

Page 36 of van der Waerden raises the question of whether the ancient Egyptians had more advanced mathematical methods than those that have survived until today. By the word “ancient”, he means before the time of Alexander the Great, after which the city of Alexandria was founded and the Greek astronomers emigrated to Alexandria where they used the mathematical methods of the Babylonians, but dressed in the Greek language rather than the Akkadian language of the Babylonian pagan priests.

He gives two reasons against this. One reason is that there are both elementary mathematical Egyptian texts and advanced texts, and the general character of the mathematics remains the same in both kinds of texts. The second reason is that the Greeks had access to ancient Egyptian mathematical and geometrical methods. The Egyptians successfully used the geometrical methods in a practical way for building purposes, and the Greeks did use selected geometrical methods of the ancient Egyptians. If the Egyptians had developed good methods for doing arithmetic, we would also find some trace of this among the many Greek writings in mathematics. But the Greeks only show use of the Babylonian methods in arithmetic. The ancient Egyptians did not use the positional base 60 number system of the Babylonians or the Babylonian multiplication tables up to 60 times 60.

Pages 353-356 of Ruggles discusses the pyramids of Giza, which are the most impressive pyramids of Egypt. Ruggles makes it clear that we do not know the methods by which the Egyptians constructed these massive monuments. In modern times several writers have made guesses concerning how this may have been done. The largest pyramid required over two million blocks, each weighing about 15 tons, and it is not known how the blocks were transported to such a height. They must have had an excellent knowledge of applied levers and pulleys, but even this supposition does not explain how they could have done it. Our lack of knowing how this marvelous feat of construction occurred is not evidence that it required advanced methods of mathematics that differs significantly from the examples we already possess. The mathematics needed for building construction is different from the mathematics that is needed for mathematical astronomy.

On pages 128-129 of Clagett, he wrote the following:

“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 (see pp. 289-290 of Swerdlow 1993), and his pioneering studies were based on his own readings of the original texts. Neugebauer first studied how to read Egyptian hieroglyphics so that he could study ancient Egyptian mathematics from the original documents. 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, primarily based on the Rhind Papyrus from ancient Egypt.

After repeated efforts Neugebauer convinced Richard Anthony Parker, the most acclaimed expert on ancient Egyptian science and calendation, to leave the University of Chicago and join him as a professor at Brown University in 1949. 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 knowledge of the time of the equinoxes by the ancient Egyptians, Neugebauer 1980 wrote 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. The reason he sought and proposed this method is simply that his studies into ancient Egyptian mathematics and astronomy did not hint at any Egyptian ability to accurately predict the time of the equinoxes.

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 this chapter, Wells 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.” Page 7 of this book edited by Walker states, “Ronald A. Wells was a Fulbright scholar in Egypt at the University of Cairo and at Helwan Observatory in 1983-4, and again at the Institute of Archaeology, Egyptology Division, University of Hamburg, in 1987-8."

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 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. The attention devoted to ancient Egypt serves the purpose of showing that ancient Israel could not have obtained knowledge of mathematical astronomy from Egypt because Egypt did not possess knowledge of mathematical astronomy.

[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 all 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.”

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, over 1000 years 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.

Furthermore, the Egyptians did not use the Babylonian positional base 60 number system, which they would have used it if Abraham had convinced them of its superiority. 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?

Scripture defines the wisdom of ancient Israel in an unconventional way in the following passage.

Deut 4:5, “Behold I have taught you statutes and ordinances as YHWH my Almighty commanded me, that you should do so in the midst of the land where you are going to possess it.”
Deut 4:6, “So keep and do [them], for that [is] your wisdom and your understanding in the sight of the peoples who shall hear all these statutes. Then they shall say, surely this great people [is] a wise and understanding nation.”
Deut 4:7, “For what great nation [is there] that has an Almighty [so] near to it as YHWH our Almighty in everything we call upon Him.”
Deut 4:8, “And what great nation [is there] that has statutes and ordinances [as] righteous as all this law that I set before you today?”

The nations of the world think of wisdom in terms of scientific achievement and the acquiring of great knowledge, but that is not the way Moses was told to proclaim wisdom to Israel. Mathematical astronomy was not to be wisdom for them. I do not doubt that the ancient Israelites had the mental capacity to be able to develop advanced mathematics, but without the collective need for this effort by Israelite society, what would motivate such an effort?

Ancient Israel could determine the calendar from observation, so
they had no need for any advanced tedious calculations.

Did ancient Israel use a positional digit system with a zero, which would enable rapid multiplication and division? On page 26 of GKC2 (the latest English edition of the Hebrew grammar book by Gesenius), the numerical value of the 22 Hebrew letters is presented. This shows one letter for the value 2, another letter for the value 20, and another letter for the value 200.

This illustrates the nature of the symbolic number system in ancient Hebrew, and shows that it was not a positional digit system with a zero. Page 30 has further comments on this system, which was used on coins in Judea from the Maccabean period (c. 150 BCE). The time of the origin of this system is unknown. This system would be a hindrance for general long division and is not useful for 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. 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.

Although the Jews were in captivity in Babylon where the pagan priests had an advanced knowledge of both mathematics and mathematical astronomy written in the complex Akkadian language with its hundreds of symbols for words (not for numbers), there is no evidence that these Jews acquired this knowledge. Ancient Jewish writings from the Dead Sea Scrolls, from Philo, from Josephus, from archeological artifacts, and from the Mishnah (c. 200 CE), give no hint that the Jews became familiar with the Babylonian mathematical methods of computation before the time of the Greek astronomer Ptolemy (c. 150) CE who lived in Alexandria, Egypt. The Talmud does claim that Mar Samuel was able to compute a calendar for many years in advance, c. 250 CE, although none of the details are known.

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, “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-BEZ-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 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 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 crescentat 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.

1. 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 Babylonia at the time of its publication c. 600 CE, not about 900 years earlier when the Babylonian astronomers derived this figure. But other factors are also used for the 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. 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 Wiesenberg. 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] Authority of the Levitical Priesthood from the Tanak

A. The Levitical Priesthood has a Role regarding the Calendar

According to the law of Moses certain activities related to the calendar are required to be performed by the Levitical priesthood. Specifically, at the beginning of each month, in the context of Num 10:1-10, notice the following activity of the priesthood.

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 appointedtimes [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.”

A partial summary of this requirement from the law of Moses is that two priests (from Aaron and his seed) were to blow two trumpets on the first day of each month, thus giving the priests a role of significance in regard to the start of the calendric unit of time called a month [2320 chodesh]. In a later chapter these Scriptures will be discussed in depth beginning with Num 10:1. At this time the question being addressed is whether this calendric activity of the priesthood stems from the authority given to the priesthood itself or from some other human authority such as a king or a Sanhedrin.

B. Anointing Oil is Symbolic of Authority upon Aaronic Priests

Consider the key wording by which Aaron and his sons become a priest.

Ex 29:7, “And you [Moses] shall take the anointing oil and pour [it] upon his [Aaron's] head and you shall anoint him.”
Ex 29:8, “And you shall bring his sons and clothe them [with] coats.”
Ex 29:9, “And you shall gird them [with] sashes, Aaron and his sons, and you shall bind turbans on them. And [the] priesthood shall be for them for an everlasting statute, and [in this manner] you shall fill [the] hand of Aaron and [the] hand of his sons.”

The hand is a symbol of power and authority. When verse nine literally states “fill the hand”, it means “to bestow authority upon”. Some translations simply have “consecrate”, which loses some of the punch.

Ex 40:15, “And you shall anoint them [Aaron's sons] as you anointed their father that they may be priests to Me. And this shall be so that their anointing shall be to them for an everlasting priesthood for their generations.”

Simply summarized, the males in lineage through Aaron shall have authority bestowed upon them as priests through a ceremony using the anointing oil upon their head. The direct Scriptures are Ex 28:41; 29:7-9; 30:30; 40:13-15.

C. The Origin and Exclusiveness of the Aaronic Priesthood

Num 3:11, “And YHWH spoke to Moses saying,”
Num 3:12, “And I, behold, I have taken the Levites from among the children of Israel instead of all the firstborn that opens the womb from the children of Israel. And [hence] the Levites shall be Mine”
Num 3:13, “because all [the] firstborn [are] Mine. On [the] day I killed all [the] firstborn in [the] land of Egypt I set apart to Myself all [the] firstborn in Israel, both man and beast. They shall be Mine, I am YHWH,”
Num 3:5, “And YHWH spoke to Moses saying,”
Num 3:6, “bring [the] tribe of Levi near and present him before Aaron the priest that they may serve him.
Num 3:7, “And they shall attend to his needs and the needs of the whole congregation before [the] tent of meeting to perform [the] service of the tabernacle.”
Num 3:8, “And they shall attend to all [the] instruments of [the[ tent of meeting and the needs of [the] children of Israel to perform [the] service of the tabernacle.”
Num 3:9, “And you shall give the Levites to Aaron and to his sons. They [are] fully given to him from [the] children of Israel.”
Num 3:10, “And you shall appoint Aaron and his sons that they shall keep their priesthood. And the layman/outsider [2114 zar] who comes near shall be put to death.”
Num 18:6, “And I, behold, I have taken your [= Aaron and his sons]
brethren the Levites from among [the] children of Israel; [they are] a gift to you [= Aaron and his sons] given to YHWH, to attend to [the] service of [the] tent of meeting.”
Num 18:7, “And you [= Aaron] and your sons with you shall keep your priesthood for everything pertaining to the altar and for that behind [the] veil, and you shall serve. I give your priesthood [to you as] a service of gift.

And the layman/outsider [2114 zar] who comes near shall be put to death.” It is seen here that only Aaron and his sons may be priests, and all Levites who are not descended from Aaron are to serve under the authority of the priests. Certain duties are exclusive to priests and other duties are for other Levites under the direction of the priests. Here a non-Aaronite is referred to as a layman/outsider [2114 zar], and if such a person attempts to come near (get close, meddle, or interfere), death shall be the punishment.

The Hebrew word zar is discussed on page 279 of HALOT where several meaning are supplied based on the context, and Num 3:10; 18:7 are listed under the general meaning “unauthorized person”, and for these verses the submeaning “not an Aaronite” is stated in HALOT.

D. Punishment by Death for Usurping the Domain of the Aaronic Priesthood

Note the following references that show the teaching authority given to the priests.

Num 3:10; 18:7 show punishment by death for violating the domain of the Aaronic Priesthood. An example of this punishment by death is seen in II Sam 6:1-8; I Chr 13:7-11. The key passage follows.

II Sam 6:6, “And when they came to Nachon's threshing floor, Uzzah put forth [his hand] to the ark of the Almighty and took hold of it because the oxen shook it.”
II Sam 6:7, “Then [the] anger of YHWH flared up against Uzzah and the Almighty struck him there for [his] error. And he died there by [the] ark of the Almighty.”

This type of event is unique, but the lesson is clear even though no other example is available. If some item, such as the two silver trumpets in Num 10:1-10, has a holy use for the priests alone, then anyone having the fear of the Almighty should refrain from meddling with it. To do so is a usurpation of authority.

E. The Teaching Authority Given to the Levitical Priesthood.

Lev 10:8, “And YHWH spoke to Aaron saying,”
Lev 10:9, “you shall not drink wine or strong drink, you nor your sons with you when you go into [the] tent of meeting so that you shall not die; [it shall be] an everlasting statute for your generations”
Lev 10:10, “so that you may distinguish between the holy and between the common, and between the the unclean and between the clean,”
Lev 10:11, “so that you [= the Aaronic priesthood] may teach [the] children of Israel all the statutes which YHWH has spoken to them by [the] hand of Moses.”

Deut 24:8, “Take heed in an outbreak of leprosy, that you carefully observe and do according to all that the priests, the Levites, shall teach you as I commanded them, so you shall be careful to do.”
Jer 18:18, “... for the law shall not perish from the priest, or advice from the wise, or a word from a prophet.”
Mal 2:7, “For [the] lips of a priest should keep knowledge, and [people] should seek [the] law from his mouth, for he [is the] messenger of YHWH of hosts.”

Note that from the wording of Deut 24:8, it is accepted that when the populace is taught the law by a priest, they are expected to do what the law says, and this gives authority to the priest.

Despite the above wording that shows the general summarized impression that the priesthood was expected to teach the people the law of Moses, this function was not exclusive to the priesthood alone, as can be seen from the Torah next.

Deut 31:9, “And Moses wrote this law and he gave [it] to the priests, [the] sons of Levi who bore [the] ark of [the] covenant of YHWH, and to all [the] elders of Israel.”
Deut 31:10, “And Moses commanded them [= priests, Levites, and elders] saying, at [the] end of [every] seven years, at [the] appointed-time of the year of release at the feast of tabernacles”
Deut 31:11, “when all Israel comes to appear before YHWH your Almighty in [the] place that He shall choose, you shall read this law in the presence of all Israel in their ears.”

Thus the reading of the law every seventh year could be from the mouth of the priests, the Levites, and the elders, although the primary teachers of the law were shown above to be the priests.

Lev 21:10 begins with the Hebrew v-ha-cohan ha-gadol, which literally means “and the priest the great”, which is commonly translated “the high priest”. The Hebrew word gadol means “great” and it shows greatness in authority. The authority of the high priest is seen in Lev 21:10, “And the high priest among his brothers on whose head the anointing oil was poured, and [hence] whose hand was filled to put on the garments, shall not uncover his head nor tear his garments”.

F. Ps 133 shows Calendric Unity via the Authority of the Aaronic 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.”
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 Aaronic priesthood (Levitical priesthood). Anointing with oil upon the head bestows authority on the priest (Ex 28:41; 29:7-9; 30:30; 40:13-15). This is saying that dwelling in unity is like the oil of authority upon the Levitical priesthood, because unity can only come about if the priesthood properly teaches the law (Lev 10:8, 11; Mal 2:7) and signals the beginning of each month through their blowing of the two silver trumpets (Num 10:1-2, 8-10). Only then can there be spiritual unity, and with individual spiritual growth, the ideal outcome of this will be the blessing of eternal life (note Ps 133:3).

The appointed-times, the days of holy convocation, were indirectly announced by this priesthood at the beginning of the first and seventh months. This was a means of promoting unity in collective worship and unity of the days of holy convocation. There could be no opposing opinions and disunity concerning the day of the beginning of a month because of the authority of the high priest to achieve unity. This priesthood that was used to achieve unity was only given residence within Israel (Num 35:2-8).

To speak of pleasantness in unity, as seen in verse 1, implies a mental peace that can only come by willing agreement with the decision of the priesthood (Ps 133:1-2). If knowledge to achieve spiritual unity is attained, it should produce uniformity in recognizing the days of holy convocation, the appointed-times.

Through the symbol of oil, Ps 133 shows calendric unity through the authority of the Aaronic Priesthood. Verse 1 shows that this unity is good and pleasant.

G. People involved in Israel's Governance before the Babylonian Exile

When considering the overall structure of ancient Israel's governance before the exile to Babylon, first there was a period of Judges, and then, during the life of the prophet Samuel, the period of kings began. After Solomon, the kingdom was split into the northern House of Israel and the southern House of Judah. The latter contained the capital city of Jerusalem where the king and the priestly headquarters were centered near the one and only Temple.

From that time onward our interest then centers on the House of Judah alone. It is clear that Israel's governance and that of the House of Judah was intended to be a theocracy (note Deut 17:14-20). The elements of the theocracy in the House of Judah were the king, the priests, certain people who the king might appoint, and the prophets who might be unwelcome to certain sinful kings.

There were also courts to hear legal cases where parties were in dispute. Deut 17:8-13 mentions the need to judge legal cases of dispute, and those who do the judging are referred to as priests, Levites, and judges in verse 9. There is no indication in the Tanak that any calendric decision was to be treated as if it were a legal case that required some non-priestly civil court.

Such a concept is contrary to the implications of Ps 133. Num 10:8, 10 mentioned above, puts jurisdiction over the calendric practice of blowing the two silver trumpets at the beginning of the months in the hands of the priesthood, and there was one high priest who had the leadership. Meddling with the duties of the priesthood by unauthorized people carried the death sentence.

There is a unique event in Num 11:16-30 that shows a selection of 70 men from among the elders of Israel. Num 11:16, 24, 25, 30 have the word elders, which is the Hebrew word zaken, having Strong's number 2205, appearing in BDB on page 278 where its first meaning is “old of human beings” and another meaning is “elders, as having authority”. The meaning of zaken is best appreciated when one considers the nature of the chain of authority through male lineage as shown by a combination of commandments. Among the ten commandments is, “Honor your father and your mother …” (Ex 20:12; Deut 5:16). The authority of the husband over his wife is seen in Gen 3:16; Num 30:6-16. These laws work together to imply that the oldest living male within a family's lineage has authority over the extended family, and he is thus surely an elder or zaken. Num 11:16 makes it clear that these 70 men were already elders before Moses began the selection, and moreover, besides being elders, they were officers. Here the word officers is the Hebrew word shoter, which is Strong's number 7860, appearing in BDB on page 1009 where it states, “appar[ently] subordinate officer, judicial, civil, or military”. This implies that these elders have had some practical leadership or management experience, but not necessarily at the top position.

Num 11:16, “And YHWH said to Moses, Gather to Me 70 men from [the] elders of Israel whom you know to be elders of the people and its officers. And bring them to the tent of meeting, and let them stand there with you.”
Num 11:17, “And I will come down and I will speak with you there. And I will take of the Spirit that is upon you, and I will put [it] upon them, and they shall bear [the] burden of the people with you. Thus you shall not bear [the burden] yourself alone.”

No further qualifications are given concerning the selection of these 70 men from among those who were already elders. There was no tribal restriction, there was no requirement of a knowledge of the law, and there was no requirement of faith. There is never any indication in the Tanak that these elders met together as one body to discuss matters among themselves, or that they had a unified label such as a court or Sanhedrin.

In Ex 18:13-27 Moses' father-in-law gave him advice to build a pyramid organizational structure of judges, so that only the very difficult cases would filter their way up the pyramid to him. This advice did not involve previously recognized elders with leadership experience. If this advice would have succeeded, there would have been no need for the subsequent complaint by Moses in Num 11:1-15, which led to the appointment of the 70 men who were already elders.

In Num 14:26-33 the punishment of death during the 40 years of wandering in the wilderness was given to all Israelites who were 20 years old and above. This death in the wilderness came to all of the 70 elders with the exception of Joshua and Caleb, if they were among these elders. One need for elders in Israel was simply the practical function of communication of basic news to all people from a central seat of government. When Joshua crossed the Jordan River there were a few million Israelites. If Joshua himself spoke loudly, only a tiny fraction of them could hear him. Since people were geographically grouped as near relatives, the most practical way to communicate with all people was through the system of elders. Joshua would speak to the elders as heads of clans (subgroups within a tribe), and they in turn would go to those who they represented in family ancestry and authority so that the news would reach everyone. Existing authority through male lineage was respected. Thus Josh 7:6 mentions the elders of Israel who were near Joshua. There is no need to imagine that there were 70 of them.

These elders were authority figures for purposes of orderly travel and communications, and they also had ancestral authority as the oldest males in their extended family.

H. The Mishnah and the Great Sanhedrin

The Mishnah (c. 200 CE) teaches that the 70 men with Moses constituted the greater Sanhedrin where it quotes from Num 11:16 discussed above. On page 383 of Danby's translation of the Mishnah, in Sanhedrin 1.6, we find (with Danby's additions in square brackets), “The greater Sanhedrin was made up of one and seventy [judges] and the lesser [Sanhedrin] of three and twenty. Whence do we learn that the greater Sanhedrin should be made up of one and seventy? It is written, Gather unto me seventy men of the elders of Israel, and Moses added to them makes one and seventy.”

Although Num 35:24 mentions “the congregation shall judge”, the Tanak never defines the congregation in this sense as the 70 (or 71) elders. It may refer to any court that represents the people in any area of Israel through history. The Mishnah interprets Num 11:16 as the first great Sanhedrin in a succession through history in order to justify a major leadership role for a body of men who are
not necessarily Levites.

Deut 17:8-13 mentions the need to judge legal cases of dispute, and those who do the judging are referred to as priests, Levites, and judges in verse 9.

The word elder is not used here, thus negating the Mishnaic supposition that a collective of 70 elders was to continuously constitute a greater Sanhedrin. If this Mishnaic interpretation were true, there would be some clear evidence of it in the Tanak, which is often occupied with political conflict.

On page 382 of Danby's translation in Sanhedrin 1.2, authority to render calendric decisions is claimed for a small committee within the Sanhedrin, and there is no tribal requirement for this committee. It appears that the Mishnah is attempting to invent an entity that controls the calendar apart from the priesthood. As stated above, this Mishnaic concept is contradicted by Ps 133.

Positive evidence that calendric unity was only to be achieved through the authority of the Aaronic priesthood does exist in Ps 133. In that psalm the unity of the brethren was to be achieved through the anointing oil upon Aaron's beard, which symbolizes the bestowing of authority upon that priesthood to bring about unity.

This authority would be contradicted by some body of non-priests who would attempt to direct priests concerning the appropriate time to blow the two silver trumpets and declare which month is the first.

I. History of Disruption and Restoration of the Levitical Priesthood

The Levitical priesthood performed specific functions associated with the sacrificial system, the calendar, teaching the people, and they were also prominent among the judges.

As seen in Jeremiah 52, when the House of Judah was fully conquered by the Babylonians, the wealthy people of Judah were taken into exile, Solomon's Temple was destroyed, and the high priest was put to death. The disruption in the priesthood was based upon the execution of the high priest and the exile of the wealthy class rather than the destruction of Solomon's Temple. From this time onward there is no historical record of the existence of the ark. The poor people who remained in the land may have included some Levites and priests. However, Ezra 2:2, 36 shows that when Zerubbabel returned to Jerusalem to rebuild the Temple, there were priests who returned with him. We have no history that preserves exactly how the priesthood functioned during the period of exile, yet the priesthood existed without an ark and without a Temple. When the Second Temple was destroyed in 70, the priests were still known and the priesthood could have continued as it had been during the Babylonian exile when there was neither ark nor Temple. Some inventiveness could have enabled the priesthood to perform their functions because during the Second Temple period, they found some means to function without an ark during the tenth day of the seventh month, the Day of Atonement. Political considerations prevented the continuation of the priesthood, yet this was a method of fulfilling the prophecy in Mal 2:3.

There was a serious complaint against the Levitical priesthood in Mal 2. The punishment to that priesthood for its continuing sin is discussed in Mal 2:3 where the eventual sentence is: “take you [= priests] away”. This language is similar to that of exile rather than a permanent abolition.

There is evidence from the Tanak that this priestly exile will be ended and the sacrificial system will be functioning again, even prior to the time of the Third Temple that is discussed in Ezek 40-48 where the Aaronic Priesthood is shown to function. This renewal of the functioning of the Aaronic priesthood is implied by the uses of the daily-sacrifice (Hebrew tamid, Strong's number 8548) in the prophesies of Daniel, especially Dan 11:31; 12:11, but also Dan 8:11, 12, 13. Through these prophesies of Daniel, the Tanak recognizes the legitimate functioning of this priesthood once again prior to the Messianic era of worldwide peace.

Thus the Aaronic Priesthood is now in a temporary exile, but not made void. During this time of exile there are no two priests to blow the two silver trumpets according to Num 10:10. No one outside the lineage of Aaron is qualified to do this. The best that could be done is to simulate the priesthood in the sense of determining what they would determine and then act accordingly. If someone would imagine differently, there is the challenge of proving who would have the authority to appoint two priests to perform this
function.

J. Authority of the Levitical Priesthood Recognized in the New Testament

The apostle Paul in the New Testament recognized the authority of the Levitical priesthood. In Acts 21:26 Paul entered the Temple and participated in a ritual that required the Levitical priesthood to perform certain duties, and thus Paul recognized the authority of this priesthood. In Acts 23:5 Paul also recognized the authority of the high priest. Heb 9:7 points out that when this was written, the high priest still functioned and entered the holy of holies once per year although there was no ark, showing that this was still a continuing practice of the Levitical priesthood. Thus this priesthood was not shown disrespect by the author of the letter to the Hebrews. Heb 10:11 shows the continuation of the functions of the Levitical priesthood while the Temple still stood. The next chapter continues this subject.

[16] Control of the Temple, and thus the Calendar, in the Early First Century

When studying the history of the calendar whose roots are embedded in the Tanak, one encounters writings from the New Testament, from Josephus and from Rabbinic literature. Then the reader is faced with the problem of determining whether all the statements one finds in these sources are historically true. There is a huge time gap from the fifth century BCE when Ezra and Nehemiah lived to the first century environment of the New Testament. Josephus was born in 37 CE, and while he wrote about events in the prior century, his sources from that time are not subject to independent checks for accuracy. Undoubtedly there were elderly folk who could give him personal recollections from the decades prior to his birth. Due to the difficulty in verifying information in Josephus from before the first century, our attention from his writings will be confined to the first century.

(A) Primary Sources of History in the early First Century

In analyzing who controlled the Temple before the war between the Romans and the Jews broke out in 66, the major primary sources are the New Testament and Josephus, and the question of whether the Rabbinic texts that begin with the Mishnah (c. 200 CE) are to be properly accepted as primary sources deserves some initial brief comment. From the destruction of the Temple in Jerusalem in 70 CE to the publication of the Mishnah c. 200 CE is 130 years. While the authors of the New Testament were personal witnesses of what they wrote (though Mark and Luke received their information from others who were personal witnesses) and Josephus was a personal witness beginning about the middle of the first century (he was born in 37 CE, but utilized other historians before him, especially Nicolaus of Damascus for events in the second century BCE), the Mishnah was not set into its written form by anyone who was a personal witnesses of events before 70 or who personally knew anyone who was such a personal witness. Except for some relatively few apparent borrowings from the Megillat Taanit (published c. 120), it is not known how the infrequent historical statements in the Mishnah and later Rabbinic texts from before the destruction of the Temple have found their way into those texts.

However, by comparing certain statements in these three sources with one another that relate to authority in Judea during the time sought, and by supplementing this with a few remarks from the Roman historians Tacitus and Trogus, we can make a reasoned evaluation on whether the use of the Mishnah and later Rabbinic texts are reliable as a historical source of events from before 70. In any case, the Mishnah falls short of being a primary source because it was not put into published form close to the time of the events we now seek (before 70 CE), and we have no record of any primary sources that it utilizes except for the Megillat Taanit, which is only a very condensed skeleton of some events, and which was completed c. 120.

Rabbinic texts may have used some primary sources for its historical statements, but this is evaluated in appendix B. In the present discussion our interest lies in which groups of Jews controlled the Temple services, especially during the first century before the war began in 66. The New Testament mentions the high priest, chief priests, Sadducees, Pharisees, and scribes. Josephus mentions these groups also, but adds the Essenes and the zealots. Since the latter two groups are never mentioned in the New Testament, they should be dismissed as candidates for having control of the Temple in the 70 years before its destruction.

(B) Branches of Modern Judaism relate to evidence on this Issue

Jewish scholars are biased in their writings and opinions, and it is important to address this in order to warn the reader concerning the literature on this subject. Scholars may be grouped based on their personal religious affinity, and this is sometimes reflected in their writing even though they may carefully avoid telling the audience their religious outlook.

Modern Judaism is divided into many groups, but these may be roughly categorized into four divisions based upon their attitude toward the Pentateuch and the Talmud. My summary is somewhat oversimplified and it pertains to the culture within the United States rather than modern Israel, but growing up as a Conservative Jew in New York City and having a grassroots feel from personal contacts, in my opinion it is not very far off base.

Certainly not all individuals within these groups conform to the characteristics to be described next, but these characterizations do approximately reflect the historical development of these divisions and the views of some major scholars from these groups. Jewish laymen sometimes tend to be more idealistic and less studied in the details of their religion, so that many of them are less likely to fit the broad description than the knowledgeable students and scholarly representatives. In discussing these divisions, the major emphasis will be on their attitude toward the law of Moses, and that is the reason for limiting the discussion to the Pentateuch within the Tanak. All of the divisions of Judaism consider the entire Tanak to be a sacred document of their religion.

The first division is Orthodox Judaism, which treats both the Pentateuch and the Talmud as inspired, and accepts the laws of the Pentateuch as they are interpreted in the Talmud.

The second division, Conservative Judaism, treats both the Pentateuch and the Talmud as sacred documents of their faith, but regards common views of archaeological interpretation as well as secular history and biblical textual criticism as valid sources for occasionally modifying their reliance on the Pentateuch and the Talmud as representing correct history. Adherents of Conservative Judaism tend to be less strict in their observance of the laws than Orthodox Jews, and their knowledge of the Talmud (excluding Conservative scholars) is typically significantly less than that of Orthodox Jews. Adherents of Conservative Judaism generally do not accept the legal interpretations of the Talmud to be authoritative in theory or in practice in their lives.

The third division, Reformed Judaism, treats the Pentateuch as a sacred document, but not the Talmud. Reformed Jews regard the laws of the Pentateuch to be interpreted figuratively or allegorically, and to be applied in a changeable way according to the times. From a literal standpoint Reformed Jews are the least observant of the laws of the Pentateuch. Reformed Jews do not regard the Pentateuch as depicting correct history.

The fourth division, Karaite Judaism, treats the Pentateuch as inspired, but the Talmud is not considered to be a sacred document. Karaites interpret the laws of the Pentateuch in a literal way, and they are strict in observing them. Karaism is the smallest of the four divisions in numbers of adherents, and their interpretation of the laws is not uniform amongst themselves. Orthodox Judaism and Karaite Judaism both represent Jewish fundamentalism, but the latter discard Talmudic interpretation.

It is to be expected that a scholar who was reared in Judaism will be biased toward the Talmud according to that rearing. Only Orthodox scholars will be heavily motivated to treat the Talmud as representing true history, although a minority of Conservative scholars will write in such as fashion that they will often appear to masquerade as Orthodox Jews. If one examines a book, a paper, or an article in an encyclopedia that was written by an Orthodox Jew, one can expect that author to use the Talmud heavily as accurate history. All Jewish scholars will downplay the New Testament. Within their writings, Jewish scholars very rarely label themselves according to their specific Jewish upbringing, but the reader who examines their works can usually decide whether or not each one appears to favor the Orthodox position. It is important to make some judgment about an author's position because bias plays a role when the reader is trying to determine which position represents correct history. It is possible to use certain criteria in order to judge whether it makes sense to treat the Talmud as if it was inspired, which is the accepted position of Orthodox Jews.

If two laymen are debating an issue and one of them uses an opinion by an implicit Orthodox Jewish scholar while the other uses a differing opinion by a Conservative Jewish scholar, the two laymen will not be able to agree because the sources that they each favor are in disagreement. That is the reason why it is so important to go back to the primary sources and discuss the place of the Talmud for historical purposes before the Temple was destroyed. After this is done and after the bias of a scholar is identified, one will know how to weigh that author's writings.

(C) The New Testament as a Primary Source

The writers of the New Testament were convicted to motivate its readers to seek eternal life according to the faith they had come to accept, but except for Paul who declared himself to be a Pharisee (Acts 23:6; 26:5; Phil 3:5), there is no clear evidence that they were personally biased for or against the Pharisees compared to the Sadducees in the subject of who controlled the Temple. Josephus devoted more personal attention to the politics of the groups and was involved in politics, so he should be expected to be far more biased than the writers of the New Testament. We will consider the matter of the bias of Josephus to some degree. From these considerations it should be clear that the most important primary source of historical information from before the Temple was destroyed in 70 CE is the New Testament, so this will be discussed first.

Obviously, favoring one primary source will produce conclusions that are biased toward that source. Any author who arrives at conclusions has no choice but to favor some source after giving reasons. Both Sadducees and Pharisees are condemned in the New Testament in the sense of having incorrect teachings (Mat 16:6, 11-12). Thus, according to the writers of the New Testament, one cannot look to either of these groups as having the original biblically correct understanding of some particular teaching of the Tanak merely because of the label Sadducee or Pharisee attached to the doctrinal opinion.

(D) Many of the Scribes were Sadducees. Mat 23:2 and Moses' Seat

Luke 20:27 [NKJV], “Then some of the Sadducees, who deny that there is a resurrection, came to [Him] and asked Him,
Luke 20:28, saying: ‘Teacher, Moses wrote to us [that] if a man's brother dies, having a wife, and he dies without children, his brother should take his wife and raise up offspring for his brother.’” [Speech continues through verse 33]
Luke 20:34 [Response to the Sadducees], “The sons of this age marry and are given in marriage.” [Speech continues through verse 38]
Luke 20:39, “Then some of the scribes answered and said, ‘Teacher, You have answered well.’
Luke 20:40, But after that they dared not question Him anymore.”

From verse 39 it is clear that scribes had been there all along, and from verses 27 and 40 it is clear that these scribes were Sadducees. In fact the Sadducees would not have asked Him this sensitive question if Pharisees had been present because that would have immediately sparked a heated debate between the two groups over their difference on this issue.

Acts 23:9 makes it clear that some scribes were Pharisees. Hence scribes included some Sadducees and some Pharisees.

On page 22 of Bar-Ilan we find the following paragraph: “Most of the scribes of the end of the Second Temple period whose genealogy is known were priests: Yosef (T. Shabbat 13:11), Yohanan (P. T. Maaser Sheni 5:4, 56c), Beit Kadros (T. Menahot 13:19), Josephus and others. It is clear that during the time of the Temple, priests, some of whom were scribes, used to manage the Temple property, contributions and gifts in addition to annual tithes (Neh 13:13; T. Shekalim 2:14-15; Josephus, War 6:387-91). The Temple as the official cultural-religious center was also the center of the knowledge of reading and writing, and because of that the priests in charge of the Temple were evidently responsible for the preservation of the Tora, its copying in general and the scribal profession in particular.” Thus in the view of Bar-Ilan, a historical expert in the realm of scribes and priests in the first century, we see the priests in charge of the Temple and the scribes heavily
represented by priests. Some writers have been unaware of the
representation of priests among the scribes and have given a distorted picture of Mat 23:2.

Acts 5:17 [NKJV], “Then the high priest rose up, and all those who [were] with him (which is the sect of the Sadducees), and they were filled with indignation.” This shows the chief priests to be included within the Sadducees at that time, although it is unclear how many Sadducees might be from outside the priesthood.

Thus, when we see Mat 23:2 [NASB], “The scribes and the Pharisees have seated themselves in the chair of Moses”, the scribes are mentioned first, and they have a major representation from among priests, which were seen to be closely equated with or within the Sadducees. Hence Matthew is not excluding the Sadducees from Moses’ seat, and the mention of Scribes (which includes Sadducees) comes first. There are three primary biblical functions of the Levitical priesthood. The first concerns the performance of the sacrificial system including personal counseling with those who bring sacrifices for personal reasons (such as to atone for their sins) and rituals at the sacred altar for the holy days, the Sabbaths, the new moons, and the daily sacrifices. The second concerns teaching the law to the people, which is shown in Mal 2:7 and Heb 7:11. The third concerns the prominent role of the priests and Levites throughout the court system of Israel according to the law of Moses (Deut 17:9; 19:17; 21:5). Thus the priests were to officiate at the holy altar, teach the people, and judge legal cases.

Let us consider the meaning of “Moses' chair or seat” from Mat 23:2. Moses did have the supreme role in the first primitive court of one judge in Israel. In Ex 18:13-26 we see the role of Moses as the civil judge rather than in the role of communicating the law to the people. Ex 18:13 has the expression “Moses sat to judge the people”. This sitting implies a chair or seat of office for judging. The Hebrew word shaar, Strong's number 8179, is normally translated gate, but it sometimes means “court”. Deut 16:18 [NKJV], “You shall appoint judges and officers in all your gates [courts]...”

Amos 5:15 [NKJV], “Hate evil, love good; establish justice in the gate [court]”. On page 1045 of BDB the second meaning of this word is “space inside gate, as public meeting-place, market”, and within this category, BDB later adds “where elders, judges, king, sat officially”. Examples of sitting in the gate (meaning court) include Gen 19:1; Ruth 4:1-2; II Sam 19:8; I Ki 22:10; II Chr 18:9; Est 2:19, 21; Job 29:7; Prov 31:23; Jer 38:7. The advice of Moses' father-in-law in Ex 18:13-26 was a pyramid structure of judges, but in Num 11:16-17, 24-25 this pyramid structure was replaced by a flat structure (equal authority) of 70 men from among the elders of the people.

See the prior chapter titled, “Authority of the Levitical Priesthood from the Tanak” for more detail on this. At the end of the 40 years in the wilderness, more details about the future court system were revealed in Deuteronomy, where Deut 17:9; 19:17; 21:5 show the prominent role of the priests and Levites throughout the court system of Israel according to the law of Moses.

From biblical examples, Moses' chair or seat sensibly means the official seat from which civil case judgment comes, a judicial function, not a legislative function. This is neither the changing of existing laws, nor the legislation of new laws, but the application of existing laws to specific cases in dispute between relevant parties who seek to bring their case to a civil court. Priests would not consider their procedures to be under the jurisdiction of a civil court. Civil justice of disputes does not include the methods and rules whereby the priests carried out their functions, which were not civil disputes in nature. This reasoning only considers the context of the Tanak applied to Mat 23:2, so the question remains as to whether, in the first century, an expanded jurisdiction existed for the main Sanhedrin in Jerusalem, in which it is assumed that Moses' seat was exercised. In a religious society certain aspects of civil laws must be derived from the law of Moses as it was understood in their day, but the question remains concerning whether the central Sanhedrin had a legislative function at all. The Sanhedrin will have to be discussed in more detail.

(E) Sanhedrin in the New Testament

The Greek word sunedrion for sanhedrin, Strong's number 4892, occurs 22 times in the New Testament. These are Mat 5:22; 10:17; 26:59; Mark 13:9; 14:55; 15:1; Lk 22:66; John 11:47; Acts 4:15; 5:21, 27, 34, 41; 6:12, 15; 22:30; 23:1, 6, 15, 20, 28; 24:20. In three of these places (Mat 5:22; 10:17; Mark 13:9) a local court is the meaning, but in all other 19 cases this is the Sanhedrin in Jerusalem associated with the Temple. In 17 of these 19 cases the Greek definite article is used, which implies that there is only one Sanhedrin associated with the Temple. The two exceptions without the definite article are Mark 15:1 and John 11:47. The context of all 22 places is consistent in showing a civil court where accusation against a party is made, witnesses for or against that party are questioned, the accused party is questioned, and a judgment for or against that party is rendered. Except for Acts 23 where the outsider Paul introduced the doctrinal issue of the resurrection from the dead in order to cause strife and detract attention from his own case, in none of the meetings of the Sanhedrin associated with the Temple do we encounter a debate over the application of the law of Moses or the meaning of the Scripture. In the only examples available, the Sanhedrin appears to be a civil court in which civil cases are relevant, not an environment for the debate over biblical doctrine. The Sadducees and Pharisees appear to try to get along with one another peaceably within the Sanhedrin, except for the case in which Paul caused a stir over doctrine. The conclusion from the New Testament is that the Sanhedrin in Jerusalem associated with the Temple acted as the supreme court to hear cases, but did not engage in legislating new additions to the law of Moses.

(F) The Parable of the Wicked Vinedressers

Luke spent considerable time with Paul (a former Pharisee) - see Col 4:14; II Tim 4:11 and the “we” portions of Acts that includes the presence of Luke as the author - Acts 16:10-17; 20:5 - 21:13; 27:1 - 28:16. Luke partially relied on Paul for some of the relations between the leaders of the Jews when he wrote. Paul, having been a Pharisee and having lived in Jerusalem, would have been an excellent first hand source of extra background information for Luke's writings.

Luke 20:9 [NKJV], “Then He began to tell the people this parable: A certain man planted a vineyard, leased it to vinedressers, and went into a far country for a long time.”
Luke 20:10, “... the vinedressers beat him ...”
Luke 20:11, “... they [the vinedressers] beat him also ...”
Luke 20:12, “... they [the vinedressers] wounded him also ...”
Luke 20:13, “... I will send My beloved son ...”
Luke 20:14, “... vinedressers ... reasoned among themselves ... let us kill him.”
Luke 20:15, “... they [the vinedressers] ... killed [him]. Therefore what will the owner of the vineyard do to them?”
Luke 20:16, “He will come and destroy those vinedressers and give the vineyard to others. And when they heard [it] they said. Certainly not!”
Luke 20:17, “Then He looked at them and said, What then is this that is written: The stone which the builders rejected Has become the chief cornerstone!”
Luke 20:18, “Whoever falls on that stone will be broken; but on whomever it falls, it will grind to powder.”
Luke 20:19, “And the chief priests and the scribes that very hour sought to lay hands on Him, but they feared the people - for they knew He had spoken this parable against them.”

The parallel passage in Mark starts in Mark 11:27 where it mentions, “the chief priests, the scribes, and the elders came to Him”. The continuous flow of the narrative goes down to Mark 12:12, “And they [chief priests, scribes, and elders] sought to lay hands on Him, but they feared the multitude, for they knew He had spoken the parable against them.” The parallel passage in Matthew begins in Mat 21:33 and ends in Mat 21:45-46, “Now when the chief priests and Pharisees heard His parables, they perceived that He was speaking of them, but when they sought to lay hands on Him, they feared the multitudes, because they took Him for a prophet.”

In this parable the phrase, “the stone which the builders rejected” is mentioned in Mat 21:42; Mark 12:10; Luke 20:17 directly before the conclusion which shows that the leaders of Israel correctly perceived He was talking about them as the builders who rejected Him (the stone), and also about them as the vinedressers who killed Him (the son). Israel is the vineyard.

In the midst of the conclusion to this parable, when He says, in Mat 21:43, “the kingdom will be taken from you”, it is clear that He is agreeing with their interpretation that they are the leaders and that the kingdom refers to Israel and especially its government.

Luke says, “chief priests and scribes”. Mark says, “chief priests, scribes, and elders”. Matthew says, “chief priests and Pharisees”. Despite these differences, all three mention chief priests first.

These leaders understood that they themselves were the vinedressers in the parable, and the vineyard was Israel. Thus the parable teaches that at the general time of the crucifixion, the leading position among Jews in Judea was in the hands of the chief priests, which were Sadducees, but the Pharisees also had some
leadership. This is the clearest statement of which group held the leading position from the standpoint of the seat of semi-autonomous government permitted by the Jews under the Roman Empire.

(G) How the High Priest Spoke to the Audience that included the Pharisees

John 11:47 [NKJV], “Then the chief priests and the Pharisees gathered a council and said, What shall we do? For this Man works many signs.”
John 11:48, “If we let Him alone like this, everyone will believe in Him, and the Romans will come and take away both our place and nation.”
John 11:49, “And one of them, Caiaphas, being high priest that year, said to them, You know nothing at all, ...”

For the high priest to say to his audience that included the Pharisees, “you know nothing at all”, it seems obvious that he had no fear of the Pharisees and there could hardly be any substance to the idea that the Pharisees had so much authority over the Temple that they could push him around as they might choose.

(H) Pilate's Understanding of the Chief Priests’ Authority

Mark 15:10 [NKJV], “For he [Pilate] knew that the chief priests had handed Him over because of envy.”

If the chief priests did not have primary authority, but instead the Pharisees controlled the Temple area, the chief priests would have had less reason to be envious of the authority exercised by the Nazarene through the miracles.

Instead the Pharisees would have played a more prominent role during the trial due to their authority, and the Pharisees would have shown envy. Note that Mark 15:10 does not say, “The Pharisees had handed Him over”, but instead, “the chief priests had handed Him over”. The last two times in Matthew that the Pharisees are mentioned are Mat 23:39; 27:62, but the trial occurred between these places. The last time that the Pharisees are mentioned in the other three Gospels are Mk 12:13; Lk 19:39; John 18:3, but these are all before the trial began. Thus the Pharisees by name seem totally absent from the trial.

(I) The Role of Gamaliel

Acts 5:34 [NKJV], “Then one in the council [= Sanhedrin] stood up, a Pharisee named Gamaliel ...”

If Gamaliel was the presiding officer of the Sanhedrin this would not merely say “one in the Sanhedrin”. The language of the New Testament shows that Gamaliel was not the head of the Sanhedrin. Appendix A refers to the Babyonian Talmud concerning the title nasi and Gamaliel along with others in his lineage.

(J) Legal Authority of the Chief Priests

Paul lets his audience know of his background as a Pharisee in Acts 23:6; 26:5; Phil 3:5, and as a former student of the Pharisee Gamaliel in Acts 22:3.

If Paul had a choice in seeking credentials for authority, he would naturally seek it from among the Pharisees rather than the high priest or the chief priests who were of the Sadducees. Here is what we find when we see where Paul went for authority. Acts 9:1-2 [NKJV], “Then Saul … went to the high priest and asked letters from him to the synagogues of Damascus so that if he found any who were of the Way, whether men or women, he might bring them bound to Jerusalem.” Acts 9:14, “Ananias said, And here he [Paul] has authority from the chief priests to bind all who call upon Your name.”

Acts 26:10, “This I [Paul] also did in Jerusalem, and many of the saints I shut up in prison, having received authority from the chief priests; and when they were put to death, I cast my vote against them.” In Acts 26:12, “While thus occupied, as I journeyed to Damascus with authority and commission from the chief priests...”

We see that Paul does not go to any supposed Pharisaic leader for legal authority, but rather to the chief priests. Paul's personal identification with the Pharisees would have caused him to go to the Pharisees for authority if they could give it.

Acts 22:30 [NKJV], “The next day, because he [the Roman commander] wanted to know for certain why he [Paul] was accused by the Jews, he released him from his bonds, and commanded the chief priests and all their council [= Sanhedrin] to appear, and brought Paul down and set him before them.” Here the Roman commander shows that he understands “their Sanhedrin” to be that of the chief priests despite the fact that in Acts 23:6 Paul perceives that both Sadducees and Pharisees were present.

Thus the chief priests were dominant. The Pharisees did have sufficient clout in the local synagogues that they could excommunicate Jews from the life of the synagogue provided there was reasonable cause (John 9:13, 21-22, 34; 12:42). However, the synagogue environment is not the Temple where the chief priests (Sadducees) were dominant.

(K) Conclusion from the New Testament

The evidence from the New Testament has been given, and the Sadducees including the high priest and chief priests are clearly dominant concerning the overall political control of civil government from the semi-autonomous viewpoint that the Romans permitted. Qualification to the Levitical priesthood was a matter of heredity, not learning, and not popular support.

Since only the priesthood was permitted to carry out the Temple services commanded in Scripture, and the priesthood was associated with the Sadducees, we would conclude that the Sadducees dominated the control of the Temple services. But there is still a need to discuss Josephus and the Rabbinic texts.

(M) The Roman Historian Pompeius Trogus

The third generation Roman citizen Pompeius Trogus wrote a history in Latin c. 20. (see pages 2-3 of Yardley and Develin). At some time within the next 200 years a person named Justin wrote excerpts from Trogus’ history, and these excerpts survive in Latin (pages 2-6). The well known early church father Augustine (c. 400) wrote that Justin wrote a brief history following Trogus (page 6).

On page 230 we find this translation of 2:16, “After Moses his son, Arruas, was made priest in charge of the Egyptian objects of worship, and soon afterwards king. And ever after that it was the practice amongst the Jews for their kings to be their priests as well. This integration of their judicial and religious systems made the Jews unbelievably powerful.” The following comment on this statement appears on page 241 of Stern, “Pompeius Trogus anachronistically depicts all Jewish history according to the conditions that prevailed during the Hasmonaean [Maccabeean] monarchy, when the king and the high priest were the same person; …” This excerpt from Trogus, who wrote in the early first century, shows that he understood the Levitical priests to exercise the judicial function. This independent primary witness agrees with Tacitus and the New Testament in attributing primacy of Jewish authority to the priests.

[17] Appointed-times and Years are known from Lights in the Sky

Gen 1:14-15 will now be examined 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 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, here is a literal translation of 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 “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.

[17] Appointed-times and Years are known from Lights in the Sky

Gen 1:14-15 will now be examined 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 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, here is a literal translation of 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 “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.

[18] A Month is a Cycle of the Moon

No discussion has yet been given concerning the meaning of appointedtimes in Gen 1:14.

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.

[19] 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 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.

[20] 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 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.”

[21] 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 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.

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 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, a literal reading of 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 are great historical monuments, namely the pyramids, that bear witness to the unchanging orbit of the earth around the sun.

Pages 333, 336-337 of Lockyer show that most of the Egyptian pyramids are oriented east-west, and the two largest pyramids at Giza 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 falls exactly east-west only on the days of the vernal equinox and the autumnal equinox. This witness of the great pyramids at Giza indicates that at the time of their construction, the orbit and axis of the earth with respect to the sun was the same as today because at the equinoxes the east-west shadow of one wall of these pyramids is perfectly aligned in the east-west direction. One would imagine that if the earth’s orbit had changed due to the miracle associated with “Joshua’s long day”, then the alignment of these pyramids would have changed, so that one wall would no longer be aligned exactly in the east-west direction. Although Egyptian chronology remains a matter of controversy, so that it is not possible to date these pyramids with certainty, all estimates are that they were built long before the time of Moses. I would conclude that the earth’s orbit did not change during the miracle of “Joshua’s long day”.

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.

[22] 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:”
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 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.

[23] 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.

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.

[24] 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.

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 “monthstart” 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 with Ps 133 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 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.

[25] Isaiah 47:13, Astrologers, the Zodiac, and the meaning of chodesh

Isa 47:13 is a most interesting verse of Scripture because it teaches much about the Hebrew word chodesh and it condemns the Babylonian astrologers, as will be shown in this chapter. I will soon provide a literal translation of Isa 47:13, and one goal of this chapter is to explain why this translation is appropriate and accurate. Several of the Hebrew words with their Strong’s number are included after the corresponding English word(s) in the literal translation because they are discussed in this chapter.

First, some remarks should be made concerning the context. Isa 1:1 mentions that Isaiah’s recorded visions were during the reigns of the Judean kings Uzziah, Jotham, Ahaz, and Hezekiah. This approximates the period of Isaiah’s visions as from c. 760 to c. 700 BCE. The Neo-Assyrian period is from c. 1000 to 612 BCE, at the end of which Babylon captured the Assyrian capital of Nineveh (see page xxiv of Rochberg 2004). Hence Isaiah lived during the time of dominance by the Assyrian Empire. Isa 8:4; 10:5-6 is a prophecy that Assyria will soon conquer some of its neighbors. Isa 30:31-33 is a prophecy that Assyria will be defeated. Babylon was south of Assyria, and the Babylonian Empire eventually occupied more than the extent of the Assyrian Empire. Isa 39:5-7 is a prophecy that the House of Judah will be defeated by Babylon. This implies that Babylon would first defeat Assyria, which fully transpired in 612 BCE. During Isaiah’s lifetime, although the Assyrian Empire was politically dominant, the Babylonian Empire also existed to its south. Isa 47:1, 11 is a prophecy that eventually Babylon would be defeated, and Isa 47:13 is a taunt directed at Babylon. The “you” at the start of verse 13 is Babylon.

On page 8 of Rochberg 2004, she wrote, “The nightly watch of the sky seems to have been standard Babylonian practice since the reign of King Nabonassar (747-734 B.C.).” Recall the above remark that Isaiah’s visions were from c. 760 to c. 700 BCE. On page 2 of Swerdlow 1998, he wrote, “Prognosticate by the new moon they [the Babylonian astrologers] did, and by the full moon, and by the appearance of the moon, and by eclipses of the sun and moon, and by the risings and settings and conjunctions of stars and planets, and by halos and clouds and rain and winds, in short, by anything in the heavens, astronomical or meteorological, that could be taken as ominous, a prophetic sign given by the gods.” When Swerdlow began with the words “prognosticate by”, he meant that based upon the conditions that prevail during the time of the events mentioned, they would make predictions about the future with the intent that they would come to pass. With this historical context in mind, here is my literal translation of Isa 47:13.

Isa 47:13, “You [Babylon] are wearied with your many consultations. Now let [the] astrologers [1895 havar] of [the] heavens [8064 shamayim] stand up and save you, those who look-intensely [2372 chozeh] at [the] stars, those who-make-known [3045 yada] at [the] new-moons [2320 chodesh], what will happen to you.”

The Jewish biblical scholar Ibn Ezra (1089 – 1164) wrote a commentary on the book of Isaiah, in which he wrote that the two Hebrew words together, hovrev shamayim [1895, 8064], mean “astrologers” (see page 216 of Ibn Ezra). This viewpoint made its way into the KJV, so that the KJV does not show the word “heavens”, which is the literal meaning of shamayim.

The Hebrew word havar [1895] only occurs in this one place in the Tanak. From this Hebrew context alone, without any outside knowledge, there is insufficient information to determine the meaning of havar [1895]. Jerome was taught Hebrew by Jewish scholars, and he translated this from Hebrew into Latin c. 390. After his death the Roman Catholic Church accepted Jerome’s translation from Hebrew to Latin (except for the Psalms) as the Vulgate, its official text of the Old Testament, which the Jews call the Tanak in Hebrew. In the bibliography, on page 180 of the Vulgate Isaiah at Isa 47:13, we see the Latin words augures caeli, which means “seers of the heaven”. In Brenton for the Septuagint at Isa 47:13, the text shows the Greek astrologoi tou ouranou, which is translated “astrologers of the heaven”.

Generally, it is recognized that Jerome’s knowledge of Hebrew was significantly better than the Septuagint translation into Greek from the Hebrew, although the Septuagint presents its own special problems because the Hebrew text from which the Septuagint was translated (this text is labeled the Vorlage) no longer exists. If we assume that the Vorlage was very close to the Septuagint that has survived, then there are many deletions and additions between the Vorlage and the Masoretic Text of the Tanak. The conclusions are that the Vorlage does not exist, and the Septuagint is not generally reliable for the purpose of determining the proper translation of the Hebrew Masoretic Text into English. With appropriate careful reasoning, there are some situations where the Septuagint can help resolve some apparently ambiguous meanings of some Hebrew words. Nevertheless, Jerome and the Septuagint agree in this instance, and these are the earliest known sources that provide a meaning of the Hebrew havar [1895].

Page 211 of BDB discusses havar [1895], and the word “astrologers” never appears in this entry, although a partially related idea is presented. BDB gives the meaning of havar to “divide” as a verb, but concerning this meaning BDB comments “so most [commentators], but dub. [= dubious, doubtful]”. BDB quotes one source that proposes the translation “they that divide the heavens”, but BDB gives no alternative. The fuller explanation given by BDB is “the distinguishing of signs of the zodiac, or other astrological division of the sky”. The RSV gives the translation “those who divide the heavens”, thus agreeing with this approach to the translation.

BDB explains that the origin of the conjectural meaning “divide” is the similar sounding word in the Arabic language, habara, which means to “cut into large pieces, cut up”.

My translation from German to English from page 184 of the short article by Josua Blau has this to say about the use of the Arabic word habara as the explanation of the Hebrew havar 1895]: “However, the Arabic habara is based upon the explanation ‘cut’; indeed the subject of habra appears to be a ‘piece of meat’ and its meaning is ‘meat in (large) cut pieces’; thus one can surely not accept this explanation of [the Hebrew] havar.” Here Blau is emphasizing the need to have a similar context in order to reliably claim that a word from one Semitic language is a cognate to a word from another Semitic language. The context is different, so he fully rejects the explanation “to cut”. Thus Blau rejects the basis behind the RSV translation “those who divide the heavens”.

The theory of using this Arabic word as a suggested cognate to the Hebrew word havar [1895] does, at least momentarily, appear to be supported by the idea of the zodiac in the explanation of BDB. In order to determine whether the zodiac lends support to using this Arabic cognate theory (to divide the heavens), it is necessary to understand the origin of the zodiac and its meaning. This needs to be compared to the time at which Isaiah prophesied (c. 760 – c. 700 BCE).

On page 31 of the book by Koch-Westenholz the term zodiac is defined. Her definition uses the word ecliptic, which is the apparent path of the sun in the sky during a complete year as observed from the earth. Constellations (recognized star groups) appear in the sky at or close to the ecliptic. Her definition of the zodiac is: “The ecliptic is divided into twelve equal parts, [called] the signs of the zodiac. The zodiacal signs are a mathematical construction and do no longer correspond to the portion of the sky occupied by the zodiacal constellations whose name they bear. The zodiacal signs are: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces.” These signs are used in horoscopes.

Concerning the origin of the zodiac, which refers to the division of the year into 12 equal parts, each originally containing one designated constellation, but no longer tied to the current location of that constellation, here is a comment by John Britton, a specialist in ancient mathematical astronomy, especially Babylonian astronomy. On page 244 Britton 1999 wrote, “Obviously the [Babylonian System A] theory [of lunar anomaly] was invented earlier, but it [this mathematical theory of astronomy] seems unlikely to have materially predated the zodiac, which seems to have appeared between -463 and -453. On balance, if we assign its [this theory of lunar anomaly's] invention to -440 +/- 15 years, we should not be too far off.”

Here Britton estimates the origin of the zodiac as 12 equally divided signs of the year between 464 and 454 BCE. On page x of Rochberg 1998, we note the following concerning the origin of horoscopes: “The appearance of horoscopes in Babylonia at the end of the fifth century B.C. [= c. 400 BCE] marks the point when the situation of the heavens at the time of a [person’s] birth came to be regarded as significant for the future of an individual.” On pages 20 and 25 Rochberg gives the year 410 BCE as the earliest known text of a horoscope. Horoscopes are based on the zodiac. Hence we see that the zodiac or horoscopes cannot be associated with any statement of Isaiah, showing a difference of 250 years. Thus the comment by BDB is out of place in its alleged association of dividing the heavens with the Hebrew word havar [1895]. Of course BDB was written before the date of the origin of the zodiac became known by historians of ancient astronomy. Thus BDB is out of date in this area. The origin of both the zodiac and horoscopes is ancient Babylon.

In an email sent by professor Lester Ness to the group HASTRO-L on June 17, 2004 he translated from the French on page 53 of the book by Auguste Bouche-Leclercq as follows, “However, it has been proven beyond doubt that the Egyptian zodiacs are all from the Roman period and freely imitate the Greek zodiac. At one blow, all the extravagant suppositions based upon their [the Egyptian’s] supposed antiquity are destroyed.” This was written to combat the erroneous claims that the zodiac originated in ancient Egypt. The Greeks copied the zodiac from the Babylonians and added some of their own ideas.

Edward Ullendorff suggested another meaning of the Hebrew word havar [1895] on pages 339-340 of his paper. He favored the two Hebrew words together, hovrev shamayim [1895, 8064], to mean “worshippers of the heavens”. He claimed that the Ugaritic word thbr (to worship) is cognate to the Hebrew word havar.

However, the Ugaritic context has nothing to do with signs or bodies in the heavens, so that there is no contextual link between the Ugaritic word and the Hebrew word. Besides, the writers who discuss ancient Babylonian astrology do not suggest that these astrologers worshipped the heavenly bodies. They made prognostications based upon what might be seen that was associated with the phenomena in the heavens. Deut 4:19, which emphasizes worship, is not specifically associated with ancient Babylon. The evidence of the greater historical context of Isaiah as well as the context within Isa 47:13 along with the translation of word havar [1895] in the Greek Septuagint, in the Latin Vulgate from the Hebrew by Jerome, and by Abraham Ibn Ezra all agree that its meaning should be the plural noun astrologers, yet the literal grammatical form of havar is that of a verb in the plural form. There is no good case for a different meaning based upon the context.

Without the contextual evidence from historical astronomy and astrology that became available c. 2000, this might still be debatable. Today's knowledge of ancient Babylonian history make it clear that havar should mean “astrologers”.

On page 302 of BDB Isa 47:13 is specifically written under meaning 1c for the Hebrew word chozeh [2372], and this verse has this verb in its plural form immediately preceding “at [the] stars”. BDB states of this context “as stargazers, in astrology”. Below the middle of column 1 on page 395 of BDB, Isa 47:13 is specifically written under the Hebrew word yada [3045], and it occurs in a plural verb form. Here BDB translates from yada to the end of the verse as follows, “who declare, at the new moons, of (the things) which are to come”. Here BDB translates yada “who declare”, but the context indicates that their declarations are predictions or prognostications. In painstakingly crawling through Isa 47:13, at last we arrive at the primary Hebrew word that provides the reason for exploring this verse in its context in detail. That is the Hebrew word chodesh [2320]. Here it occurs in the plural, and it is preceded by the single letter lamed, which is a preposition that is pronounced “l”. Pronounced together it is leh-chadasheem.

The question arises concerning whether leh-chadasheem means “every month (i. e., monthly)” or “at the new moons” in Isa 47:13. Consider the following factors.

(1) This plural form of chodesh with this preposition lamed occurs in five other places in the Tanak. These are I Chr 23:31; II Chr 2:4; 8:13; 31:3; Ezra 3:5. This preposition is flexible and its meaning depends on the context. It often means at, for, or on”. In all six cases (Isa 47:13 being the sixth case) it may be consistently translated “at [the] new-moons”. In the five examples outside Isaiah the context prevents it from meaning “every month”.

(2) The translation “every month” is usually given in Num 28:14; I Chr 27:1; Est 3:7 where chodesh in the singular occurs twice in all three verses, and the preposition lamed is absent before these three double cases. The end of Num 28:14 literally means “month on month for [the] months of the year”. In the Hebrew it is “chodesh [singular] b-chadshoh [preposition bet and singular] l-chadshay [preposition lamed and plural] ha-shanah”. Here the plural form of chodesh is different from the plural form in Isa 47:13, though both have the preposition lamed. These three consistent examples show that the expression that is literally “month on month” (no lamed and no plural) means “every month”; thus there is no need for another expression to mean every month.

(3) In theoretical Hebrew grammar it would be a possibility for lehchadasheem in Isa 47:13 to mean “every month”, but there is no biblical context in which this is an example that is implied by the context. As already stated above, on page 395 of BDB, Isa 47:13 is quoted to end as follows: “who declare, at the new moons, of (the things) which are to come”. Yet BDB contradicts itself on this, because on page 516, column 1, 9 lines from the bottom of the page, BDB states “every month” for leh-chadasheem in Isa 47:13. The Hebrew preposition lamed is very flexible, having a wide variety of meanings, so this is given as a grammatical possibility. Nevertheless, no known context implies that this was a method that was in fact used in the ancient Hebrew language to mean “every month”.

(4) Near the beginning of this chapter quotations from Rochberg and from Swerdlow were given to show that during the era of Isaiah, on each night the Babylonian astrologers examined the sky for anything unusual, and then such unusual events were used as the basis for prognostications. It would be needlessly redundant for the end of Isa 47:13 to mean “monthly” when in fact the examination of the heavens was a nightly matter. However, prognostications were made for every new moon even if it was a very typical new moon. More emphasis was placed on the new moons because that was of central importance to the Babylonian calendar since it began each month. Translations of reports to the Assyrian kings by those who supervised the nightly watchers of the skies that includes the time of the later life of Isaiah may be found in the book by Hermann Hunger 1992. The prior quotation by Swerdlow is almost a summary of Hunger’s book. The above considerations provide good reasons to reject the proposal found in some translations that leh-chadasheem in Isa 47:13 means “every month”.

Thus the following is an accurate literal translation. Isa 47:13, “You [Babylon] are wearied with your many consultations. Now let [the] astrologers [1895 havar] of [the] heavens [8064 shamayim] stand up and save you, those who look-intensely [2372 chozeh] at [the] stars, those-who-make-known [3045 yada] at [the] new-moons [2320 chodesh], what will happen to you.”

The NRSV reaches an accurate literal sense of the whole verse. Isa 47:13 [NRSV], “You are wearied with your many consultations; let those who study the heavens stand up and save you, those who gaze at the stars and at each new moon predict what shall befall you.”

Isa 47:13 shows that the Babylonian practice of predicting the future of nations and the future of kings by what is seen in the heavens is sinful. An example of the type of prognostication that was made by Babylonian priests is found on page 140 of Hunger 1992, catalogued as RMA 30, “If at the moon’s appearance its right horn becomes long, its left horn short: the king will conquer a land not his own.” On the same page RMA 37 has, “If at the moon’s appearance in intercalary Adar ([13th month] XII/2) its horns are pointed and (the moon) is red: the ruler will become strong and subdue the land.” More normal appearances also provided predictions. Babylon had a pagan priesthood, which did not use two silver trumpets to announce the start of a month. The Babylonian priesthood spread into Assyria so that the border between Babylon and Assyria was somewhat artificial to their priesthood. Before Babylon conquered Assyria’s capital city, Nineveh, in 612 BCE, this priesthood performed their nightly observations of the heavens and made their first forays at mathematical astronomy. The kings of Assyria recognized the supposed powers of this priesthood and received letters from this priesthood. One letter that is labeled number 303 (also labeled Harper 894) on page 208 in the book by Pfeiffer, was sent from an authoritative priest to the king of Assyria that contains the following: “On the 30th I saw the moon, it was in a high position for the 30th day; presently it will be as high as it stands on the 2nd day. If agreeable to the king my lord, let the king wait (for a report) from the city of Ashshur. The king my lord may then determine (for us) the (first) day (of the month).” The context of this letter mentions the phrase “saw the moon” as a contrast to not seeing the moon, so that this must refer to the first sighting of the crescent by the observer. Since this mentions that the moon was seen about as high in the sky as for a second day old moon, the author suggests that the king wait for a report from another location where perhaps the moon might have been seen one day earlier. The sighting was near the end of the 30th day of the month.

Here is a similar example from page 75 of Hunger 1992, where the completion of a damaged word in square brackets is by Hunger. It is catalogued as RMA 76: “We watched on the 29th day; the clouds were den[se], we did not see the moon. We watched on the 30th day; we saw the moon, but it was (already) very high. The (weather) of the 29th day has to do with it. What is it that the king my lord says?” Here the author suggests that if the weather had been clear one day earlier, it would likely have been seen. He wants the king to decide which of the two days should start the month. In both examples the Assyrian king was to officially declare the first day of the month on the basis of the information provided.

These examples and others like them make it clear that the sighting of the new crescent began the first day of the month in Assyria and Babylon. Because Babylonian prognostications were made for every Babylonian new moon regardless of whether anything unusual was seen at that evening, Isa 47:13 shows that the Hebrew word chodesh, new-moon, is also applicable to the Babylonian new moon!!! This shows that the fundamental concept that underlies the Israelite new-moon and the Babylonian new moon are the same. Since the Babylonian new moon day began with the sighting of the new crescent, provided that there was subsequent official recognition of this sighting, but without allowing a month to have more than 30 days, the same concept should apply to the biblical new-moon. Isa 47:13 is not the only evidence to be presented for this conclusion.

[26] The Biblical New Moon relates to the Sighting of the New Crescent

Without using Isa 47:13, we have seen that a month is a cycle of the moon, and the full moon typically occurs about 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 discernible candidates for the biblical new moon that are available from this information are the old crescent and the new crescent. Isa 47:13 points to the new crescent. Gen 1:14 puts emphasis on the “lights”, that is, what can be seen.

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 a previous chapter it was mentioned that the 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. 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, which is the time that the Sabbath begins and 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 same concept as the Babylonian calendar.

This evidence from Ezra 6:15 and Neh 6:15 is also in harmony with the conclusion from Isa 47:13, yet the reasoning from the books of Ezra and Nehemiah is independent of Isa 37:13. 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.

[27] 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 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.

[28] Did the Jews use Calculation for their Calendar in the First Century?

On page 302 of Neusner's translation of the Mishnah the section Rosh Hashannah 2:8 appears, which is 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.”
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.
(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 to have occurred 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.

[29] The Biblical Year is a Whole number of Biblical Months, 12 or 13

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 Tanak dealing with calendric 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 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.

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, Parker 1955, and Porten 1996). 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 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.

[30] 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]”.

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] newmoon, 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”.

In these verses the word “tomorrow” is translated from the Hebrew word machar, Strong's number 4279. This word refers to the next daytime, which begins in the morning rather than sundown.

According to the choice of Hebrew words in these verses, the beginning of the festivity relating to the new moon is in the morning rather than at sundown. In these verses there is no reference to the standard Hebrew word for day, which is yohm, Strong’s number 3117. The use of the Hebrew word for new moon in these verses is not referring to a 24-hour day, but instead it refers to the time of festivity.

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 hat 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 Tanak. 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 Tanak 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 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 newmoon 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.”

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.

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] newmoon [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 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. 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.