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A Statistical Solution to the Star of Bethlehem Problem
by David A. Pardo

Note P.G.: See my own views on the same subject: "The Star of Bethlehem: A Scenario organized by Essenian Astrologers", (abstract in English, complete translation soon available) and the discussions at Hastro (History of Astronomy Discussion Group, specially March 1997 & January 2001, David Pardo (Seattle) can be contacted at

      The purpose of this paper is to suggest a possible solution in arriving at the as yet unknown date of birth of Christ. Christ, it will be argued, was born between February 19 and March 20, 7 BC with a higher probability for the event in the latter part of the interval. The paper will provide a consistent answer to (1) the appearance date of the "star" which will be argued was the triple Jupiter-Saturn conjunction in 7 BC (2) how the Christ child was located and (3) the date of the "tax" recorded in Luke 2:4-6.

     Research has narrowed down the likely time periods for the nativity to three-3 to 1 BC, 6 BC, and 7 BC. Moreover, the celebration of Christmas on December 25 has been dismissed as a Mithraic holiday borrowed by the Christian Church. The 3 to 1 BC interval contains several important astrological events. The problem is that Josephus, the Roman historian, explicitly implies that Herod died in 4 BC. A later date is further discounted by the numismatic evidence. As a well known counter argument, it has been calculated that from Josephus' description there was not enough time to bury Herod. There is a simple explanation, however. The Jewish people wanted to dispose of the body and memory of this king as soon as possible because of what he did. The 3 to 1 BC argument, like a 4 BC argument, is factually weak. The 6 BC dating also contains an important astrological event, the massing of planets in the sign of Aries, not Pisces. The problem here is that we know with accuracy and reliability from archaeology that a universal census/tax or lustrum for Roman citizens at least was implemented by Caesar Augustus in 8 BC, although preparations and possibly the census had begun in the preceding year. There is no known universal tax for 6 BC. [1]  This immediately rules out the 6 and 5 BC dating, since the tax became due in 7 BC latest. We are left with the 7 BC argument.

The 7 BC Date

     In order to show that the 7 BC date has the greatest statistical explanatory power, we must look to interpreting the relevant passages in the gospel of St. Matthew and the gospel of St. Luke. The argument presented here will consist of two parts: a mathematical theory and an administrative theory. The argument is fully consistent with the New Testament account of the sequence of events that followed the nativity. In other words, a "tax" takes place; the child is taken to Jerusalem to be "presented"; the wise men arrive and depart; the family leaves for Egypt; the "innocents" are slaughtered; the family returns to Nazareth.

A. The Mathematical Theory

The following facts or chronological inferences can be drawn from Matthew 2:1-11,2:12,2:16.:

1. The wise men saw something in the sky before coming to Jerusalem from the East.

2. The wise men's journey was motivated probably to confirm an astrological, scientific or religious belief. They may have been experimental research scientists.

3. The wise men believed the child was already born when they arrived in Jerusalem.

4. The wise men did not know the exact location or "city" where the child had been born until they came to Jerusalem and asked.

5. Herod and his court must have been convinced that these wise men were very intelligent and knowledgeable about astronomy and astrology.

6. Bethlehem was a much smaller than average "city" or municipality in population. The wise men discovered or asked for the approximate population which, our taking the text literally, may have been the smallest in Herod's kingdom.

7. The Jewish religious, scientific and academic establishment did not see or understand what the wise men saw and understood.

8. The wise men did not tell Herod and his court how they would locate the child.

9. A search for the child might be necessary.

10. The wise men hurried to Bethlehem.

11. The wise men did not expect to find the child, even less so with his mother Mary.

12. The child was less than or equal to two years old when the wise men saw the "star". The child may have been much less than two since Herod was not taking any chances.

13. A registration took place ending at the first appearance of the "star" since there is no evidence that there was a poll tax at the time. The registration asked for at least the location of current residence, the name, and the current age of everyone in Herod's kingdom.(We must accept Matthew's account here regarding the slaughter of the "innocents", unless there is reason, either textual or historical, to believe otherwise).[2]

     To explain the passage and its inferences four assumptions will be made. These assumptions are well known to the astrologer.

     1. The currently known universe began and time was created. "Something" created time. This is a standard First Cause argument, which is fully consistent with current astronomical and scientific data, the book of Genesis, and Mesopotamian creation myths.

     2. If "Something" created time, it is logical that the movement of the stars and the actions in human history are already known by that "Something". This assumption follows from assumption 1, given human logic. This is the theological argument of predestination, not determinism.

     3. It is logical then to suppose that the movement of the stars and the actions in human history are directed as one. The unity of Creation, not pantheism, has profound aesthetic appeal to the scientist and the theologian.

     4. Since 8 BC, the zodiac has been the most statistically accurate representation known among humans in the Western world of how the movement of the stars and the actions of human history are directed as one. [3]

If the human interpretation of the zodiac had 100% predictive power, then we would have, among other things, the following:

a. philosophically, there would be no free will from the human perspective.
b. financially, the best astrologers would have inside information.
c. poetically, life would not be life as we know it..

      7 BC marked a well known, important astrological event whose significance has been well documented. [4]  There was a triple conjunction of Jupiter and Saturn in the sign of Pisces. This event occurs approximately once every 900 years. By the precession of the equinoxes we know with a high degree of confidence that the age of Virgo/Pisces began earliest 300 BC and latest 300 AD. Thus, we have an astronomical landmark that pinpoints to the year a possible new astrological age.

     The non-periodic triple conjunction began on the evening of May 27 and lasted over about a 7 month period, given the quadrant with opposite vertices latitude 33 N longitude 44 E and latitude 30 N longitude 48 E. [5]  Azimuth readings for this event are not considered appropriate. By June 27 the apparent velocity of Saturn was slowing; by July 7 the planet could be observed to be at its first stationary point. By July 15 Jupiter, rising above Saturn, was at its first stationary point. In principle, the wise men could have set on their journey by July 15 since it would be preferable if they did not delay, avoiding the possibility the child may have left his place of birth. [6]  We can speculate on the time it took for the wise men to reach Jerusalem. For example, from Karbala at c. latitude 32 degrees 40 minutes N longitude 44 E the distance is c. 562 miles as the crow flies. The maximum distance traveled from Mesopotamia probably was not more than 750 miles. Pliny in Natural History 12, 109 declares that a camel can travel 25 Roman statute miles( c. 28 kilometers) in a day. A modern camel travels in a working day on average 25 miles so that the wise men could have arrived in Jerusalem as early as August 15. [7]  Throughout, the wise men may have been following the "star", in other words, checking the progress of the triple conjunction.

     To the wise men the question was not one of statistical prediction and timing of future events, but one of location-which explains why they had to ask for directions in Jerusalem. They did not have information on the first name of the child, particularly since there was confusion among Jewish contemporaries about the number and type of messianic figures. They did not have a personal description or the time of day of the child's birth. Since there is no known way of precise identification of an individual without some information, the wise men must have reasoned that the criterion for selection was contained in the zodiac. In other words, if the age of Virgo/Pisces began with an astronomical event in Pisces, why would not the child who inaugurated that age also be a Pisces and his mother, the alma, the young maid, be a Virgo? Undoubtedly, this question must have been posed by Hellenistic astrologers who had abandoned the old Babylonian system. The search strategy could then be described as in table 1. Note that here and in the rest of the paper, statistical independence in astrological signs will be assumed, that there are 12 signs in the zodiac, and the possibility of twins is considered inconsequential.

Table 1: The Search Strategy of the Wise Men
Search Priority

     The wise men could have begun with the hypothesis that the child, a boy, was born between February 19 and March 20, 7 BC. If the child was presumed to be a Virgo, he could not yet have been born given the August 15 arrival date. His estimated date of birth would have had to be calculated. Virgo as a boy also does not seem logical. The wise men may have been prepared to go through the complete suite of strategies if at each stage of the search there was no expected outcome. In that case, if the population of Bethlehem between February 19 and March 20, 7 BC was 2,880 with a net birth rate (e.g. the number of children reaching the age of at least six months for every hundred people) of 1% at a minimum, let us say, then there would be at least a 70 percent chance of finding two or more boys that would yield a positive outcome. This probability assumes no demographic movement. Clearly, the wise men must have been hoping that the first search strategy would yield the desired outcome which would leave little room for misidentification. The first search strategy fits the passage in Matthew.

     The wise men went directly to Bethlehem since the child could have left with his mother after the "tax". That there was considerable demographic movement during the "tax" was not a concern, however. A woman during late, albeit perhaps here unwanted, pregnancy does not travel. Hence, the wise men could use the population estimate of Bethlehem prior to or after the "tax" in any of their calculations. Although the wise men did not know it, the mother had to leave Nazareth for an extended period of time because of the "unusual" circumstances behind the birth of the child-a situation intimated in Mary's song as expressed in Luke 1:47-55.

     Geometric and Poisson probabilities for finding the child under the worst case scenarios are given in table 2. [8]  They were calculated with the following data: (1) Shortly before the fall of Jerusalem (the spring of 70 AD) probably not more than 2,350,000 to 2,500,000 Jews lived in Palestine and the number of "cities" functioning as more or less autonomous municipalities lay between 300 and 400, giving Bethlehem a population in 70 AD no greater than 8,000. [9]  (2) A stable Jewish population in Palestine existed growing at the rate of r (Lotka's r) with minimal migration. In fact, the Jewish population was growing quite quickly-and this was not just the result of proselytixing. [10]  (3) The infant mortality rate was 30%, the death rate was 4%, and the crude stationary birth rate was equal to or greater than 4%. [11]  The wise men could have arrived around August 15 or thereabouts so that the infant mortality rate is only an approximate measure here. We know, however, that death in infants occurs most often in the early or late neonatal stage. Birth trauma ranks as the most important factor, above hygiene, sanitation, nutrition and infectious diseases so that the infant mortality rate can be used as a proxy for the net birth rate.

Table 2: Scenarios given Christ is a Male Pisces and his Mother is a Virgo
(February 19 to March 20, 7 BC)
Population Growth Rate
Population of Bethlehem
Poisson Probability. No Child
Poisson Probability. One Child
Geometric Probability. No Child
Geometric Probability. One Child

     Neither the Poisson nor geometric probabilities yield results that uniquely identify the child. There is only an 81.67-87.86% Poisson probability of finding one or no child, while the geometric probability gives 39.50-64.19%. Notice, however, that even here there is a greater chance of finding no boy than one. This fits the recorded reaction of the wise men when they eventually found what they were looking for.

    Misidentification is dramatically reduced under the following conditions:

1. The population growth rate increases and/or the death rate decreases. At a growth rate of 1%, the population of Bethlehem in 7 BC would be 3741 with a Poisson probability of 63.47% for no child and 28.86% for one child, while the geometric distribution yields 54.54% and 24.79% respectively.

2. The wise men before coming to Jerusalem must have realized that the child could have been born in a highly populated "city". Other criteria such as ensuring the child's Jewishness, the estimated time of birth, the presumed lineage, and particularly the first name as suggested in the Old Testament would have to be used. There are only two messianic names mentioned in the Old Testament. [12]  Lauterbach states that in one and the same family no two persons could conceivably have one and the same name. [13]  The name itself is usually given on the day of circumcision. In the Talmudic tradition, although Maimonides does not mention it, a child who dies before attaining the age of eight days should also be circumcised over his grave with a flint or a reed and should be given a name as a memorial. [14]  Hence, with an average of six live born children per woman, half female and half male, the maximum average theoretical frequency of either messianic name would be 1 in 2-information that could be used. Since Matthew does not suggest that the wise men asked for any information other than the basic demographics of Bethlehem, we could infer that the actual population of Bethlehem in 7 BC was much less than 8,000.

3. Since the slaughter of the "innocents" is only recorded by Matthew, the number of baby boys murdered in cold blood must have been small. If the population of Bethlehem were 8,000, roughly 220 or more would have been killed, which almost certainly would have caught the attention of Josephus among others.

     It would not be unreasonable to conclude that Bethlehem's population was roughly 2,880 or less with a net birth rate of c. 3%. ( Assume, for example, a 1/4 infant mortality rate, a birth rate of 4.2% and a death rate of 3.7%. Then backtrack to 7 BC after using the normal technique of averaging a high and low population as of spring 70 AD. This gives an average of 4858 for each "city". Since there is positive skew and. Bethlehem was the smallest "city", deduct c. 2, 000. The approximations make sense here since the wise men could have, but did not, ask for the name of the child). The Poisson probability of finding one or no child would now be at least 96.3%, while the geometric distribution yields at least 91%.

     The search in Bethlehem had to be quick. The fastest way would be to consult a town council, if there was one, on the birth of a boy between February 19 and March 20, 7 BC in Bethlehem during the general time of the "tax". Next, after the wise men had considered the candidates, the astrological sign of the mother could be checked by the wise men asking her husband, for example. In the event that the mother and her child had left Bethlehem, relatives would have been contacted. We must argue here that most, if not all, Jewish adults over the age of 14, let us say, knew the signs of the zodiac and their own sign and at least those of their own children.

B. The Administrative Theory

     It is well known that the King James Version of Luke 2:1-6 is not the only translation that tries to stay faithfully to the original text. Some of the possible translations for the text in parentheses are: (1) This census preceded that held when Quirinius was legate of Syria(i.e. in 6 AD) (2) This was the first census in Judea that was held when P. Sulpicius Quirinius was legate of Syria(i.e. in 6 AD) (3) This was the first of two censuses held when Quirinius was legate of Syria. The word apografomai (apographomai) means to register or record, not tax. Hence, the general sense is that there was an enrollment prior to taxation or the beginning of a census made before its completion by Quirinius. Using this last interpretation, it will be argued that there were three tax related events referred to in this passage: the universal tax for Roman citizens at least and decreed by Augustus, a registration in 7 BC for Jews, and a census conducted by Quirinius in 6 AD. Luke, although not a political economist, probably knew the reason for the registration in 7 BC. [15]

     The universal tax decreed by Augustus sets the stage for the registration in 7 BC. Luke, undoubtedly, wanted to link the two to highlight the fact that something wonderful and of global significance was about to happen in a world such as ours. Since the two events were chronologically close to each other, he merged the two events. Luke also may have inserted the passage because he surmised that Augustus was the real mastermind behind the 7 BC registration.

The reasons for the 7 BC registration here were:

1. Augustus wanted to prepare Herod's client kingdom for incorporation as a procuratorial province of Syria in 6 AD. [16]  With such a complicated personal situation in Herod's family, with many Jews asking for provincial status [17] , with all the inevitable competing claims for Herod's throne, the emperor must have asked himself the question: what was going to happen in Judea after Herod, a "Third World" strongman and a puppet of the Romans, died? Augustus was leaving the "Syrian option" open, anticipating events with his usual tact and brilliance.

2. Herod wanted an accurate count of the population for the writing of his will. Will 3 written in 12 BC suggests that Herod was declining in vigor and wished to give up rule. [18]

3. Herod wanted to redeem himself in the eyes of the Jews for earlier burning the Temple genealogies.

     In effect, a deal was struck between Herod and Augustus: cooperate and institute the registration and the Romans will honor your will by giving your heirs a chance to rule. We know that the Romans and Herod discussed at least once in private, for instance, Herod's conversation with Varus in Josephus' Antiquities 17,5,2 and 17,5,7. Augustus and Herod, both by now highly experienced in political matters, must have had serious doubts about all of Herod's children. If Herod's heirs ruled well then, the client kingdom would not be incorporated into Syria and Herod's heirs would also have an accurate count of the population if they wished to introduce a poll tax. [19]

     The general problem that Augustus like any government must have been faced with was how to extract the maximum of taxes peacefully without encouraging an underground economy and killing incentives for the Roman Empire's population to work. The emperor was acutely aware of past injustices in the tax system in the provinces. He had mitigated the principal-agent problem by carefully choosing and controlling procurators and governors and by minimizing the role of the publicani. In interests of fairness he could not, however, introduce a graduated income tax since a person's occupation and how much that person earned were not known. Furthermore, such a tax would probably be complicated thereby introducing the possibility of "loopholes" that would arouse animosity. The poll tax was the solution, and he knew the Jews would justifiably see it as extortion since there is no evidence that the Romans gave anything anywhere in return. To make the poll tax successful in the first cycle, Augustus needed to:

1. determine the names, ages and residences of everyone in Herod's kingdom.

2. collect accurate data for the poll tax (and bloc assessments) without a revolt.

3. coax all the inhabitants to register willingly and not to lie.

     If the Romans were preparing a census for Syria in 6 AD, the most appropriate time for them to determine the ages of those Jews over twelve in Herod's kingdom would be in 7 BC. [20]  We know that all men from fourteen to sixty five and all women from twelve to sixty were obliged to pay a tributum capitis in the Syrian province. The age counted from the date of declaration. Hence, a baby girl declared at the 7 BC registration would pay the poll tax in 6 AD. [21]  The client kingdom, like the rest of Syria, would be on a possible twelve year census cycle. [22]

     There is no historical evidence, if the 7 BC registration occurred, that there was unrest. This is highly unusual, particularly in such an "unruly" territory, suggesting that the Romans had anticipated a revolution (perhaps learning through their experiences in Gaul among others) and staved it off. There is also no historical evidence that the Romans repeated such an event. It can be surmised that the reasons why the Romans were reluctant to institute a registration in other territories that became provinces were two fold. First, the population in the main would lie or would not register which would make a poll tax difficult to collect in the first cycle and, second, the Romans in many cases inherited an already existing tax gathering system. For example, in Egypt, the Romans continued the poll tax from their Ptolemaic predecessors. [23]

     It will be argued that Augustus and Herod were presenting the 7 BC registration as a genealogical service to the Jews. After 6 AD, the data gathering in the client kingdom for taxes and for the issuance of fines could follow the Syrian or Egyptian model. All Jews fell for the ruse since the Pharisaic conceit of nobility of learning had not yet supplanted the Sadducaic conceit of priestly nobility. The peasants and the working class must have been particularly susceptible to the registration since they must have despised and envied the grandees of an ungenerous plutocracy, bureaucracy, academia and priesthood. Without a "fount of honor" they now had the opportunity to show their own pedigrees. [24]

     .The very division of Israel into "houses" presupposes among them the existence of well authenticated genealogies at least some of which are mentioned in the Old Testament. Herod could have ordered the high priest, who would presumably be knowledgeable in genealogies, to assemble a list of "houses". [25]  Registration would take place at the ancestral "city" so as not to arouse suspicion. [26]  Tainted, prohibited, or void marriages would also have to be noted, thus explaining why the heads of household among others had to be accompanied by their wives.

     It will be argued that the registration took place c. March 1 to June 1, decreed perhaps at the end of 8 BC. The date of conclusion fits St. Matthew's account and Josephus' account of the 6 AD census/tax. [27]  We can also infer that Mary came to Bethlehem at the beginning of the registration period, otherwise she would have had her child at home before venturing to travel. To get an accurate count as of June 1, the window of registration time was probably not more than around three months since women in their sixth month of pregnancy could still travel, although with difficulty and not in complete safety. The possibility of not registering a child born before June 1 would be almost entirely eliminated.

With such a scheme as this Herod must have been deeply "troubled" at the arrival and the questions of the magi.

The Music of the Spheres

      The theory here implies that the dawning of an astrological age is accompanied by a major turning point in religious development Effectively, there is a music of the spheres in that the inauguration of a new age is marked by a religious figure whose birth sign coincides with the sign or opposite sign of that age. Furthermore, one of the religious figure's parents or children has the astrologically opposite sign. [28]  There is considerable disagreement through an examination of the precession of the equinoxes when exactly an astrological age begins. However, there is a general consensus within approximately two to four hundred years. The age of Taurus, the A, the ox, started around 4,400 BC possibly contemporaneous with the invention of the ox-drawn cart. It is extremely unlikely that we can find evidence that an important religious figure was born at this time in the sign of Taurus. Ideally, we would like to demonstrate that (a) a Libra/Aries birth combination happened contemporaneous with an important religious development in the age of Libra/Aries (b) the age of Virgo/Pisces could have begun in 7 BC from biblical chronology and (c ) the Leo/Aquarius combination has been predicted and could likely be fulfilled. Obviously, we do not have definite data yet on this last combination just as we do not have definite data yet for Cancer/Capricorn and Gemini/Sagittarius. [29] Table 3 displays the probabilities of the predicted combination contemporaneous with that astrological age. [30]

Table 3: Sign Configurations
Sign Pair
Beginning Date of Age
Joint Probability
2200-2000 BC
100 BC-100 AD
2000 -2200 AD
4000-4300 AD

     We know that an important development, the formation of the Jews, occurred c. 2,100 BC. From biblical chronology the patriarch Abraham could have been born in 2,168 BC, assuming that the construction of the first Temple began in 967 BC and that recorded years in the Bible are not just half-years. The exodus would have taken place in 1,446 BC with Joshua's crossing of the Jordan around 1,405 BC. Ideally, what must be shown through the bible, Jewish folklore, or tradition is that Abraham was a Libra and his son Isaac was an Aries or vice versa.

     It is well known in rabbinical circles that Isaac was born on Nisan 15 at Passover, a very probable Aries. [31]  There is then a 1/6 probability that this event date could have occurred accidentally. Abraham's birth date is problematic since there is no direct evidence. The 83.33% explanatory power of the theory is, in fact, at a minimum because:

1. A joint hypothesis has been presented here where the dating of the astrological landmark itself must be taken into account.

2. The time of year of Abraham's birth date is narrowed down to either Nisan or Tishri if one considers the controversy in the Talmud Bavli (Rosh Hashana 10b-11a) between Rabbi Eliezer and Rabbi Yehoshua (1st-2nd C. Yavneh). [32]

3. The Old Testament Jews may have known of the precession of the equinoxes. [33]  Abraham, for one, has a reputation for being a world class astronomer-and he could not have missed this knowledge. The fact that he may have been born in Libra could have been additional motivation for him to break with the prevalent Taurine astrology of the Chaldeans.

4. Second Temple Judaism predicts that, when Greenwich mean time is taken into account, an important religious figure will be born on the ninth or, technically, the tenth of Av in Leo. This prediction, invalidating all current Jewish and Christian theology, would be irrelevant here if based on an a priori informed speculation that is not realized either in this or the next astrological Great Year. However, as of now it does fit with the original Old Testament scenario of four key eschatological players-a man with the spirit of Elijah (John the Baptist?), a prophet ("the Prophet" in Islam?), a priestly and a political figure. The last two, known as the "star" and the "scepter", are supposedly linked psychologically.

     (b) If we reason numerically from the precession of the equinoxes then 7 BC marks the most probable year of the birth of Christ. Given the Temple dating of 967 BC, using a date later than 7 BC for the birth of Christ would only widen an expected statistical discrepancy between biblical and astrological chronology. If the construction of the Temple began latest in 957 BC, then from biblical chronology the interval of time from Abraham's birth in an assumed Tishri to Christ's birth would coincide with a hypothetical age of Aries to less than a year. Currently, based on the number of sidereal days in a cycle, there are c. 25806 solar years for the pole star to return to its original position, giving a mean of 2150.5 solar years in an age-which is consistent with the Abraham-Christ interval. [34]  Under this scenario, however, 6 BC could not be ruled out.. We can also forecast the age of Aquarius to begin in 2,144 AD if premillennialism is discounted.

     (c) Most philosophical historians--from Vico and Spengler to Toynbee and Durant--agree on the Platonic and Aristotelian observation that the broad contours of history follow certain patterns. In the case of Toynbee, for example, each "civilization" repeats an irreversible sequence of political stages and each one is associated with a specific type of economic structure. The political system mutates when the underlying economic power base changes. Thus, the agrarian stage is loosely linked to kingship, feudalism to aristocracy, and commercialism to democracy. Social and cultural values naturally change in importance as reflected in architecture, for example. A dies irae, a police state and/or bureaucratic dictatorship, follows at first unnoticeably. The universal state that has emerged from this "time of troubles" provides the creative internal proletariat with the opportunity to found a new world religion that is both rooted in revelation and built on past spiritual tradition. Through a new religious text and/or a new set of moral rules the ethical foundation for the next civilization is now laid, while the existing socio-economic system eventually degenerates into a caste society. The civilization dies. [35]  This fits with the introduction of a Leo/Aquarius figure. Today the conflict between those with personal physical or financial capital and those without, both within nation-states and between nation-states, has been aggravated by technologies which undermine traditional social, religious and national/regional political institutions. The signs for a universal state are here, and the global village is poised to embrace a new myth that gives new purpose and new meaning. It is this myth first propagated by the working and middle class, which could counter-balance and outlast the emerging universal state and continue to at least the end of the Aquarian age. [36]

     The implications of the argument suggest that a mythological dimension to the universe exists. Numerical analysis must be balanced by an appreciation of the principles behind the universe, which are not necessarily just the principles of theoretical physics. [37]  A star calendar could, in fact, be developed here perhaps through a new religious text. [38]  Such a calendar would be based on mythology without foreclosing the future possibility of a universe different from the one we know today. The calendar, implying that historical time is predominantly cyclical, could provide some linearity since the pole star does not return exactly to its original position. [39]


     A fully consistent, two part theory has been given for setting the birth of Christ in Pisces in 7 BC with a greater probability for the latter part of the time interval. Since there is no historical fact for the month, let alone the exact date of birth, any evidence for the validity of this theory must point to the event indirectly. The statistics and supporting circumstantial evidence, although hampered by missing data, give at least 83.33% explanatory power.

     One implication of the theory is that in the foreseeable future there will be another major religious innovation inaugurated by a person whose astrological sign is Leo(born on the 9th or 10th of Av) with an immediate family member, preferably father or son, as an Aquarius. This would suggest that the Christmas event is not a theological singularity. Although human behavior may not change, holiday dates and the calendar itself may have to be modified.

[1]  Hardy, E. G. , Monumentum Ancryanum, Clarendon Press, Oxford, 1923 and Fairley William, Monumentum Ancryanum Deeds of Augustus, Dept. of History at the University of Pennsylvania, Philadelphia, 1898 « Text

[2]  The psychological content and style of Matthew's passage should be contrasted with John 19:35. « Text

[3]  Genesis 1:14 does not deny the validity of astrology. Deuteronomy 18 10:12 also fails to consider the very probable situation that the wise men paid out of their own pockets to do work for the sake of knowing. « Text

[4]  See, for example, pp. 315 in Finegan, Jack, Handbook of Biblical Chronology, Hendrickson Publishers, Peabody, Mass, 1998. Note that there is no astrologically argued event for the Prophet Muhammad. Also, the "star and the crescent" on the Turkish flag and witnessed in astronomy does not refer to a religious phenomenon. See Bahali, Kassim, "The Birth of Muhammad PBUH: A Computer Analysis", unpublished paper translated from the Malay. « Text

[5]  Chevalley, Patrick, Sky Charts-Cartes du Ciel, freeware 1999-11-28 version 2.44, « Text

[6]  There are other reasons for believing an early journey. (1) The longer the wise men stayed in Bethlehem, the more confident they would be that the child reached adulthood. (2) Herod could be be more certain in locating and murdering the child. It is also conceivable that the wise men anticipated the completion of the astronomical event. The 7 BC triple conjunction gives c. 40-45 arc minutes separating Jupiter and Saturn at their simultaneous second stationary points. Using the magnitude of Ptolemy's combined Jupiter-Saturn arithmetic average errors of 35' in celestial longitude, the wise men could have predicted the triple conjunction at Jupiter's first stationary point. For a data description see Thurston, Hugh, Early Astronomy, Springer Verlag, New York, 1994 pp. 169-170. Notice that Ptolemy does not give the best possible parameter fit. The words "stood over" in the King James version could then refer to the second stationary point of Jupiter-Saturn in 7 BC which would fit with the original Greek. « Text

[7] « Text

[8]  Although there is no written evidence of statistical calculation beyond truncated numbers and series, arithmetic means, frequencies, minima and maxima before the Middle Ages, statistical reasoning began in pre-Christian times. See, for example, Daniel 1:14-16 on the design of experiments; Rabinovitch, Nachum, Probability and Statistical Inference in Ancient and Medieval Jewish Literature, University of Toronto Press, 1973; Trenerry, Charles, The Origin and Early History of Insurance, Studies in Economics and Political Science of the London School of Economics, vol. 87, 1926. Calculating roughly with the use of the geometric distribution where the average chances of finding and not finding the child serve as the parameters is very plausible and simple, requiring only one multiplication. It is also only one step away from the Poisson, the distribution of choice. « Text

[9]  Encyclopedia Judaica, Macmillan Company, Jerusalem, volume 13, 1971, pp. 869-871 « Text

[10]  Ibid., pp.869-871. Note that a case cannot be made by maximizing the number of children with respect to r in the equation for the population of Bethlehem

Nt = No ert (1)

where Nt = the population of Bethlehem at time t
No = the population of Bethlehem in the spring of 7 BC
r = the population growth rate
t = the number of years

and in the equation for the number of children born in Bethlehem in 7 BC and surviving through the first year as:

X = No [(g + r)(1 - d)] (2)

where X = the number of children
g = the crude stationary birth rate
d = the infant mortality rate
Substituting (1) into (2) we would have:

r = (1 - gt) / t (3)

With t as 76 for the interval between 7 BC and 70 AD and with g set at 4%, we find a negative growth rate of c. 2.68%. We know from history that (1) the growth rate was positive so that any calculation must begin with r > 0 and (2) a population of 61,315 for Bethlehem in 7 BC, given N76 is 8,000, is highly improbable. The population of Jerusalem under Herod has been calculated to be c. 40,000. This does not include the Temple Mount. Broshi, Magen, "Population de l’ancienne Jérusalem", Revue Biblique, 82:5-14, 1975. « Text

[11]  Bagnall, Roger and Frier, Bruce, The Demography of Roman Egypt, Cambridge, 1994 conclude that the crude birth rate in Roman Egypt was 44.1 to 1000, the death rate 42.1 to 1000, and the infant mortality rate about 1/3, giving a stable growth rate of .2%. Parkin, Tim, Roman Demography and Society, Johns Hopkins University Press, Baltimore, 1992, on the other hand, is more optimistic about the Roman population at large. He arrives at a crude birth rate of 40 to 1000 and a death rate of 40 to 1000 giving a stationary population. 30% of the original birth cohort died in the first year. All agree that the Roman population experienced a "high pressure" regime. Using Parkin's data in computing Bethlehem's population appears more appropriate for a number of reasons. Roman Egypt was urbanized and densely populated and, so, susceptible to death by plague or infectious disease. It was not particularly hygienic or sanitary. Furthermore, a crude birth rate much higher than 44.1 to 1000 with a gross reproductive rate of 5-6 children per mother, live born, approaches the fastest national birth rate in the modern world. (In 1998 Niger had a 5.3% crude birth rate, c. 7.4 children/woman which is about half of the theoretical maximum of 15 children/woman. ) Parkin's death rate probably marks the upper bound for the Jewish population in Palestine. The Jews were living in a primarily agricultural region and their religion contained a code of health. « Text

[12]  The name in Jeremiah 30:9 is non-existent among Talmudic rabbis, unlike that in Zechariah 6:11-12. « Text

[13]  Lauterbach, Jacob, Studies in Jewish Law, Custom, and Folklore, Ktav Publishing House, 1970, pp. 34 « Text

[14]  Klein, Isaac, A Guide to Jewish Religious Practice, Jewish Theological Seminary of America, New York, 1979 « Text

[15]  Various arguments have been advanced using a c. 7 BC dating, but all explanations as yet have not been fully satisfactory. For example, Heichelheim, F. M., "Roman Syria" vol.4, part 2 pp.161-162 in An Economic Survey of Ancient Rome, Editor Tenney, Frank, Johns Hopkins, Baltimore, 1938 proposed that Herod determined the resources of his kingdom so that he could write his will. Unless a poll tax was planned, this does not appear to make much sense since tax was imposed through the tributum soli which had been in existence in the client kingdom from 63 BC when this tribute had first (and through 30 BC) been paid to Rome. Numbering the population probably was not a chief concern of Herod and, even if it was, why did individuals have to return to their ancestral city? Another argument has been advanced that there was a tax in 7 BC when the Jews in Palestine had to return to their ancestral city and the Jews abroad paid their taxes at their place of residence. The argument goes that, the Roman administration wanted to reduce tax evasion and, second, it wanted to identify all Jews who, by not paying their taxes, would therefore be considered enemies of the Roman State. By using or borrowing a written copy of Jewish genealogy, Caesar Augustus may have persuaded the Jewish establishment that it was in its interest for the Romans to check the validity of the genealogy through the administration of the tax. In order for this to occur, a written, but not necessarily complete, genealogy for all the Jewish people must have existed since the approximate time of the heroic age. This genealogy must have contained the birth or "presentation", the death, the marriage and/or divorce along with the male marriage partner's name of every Jewish person as of 8 BC except for those who had not had time to be recorded. Second, at least one written copy of the genealogy must have existed and this copy must have listed the genealogy by ancestral city. It is possible that with a complete record of a population to check against Caesar Augustus could have identified all tax evaders. However, there are several problems with this argument. (1) Augustus was dealing with a client kingdom so that it is improbable that he would have levied a tax. (2) Julius Africanus in the Epistle to Aristides 5 states that Herod, when first becoming king, burnt the genealogical register in the public archives. Because Herod could not trace his genealogy to the liking of the Jews, he thought he could be an aristocrat if no-one else could trace his descent. According to Africanus some Jews, however, kept private records. (3) Jews were scattered not only over the whole Roman Empire. They also lived beyond the Euphrates, in Yemen, and Ethiopia among other places. With a complete genealogy one could not distinguish a tax evader from someone who lived outside the Empire. (4) Genealogies in large populations are much more easily transmitted through oral tradition. « Text

[16]  Planning twelve years in advance on routine procedures such as a census is a normal matter of state policy, particularly for Augustus. All agree that the emperor was an administrative genius, modest(perhaps to avoid the fate of his step father), where possible averse to bloodshed, and brilliant in his efficient and novel bureaucratic solutions. Above all, Augustus was patient-festina lente! « Text

[17]  The Romans realized full well that by Herod's death in March 4 BC many Jews under Herod had had enough of his rule. See Josephus' Antiquities 17,11,2. « Text

[18]  Richardson, P., Herod King of the Jews and Friend of the Romans, University of South Carolina Press, 1996, pp. 35. Richardson pp. 18 has also speculated that by 7 BC Herod now in his late sixties may have had tertiary syphilis, a condition that must have impressed Augustus and the Romans with a sense of urgency « Text

[19]  Herod knew Augustus would keep his word (Suetonius 12 Caesars 2,42). This may explain in part Herod's generous bequest to the Augustan family. Predictably, the emperor confirmed Herod's testament with minor changes such as making Archelaus only ethnarch with the proviso that he must govern well. Josephus' Antiquities 17,11,4 « Text

[20]  Some have questioned whether a census was carried out in Syria just before or at the same time as the one in Judea in 6 AD. See Dabrowa, E., The Governors of Roman Syria from Augustus to Septimius Severus, Dr. Rudolf Habelt GmBH, Bonn, 1998, pp. 29 « Text

[21]  The Judean census under Quirinius took place between September 2, 6 AD and latest September 1, 7 AD. The unrest may have delayed its completion. Thus, the existing eligible portion of the inhabitants as of the 7 BC registration would have to pay the poll tax. This suggests that the 7 BC registration concluded before September 2. « Text

[22]  Heichelheim, F. M., "Roman Syria" vol.4, part 2 pp. 237 in An Economic Survey of Ancient Rome, Editor Tenney, Frank, Johns Hopkins, Baltimore, 1938, quoting Ulpian, seems to imply that there was a periodic Syrian census. This is possible since a periodic census can be found also in Egypt, but in intervals of fourteen years. Men between fourteen and sixty five were subject to the poll tax, while women were exempt from it. See Bowman A., pp. 691 in Cambridge Ancient History, vol. 10(2nd edition) editors Bowman, A., Champlin, Edward, Lintott, Andrew, Cambridge University Press, 1996 « Text

[23]  It is curious that Augustus did not make any changes to the convoluted Egyptian census and tax system as described in Wallace, Sherman L., Taxation in Egypt From Augustus to Diocletian, Princeton University Press, Princeton, 1938, pp. 96-134. Perhaps he did not want to risk bureaucratic unemployment. There is evidence, however, that the bureaus did try to simplify lists, ibid. pp.101-102 « Text

[24]  Much mischief must have been done in speculation on family origins and pedigrees after the genealogies had been burnt. Animosity and conceit among the Jews about genealogy was such that it was remarked that nine hundred camel loads of commentary existed on 1 Chronicles 8, 37-1 Chronicles 9,44 alone. The Talmud states that "when men quarrel among themselves, they quarrel over birth". Casting doubt upon a leading family's pure descent might even have been greeted with force, particularly since property rights were at stake and the great sages had cautioned that "a family once mixed up remains so". Unfortunately, the Jews forgot to consider that patrilineal descent can only be determined with certainty through DNA. Testing with the remains of one's ancestors, although available just recently, is not the only proof. There is the possible genetic transmission of auditory memory accessed through a psychological mechanism--raising an interesting issue. If the concept of reincarnation has been confused with this, a hypothesis that can be scientifically tested, then a major dogma of Eastern religion must be abandoned and placed into the category of speculation at best. It also raises questions about whether Darwin is telling the whole truth. « Text

[25]  Pomykala, Kenneth ,The Davidic Dynasty: Tradition in Early Judaism, Society of Biblical Literature, 1995 pp. 122-123 argues that there were many houses, that of David being a rather large social group akin to a clan which, while genealogically related to the pre-exilic family of David, was not to be identified with the pre-exilic royal house. « Text

[26]  Administrative expenses for Herod would also be approximately the same whether the inhabitants registered at their current residences or in their ancestral "cities", assuming a genealogical list were to be constructed by ancestral "city". « Text

[27]  A June dating gave Herod the clerical time to sort and collate registration records before the arrival of the magi. « Text

[28]  Roman Mithraic Zurvans also depict each successive astrological age contemporaneoous with each spiral of history. « Text

[29]  We can speculate on the Cancer/Capricorn figure--the Three Taverns. The Capricorn might be a consummate musician/artist, an Orpheus/Pan and/or a Dionysian dancing king reacting to the sterility associated with the future predominance of scientific procedure. Perhaps in "passing through the waters" he encounters Typhon. For a possible character study see Cronin, Archibald, A Thing of Beauty, Little Brown, Boston, 1956 « Text

[30]  A Libra/Aries probability of .2019 instead of .0139 under the worst case scenario of 12 children where at least one son or daughter were born in one of the two signs and the mother and/or father were born in the astrologically opposite sign is misleading since Abraham and Isaac are the relevant a posteriori figures. « Text

[31]  The possible modern dates of birth of Isaac are given below with the use of Lee, Scott, Calendar Conversions ~scottlee/calconvert.cgi, and under the assumption that the building of the Temple started between the generally accepted dates of 968 BC and 957 BC. For the argument of the 967 BC April/May dating of the Temple see Finegan, Jack, Handbook of Biblical Chronology, Hendrickson Publishers, Peabody, Mass., 1998 pp. 249. Note that these dates are calculated based on the assumption that Abraham was in his 101st year when he fathered Isaac, that Isaac was in his 61st year when he fathered Jacob, and Jacob was in his 131st year in Genesis 47, 9. There is a certain amount of ambiguity in dating Jacob's age when he met the Pharaoh. If Jacob was in his 130th year, Isaac could have been born an Aries, March 23, 2066 BC.

April/May Temple Dating Isaac's Birth Date
957 BC March 12, 2057 BC
958 BC March 25, 2058 BC
959 BC April 4, 2059 BC
960 BC March 16, 2060 BC
961 BC March 26, 2061 BC
962 BC April 8, 2062 BC
963 BC March 19, 2063 BC
964 BC March 30, 2064 BC
965 BC March 12, 2065 BC
966 BC March 23, 2066 BC
967 BC April 3, 2067 BC
968 BC March 14, 2068 BC

« Text

[32]  Vettius Valens in Anthologiarum Libri, 2, 28-29 cites Abraham as an expert on the ninth of the twelve loci which are used in Greek horoscopes. However, even if Abraham were preoccupied with the ninth locus because it somehow related to his geniture, there is not sufficient information to determine the time of year of his birth. Furthermore, some have questioned Valens' credibility. Ideally, a connection should be made between Abraham's birth date and the festival days of Sukkot. There is general agreement that the early Israelite settlers in Canaan found the pagan natives celebrating an agricultural thanksgiving festival at the end of the harvest time and that Sukkot, like Passover, is not an original Israelite invention. (MacRae, George W. , "Meaning and Evolution of the Feast of Tabernacles", Catholic Biblical Quarterly 22:251-276 1960) The Book of Jubilees 16,16 states that Abraham was the first person to celebrate Sukkot. The question that we must ask is why would Abraham have celebrated a variant of a pagan festival, knowing from Genesis 24,3 that he did not approve of the Canaanites. Or why would he have established Sukkot in the first place? Pre-Mosaic Sukkot-and possibly Passover-may have merged ideas, just as these festivals did in the post-Mosaic period. « Text

[33]  The ancients used equinox markers eons before Hipparchus although an accurate determination of the rate of precession had to await the astronomer. Worthen, Thomas, The Myth of Replacement: Stars, Gods. and Order in the Universe, University of Arizona Press, Tucson, 1991 pp. 174. Thus, tradition has it that the shofar cannot be made of anything Taurus because of the imagery of the golden calf. More concrete evidence can be found in the declaration of Jeroboam I in 1 Kings 12:28-33. He sets the day of his festival in Scorpio/Taurus which "became a sin for the people". The transition from the Scorpio(or Serpens)/Taurus stage is also apparent in the Aegean world. Apollonius tells us that in the bronze age story of Jason and the Argonauts the heroes sail for Colchis in search of the golden fleece guarded by a giant serpent. Mythology also tells us that in the Minoan world, the Minotaur, symbolizing the union of established state and religion, was destroyed by Theseus. « Text

[34]  A tiny adjustment has to be made since the speed of the precession of the equinoxes is variable and the period is decreasing slightly. And, technically, of course, it can be argued that the pole star does not return to its exact position and an age may be a century or two more or less than the mean of 2150.5 years. « Text

[35]  It has been well argued that the culprit for the observable cycles of history is economic utilitarianism, the pleasure/pain principle in all its variations, not money. History moves forward materially by the invisible hand of Adam Smith or, more universally, in Hegelian terms the "cunning of reason". The question that must be asked is why the current educational, particularly social scientific, establishment is teaching and practicing a philosophy that is both normatively sophistical and positively inaccurate. It also is not clear in a philosophical sense that economic agents are in reality acting rationally. « Text

[36]  A method has been given in Pardo, David, "Religion, Supercapitalism and the Negative Capital Tax", unpublished working paper, to postpone the inevitable development from democracy to the emergent universal state. Since "virtue is its own reward"(the philosophical version of the Christian message) is unattainable globally because it entails a prisoner's dilemma, the long term tension between democracy and capitalism could be eased by efficient and direct government policies to co-opt all citizens through personal savings. There is enough flexibility in the concept to implement it on a truly global scale. « Text

[37]  To be expected then, mathematics and physics are replete with numerical oddities. Transcendental numbers such as p and "e" , for example, are indefinite, so also are the fine structure and Euler constants. The Pythagoreans must have known that something was wrong when Hippasus or the Hindus discovered that the diagonal to a pentagon's side is irrational. All is not number. « Text

[38]  For a possible universal language for this text see Pardo, David, "The Common Heritage and the Future of World Religion" pp. 277 in The Maltese Islands on the Move, edited by Vella, Catherine, Central Office of Statistics, Malta 2000. The rationale for the use of Hebrew letters rests on the fact that these letters also represent numerical values and on the assumption that the idea of the Torah existed before Creation. Interestingly, the language has poetic, musical and mathematical possibilities. « Text

[39]  An astrological calendar would be much easier to use than our current calendar because it would not be based on an arbitrary date and the number of days for the months would be easier to remember. Unlike the myriad of calendars based on the perceived birth dates of religious figures or the quirks of history, an astrological calendar would represent cosmic time. Since such a calendar operates sidereally and tropically, it would not exclude the possibility that time could run backwards. The calendar could in principle start exactly on the spring equinox in 7 BC, corresponding to the autumn equinox in the southern hemisphere. The rationale for this date is that Pisces starts the Great Year of astrological ages, while Aries starts the solar year. The day for the solar leap year could be added to Pisces. Hence, a date such as 1/1/0 could mean the month of Aries, solar day 1, with the 0 meaning the first year of the Great Year. A number would also have to be specified for the particular Great Year. Alternatively, the 0 could signify the first year of the age if the sigil of that age was added. Fitting nicely with the mean length of the seasons, this star calendar, however, would be about six years out of sync with current estimates of the complete precessional cycle. « Text

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David A. Pardo: A Statistical Solution to the Star of Bethlehem Problem
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