Posted April 15, 2006
Modern academic study of the Bible operates within a conceptual framework far removed from the ideas about the Bible's origin hallowed by religious traditions, the Jewish tradition included. This departure from tradition took place some two or three centuries ago, and even though the reasons for this departure are explained in any academic introduction to biblical studies,  it is not common to find in the current biblical scholarship discussions which would raise issues posing a direct difficulty for some point of traditional Jewish belief. For example, nobody still bothers to prove that the Pentateuch was not written by Moses, and even the question of Moses' very existence is not discussed in historical terms. But sometimes a recent article in an academic journal can highlight the problematic nature of the traditional belief regarding the origin of the Pentateuch, and if that article succeeds in spawning a discussion, it may become evident that even in the academe there still are circles who fail to fully realize the implications of the knells sounding the intellectual death of the traditional belief.
One such discussion was published during the last decade  in the journal Vetus Testamentum, and has to do with the number of the Israelites reported to have participated in the Exodus from Egypt and in the subsequent wanderings in the Sinai desert. This number is given in Exodus 12:37 as "six hundred thousand men on foot, besides women and children," and in Exodus 38:26 it is specified as "every one who was numbered in the census, from twenty years old and upward... six hundred and three thousand, five hundred and fifty men." In Numbers 1, a detailed census is given, said to have been conducted a year after the Israelites' departure from Egypt (Numbers 1:1). This census resulted in the same number of the Israelite males over 20 years old: 603,550, but now the count explicitly excluded Levites (Numbers 1:45-47, and see also 2:32-33). The approximate number of 600,000 is given again in Numbers 11:21, and finally, Numbers 26:1-51 provides the details of another census, taken while the Israelites were camping in Transjordan, preparing to enter to the Promised Land (40 years after the Exodus, according to Numbers 14:33-34, however, the date of the census is not mentioned explicitly). According to this last census, before their entry into Canaan the Israelites numbered 601,730 males over 20 years old (Numbers 26:51), once again excluding the Levites, who were counted separately (Numbers 26:62).
The manifest implausibility of these numbers was known in biblical scholarship long ago. However, in 1995, Eryl W. Davies published in Vetus Testamentum an article surveying both the difficulties presented by these large numbers and the discussions of these numbers by earlier scholars.  Since almost none of the earlier discussions mentioned by Davies supposed that the census data of the Israelites in the books of Exodus and Numbers reflect in some way the number of the Israelites who took part in the Exodus or in the wanderings in Sinai,  these discussions need not concern us here. As for the difficulties raised by the census numbers, Davies mentioned the following:
To the difficulties mentioned by Davies one may add that, according to Exodus 12:38, the Israelites did not leave Egypt alone and empty-handed, but "also a mixed multitude went up with them, small cattle and large cattle, very much livestock." In addition, since the Israelites must have brought with them "tents, bedding, cooking and eating utensils, and tools -- which could hardly be carried by people traveling on foot,"  they would have to use at least a limited number of transport wagons drawn by animals. On these grounds, an 18th-century German scholar, Herrmann Samuel Reimarus, set out to calculate the length of the column that would be formed by the marching Israelites, supposing that the number of people was 3,000,000, the number of livestock 900,000, and the number of transport wagons 10,000, that each row in the column consisted of fifty people abreast or of such number of animals or wagons which would require the equal width of space, and that each row in the column marched at a distance of three steps from the preceding and the following rows. His calculations brought him to conclude that the length of such column would be 49 German miles,  which equals to 245 English miles, or almost 400 km.  Even though Reimarus's figure of 3,000,000 persons may be too high,  reducing it by a third (to the minimal figure of 2,000,000 persons), and reducing correspondingly the figures for livestock and wagons, would result in a column of 164 English miles, or over 260 km, in length. Given the marching speed of three miles per hour -- a speed which could be expected only of healthy persons in their prime -- it would take such a person, marching at the end of the column, 54 hours to reach a camping place at the column's head.
On the other hand, according to the Pentateuchal description of the Israelites' sojourn in Egypt, they must have dwelt in the easternmost part of the Nile delta, in the vicinity of the city of Ra'amses -- Pi-Ramesse (modern Qantir), named after the renowned pharaoh Ramesses II, who built that city as a royal capital for himself and his successors.  Thus, Joseph is reported settling the clan of Jacob in "the land of Ra'amses" (Genesis 47:11), and at the start of the Exodus itself, with Egypt struck by the plague of the firstborns, the Pharaoh is portrayed waking up at night and demanding an immediate departure of the Israelites from Egypt (Exodus 12:30-33) -- a demand that is carried out on that very day, with the whole people of Israel marching "from Ra'amses to Succoth" (Exodus 12:37), so that no time must have been spent on gathering the Israelites from distant settlements to the capital. Now, given the knowledge of the irrigation and melioration techniques at different stages of ancient Egyptian history, and given the amount of cultivable land in different areas of Egypt that such techniques allowed, scholars have figured out that in the late second millennium BCE, the whole Nile Delta -- not merely the easternmost part thereof -- could produce food sufficient only for about 1.2 million persons.  It was simply impossible for 2,000,000 Israelites to have lived there prior to the Exodus. Nor would it be feasible to lead a population of 2,000,000 Israelites into the land of Canaan, which, even under the best possible agricultural conditions and with the use of the most advanced agricultural techniques available in the ancient world, could not have borne enough produce to sustain more than about one million persons. 
Thus, the numbers of the Israelites taking part in the Exodus and in the wanderings in Sinai, as specified by the Pentateuch, are totally infeasible. And yet, in 1998, Vetus Testamentum had published an article by Colin J. Humphreys, which tried to make at least some sense of these numbers.  Humphreys's study invoked some criticisms, published in 1999,  to which he responded with yet another article in 2000.  The same year, another criticism of Humphreys's approach was published,  and in 2001, the discussion ended up with an article of Gary A. Rendsburg, essentially endorsing Humphreys's approach. 
The essence of Humphreys's approach rests on three premises. First, there is at least one figure in the censuses of the book of Numbers, which "stands out as being entirely reasonable."  Numbers 3:14-39 reports about the census of the tribe of Levi, conducted separately from the census of other Israelite tribes. This census is summarized with the figure of 22,000 Levite males over one month old. Then, Numbers 3:40-43 reports about the census of the firstborn sons over one month old in the whole Israelite population, which resulted, as noted above, in the figure of 22,273 persons. The surplus of the firstborn sons over the Levites, amounting to 273 persons, is mentioned explicitly in Numbers 3:46. It is this figure which Humphreys took as fully reliable. 
Second, Humphreys supposed that the numerical strength of the tribe of Levi was approximately 1/12 of the numerical strength of the whole Israelite population, or 1/11 of the original outcome of the censuses described in Numbers 1 and 26, which did not include Levites. 
Third, Humphreys suggested that in the figures for individual tribes, provided in the censuses of Numbers 1 and 26, the Hebrew term 'elef, usually translated as "thousand," should be understood as "a group of men, a troop" -- a meaning somewhat close to that of "family, kin group," which is well attested for 'elef in the Bible. Thus, when the number of males over 20 years old in the tribe of Reuben, for example, is given in Numbers 1:21 as "forty-six 'elefs, five hundred,"  in Humphreys's view it means 46 troops, consisting of 500 persons in total.  This suggestion, of course, is not new with Humphreys and goes back to W. M. Flinders Petrie, who made it, in a slightly different form, back in 1906, and whose precedence Humphreys acknowledged.  What was new with Humphreys was the connection of this suggestion with the two mathematical premises mentioned above.
However, the first two premises of Humphreys do not square well with the proposal that the term 'elef in the Pentateuchal censuses means "troop" rather than "thousand," and the latter proposal itself turns the portions of the book of Numbers, which speak of the censuses, into an irremediable disorder.
To begin with, when Numbers 3:43 says that the number of Israelite firstborn sons was "twenty-two 'elefs, two hundred and seventy-three," this should, according to Humphreys's approach to the meaning of the term 'elef, be read as 22 troops consisting of 273 persons in total. Hence, the idea that there were 273 firstborns more than Levites (as per Numbers 3:46) would mean that there were zero Levites over one month old -- or in other words, the whole thing would make no sense.
One might object that there would be no reason to register "troops" formed of males starting from the age of one month. But then the same is true of the "troops" of the Levites mentioned in the census of the tribe of Levi in Numbers 3:14-39 -- that is, if the figures of "seven 'elefs, five hundred" for the clan of Gershon (v. 22), "eight 'elefs, six hundred" for the clan of Kehath (v. 28),  and "six 'elefs, two hundred" for the clan of Merari (v. 34), are to be understood based on the meaning 'elef = "troop," as Humphreys suggested explicitly.  Humphreys's idea that for the Levites, exempted from military duties, a "troop" was merely a team of workers in the Tabernacle still does not explain why 30-day old babies would be enlisted in such teams.
Moreover, Humphreys's way of interpreting the census data for the Israelite tribes in Numbers 1 and 26 means, in effect, that the figures of 'elefs may be disregarded and that the numerical strength of the tribes (in the terms of males over 20 years old) should be determined based on the figures for hundreds and tens. The numerical strength of the tribes, calculated in this way, was given by Humphreys in Tables 2 and 4 of his article from 1998.  And according to these tables, a given tribe could number from 200 to 700 males over 20 years old according to the census of Numbers 1, and from 200 to 730 males over 20 years old according to the census of Numbers 26. It might be reasonable to suggest that the numerical strength of the tribe of Levi would fall somewhere between these figures, but there is absolutely no ground for the idea that the tribe of Levi would be closer to the average tribe magnitude than to the smallest or the largest of other tribes. In other words, it is impossible to derive the numerical strength of the tribe of Levi (in whatever terms) from the numerical strength of the total Israelite population, assuming the former to be about 1/12 of the latter.
But most importantly, the understanding of 'elef as "troop" or "work team" does not square with the censuses in Numbers 1 and 26 themselves; nor does it square with the Levitical census in Numbers 3:14-39. In chapters 1 and 26, beside the figures for individual tribes, a summary figure is given: 603 'elefs, 550 (Numbers 1:46) and 601 'elefs, 730 (Numbers 26:51). Now, these figures make sense only if the term 'elef in the censuses is understood as "thousand"; otherwise, summation of the figures specified for individual tribes yields 598 'elef-"troops" consisting of 5,550 persons in Numbers 1, and 596 'elef-"troops" consisting of 5,730 persons in Numbers 26.  Humphreys's solution to this difficulty was to suggest that initially, the summary figures given in the two censuses were just these; but since the term 'elef was used in the summaries in two distinct meanings: for "troops" and for "thousands" (in denoting 5,000 persons in each summary), a later copyist mixed up the two meanings and mistakenly summed up the figures for two different kinds of 'elefs. The same explanation was offered by Humphreys for the fact that the Levitical census in Numbers 3:14-39 ends up with the summary figure of 22 'elef Levites, rather than with 21 elef-"work teams" consisting of 1,000 persons, as the summation of the figures for different Levitical clans would demand. 
This suggestion of Humphreys looks rather contrived in itself.  But problems do not end here. As pointed out by one of Humphreys's critics, Rüdiger Heinzerling, there is another Levitical census in Numbers 4:34-48, which counts not all the males over one month old, but only those who were required to perform their duty in the service of the Tabernacle -- males from 30 to 50 years old.  For obvious reasons, the number of Levite males from 30 to 50 years old (in Numbers 4) should be considerably smaller than the number of all Levite males from one month and up (in Numbers 3). Yet, for the Levitical clan of Gershon Numbers 3:22 gives the figure of 7 'elefs, 500, while Numbers 4:40 gives the figure of 2 'elefs, 630. For the Levitical clan of Kehath, Numbers 3:28 gives the figure of eight 'elefs, 600,  while Numbers 4:36 gives the figure of two 'elefs, 750. And for the Levitical clan of Merari, Numbers 3:34 gives the figure of six 'elefs, 200, while Numbers 4:44 gives the figure of three 'elefs, 200. If only the figures of hundreds are of numerical significance ('elefs being mere "working teams," into which the relevant number of persons were organized), then for every Levitical clan, the number of males aged 30 to 50 years turns out as higher or equal to the number of males aged one month and more -- which is patently absurd. 
Hence, in the context of the Levitical censuses, there is no escape from understanding the term 'elef as "thousand," which means that the total figure of Levitical males aged 30 to 50 years is given in Numbers 4:48 as 8,580, and the total figure of Levitical males aged one month and more is given in Numbers 3:39 as 22,000. Correspondingly, the information that the number of the Israelite firstborn sons over one month old exceeded the number of the Levitical males over month old by 273, as told in Numbers 3:46, means that there were 22,273 Israelite firstborn sons. And the figures of 22,000 Levite males and 22,273 firstborn sons leave no place for the notion that the non-Levitical tribes numbered only a few hundred males -- even if concerning these tribes, the census figures reflect the numbers of males aged 20 years and more, rather than those aged one month and more. In other words, Humphreys approach, intended to salvage at least some measure of historical reliability from the Pentateuchal figures for the number of the Israelites who took part in the Exodus and in the wanderings in Sinai,  is simply baseless.
But does the glaring implausibility of the Israelite census numbers in the Pentateuch mean that the Pentateuch was not written by Moses during the wanderings in Sinai, shortly after the Exodus from Egypt? Some words of caution are in order. In the article which started the recent discussion in Vetus Testamentum, Eryl W. Davies, after having pointed out the difficulties with the census numbers and having criticized a number of solutions which different scholars proposed for this issue prior to 1995, concluded that these numbers "are purely fictitious and were simply invented."  Then, however, he proceeded to note that invention of fictitious numbers was fairly common in literary works of the ancient Near East intended to narrate historical events, and brought a number of examples for this phenomenon.  One of Davies's examples is the inscription of Sennacherib, king of Assyria, stating that during his military campaign against the kingdom of Judah (in 701 BCE), the Assyrian king took from that kingdom 200,150 captives and drove them into exile.  Now, the whole population of the kingdom of Judah at that time probably did not amount to 200,150 persons. Archaeologists estimate the population of the kingdom of Judah a generation before Sennacherib's invasion as only about 110,000 persons.  Nevertheless, Sennacherib's account of his campaign against Judah was written little more than a decade after the actual campaign, and there is no doubt that the campaign itself is a real historical event -- even though the number of the exiles from Judah is fictitious.
However, in the historical narrative of the Pentateuch, the numbers of the Israelites who took part in the Exodus and in the wanderings in Sinai are more than just numbers. They form and integral part of the narrative itself, so that abandoning these numbers as fictitious deprives other elements of the Pentateuchal narrative of any real historical foundation. For example, as mentioned above, the census of the Levites in Numbers 3:14-39 and the census of the firstborn sons in Numbers 3:40-43 gave rise to the notion that the number of the firstborn sons exceeded the number of the Levites by 273 persons. Since the Levites were called to cultic service in the Tabernacle (the portable sanctuary during the Israelites' wanderings in the Sinai desert) in lieu of the firstborn sons, the 273 "extra" firstborns that could not be replaced by Levites had to redeem themselves by payment of silver -- and the Pentateuch duly records the collection of silver, five shekels from a person, and its payment to the family of Aharon the Priest, Moses' brother (Numbers 3:44-51). If the numbers of 22,000 Levites and 22,273 firstborn sons are fictitious -- as they probably are  -- then the events described in Numbers 3:44-51 could not have taken place.
Or, in Exodus 38:21-31, there is a description of the collection of precious metals from the Israelites soon after the Exodus for casting different cultic vessels and constructional elements of the Tabernacle. Part of this description is the account of silver, which was collected from all the Israelite males over 20 years old according to the quota of half a shekel per person (based on the commandment given by God to Moses in Exodus 30:11-16). The number of the persons who contributed half a shekel each is specified in Exodus 38:26 as 603,550, and the following verses enumerate in detail the amounts of silver thus collected that were used for casting different constructional elements of the Tabernacle (Exodus 38:27-28). If the number of 603,550 Israelite males over 20 years old soon after the Exodus is fictitious -- as it certainly is  -- then the account of silver collection and use in Exodus 38:25-28 is also fictitious.
Now, if Moses had written down the Pentateuch (as revealed to him by God) and distributed it among the Israelites,  those of them who would be able to read it would clearly recognize that their people did not number over 600,000 males aged 20 years or more, nor 22,000 Levite males aged one month or more, and that correspondingly, some portions of the Pentateuch could not be describing any real events, even though these portions were phrased as historical narratives. It is difficult to assume that God would reveal to the Israelites, through Moses, a text, some elements of which would be naturally perceived as untrue, both by its initial audience  and by any subsequent readers capable of comparing different parts of the relevant text and of performing some basic calculations. Hence, the unfeasibility of the Pentateuchal numbers of the Israelites who took part in the Exodus and in the wanderings in Sinai constitutes clear evidence that the notion of the origin of the Pentateuch, endorsed by the Jewish tradition, is incorrect, and no numerical trickery can alleviate this conclusion.
 For an example of such explanation, see Alexander Rofé, Introduction to the Composition of the Pentateuch (The Biblical Seminar, 58; Sheffield: Sheffield Academic Press, 1999), pp. 11-27.
 Lest some readers object to the presentation of a decade-old discussion as "recent" in the title of this essay, it should be noted that for an academic field operating, to a large degree, within a conceptual framework set down in the 18th-19th centuries, a decade-old discussion may be duly classified as recent.
 Eryl W. Davies, "A Mathematical Conundrum: The Problem of the Large Numbers in Numbers I and XXVI," Vetus Testamentum 45 (1995), pp. 449-469.
 The only exception is the discussion by W. M. Flinders Petrie, in the beginning of the 20th century, which included an attempt to solution of the problem made along lines that will be discussed below.
 Davies, "A Mathematical Conundrum," pp. 449-450.
 Davies, "A Mathematical Conundrum," p. 450, n. 6. Actually, the marching column would have been much longer -- see below.
 Davies brought also examples from the book of Judges ("A Mathematical Conundrum," p. 450). But since the chronological scheme of the historical narrative of the Bible demands some years to have passed between the initial invasion of Canaan and the events described in the book of Judges, these examples are omitted here.
 See Davies, "A Mathematical Conundrum," p. 450. Davies added to the counts of Numbers 1 and 26 also 50% of the numbers given for the tribe of Manasseh (these 50% amounting to 16,100 men in Numbers 1 and 26,350 men in Numbers 26); but it is not clear that "half the tribe of Manasseh" mentioned in Joshua 4:12-13 included exactly one half of the tribe's members, rather than, for example, one half of the clans which comprised the tribe, and whose numerical strength cannot be gleaned from the censuses. In any event, the numbers given for the tribes of Gad and Reuben in Numbers 1 and 26 considerably exceed the number given for these two tribes and "half the tribe of Manasseh" in Joshua 4:12-13. It should be noted that in the censuses of Numbers 1 and 26, the males over twenty years old are explicitly defined as those obliged to go out to war (yotze' tzava', Numbers 1:3, 26:2), and in Numbers 32:16-18, 26-27, the tribes of Gad and Reuben (Manasseh not mentioned at that point!) promise Moses that only their women and children would remain in their tribal inheritances in Transjordan, while all the men eligible for war would take part in the invasion of Canaan.
 Davies, "A Mathematical Conundrum," p. 451. Davies (ibid., n. 8) quotes the study of A. Lucas ("The Number of Israelites at the Exodus," Palestine Exploration Quarterly 76 , p. 167), which, on the basis of population growth in Egypt in the early twentieth century CE, estimates that the seventy-persons strong clan of Jacob could have increased to 10,363 persons at most in the period of 430 years mentioned in Exodus 12:40-41. And it has to be mentioned that first, the medical treatment available to an average Egyptian in the early 20th century CE was considerably better than the medical treatment available in ancient times, and second, the Jewish tradition postulates that the Israelites' sojourn in Egypt lasted 210 years rather than 430 (Midrash Seder Olam Rabbah, chapters 1, 3).
 Davies, "A Mathematical Conundrum," p. 451.
 Lester L. Grabbe, "Adde Praeputium Praeputio Magnus Acervus Erit: If the Exodus and Conquest Had Really Happened," Biblical Interpretation 8 (2000), p. 25.
 The German mile was defined as equal to 10,000 steps (ibid., p. 26).
 Ibid., pp. 24-26.
 Or it may be not, since the number of the "mixed multitude" that accompanied the Israelites is not specified in the Pentateuch.
 For identification of the city of Ra'amses, see James K. Hoffmeier, Israel in Egypt: The Evidence for the Authenticity of the Exodus Tradition (New York - Oxford: Oxford University Press, 1996), p. 117. The name of the city of Ra'amses has a problematic implication for the Jewish tradition. According to the midrash Seder Olam Rabbah (chapter 3), the period of 400 years mentioned in Genesis 15:13 was the period between the birth of Isaac and the Exodus from Egypt. Now, Isaac is said to have been born when Abraham was 100 years old (Genesis 21:5), and Seder Olam Rabbah (chapter 1) places the birth of Abraham 48 years after the Tower of Babel incident, and places that incident 1996 years after the Creation of Adam -- which yields year 1948 from the Creation as the date of Abraham's birth, and year 2448 from the Creation as the date of the Exodus. Year 2448 from the Creation is 1313 BCE. But on the other hand, Ramesses II reigned in 1279-1213 BCE (see Kenneth A. Kitchen, "Egypt, History of (Chronology)," The Anchor Bible Dictionary, [New York: Doubleday, 1992], vol. 2, pp. 327, 329). So, if the Israelites' sojourn in Egypt ended in 1313 BCE, they could not have built the city of Pi-Ramesse, named in the Pentateuch Ra'amses, as they are said to have done in Exodus 1:11; nor could they move from that city to anywhere, as they are told to have done in Exodus 12:37, Numbers 33:3, 5.
 Karl W. Butzer, Early Hydraulic Civilization of Egypt: A Study in Cultural Ecology (Chicago and London: The University of Chicago Press, 1976), pp. 83, 93-96.
 Magen Broshi, "Methodology of Population Estimates: The Roman-Byzantine Period as a Case Study," in: idem., Bread, Wine, Walls and Scrolls (Journal for the Study of Pseudepigrapha Supplement Series, 36; Sheffield: Sheffield Academic Press, 2001), pp. 86-92. As the title of Broshi's article indicates, the maximal possible magnitude of the population of Canaan/Palestine in the ancient times was reached only in the Roman-Byzantine period, that is, in the 4th-7th centuries CE. In the period after the alleged conquest of Canaan by the Israelite tribes (the period which is defined, in archaeological terms, as Iron Age I, and the beginning of which is conventionally set to 1200 BCE), the total population of Canaan was, according to archaeological estimates based on the number and the size of the settlements known from that period, only about 60,000-70,000 persons (Magen Broshi, "The Population of Iron Age Palestine," in: Bread, Wine, Walls and Scrolls, p. 80).
Admittedly, Broshi's data apply only to the territory situated west of the Jordan River, which is less than the territory allotted, according to the Bible, for the settlement of the Israelite tribes after the Exodus. As mentioned in n. 8 above, the tribes of Gad and Reuben, and half the tribe of Manasseh, are told to have been allotted territories in Transjordan, to the east of the Jordan River. However, if we take the total of 601,730 males over 20 years old in the census of Numbers 26:51, taken before the Israelites' entry into Canaan, and subtract from it the figures for men over 20 years old from the tribes of Gad (40,500; Numbers 26:18), Reuben (47,730; Numbers 26:7), and the whole tribe of Manasseh (52,700; Numbers 26:34), we arrive at 460,800 males over 20 years old that must have settled to the west of the Jordan River after the Israelites' entry into Canaan. In fact, this figure is underestimated, as it includes neither the half of the tribe of Manasseh which was allotted territory west of the Jordan River, nor the Levites who must have settled in Levitical cities west of the Jordan River (the Levites were not included in the total specified in Numbers 26:51). Even so, however, the number of 460,800 males over 20 years old corresponds to about 1,500,000 total Israelite population that would have to settle in the land of Canaan to the west of the Jordan River -- considerably more than this land could ever have sustained in the ancient times.
 Colin J. Humphreys, "The Number of People in the Exodus from Egypt: Decoding Mathematically the Very Large Numbers in Numbers I and XXVI," Vetus Testamentum 48 (1998), pp. 196-213.
 Jacob Milgrom, "On Decoding Very Large Numbers," Vetus Testamentum 49 (1999), pp. 131-132; Mark McEntire, "A Response to Colin J. Humphreys, 'The Number of People in the Exodus from Egypt: Decoding Mathematically the Very Large Numbers in Numbers I and XXVI'," Vetus Testamentum 49 (1999), pp. 262-263.
 Colin J. Humphreys, "The Numbers in the Exodus from Egypt: A Further Appraisal," Vetus Testamentum 50 (2000), pp. 323-328.
 Rüdiger Heinzerling, "On the Interpretation of the Census Lists by C. J. Humphreys and G. E. Mendenhall," Vetus Testamentum 50 (2000), pp. 250-252.
 Gary A. Rendsburg, "An Additional Note to Two Recent Articles on the Number of People in the Exodus from Egypt and the Large Numbers in Numbers I and XXVI," Vetus Testamentum 51 (2001), pp. 392-396.
 Humphreys, "The Number of People in the Exodus from Egypt: Decoding Mathematically the Very Large Numbers in Numbers I and XXVI," p. 201.
 Ibid., pp. 201-202.
 In the Hebrew text, there is the conjunction wa- between the number of 'elefs and the number of hundreds: shishshah wa-'arba'im 'elef wa-chamesh me'ot. The most common meaning of wa- is additive, "and" -- so it might be possible to claim that the use of this conjunction means that the number of hundreds is to be added to the number of 'elefs in order to obtain the full figure, rather than be understood as equivalent to the number of 'elefs. However, the matter is not sufficiently clear, since the conjunction wa- may also have an explicative meaning, equivalent to the English "to wit" (see E. Kautzsch [ed.], Gesenius' Hebrew Grammar [second English edition; translated by A. E. Cowley; Oxford: Clarendon Press, 1910], §154a, n. 1b). The potential ambiguity of the conjunction wa- is best rendered, in the examples quoted in this essay, by the English comma.
 Humphreys, "The Number of People in the Exodus from Egypt: Decoding Mathematically the Very Large Numbers in Numbers I and XXVI," pp. 199-200, 203-204, 206-207.
 Ibid., p. 198, n. 6. Petrie's suggestion, and its development by other scholars prior to 1995, was discussed by Davies, "A Mathematical Conundrum," pp. 460-466 (see above, n. 4).
 The ancient Greek translation of the Bible (the Septuagint) reads here "eight thousands (= 'elefs) and three hundred," and in Humphreys's words, "Most commentators accept that 8,600 [in the Masoretic text] is a corruption of 8,300 or else the numbers do not add up to 22,000" (Humphreys, "The Number of People in the Exodus from Egypt: Decoding Mathematically the Very Large Numbers in Numbers I and XXVI," p. 213). This hypothesis of textual corruption is, of course, based on the understanding of the term 'elef in the context of the Levitical census as "thousand" -- hence the total of 22,000 in Numbers 3:39. Yet Humphreys, while rejecting this understanding, nevertheless assumed the correct figure for the clan of Kohath to be "eight 'elefs and three hundred" (ibid., Table 3).
 Humphreys, "The Number of People in the Exodus from Egypt: Decoding Mathematically the Very Large Numbers in Numbers I and XXVI," pp. 204-205, and p. 213, Table 3.
 Ibid., pp. 212-213.
 Humphreys, "The Number of People in the Exodus from Egypt: Decoding Mathematically the Very Large Numbers in Numbers I and XXVI," pp. 206-207; idem., "The Numbers in the Exodus from Egypt: A Further Appraisal," pp. 323-324.
 And besides, it violates one of the principles of Jewish belief as stated by Maimonides -- namely, that the whole Torah (Pentateuch) was revealed by God to Moses, and that no verse of it may be assumed to stem from other than divine origin (Moses Maimonides, Commentary to the Mishnah, foreword to the tenth chapter of Tractate Sanhedrin, principles eight and nine).
 Heinzerling, "On the Interpretation of the Census Lists by C. J. Humphreys and G. E. Mendenhall," pp. 250-251.
 Or, rather, eight 'elefs, 300; but the acceptance of this version is dependent on the notion that 'elef in the context of the Levitical census means "thousand" (see above, n. 29), hence it is not endorsed here. The version with 300 was, however, endorsed by Heinzerling.
 It is interesting to note that Gary A. Rendsburg, in his article of 2001 endorsing Humphreys's approach, referred to Humphreys's latest article on the topic under discussion, published in 2000 (Rendsburg, "An Additional Note to Two Recent Articles on the Number of People in the Exodus from Egypt," p. 396, n. 8), but failed to refer to the article by Heinzerling, which raises this literally lethal difficulty for Humphreys' theory -- even though Heinzerling's article was published in the same year and in the same volume of Vetrus Testamentum as Humphreys's (see above, nn. 20-21).
 Humphreys openly admitted that this was his intent ("The Numbers in the Exodus from Egypt: A Further Appraisal," pp. 326-327).
 Davies, "A Mathematical Conundrum," p. 466.
 Ibid., p. 467.
 For the translation of this inscription, see A. Leo Oppenheim, in: James B. Pritchard (ed.), Ancient Near Eastern Texts Related to the Old Testament (third edition; Princeton: Princeton University Press, 1969), pp. 287-288. This campaign of Sennacherib is the same as the one described in the Bible (II Kings 18:13-19:37), except that according to the biblical version -- at least in its plain and continuous reading -- the campaign ended with a disaster rather than a victory for the Assyrians. The question of the historical reality behind the biblical and the Assyrian records, however, is outside the scope of this essay.
 Magen Broshi and Israel Finkelstein, "The Population of Palestine in Iron Age II," Bulletin of the American Schools of Oriental Research 287 (1992), pp. 51-52, 54.
 "Probably," since the arguments specified in the beginning of this essay point toward the unfeasibility of the numbers of over 600,000 Israelite males over 20 years old during the Exodus and the wanderings at Sinai, rather than toward the unfeasibility of the numbers of 22,000 Levites or 22,273 Israelite firstborn sons over one month old. However, if the census numbers for non-Levitical tribes are fictitious, there is no reason to treat the census numbers of the Levites as reliable.
 It is interesting to note that the number of 603,550 Israelite males over 20 years old is the same as the summary figure of the census given in Numbers 1:46. However, the latter figure did not include the Levites (Numbers 1:47), whereas in Exodus 38:25-28, or in Exodus 30:11-16, where the commandment regarding the collection of half a shekel from every male over 20 years old is given, there is no hint of exclusion of the Levites from the duty of payment. Hence, the use of the number of 603,550 persons in both these cases, despite the different scope of the population to which the number is applied, reveals that we are dealing with an artificial, schematic figure rather than with a real and reliable census datum.
 See Deuteronomy 31:24-26. Of course, these verses tell only about the deposition of a Torah scroll beside the Ark of the Covenant in the Israelite sanctuary (if "this scroll of the Torah" in v. 26 refers to the whole of the Pentateuch, as accepted by the Jewish tradition; how this reference could include chapters 32-34 of the book of Deuteronomy is another question). But the phrase "that it may be there for a witness against you" (we-hayah sham bekha le-'ed) in Deuteronomy 31:26 implies some measure of public accessibility to the text of the Pentateuch. According to later traditional sources, Moses gave a Torah scroll to each tribe of the tribes of Israel (Midrash Pitron Torah [ed. E. E. Urbach; Jerusalem: Magnes Press, 1978], p. 294; Moses Maimonides, Commentary to the Mishnah, introduction to the section Zera'im).
 The perception of the initial audience is important in this regard, since in those cases in which some statements in the Pentateuch contradict the findings of natural sciences, it may be supposed that in speaking about the natural world the Pentateuch employed the notions which were current among the ancient Israelites -- such as the notion that the hare and the hyrax are ruminant, as told in Leviticus 11:5-6 and Deuteronomy 14:7. This point has been discussed in an earlier essay by the present author: "Of Hare and Hyrax, of Torah and Science: Thoughts about The Camel, the Hare and the Hyrax: A Study of the Laws of Animals with One Kosher Sign in Light of Modern Zoology (Southfield, Mich.: Targum/Feldheim, 2004) by Rabbi Nosson Slifkin."