Introduction

Numbers tend to both impress and confuse a lot of people. Because numbers lack emotive content, because they are simply symbolic representations of very real things like cars in a parking lot or people at a baseball game, numbers tend to be viewed as unbiased witnesses to indisputable facts. People trust numbers. However, numbers can be misleading. Numbers can be manipulated. Frankly, numbers don’t always tell the unbiased truth.

Mark Twain once observed [1],

Given the stated facts, one should stand in slack-jawed amazement at Mr. Twain’s observations. However, it is obvious to “any calm person, who is not blind or idiotic,” that the famous author didn’t take into account every important factor in the evolution of the Mississippi River when he wrote this paragraph. While Mr. Twain’s carefully selected criteria did indeed bear out his conclusion of an extremely long Mississippi of the distant past and an impossibly short Mississippi in the distant future, his numbers didn’t reflect the true facts. Sometimes, mathematical extrapolations lead to false conclusions. [2]

Now consider the average biblical inerrantist. Biblical inerrancy proponents claim the Bible is completely without error. Most believers who subscribe to the doctrine of biblical inerrancy assert that the Bible is the work of an almighty supernatural being. If God had written the above paragraph regarding the Mississippi River instead of Mark Twain, these believers would have been satisfied that the conclusions were solid facts. Indeed, some time in the distant past the Mississippi River stretched over one million three hundred thousand miles into the Gulf of Mexico. Such a belief in the infallability of scripture is printed in the popular Chicago Statement on Biblical Inerrancy, often cited by such advocates. In part, the Statement reads,

And,

This omniscient deity chose the very words of scripture so that it would accurately reflect his will of what would be written. Because the Bible is ultimately the work of a perfect unerring god, the Bible itself is a perfect unerring document. The Bible is a reflection of the divine being. If the Bible reports that the universe and all within it was created in a six-day period, then that is exactly what happened historically, according to the inerrantist. If the Bible claims, under divine influence, that a flood once inundated the entire planet killing all living creatures save a handful of representatives on a tiny ark, then that is exactly what happened, supporting scientific evidence or not. If the Bible tells us a man was killed on a cross and that this man then rose from the dead three days following internment in a rock-hewn tomb, the inerrantist has no reason to doubt this claim because the story came from a document inspired by an omniscient being. Likewise, if the Bible tells the story of a mass exodus of former slaves from the Nile delta following a series of miraculous signs from the almighty deity, and if the Bible places the number for the exiting slaves at something near 3 million people, most inerrantists do not even entertain the possibility that this number could be falsely exaggerated or in some way not historically accurate. After all, the Bible is the work of a god that cannot err and would not resort to exaggerations simply to prove a point or advance an agenda. Whatever else this god may be, it certainly has a high degree of integrity. If the Bible makes a historical claim that nearly 3 million people were freed from Egyptian bondage in the distant past, then that is exactly what the deity intended to say. If there is any error reading the Bible the error exists in the fallible human interpretation of the divine intention, not the other way around. If stories in the Bible strain credulity it is the limited human mind that is blamed for simply not being able to conceive of something as great as the activities of the divine being.

Over 300 years ago, however, a critical reader of the biblical text understood that there were numerous problems with the biblical tale of the Hebrew exodus from Egypt if the narrative was read as a literal interpretation of factual history. Hermann Samuel Reimarus, a German philosopher of the 1700’s, wrote:

Most modern readers of the text who are not Bible inerrantists have followed Reimarus’ lead and reject the historicity of the story of former Hebrew slaves exiting the eastern Nile delta some 3400 years ago. Despite inerrantist claims to the contrary, the fanciful tale is just too incredible to believe. However, some resolute fundamentalists, both Jewish and Christian, hold fast to the belief that the Bible tells a true and accurate story of how the early Israelites were freed from the land of Goshen by the Hebrew deity Yahweh and how they set upon a 40-year journey into the Sinai wilderness.

Of particular interest to me, and what is the subject of the article which follows, is the claim first mentioned in Exodus 12:37 that an astounding number of these former Hebrew slaves set out upon that Sinai trek. The passage reads [4],

In reckoning the total population of former Hebrew slaves leaving Egypt, the number begins by counting “men on foot.” This designation correlates to young men over the age of 20 (otherwise known as “of military age”). Details of this population figure is actually given in Numbers 1:1-50 where Yahweh is said to have given the command to Moses to count the people who had just come out of Egypt into the Sinai wilderness. According to the text, this occurred “on the first day of the second month, in the second year after they had come out of the land of Egypt.” This figure would have been virtually identical to the “estimated” number of people given as a “rounded” number in Exodus 12:37 two years prior. In Numbers 1:46 the reported population is given as a more precise figure of “six hundred three thousand five hundred fifty.” However, it is noted that this figure does not include the Levites [5] (a tribe of Hebrews separated out from the general population for purposes of priestly work), and in verse 3 it is specified that only men “from twenty years old and upward, everyone in Israel able to go to war” were to be counted. Since the number only counts young men able to go to war, this obviously leaves out women, the elderly and (as mentioned in the text of Exodus 12:37) children of both genders. Many students and scholars of the text calculate the number of women of similar age to be roughly the same as that of the men. Therefore, the young population of Hebrews would be placed at 1.2 million who left Egypt following the tenth plague. That number is then doubled to account for the elderly and children of both sexes so that the total population figure for the freed Israelites comes to nearly two-and-a-half million. The text of Exodus 12:38 claims that another untold number of people (a “mixed crowd”) also left with the former Hebrew slaves. In some estimations, therefore, the total number of people leaving Egypt with Moses was nearly 3 million!

If numbers can be misleading or used for purposes other than presenting the facts, the best way the truth of the matter can be uncovered is to dig for the reality behind the figures. In the following critique I will examine three different explanations for the Israelite population figure given in Exodus 12:37 (and echoed in Numbers) offered by those who want to salvage the historicity of the exodus narrative. The first, co-authored by James Patrick Holding [6] and Brent Hardaway, takes the biblical text at face value. They argue that the population figure given in the narrative is historically plausible and develop a mathematical calculation to “prove” their position. The second explanation for the astounding population figure is one offered by numerous sources but detailed by Colin Humphreys, a Cambridge physicist and author of a book arguing for “natural causes of the biblical stories,” particularly the “miracles of Exodus.” This position basically posits that a scribal error crept into the original text of Exodus and that what readers today encounter as a population figure for the Israelite males of military age in the hundreds of thousands actually originally read as a population figure of merely a few thousand. Finally, I will look at an explanation that also accepts the high population number but does so by attributing the figure to an ancient Near Eastern literary device.

“Real” Numbers

One method to account for the phenomenal census numbers of Exodus is to simply accept them at face value. James Patrick Holding, an Internet Christian apologist, penned an article with Brent Hardaway in which they try to defend some of the logistics involved with the biblical exodus, including a calculation meant to show the plausibility of the exodus population. They begin their proposal by asking a question anyone critical of the biblical text would ask, namely, how could a group of 70 Israelites explode into a nation of nearly 3 million people in merely 430 years, as the text suggests? [7]

Holding & Hardaway go on to claim that the purpose of their essay is to “examine some common objections to the practical historicity” of the exodus. However they immediately, and without much explanation, continue by saying they are going to exclude any study of “issues dealing with archaelogy [sic].” Their claim is to examine only the “mass movement of people…within the context of what is claimed in the Bible.” However, in order to understand the “practical historicity” of any given event, one must of necessity deal with disciplines that inform such practical historicity. In other words, and as I understand the term, a practical history is a history that accords with actual fact. History is the aggregate of past events as best as can be chronologically arranged from the available evidence. That evidence is ascertained from a myriad of sources, including material culture, which is the part and parcel of the archaeological trade. To ignore archaeological evidence when claiming to be studying the “practical historicity” of an event is to blind one’s study to a vast amount of important and highly relevant information.

More specifically, what is claimed in the Bible must necessarily be compared to what happens in the non-literary world humans inhabit if what is claimed is supposed to have occurred in the real world of the ancient past. Archaeology is the study of the remains of the ancient past and can shed a great deal of light on the stories contained in the Bible, if those stories are supposed to have occurred in the real past. The importance of archaeology (and other relevant scientific fields) is even more forceful when someone wishes to consider the “practical historicity” of the exodus, as given in the supposed “historical” narrative context of the Bible. To find this “practical history,” one must necessarily compare what is being claimed with what real history has to say. Therefore, to claim to study the “practical historicity” of the exodus event within the context of what is claimed in the Bible is also to commit oneself to a study of the Bible in the context of its own claimed historical setting. If the narrative context of a biblical story claims that event X happened at time Y, what use is the practical historicity of the claim if event X at time Y is not researched to have been a real event independently witnessed by archaeological debris? As William Dever observed in his book, What Did the Biblical Writers Know and When Did They Know It?,

To sanitize their study by refusing to look at the archaeology of the ancient Near East is to sever a huge mountain of evidence. Why Holding & Hardaway want to skip over this important field of contribution is not made known in their text. However, in critiquing their study, I will of necessity be looking at any and all evidence which informs the “practical historicity” of the exodus event as narrated in the Bible. To take only the biblical context as a source of study severely biases the investigation and will likely only produce a very lopsided outcome. It is not an honest study, as it does not take into consideration important and imperative sources of information.

After their puzzling claim to study the “practical historicity” of the exodus event without wishing to consult the archaeological data, Holding & Hardaway go on to look at the bare figures the Bible reports for the original clan of Hebrews that entered the Nile delta and how they plan to illustrate how such a small figure could have grown to such a staggering population. They first draw attention to Genesis 46 and the number of sons born to the patriarch Jacob. They give that figure as 51. Holding & Hardaway then make a very strange assumption. They write, “If we assume that there was one female born for every male, we would have 102 children. That comes to a total of 8.5 children per family.” The oddity of this statement is the assumption that for every male born there was an exact corresponding female produced for subsequent pairing purposes. They assert later in their article, again prompted by information from the biblical text, that the Israelites residing in Egypt did not marry foreigners but chose mates from within the same family of exiles. Such an assumption that for every male born there was a corresponding female begs the question of whether or not such a biological oddity is true. In order for Holding & Hardaway's calculations to work, for every son born there must have been a corresponding daughter born in another family (if we are to assume that incest was avoided). Holding & Hardaway give no independent information collaborating this assumption but instead simply assert their opinion and then build the rest of their calculations upon it.

Additionally, Holding & Hardaway’s assumption that each of Hebrew families will consist of 8.5 children is actually at odds with the biblical text they are attempting to defend. When studying Genesis 46 it will be noticed that some of Jacob’s children, contrary to Holding & Hardaway’s blanket assumptions, had far fewer than the average 8.5 offspring. For example, Perez only had two sons, Levi had three, Zebulon had three, Judah only had three that lived, Beriah only had two, and Joseph only had two. So, actually half of Jacob’s children had far fewer than the 8.5 average that Holding & Hardaway propose for their calculations.

To make their argument they relate the impressive prowess of the patriarch Jacob to a world record holder, Mr. Samuel Mast (Holding & Hardaway actually give his name as Samulel Must, but this is incorrect). Holding & Hardaway found this gentleman in the Guinness Book of World Records and claim that he illustrates “the population possibilities” of ancient Israelites in captivity. Mr. Mast is recorded as having died in 1992 with the most living descendants. What is strange with this example from the outset is that Holding & Hardaway had to reach into the Guinness Book of World Records to find an example to use to “average” out their calculations of how many descendents a character from a literary narrative would have.

Holding & Hardaway report that the Guinness Book of World Records records that Mr. Mast had 11 children, 97 grandchildren, 634 great-grandchildren and 82 great-great grandchildren. They then ponder what would have happened to Mr. Mast’s family, given this propensity to propagate, if they had moved to a foreign country and had “continued to live and multiply for 430 years at the same rate.” However, it seems to have escaped both Mr. Holding’s and Mr. Hardaway’s attention that the Guinness Book of World Records records unique events, and in this case is not relating something that is typical and extends through generations. Even what occurred to Mr. Mast is singularly unique even in his own family (otherwise he’d hold the tying record or would have been outdone by one of his progeny)! Another critic of Holding & Hardaway's article questioned why what occurred to one man's family (either Mr. Mast or Jacob) does not occur to everyone else's family. Their response, if realized, would even make it more impossible for Jacob's family to have populated as Mr. Mast's did. The question was posed to them:

Holding & Hardaway respond:

A lottery held does not necessitate a lottery won. Not all lotteries are won every week they are played. Holding & Hardaway propose, however, that every single family in every generation wins the “population lottery” over 430 years of playing the game!

But the reality is, not everyone in a family unit all win the same lottery, every year, for over four centuries. Certainly a patriarch here or there may have had a larger family than normal, but not everyone which is the requirement if Holding & Hardaway's calculations are going to work!

The mention of Mr. Mast is a wonderful anecdote but is irrelevant to the discussion underway. In addition to the singularly unique instance of Mr. Mast's accomplishment (which landed him as the only person to have had such "luck" in the Guinness Book of World Records, someone who lived in the 20th century cannot be compared to someone who lived nearly 4000 years ago. The worlds these men came from as they relate to mortality rates are fundamentally at odds. While Holding & Hardaway’s irrelevant distraction is interesting for its own sake, they make a number of fundamental errors in trying to use Mr. Mast as an average Hebrew in the Early and Middle Bronze Ages. One of these fundamental errors is in assuming that a family’s propensity to dispense children like Mr. and Mrs. Mast’s was carried out for 430 years (i.e. “the same rate”)!

Using Mr. Mast as a template for Jacob and his family in Egypt, Holding & Hardaway next calculate from the Mast’s 11 children, assuming each found a mate, that at the end of Mr. and Mrs. Mast’s child-bearing years their family’s total population would have numbered 24. This means of course that Mr. Mast and his wife should only be bearing children in the first generation. This would have been all well and fine if Holding & Hardaway had followed through with this assertion. However, as will be noted below, Holding & Hardaway’s calculations continue to have Mr. Mast and his wife bearing children through a total of three generations! Holding & Hardaway establish below that a generation is 29 years (but they give no indication as to why they have arrived at this figure). That means that Holding & Hardaway have forced the originating parents (and they continue this trend all the way through their scenario) to bear children for 87 years! However, even Holding & Hardaway seem to notice --even for the briefest of moments--the ridiculousness of this scenario. Answering a criticism of having grandparents live long enough to witness great great grandchildren born, Holding & Hardaway respond, "On average, a person would die sometime in the generation that his grandchildren was born. Some would die later, some sooner." So, it seems that Holding & Hardaway realize the absurdity of allowing everyone in Jacob's family to bear children for three generations but they nonetheless allow this absurdity to drive their calculations. Did the reader notice, however, that their answer does not address the criticism leveled against their calculations? The critic noted that Holding & Hardaway's calculations had everyone in Jacob's family, for 430 years, live until they saw their great, great grandchildren born. Holding & Hardaway respond only by noting that the average person lives to see his grandchildren born. This is only two generations into a family while the critic questioned Holding & Hardaway's four generation extension!

Having created this calculation, Holding & Hardaway assume for the benefit of their argument that each family descended from the original Mr. and Mrs. Mast continues “to procreate at a rate of 4.5 births per person.” They acknowledge parenthetically that this “works out to about 10 children per family.” But why do Holding & Hardaway assign this arbitrary number for the number of children born per couple? It is clear that such an assumption fits their scenario and reflects the “true-life, modern-day Jacob,” but is it at all typical that families generate “about 10 children” each? Even Mr. Mast’s family did not do this. His children had on average 8.8 children of their own (assuming, of course, that each child was in fact married –something we don’t know). In turn, these grandchildren had 6.5 offspring each (again, assuming that each child was married). The number of children per family declined after Mr. Mast’s own prolific seed spreading. The fact is, as noted from the archaeological evidence (which Holding & Hardaway admit they avoided in writing this article) reported on the University of Pennsylvania Museum of Archaeology and Anthropology website,

I confirmed this brief assessment in the book, Families in Ancient Israel. Keep in mind that Holding & Hardaway are asserting that each couple had 9 children each generation over three generations [(2 x 4.5) x 3]. That would equate to 27 children per female in a lifetime. The fact is, biblical, archaeological, and ethnoarchaeological research simply does not support their assumptions. In the book, Carol Meyers, Professor of Biblical Studies and Archaeology at Duke University, wrote,

Dr. Meyers is arriving at her figure of fifteen by adding together two nuclear families. In Holding & Hardaway’s estimation, they are only looking at the size of one family. Dr. Meyers’ research confirms that the average family size in ancient Israel consisted roughly of seven people. Even fifteen for the extended family of the typical living compound does not come close to the two parents plus twenty-seven children per lifetime that Holding & Hardaway envision for their ideal “nuclear” Mr.Mast-like family.

Granted, the data that Dr. Meyers uses above came from research done on “early Israel,” which “designates premonarchial Israel,” (p. 2) that is, prior to the 10th century BCE. Given this fact, Holding & Hardaway may wish to argue that this does not indicate a more “established” population of Hebrews that enjoyed the benefits of living in Egypt as opposed to the pioneering spirit of the earlier Israelites, prior to the establishment of the United Monarchy. Since this is a possibility I will also take a look at the nuclear family size (how many offspring a typical family had rather than the size of an extended family) from Joseph Blenkinsopp’s article, “The Family in First Temple Israel,” also from Families in Ancient Israel.

Again, even later in Israel’s history when the population was more established, the large families that Holding & Hardaway need to grow the Hebrew crowd in Egypt simply did not exist as a rule. In fact, according to Blenkinsopp, John A. O’Brein Professor of Old Testament at the University of Notre Dame, only royalty or the very affluent with “sufficient wealth to maintain several wives or harem women” had the ability to grow large families per generation. And remember, Holding & Hardaway’s calculations only have one female being born for each male. Even if a number of Hebrew men in Egyptian exile had large harems or several wives, that would have necessarily taken potential mates away from other men in the group. It’s not the number of males possible, it’s the number of available women able to birth children that drives population figures.

Adding to the scholarly opinion, Robert and Mary Coote note in their book, Power, Politics, and the Making of the Bible, “People lived in patriarchal extended families [in the biblical period: c1250bce-550ce], whose number and size were limited by the hardships endemic to life at the subsistence level: famine, disease, poverty. If she survived to childbearing years (her chances were not so good as a boy child’s), a woman might give birth to as many as five to eight children, spaced by postponing weaning, of whom only a few, if any, would survive early childhood.” (pp. 13-14).

So, archaeologically speaking, Holding & Hardaway’s idealized numbers seem to be the product of wishful thinking and avoidance of the real data.

Holding & Hardaway further their population calculations by assuming that each generation lasted 29 years [8]. They conclude “the descendants that give birth in generation X…would pass away in Generation [sic] X+2, when their grandchildren were being born.” However, I see another major error here with this assumption. If a generation lasts 29 years that would place those of the originating generation in their late 80’s for their deaths because, as will be noted later, the dying are not counted until the end of the third generation in Holding & Hardaway’s calculations. Where are their sources for coming up with these figures? Who can they quote that will authenticate these assertions?

In point of fact, I wrote to the British Museum’s Department of Ancient Egypt and the Sudan regarding New Kingdom [9] life expectancies and received a reply from assistant curator, Dr. Neal Spencer, who responded that the “average age at death” for Egyptians during the New Kingdom was probably in the neighborhood of 40. Authors Rosalind M. and Jac. J. Janssen note an inscription from an Egyptian source written circa 100 A.D. in their collaborative effort, Getting Old in Ancient Egypt,

The authors then note that while the “ideal lifetime is here a hundred years...note that at forty a man is said to have reached old age!” (pp. 62-63). R. & J. Janssen spend the next few pages in their book discussing other inscriptions that seem to indicate that, at the very least, some ancient Egyptians lived well beyond the age of 40. But it is important to note that these individuals are few and that each one of them held some important position in the Pharaonic government and were therefore privileged to a life of relative ease compared to that of the average citizen. An important consideration is that such elites likely had access to better healthcare. However, the authors make sure to point out that while the ideal age of death for the ancient Egyptian was somewhere near 110 years, “the actuality in terms of age attainment fell somewhat short of the desire. The real and the ideal lifetime were indeed completely different matters in Ancient Egypt.” (p. 69)

Because their book did not mention the average life expectancy of an ancient Egyptian, I wrote to Ms. Janssen and asked for her opinion. She returned, “The average life expectancy FROM BIRTH was 25 for men, and 21 for women – but these are figures obtained from Graeco-Roman census lists. However, in the New Kingdom I think that it would not have been much different. Obviously if you exclude the high infant mortality, and go to life expectancy at 1 year, then the figures would be much higher - at least 33 for men and 30 for women - the figures given in a recent general book by Teeter and Brewer.” [10] [11]

Of course, these are average expectancies and undoubtedly there were some people who may have lived into their 60’s or even 70’s. But, by the same token, there were plenty of people who died long before they had a chance to turn 40. Besides, those people fortunate enough to make it to “old age” were likely from the aristocracy with access to the “best medicine” available at the time and spared the day-to-day hard labor to which the average person was exposed as previously noted. Therefore, it is highly unlikely that the Hebrew crowd under Egyptian slavery “multiplied and spread” “the more they were oppressed.” (Exodus 1:12)

Stephen Moore and Julian Lincoln Simon note in their book It’s Getting Better All the Time: 100 Greatest Trends of the Last 100 Years, in which they study the demographics of the United States over the last century,

Look at the strides modernity – with its advances in medicine and higher standards of living-- has made in just the last 100 years. Imagine the conditions over 4000 years ago and try to fit Holding & Hardaway’s imaginative mathematics into this equation. We will have additional opportunity to discuss Moore and Simon’s findings as they relate to the biblical exodus population figures as this critique continues. However, it may be interesting to note that the conditions these authors mention for American blacks of the past centuries, as well as figures for the “less developed” countries, would likely be the data more accurate to apply to ancient populations.

Returning to their inventive calculations, Holding & Hardaway produce a “formula” by which they plan to stick their biblical population numbers based upon the data acquired from their discussion of Mr. Mast. That formula looks thus:

Following, Holding & Hardaway speculate (based on the biblical data) that after the first generation of children, the adults begin to intermarry so that “no one is added to the clan via that route.” Their formula then looks thus:

Notice here that Holding & Hardaway are allowing for no deaths in this second generational snippet (that is, in 58 years [29 + 29], not a single individual has died either in infancy, to childhood diseases, in childbirth, to accident or by any other means) and that the original two parents, who already birthed 11 children in the first generation, birth an additional 9 in the second. Even the example Holding & Hardaway start with, the Guinness World Record holder Mr. Mast, did not have 20 children so Holding & Hardaway have deviated from their “true-life, modern-day Jacob” already.

Proceeding with their scenario, they show the calculations for the third generation:

Notice now that Holding & Hardaway finally kill off Mr. and Mrs. Mast. However, they don’t do this until they have counted them in the original group of “starting population” for generation three that are still producing 4.5 babies each! Holding & Hardaway obviously don’t realize that they have Mr. and Mrs. Mast far surpassing even the Guinness Book of World Records! Following Holding & Hardaway’s calculations, Mr. and Mrs. Mast have had a total of (11 + 9 + 9 =) 29 children before they are finally released at the end of the third generation (and if Mr. and Mrs. Mast started out as newborns at the beginning of generation 1, they died at the age of 87)! And, surprisingly enough, Holding & Hardaway’s math gets even more bizarre.

In their article, Holding & Hardaway realize that people producing offspring at this phenomenal rate stretches the imagination. They comment, “Now, if this rate continued, the population at the end of 430 years would be over 50 billion (if you don’t believe me, do the math).” I agree. Please “do the math,” but do it considering mortality rates, population densities and the historical estimates of world and ancient Egyptian populations I will detail shortly. They realized the absurdity of their “math” because they acknowledge their proposed population would escalate to astronomical proportions even before Moses was born. In fact, their calculations skyrocket past the total population of the world in the 21st century! Most would think this absurd escalation in the population figures would have clued either Holding or Hardaway into looking at mortality rates, but it didn’t. In fact, they merely claim that the reason they are stopping this absurd growth in the Mast family is because they need to save Mr. Mast some Christmas money. Holding & Hardaway amend their calculations so that starting in the fourth generation each family drops to having only four children. Instead of 4.5 children per person (or 9 per female), they alter their formula to 1.15 [sic] children per person (I believe they meant to write 1.5 children so that the outcome would be 4 children per female).

But there is a biblical problem with dropping off the prolific population growth that starts Holding & Haradway’s calculations. They have already given a starting formula that gives a certain number of children being born per family to Jacob’s initial kin. Now, only three generations into 430 year sojourn (that is, according to Holding & Hardaway’s assumption of 29 years per each generation, only 87 years exiled in Egypt), the Hebrew population growth begins to dip. But is that what the Bible tells us? Not at all. And recall, while I disagree with the historical reliability of the Old Testament story of the Exodus, Holding & Hardaway are suppose to be attempting to defend its “practical historicity.” The Bible quite clearly states that the Hebrew growth rate did not drop by more than half, as Holding & Hardaway are proposing in order to “save some Christmas money” by the fourth generation in captivity. As a matter of fact, the Bible clearly states the Hebrew population growth actually increased as time went on.

But the more they [the Hebrews] were oppressed, the more they multiplied and spread so that the Egyptians came to dread the Israelites. (Exodus 1:12, emphasis mine)

If someone is going to use an example as an analogy then they should have the integrity to stick to it. When they start changing the information to suit their needs then any example they choose is pointless.

The fact is, at the time of the biblical exodus (c. 1447 BCE) the total population of Egypt was estimated at between 3 million (according to Neal Spencer) and 5 million (according to another source). Recall that the biblical narrative claims that upwards of 2.5 million people left the Nile Delta during the Hebrew exodus. Using these numbers, the Bible is therefore claiming that between 60% and 100% of the Egyptian population fled the land and went on a 40-year-long trek through the Sinai wilderness without leaving a visible trace behind or anyone at the time noticing! So, yes, by all means “do the math.”

Holding & Hardaway’s mathematics reflect the same miscalculations creationists make when trying to estimate the age of the earth by looking at population growth (see Exponential Population Growth). It is known that Mr. Holding has articles [12] placed on AiG (Answers in Genesis), a faith-based Internet Christian ministry that maintains the earth’s age as somewhere near 6,000 years, so the misleading calculations may be more than simply an oversight.

Now, of course Holding & Hardaway’s calculations assume, again, that each person in each generation is fully healthy, paired with a member of the opposite sex and able to conceive and bear live children that live to adulthood. It also assumes that people have children for three generations! Unfortunately for their argument, the real world doesn’t work this way.

Following through with their proposed changes, Holding & Hardaway present their calculations supporting the “practical historicity” of the exodus population claim thus:

They conclude this portion of their article by stating, “At the end of 15 generations, which would not even take the full 430 years needed, the total population is well over the 3 million most commentators suggest as the total population and without any strain to credulity, or even any miraculous intervention. Skeptical objections to the growth of the Israelite population are simply unreasonable.”

Although Holding & Hardaway's calculations are used to support their contention that there is nothing unreasonable about the Bible’s assertion that from 70 offspring of Jacob, a tribe of nearly 3 million was spawned in the short time of 430 years, their math --like Mark Twain's speculation on the evolution of the Mississippi River-- is based on carefully selected criteria. What is unreasonable in their calculations is that they expect there will be this staggering number of births while ignoring the facts of infertile couples, miscarriages, deaths in childbirth and infant mortality. Their calculations are based upon the unsubstantiated assumption that ancient life expectancy for the Hebrew slaves was 87 years and that not a single death occurred until each individual in the population was responsible for a grossly exaggerated number of offspring! Ironically, Mr. Holding wrote elsewhere of a skeptic’s attempt to criticize other numbering issues in the Bible, “It's not just a numbers game, folks. Think out of the box! But that is what our critic does not do, and his argument doesn't gain credibility by repetition.” This is sound advice and wise criticism. It is unfortunate that Mr. Holding did not follow it when considering the solution he and Mr. Hardaway presented to the population numbers of the exodus.

What both Holding & Hardaway have failed to do with their imaginative math (and, amazingly enough, readily admit it when they say they will not be looking at the archaeology of the issue) is consult the real world statistics of ancient populations (i.e., look at the hard data). For example, according to Meir Bar-Ilan, Senior Lecturer at the Talmud Department and Jewish History Department at Bar-Ilan University in Israel,

He concluded his study thus,

Now, recall, this is only a study of infant mortality rates. Dr. Meyers had remarked earlier that as many as one in every two births did not survive until the age of 5. So, the infant mortality rate for the ancient Hebrews may have been as much as 50%.

Moore and Simon note in their study of US demographics over the last century,

It must be carefully noted that these early figures are taken from data a mere 100 years old. Conditions even 100 years ago surpassed conditions facing populations 4000 years ago.

Noting ancient and modern conditions of motherhood and childbirth, Sarah Blaffer Hrdy, emeritus professor of anthropology at the University of California at Davis, wrote in her book, Mother Nature: A History of Mothers, Infants, and Natural Selection,

Note the “average number of children per woman (1.6)” is dramatically different than the 4.5 per person authored by Holding & Hardaway.

In addition to infant mortality, we do not know the percentage of women in the ancient world who died (thus removing them from the pool of females able to bear further children) while giving birth. Again, Moore and Simon note of conditions in the last 100 years in America,

Holding & Hardaway did not even take the time, it seems, to consider the obstacles facing their calculations and yet they felt justified in claiming that the astronomical population figures for the exodus refugees neither strains skeptical credulity nor requires miraculous intervention.

What of birth defects? Given the environmental conditions facing pregnant women in the ancient past, the lack of prenatal care and modern medicine to detect and in some cases correct congenital birth defects, how many children were born that had severe physical or mental defects that either killed them early in life or rendered them sterile or in some other way unfit to reproduce? And what of children who didn’t survive to the age of 19 as indicated above? What percentage of the population died out long before they could sire Holding & Hardaway’s desired 27 children per couple?

We also don’t have the figures for the number of men who actually were married and sired children. Surely, unlike Holding & Hardaway’s ideal scenario above, not every male and female from each generation married and produced children. Even from those who did marry, how many couples were infertile? Calculating this average on an ancient population is impossible, but according to the American Society for Reproductive Medicine, Centers for Disease Control and Prevention, infertility affects 10% of the current U.S. reproductive age population. The percentage of the reproductive population of ancient Egypt which was infertile had to be much higher (considering the fact that in every other such statistic they outmatched current numbers as well). The figures from the U.S. are taken from an age in which modern medicine has seriously curtailed, and in some instances wiped out, diseases and abnormalities that in bygone days would have rendered males and females sterile. Unfortunately for calculation purposes it is not possible to determine the percentage of the ancient population that could not have children (but the Bible gives us a hint that the number must have been fairly high since there is story after story of “barren” women. In addition, fertility rites and amulets were abundant in the ancient world. This is further evidence that infertility and infant mortality rates were quite high in the past).

Another consideration that Holding & Hardaway fail to note is the number of men that may have died before siring children, leaving widows who may or may not have found subsequent mates. And what about unmarried women? Surely there were a percentage of females who never paired off and thus were denied a chance to bear children. All populations contain people who suffered from these realities. We know ancient Hebrews did because the Bible mentions them.

Holding & Hardaway also do not consider the fact that not all pregnancies end in live births. There is a certain percentage of miscarriages in every 1000 confirmed pregnancies. Using today’s figures would be most generous to Holding & Hardaway’s calculations. This generosity is borne out due to the fact that today’s women have access to prenatal care and a healthier lifestyle (less intensive labor, proper diet, modern medicine) that was not available to their sisters toiling under the hot Egyptian sun. Recall that, according the Hebrew story, these women were subjected to what amounted to torture. Exodus 1:13-14 states,

According to a leading website on pregnancy and childcare, at least one in 10 known pregnancies ends in miscarriage. That is a staggering figure even today. Who knows what the figure was in the distant past? According to estimations, African-American “slave mothers suffered high rates of spontaneous abortions, stillbirths, and deaths shortly after birth. Half of all slave infants weighed less than 5.5 pounds at birth, or what we would today consider to be severely underweight.” These conditions in fact would more approximate the conditions of those Hebrew slaves in Egypt, but the truth is, we don’t know what the real figures would have been. [13]

What Holding & Hardaway also fail to take into account is the actual population density that can be supported by a given area. Without international trade, the influx of foreign food, goods, and modern food preservation techniques, an urban area can only subsist on what the immediate rural areas can supply it. In modern Egypt, large populations are supported by imported food and goods as well as improved farming techniques, proper and extended food storage that were unavailable to the ancient world. In the Egypt of c. 1400 BCE, a population could only inhabit as much of the land as the land itself would allow. Certainly one can calculate numbers all they want. Numbers do not require space or sustenance. Unfortunately for Holding & Hardaway’s purposes, the Hebrew slaves as well as their Egyptian masters had to live somewhere and that somewhere had to be able to support them.

Archaeological research of ancient urban areas also gives scholars important data from which to estimate the population size of major cities. For instance, according to Tertius Chandler’s book, Four Thousand Years of Urban Growth: An Historical Census, the first city in the world to reach a population size of 200,000 was Babylon in 612 BCE (p. 524/527). That is over 830 years after the biblical Exodus (c. 1447 BCE). A population of nearly 3 million didn’t exist in an urban population until the mid 19th century in London, England (p.526-527)! In fact, during the supposed time of the biblical exodus, Egypt’s largest city, Thebes in 1360 BCE (the closest date Chandler’s book offers), only contained about 80,000 people (p. 460). The delta city of Avaris (which some believe was either one of the cities the Hebrews built, rearranging Egyptian chronology or throwing the Bible’s figures out altogether, or a literary prototype for the biblical city of Rameses) had only 100,000 people c. 1600 BCE (ibid). Where did these over two-and-a-half million Hebrews come from when no single native urban population in Egypt even approached this staggering figure? If researchers can estimate the 80,000 people of Thebes in 1360 BCE from archaeological remains, they surely could find evidence of the nearly 3 million in Goshen in c. 1447 BCE. Strange that no such evidence exists if the Bible is recounting in error-free detail the history of ancient Israel.

Of course, these are questions, calculations, data and considerations that Holding & Hardaway do not answer or dare venture to contemplate in order to pretend that the growth of Hebrew slaves in ancient Egypt as recorded in the Bible does not “strain” credulity or require the miraculous intervention of the Hebrew god.

Consider the following calculations in reply to Holding & Hardaway’s magical numbers above:

In modern Egypt, the growth rate is estimated to be 2.1%. Between 1990-2000, the growth rate was 1.9%. However, we shouldn’t use these figures (or even their mean) to determine the growth rate of the Hebrew population in Goshen for a number of reasons. First of all, in modern Egypt, the infant mortality rate for the decade of the 90’s was near 5%. From the analysis above, we know that this rate was at least 30% in the ancient world. In modern Egypt, life expectancy is near 70 years. Most ancient Egyptians didn’t live past 40.

Why else can’t the population growth rate be 2% or above? Because, at that rate, the population will double in size every 35 years. This is certainly not the rate at which any ancient population exploded, especially not sustained over 430 years. Such a growth rate was not even possible until the 1700’s when advances in hygiene, agriculture and medicine were able to lower mortality rates and increase life expectancy. The balance between life and death was broken and starting in the 1700’s more people were born and lived longer lives than the number of people who died. In less than 200 years, the world’s population went from 1 billion people to 6 billion. But even in the modern world, it is rare for any one country to sustain a 2% growth rate for any great length of time. And it is certain that NO single modern culture (not to mention any ancient culture) has sustained a 2% growth rate over a 400-year period. Fluctuations in population growth rates are the only constants.

But, even though I detail why current population growth rates should not be applied to the ancient Hebrews of Goshen, I nonetheless want to show what those calculations would look like to demonstrate the incongruence between factual history and the biblical exodus story. In order to do this, I will need to use a simple formula for calculating a starting population multiplied exponentially by the percentage rate of growth each year multiplied by the number of years under consideration (in this case, 430) to tabulate my results. Here is what the formula will look like:

S*e^(P*Y) = A
S is the beginning population.
P is the percentage increase per year
Y is the number of years
And A is the final population

So, let us first consider an estimated growth rate of 1.9% --the growth rate of Egypt in the 1990’s of the Common Era. Recall that the initial population (S) entering Egypt according to Holding & Hardaway was 70.

70*e^(P*430)
P = 0.019
A= 247,334

At the average population growth rate in the last decade, applied to the Hebrew family that first entered Egypt and then began to multiply, in 430 years, even at 1.9%, the end figure does not equal the nearly 3 million needed to defend biblical inerrancy. Even if the final figure only applied to males in the population (even though the starting figure did not), this still isn’t enough to get to the number biblical inerrantists need. Consider doubling that figure to account for the women. Add it in again to account for the old. Add it again to account for the young. You still will only arrive at 989,336, a far cry from the millions that supposedly left Egypt according to the biblical tale.

Now take the 2002 estimated population growth rate for Egypt at 2.1%:

70*e^(P*430)
P = 0.021
A= 584,490

Ah, now this is much better! The Bible records that 603,550 males of military age came out of Egypt (Numbers 1:46). The number arrived at above considering a growth rate of 2.1% is off only by less than 20,000 (if the number is only to be applied to males). However, the number of Hebrew males of military age was necessarily higher than the 603,550 figure because this number does not include the men from the house of Levi (Num. 1:47), but why quibble? Now, if the number is quadrupled to allow for females, the young and the elderly (remember, Holding & Hardaway did not do this with their figures. They simply assumed all genders and ages at the end of their calculations. I am being more than naively generous), you arrive at 2,337,960 for the total population at the end of 430 years if you assume a constant growth rate of 2.1%. This is still less than the needed 3 million but why quibble over slightly less than a million people? (Besides, Holding & Hardaway did initially state that the number of Hebrews leaving Egypt was between 2 – 3 million.)

But therein lies the problem. As noted earlier, no population in the history of humankind has ever maintained that growth rate for such an amount of time. Although we can’t know the figures for almost another decade, what will the average population growth rate for Egypt be in the year 2010? Will it maintain at 2.1% or will it drop? Will it rise? There is no way to know for certain, but statistics lead one to conclude that the rate will likely not remain constant over a great deal of time.

Undoubtedly biblical inerrantists could go get another population growth percentage that will assist them in their calculation from some other modern country like Libya or Jordan, but like I stated, these are not consistent growth rates. So, before I close this calculation section using real figures, I want to take a look at the estimated percentage for population growth as it applied to the ancient Egyptians. This number should be far more applicable to the Hebrew population in Goshen than any modern figure. However, the percentage growth rate is almost impossible to calculate given the nature of the type of study. Ancient Egyptians simply didn’t take a regular census and record it for later generations. When I questioned Dr. Spencer of the British Museum in a follow-up e-mail, he declined to give me an estimated growth rate but commented instead, “the growth rate was significantly lower than modern Egypt, due to the high mortality rate (seemingly experienced in most ancient societies).” I also queried Dr. Roger Bagnall, Professor of Classics and History at Columbia University and co-author of The Demography of Roman Egypt (Cambridge, 1994), and he responded,

However, according to one source, the population growth rate for ancient Egypt may have been around 0.1%. Using this figure, the calculation for Holding & Hardaway’s initial 70 population would be:

70*e^(P*430)
P = 0.001
A= 108

No comment is necessary other than to note that this calculation lines up with the estimation that ancient populations took 30 to 60 generations to double in size, not less than one generation as Holding & Hardaway’s calculations maintain.

In closing this section, I would like to take a look at one more percentage rate that might get biblical inerrantists off the errancy hook. I have looked at the estimated population growth rate of ancient Egypt. I can imagine objections about my source. So, I was generous and used the population growth rate for Egypt in 2002 using a source beyond reproach. However, I can again hear objections that those figures reflect a very tiny portion of Egypt’s history. Other countries today have growth rates as high as 3.5% (Oman). This is true, but those high rates are accounted for because of the benefits of modern medicine among other considerations not applicable to the world of the ancient Hebrew slaves in Goshen. The numbers in various countries deviate for a variety of reasons. To apply the highest rate one can find for population growth in the modern world to the ancient world of the Hebrew slaves and extend it over four centuries is absurd and unwarranted. So, with this in mind, I have decided to make one final calculation. Instead of finding the lowest number for population growth, and instead of taking the highest, I will take the current population growth rate for the entire world (1.3%) as a mean and apply it to the very tiny population of Hebrews in the Nile delta nearly 4000 years ago.

70*e^(P*430)
P = 0.013
A= 18,741

Again, comments are hardly necessary.

One enormously begged question that Holding & Hardaway do not answer in their study is what happened to this population growth? If they are correct in assuming that the population growth remained constant over 430 years, why would this trend have changed in any dramatic way following the exodus? Even if there were a brief interruption due to the Sinai wandering and early conquest years, why didn’t the population boom given in Holding & Hardaway’s calculations pick up again in the years following? Why does the Bible not report millions upon millions of people living in the days of David and Solomon? As a matter of fact, it appears the rapid growth in population came to a crawl following the years in Egyptian captivity for 2 Samuel 24:9 reports that there were 800,000 soldiers in the northern kingdom of Israel and 500,000 in Judah. That makes a military population of Hebrews somewhere near 1,300,000. Doubling that number for women and doubled again for children and the elderly, the total population of the kingdom would have been 3,900,000. This is not even double the population figure for the crowd that left Egypt: 2,414,200. Recall that the Bible claims the Hebrew population started out at just 70 and in 430 years time grew to this staggering figure. The time separating the exodus from David’s census is roughly another 400 years. What was it about being a Hebrew slave in Egypt that made the Israelite people so fertile and productive? What was it about being their own nation that pulled the reigns in on the prolific childbearing? In addition, why did was this population explosion only limited to the enslaved Hebrews and did not seem to affect the native Egyptian citizenry?

Confusion Over Words

If the biblical inerrantist realizes the absurdity of accepting as historically “practical” the exaggerated population figures of Exodus and Numbers, they may take another stab at salvaging their belief in the error-free, divinely inspired book of God. Above I noted that biblical inerrantists “claim the Bible is completely without error. Most believers who subscribe to the doctrine of biblical inerrancy assert that the Bible is the work of an almighty supernatural being. This omniscient deity chose the very words of scripture so that it would accurately reflect his will of what would be written. Because the Bible is ultimately the work of a perfect unerring god, the Bible itself is a perfect unerring document.” With this paradigm in mind, recall that almost every inerrantist would readily agree with the Chicago Statement of Biblical Inerrancy. While maintaining a belief that the Bible is without error, some inerrantists nonetheless recognize that it has developed through the hands of more than a few translators. Regarding the error-free nature of the scriptures, the Chicago Statement says, “the whole of Scripture and all its parts, down to the very words of the original, were given by divine inspiration”(Article VI). Here, some inerrantists believe they have found a loophole through which virtually any discrepancy in the Bible can fit. For instance, if the biblical text in one book says that 4,000 horses fit into Solomon’s stalls (2 Chr. 9:25) but another book claims a staggering 40,000 did (1 Kg. 4:26), a biblical inerrantist can claim that, in the original autographs (i.e. in “the very words of the original”), the two figures agreed. Some inerrantists believe, in the face of insurmountable problems in the current text available to readers that there once existed a copy of the Bible --the original copy-- that was error-free. If there are errors to be found in the current text of the Bible –errors of numbers, for example—these errors did not exist in the original form of the text but were later interpolations, intentional or otherwise, inserted by scribes copying the text penned centuries after the originals.

This line of reasoning, using this loophole, is sometimes used to explain the whopping population figures found in the book of Numbers. Some apologists claim that the Hebrew word used to denote the “thousands” place in such passages as Numbers 26:51, “This was the number of the Israelites enrolled: six hundred and one thousand seven hundred thirty,” doesn’t really mean “thousand” at all. According to this theory, the Hebrew word for “thousand,” ‘eleph (or ‘lp), used in modern translations of the Bible has been based on a misunderstanding.

Probably the most coherent and detailed defense of this line of reasoning comes from an unlikely source. Not a biblical inerrantist himself, Dr. Colin J. Humphreys, Cambridge professor of Physics, authored an article in the Old Testament journal Vetus Testamentum (vol. 48 [1998], pp. 196-213) “The Number of People in the Exodus From Egypt: Decoding Mathematically the Very Large Numbers in Numbers I and XXVI” in which he argues that the extraordinarily large population figures in Numbers “…arises because the ancient Hebrew word ‘lp can mean ‘thousand’, ‘troop’, or ‘leader’, according to the context.” (p.196) Dr. Humphreys’ basic argument is simply that “thousand” should be read as “clan” or "troop" and that this misunderstanding did not exist in the “original autographs.” I will detail Dr. Humphreys’ argument momentarily but the summation of his article is that “[t]he total number of men, women and children at the Exodus was about 20,000 rather than the figure of over 2 million apparently suggested by the book of Numbers.”(ibid)

Of course, a figure of about 20,000 leaving Egypt squares better with the population increase formula I gave above if the population growth rate were somewhere near the modern 1.3% increase for the entire world. The biblical inerrantist, using Dr. Humphreys’ reasoning, may still claim divine inspiration of the Bible while excusing the literal reading of the population figure of 2-3 million. Following the lead of the Chicago Statement on Biblical Inerrancy, a biblical inerrantist could use Dr. Humphreys’ reasoning and claim that, in the original autographs, the actual population numbers were far more reasonable. Human hands have corrupted the copies of scripture that have come down to us.

Dr. Humphreys summarizes his lengthy calculations from his Vetus Testamentum article in his recent book, The Miracles of Exodus: A Scientist’s Discovery of the Extraordinary Natural Causes of the Biblical Stories. Never mind, for a moment, that if there are “natural causes” for the miraculous, “extraordinary biblical stories” that this of necessity nullifies the essential point of these biblical tales: the demonstration of Yahweh over the very powers of nature itself as a demonstration of the deity’s universal sovereignty. By finding “natural” explanations for the extraordinary biblical stories, Dr. Humphreys has virtually taken away from the inerrantist the ability to claim Yahweh’s supernatural authority over history, nature and, ultimately, humankind. Nonetheless, Dr. Humphreys explains how he came up with his theory and why the word translated “thousand” in the book of Numbers needs to be (re)translated “troops” in order to solve the otherwise unbelievable population figures for the Israelites who left Egypt in the exodus.

Dr. Humphreys writes of what prompted his calculations,

And then, summarizing his earlier paper,

I interrupt here because I wish to detail some of the assumptions Dr. Humphreys used in his “mathematical analysis.” He stated in his Vetus Testamentum article,

Dr. Humphreys calculates his figures based upon the “small amount of available evidence” which turns out to be the Bible itself! How can one hope to prove the objective accuracy of the Bible by assuming the Bible itself to be accurate? Dr. Humphreys may believe there is a “small amount of available evidence” for family size in ancient Israel, but as explained in detail above when considering the sanitized calculations of Holding & Hardaway, the archaeological evidence (which is abundant) is clear: family size at the supposed time of the exodus would not have accommodated “8 or 9 men per family” as Dr. Humphreys surmises. This would have made the average Hebrew family (assuming, of course an equal number of daughters to keep the pool of potential mates consistent) 18 or 20 members large! Of course, such an assumption is based upon an “average” which does well for easing the burden of creating a calculation but rarely reflects reality as we saw in our study of Holding & Hardaway’s mathematics. In the real world of families, Dr. Humphreys male average would of necessity include families with only 1 or 2 male children while other families had boys numbering in double digits not to mention the inclusion of families populated only of daughters as well as childless couples! Dr. Humphreys may feel this is a reasonable assumption given that he has accepted the biblical assertion that the Hebrews under intense forced labor nonetheless “multiplied greatly,” but studies detailed above indicate he would be wrong. People under enormous stress and hardship do not tend to multiply greatly. And even if the members of such a society do tend to attempt procreation at a higher rate than those of a more relaxed society (e.g. the Egyptians themselves), the hardship of their lives (nature of their labor, inadequate housing, poor –if any—healthcare, poor diet, etc.) tends to create higher mortality rates, both among the women giving birth and the children themselves. It is plain that Dr. Humphreys, like Holding & Hardaway above, has not taken into consideration the rich details offered by such relevant disciplines as archaeology and anthropology in considering the practical application of his mathematics. Nevertheless, Dr. Humphreys continued to explain his calculations in The Miracles of Exodus:

I simply cannot comment with much authority on the interpretation of Hebrew words or terms. I am not a Hebrew scholar but it must also be noted that neither is Dr. Humphreys. As for his calculations, given the data he wished to include, they stand very well in my limited opinion. Because I do not wish to get into a detailed study of whether or not ‘eleph should be rendered “thousand” or “troop” here based solely on an understanding of ancient Hebrew–other than to note that one should hold in high suspicion arguments concerning the meaning of ‘eleph when such arguments try to reduce the overall numbers of those involved in the exodus to something more rationally credible. This is assigning an intention to the original authors that the argument cannot possibly know as fact. Such an argument is mere speculation. I nonetheless want to seek out an alternative explanation for why the number of Israelite children –the 273 figure that struck Dr. Humphreys so “forcibly”—is much smaller than the other numbers in Numbers.

In an Old Testament commentary reprinted in 1981 from a 19^th century publication, theologians C.F.Keil and F. Delitzsch account for the odd number of “firstborn Israelites who exceed the number of the Levites” and why they differed so radically from the other population figures in Numbers. Because their argument is quite intricate, I wish to reproduce it below. The keystone upon which their argument rests is highlighted in red:

Without resorting to assuming which meaning of ‘eleph the original author had for the word in the book of Numbers, Keil & Delitzch seem to demonstrate that, given the context of the Bible narrative itself, the unusual number of 273 has a reasonable explanation. I leave it to the reader to decide who has presented the more acceptable argument; Dr. Humphreys or Keil & Delitzch. I, of course, do not believe either of the figures to be accurate, given the legendary nature of the tale itself and what current archaeological data offers as to Israelites origins.

Returning to Dr. Humphreys discussion, however, I do not want to comment any further than I have on the limited use of external data Dr. Humphreys considered in creating his calculations, either. For the sake of argument, I want to grant for the moment that Dr. Humphreys is correct and assume that Keil & Delitzsch are mistaken: in the original autographs, ‘eleph was intended to be read as “troop” and not, as later editions of the Bible have translated, “thousand.” It is important for a discussion of biblical inerrancy to realize that Dr. Humphreys accepts, at least in its bare bone version, the Documentary Hypothesis. He notes in his book that

Such assumptions, according to Dr. Humphreys, give him reason to conclude that,

Of course, physicist Dr. Humphreys claims to have understood the meaning of the ancient Hebrew word sometime in the late 20^th century CE but in some way insinuates that the proper translation of ‘eleph was completely lost on the native-speaking editor(s) of the book of Numbers. But there is another facet of biblical inerrancy that hasn’t been looked at yet. Most biblical inerrantists will claim that Moses authored the Pentateuch, as Dr. Humphreys lightly touched upon in the above quote, and almost universally reject the Documentary Hypothesis [14]. While Dr. Humphreys may be assumed to have successfully argued that the “original” copies of Numbers had “troop” instead of “thousand” interpreted for ‘eleph, this theory does not explain the large population number given in the book of Exodus—also believed to have been authored by Moses according to most biblical inerrantists.

In Exodus 12:37 it is said “The Israelites journeyed from Rameses to Succoth, about six hundred thousand men on foot, besides women and children.” Substituting “troop” here for “thousand” renders this passage, “The Israelites journeyed from Rameses to Succoth, about 600 troops on foot, besides women and children.” But how many men were in a troop? Dr. Humphreys does give us an idea in his book. He had claimed that his figures reached a conclusion that only 5,550 men (instead of 603,550) traveled from Egypt into the Sinai desert. If there were 600 troops that would mean on average each troop consisted of roughly 9 or 10 men. Of course, as noted above, averages are found because there are going to be some troops with significantly more members and some with significantly less. Dr. Humphreys believes he has demonstrated in his article and book via archaeological evidence [15] that this average troop size was historically accurate. However, there is a clue in the book of Exodus that calls into question Dr. Humphreys theory if we thus far find his argument acceptable–at least as if it were extended outside the book of Numbers and into the book of Exodus.

In constructing Yahweh’s tabernacle, Moses is said to have extracted monetary contributions for the cost. The money is gathered under the pretext that the collection will protect the “donators” from some sort of plague which would have resulted from the registration. This money came from all the male Israelites who had left Egypt and who had been counted in the census under discussion. According to Exodus 30:11-13,

Recall that those who are numbered in the census are males 20 years and older, capable of military service. It is important to note that, in the conversion of monetary values, a full count of 3000 shekels came out to be a talent [16]. The next we hear of this money is in Exodus 38:25-26 when the materials for the tabernacle is being tallied. This passage is most significant in determining the number of young adult males in the Israelite population. The passage reads,

Knowing that 3000 shekels is needed to constitute a talent, we can calculate that there were 603,550 half shekels collected from those “counted in the census,” a number matching exactly the population figure given in Numbers 1:46. [17] However, recall that Dr. Humphreys suggests that the word ‘eleph found in Numbers should be translated “troop,” not “thousand.” Doing so, then, renders the passages from Exodus 38 as a complete contradiction to the passage from Numbers. It would seem, however, that the author of Exodus believed the population figure in Numbers was literally “about 600,000 men” (Ex. 12:37) and reflected exactly the census numbers found in Numbers 1:46 in his verse 38:25-26. The conundrum facing the biblical inerrantist is therefore laid bare. If the inerrantist tries to claim, as does Dr. Humphreys, that there was an editorial mistake in the book of Numbers and that the word ‘eleph should be translated “troops” instead of “thousand,” how then do they account for the exact match in numerical calculations presented in Exodus 38:25-26 which conclude the monetary contribution from the congregation of male Israelites is 603,550? The author of Exodus (most biblical inerrantists assume this was Moses) makes a calculation that takes literally the (“current”) rendering of ‘eleph in the book of Numbers (also assumed by inerrantists to have been authored by Moses). If the same author is responsible for both books, how could he have meant ‘eleph to mean “thousand” in Exodus but “troops” in Numbers?

Even if it is assumed that later editors changed Exodus after the misinterpretation of ‘eleph in Numbers, a problem is presented in light of the claim of biblical inerrancy. Such a defense may claim that ‘eleph in Numbers originally meant “troop” and therefore only 5,550 males of military age left Egypt at the exodus. It was after an editorial change in Numbers which rendered ‘eleph as “thousand” that another editor discovered a numerical discrepancy between the population figure in Numbers 1:46 and the monetary figures in Exodus 38:25-26 and so altered the Exodus passage so as to reflect this correspondence. However, we have now launched ourselves into a realm most uncomfortable for a great many biblical inerrantists. To assume a later editorial mistake, such as adding an extra zero to the number of Solomon’s stalls is one thing, to assume later editorial rewriting of entire passages to create narrative harmony is another. First of all, such an argument assumes that an original copy of the Bible existed which is markedly different than the one we have today. In arguing that certain words and passages in our copies of the Bible were different in the originals is assigning an intention to the original authors that the inerrancy defendant cannot possibly know as fact. As stated earlier, such an argument is mere speculation. How can anyone prove what the “originals” really looked like?

Secondly, such an argument assumes that there was an isolated scribe (or school of scribes) who, in copying from the “originals,” misunderstood the intention of ‘eleph and interpreted it falsely. This argument obviously assumes, but does not postulate how, this scribe (or group of scribes) was ignorant of the term ‘eleph as it related to “troop” and so mistook it for “thousand.” Again, the argument assumes the native speaker(s) misunderstood a word from his (their) own language but that later speakers of English were able to detect the error (and did so knowing the full range of meanings for ‘eleph!). Further, the argument assumes it was this scribe’s copy, and no other, that became the copy from which all other translations were derived. How likely is such a scenario? Even if we grant that this editorial mistake occurred from this one scribe (or school), how is it that his (their) slip went unnoticed by his (their) community? Was this copy never read to a congregation who, familiar with the “original,” did not catch the mistake? It seems like quite the stretch of the imagination to have such a major error creep into a text and go unnoticed so much so that this single erroneous copy became the master copy from which all other translations were made.

Furthermore, this editorial oversight could not only have been isolated to the books of Numbers and Exodus. It must have permeated the entire Hebrew Bible. Consider, for example, a few passages from Joshua. In 4:13, 7:3, 7:4, and 8:3, 12 and 25, men grouped in thousands are recounted. Granted, the numbers as we have them in the text today are no more believable than the exodus population figures from Numbers. However, that is not the point. Dr. Humphreys’ assumption is that the editorial blunder by an inept scribe (or school of scribes) was potent enough to completely rewrite significant portions of scripture. Consider also the book of Judges. This “mistake” did not only invade the Pentateuch but also crept into other passages of scripture. See 1:4, 3:29, 4:6,10, 14, and 5:8. For special consideration, I will reproduce Judges 15:15-16 in which the word ‘eleph denotes a “thousand” as it relates to a number of men:

What now of the great feat of Sampson? Did he kill a measly 10 men, a mere troop? When do we stop assigning “troop” to ‘eleph when we find it translated “thousand” in the scriptures? When it suits our purposes? When it makes certain claims more palatable?

In addition, this awkward explanation does not account for the exaggerated numbers assigned to objects other than men of military age in the book of Numbers. Chapter 31 details the quantity of sheep (vv. 32, 36, 43), cattle (vv. 33, 38, 44) and donkeys (vv. 34, 39, 45). Are we to believe that the editor that mistook ‘eleph for “thousand” instead of “troop” in 1:46 got it right in these other verses? Why did he consistently make the mistake early in the book but then became more sharp-eyed later?

It may be assumed, given the difficulties presented above, that the “mistranslation” of ‘eleph by the scribe(s) was intentional. Postulating such a possibility relieves the argument from explaining why the error was never caught by those more familiar with the text. It also explains why the mistranslation was not due to a misunderstanding of the language. It is possible that the scribe(s) were deliberately exaggerating the figures (via some literary convention) for some (theological?) purpose. I will address below, in the following section, why such an explanation is unsatisfactory for an advocate of biblical inerrancy.

Thirdly, the assumption of this argument is that a historical exodus of Israelites left Goshen before being led to the land of Canaan. The implied acknowledgement of this argument is that the number of Israelites involved in this exodus, as reported currently in the Hebrew Scriptures, is admittedly inflated. The argument concedes that there is no historical evidence to support the current biblical assertion that upwards of 2 million former slaves exited the eastern Nile delta for a 40-year trek through the Sinai wilderness. Admitting this historical error, those who argue in favor of rewriting the Hebrew script as we currently have it postulate this editorial error to explain away the apparent discrepancy between the biblical text and historical realities. What this implies, fourthly, is that the deity in charge of inspiring the original, “historically accurate,” texts did not, or was incapable of, assuring that the inspired documents were kept free from later error. If the deity could ensure an original error-free copy of the divine script, why didn’t the supernatural inerrancy carry over into the copies?

Why would one believe the “original” manuscripts to have been delivered by divine inspiration without error, but that copies of these originals were allowed to conform to the frailty of human imperfection? Isn’t the Hebrew deity a good steward of his word? Is this even consistent with what inerrantists claim about the deity Yahweh? Inerrantists believe that the Bible was inspired by Yahweh. It is almost blasphemous to assume that someone tampered with and corrupted what an omniscient, omnipotent deity wished produced. It is natural to assume that if this deity is real, it would have protected, preserved and safeguarded its work. If it is argued that later editors made mistakes in copying the inspired word, how can this Yahweh be omniscient or omnipotent and yet be unable to protect his own work? If Yahweh could not protect the textual integrity of the Bible, how could he protect anything he says? Are subsequent generations –those following the generation of those who heard or read the word in its “original” form—simply to rely upon the assumptions of apologists who, like the pious but mistaken editors of the originals, have no real idea (and are obviously not under divine inspiration because, again, why are the apologists inspired while the translators/editors are not?) what was intended in the original copies? It seems impossible that modern apologists are insightful enough via the Holy Spirit to see into the past and reconstruct the “original” intention of the text while the very men with their hands on the so-called "original" sacred texts remained blissfully ignorant of Yahweh’s true intention while making their copies from them.

Some inerrantists may claim that Yahweh left it within man's "free will" to handle the texts as they saw fit. Yahweh does not "force" his will upon anyone and he "allowed" those entrusted with the "original" texts the "freedom" to corrupt them with human nature. However, that begs the question of why Yahweh imposed his "will" upon the supposedly inspired "original" copies that were penned in defiance of human free will and tendency toward fallibility. Why were the "originals" penned under direct influence but that the copies were not? There seems no reason for this to have occurred.

Besides, if an inerrantist claims that the numbers in Exodus and Numbers arrived in their current form due to some editorial tinkering, it is incumbent upon them to produce verifiable and convincing evidence that these passages were added into the original script much later in their compositional history. In my studies of the issue, I have not yet seen an adequate, much less a convincing, argument for such editorial tinkering. I have read many assertions, but little in the way of documented evidence.

Hyperbole

If troubled by the implications of later editorialization of the sacred text, inerrantists can still claim that the inflated numbers of Exodus/Numbers do not –and were never intended to—literally reflect historical reality. A few inerrantists will agree that the census numbers for the Israelites leaving Egypt are unbelievably high. They state, however, that such extraordinary numbers are not, as we have them, a historical tally of the population as Holding & Hardaway argue nor do they speculate upon the trials the “original” texts encountered on their journey to the modern reader as does Dr. Humphreys. They do not presume a prior “pure” copy of the text which had the actual population figures and assume later editorial deletions or additions to these figures by later copyists. Such inerrantists assume that the biblical text we have today is by and large a faithful copy of the originals, believing (as I think they are obliged to) that their god would assure the accurate transmission of his message. However, such believers also recognize that the Bible is a product of a certain time and was produced by a particular culture. Under this influence, these inerrantists claim that the inflated exodus population figures are simply a form of hyperbole, a literary practice common in the ancient Near East, they say. Hyperbole is a figure of speech in which exaggeration is used for emphasis or effect, as in I could sleep for a year or This book weighs a ton. (American Heritage Dictionary). To exaggerate is to “represent as greater than is actually the case.” It is to overstate an intended position such as to make the size of an enemy force larger than it really is or to overstate one’s importance in a matter.

An inerrantist claiming this viewpoint may say that behind the numbers we find in the text today lay the true population figures. The numbers have simply been inflated for literary and theological purposes. For example, an inerrantist might theorize that the population figure of 603,550 found in Numbers 1:46 is actually the true population figure multiplied by 100. Other population figures may also have been multiplied by 100 or perhaps in some cases by 10. Other inerrantists of this thinking may not attribute a mathematical formula to arrive at the “true” numbers of the exodus, but may simply assert that the numbers as they are presently given are hyperbolic and leave it at that, not speculating on the “real” exodus numbers. Either inerrantist will claim that the inflated figures were inspired by Yahweh to be included in the text as a literary device understood by the ancient audience. This literary device simply underscored the miraculous power of the almighty. There is no reason for modern readers to get excited or bothered over the exaggerated figures since they need only be understood as an ancient literary device. To understand this device accurately, they may claim, modern readers need simply to encounter the text within its ancient Semitic context.

But what trouble this “literary device” has caused! Clearly, there is no indicator in the texts of Exodus or Numbers that the population figures are to be understood as hyperbole. Skeptics and believers alike have read the narratives over the centuries as literal figures of the exodus population. Many skeptics have rejected scripture based partly on the absurdity of these numbers. I would imagine that some believers have lost their faith because they found that the numbers in Exodus and Numbers were historical impossibilities. They reason (rightly, in my opinion) that if the Lord could not get the facts of the exodus straight, how could they trust the Lord in more “important” matters?

How do we know when hyperbole ends in scripture and a literal reading begins? Even though there is no clear indication in the texts themselves that the exodus population figures should be understood as hyperbole, how do these inerrantists nonetheless determine that the numbers are hyperbolic exaggerations? The answer, of course, is the recognition that the numbers are simply too outrageous to be believed. But this is a modern realization. How do the inerrantists determine that the ancients who initially heard these stories understood the figures to be literary devices simply meant to underscore the majesty of their god? As in assigning editorial mistakes to later copyists, this theory is also pure speculation. The only reason modern apologists claim the exodus population figures are hyperbolic exaggerations is because they themselves recognize the absurdity of the numbers. As William Dever noted in What Did the Biblical Writers Know,

As far as I’m concerned, a clear example of hyperbolic language is found in Genesis 13:6, “I will make your offspring like the dust of the earth; so that if one can count the dust of the earth, your offspring also can be counted.” I may have granted that Exodus 12:37 is hyperbolic language if the rounded number of “about 600,000 men” was not followed in Numbers by an exact figure. If we must consider 603,550 to be a hyperbolic exaggeration I cannot conceive of a single claim made in the Bible--that unless supported by independent, verifiable and objective evidence--that cannot also be viewed as hyperbolic. What of the parting of the Red Sea? Surely such a story also mismatches with historical reality. Is this a case of hyperbole as well? And what of getting water from a rock? Or bread falling from the sky? How about each of the plagues that befell the Egyptians? None of these events occurred in history at least as far as they are recorded in the biblical text nor do such spectacular demonstrations of divine power exist today. Are we safe, therefore, in ascribing to each of these events the label of “hyperbole”? If the criteria for spotting hyperbolic language is the absurdity of the claim, then not even the resurrection of Christ is saved from such a label. I am certain no inerrantist is willing to allow the game to travel this far. Again, then, what are the criteria for determining a particular claim in the Bible is hyperbolic literature and which is not?

Another question arises considering the argument that the population figures for the exodus are hyperbolic exaggerations. Why did the omniscient deity inspire the text to be written in such a fashion? Why did this deity allow the expression of his story to be clouded from future generations by men writing in ancient literary forms? Was it not possible, or did it not occur to the god, to have the text written in unambiguous language? Did the culture that produced the original text not write in ways that simply expressed the bare truth of a given situation? If there were only 6035 men of military age (or some other more believable number) who left Egypt at the exodus, was it not in the literary repertoire of the ancient writers to plainly express this fact? Were they forced, by some cultural/temporal literary rules, to express this number hyperbolically? Would their audience simply not have gotten the point of the story from the plain facts? It seems impossible that this was the case.

The problem is compounded when it is realized that this claim of hyperbolic language used for the population figures of the exodus was a claim completely unknown to those intimately familiar with the text in the ancient world. For example, St. Ephrem the Syrian (303-373 CE), an early Church Father, wrote, “Six hundred thousand men left Rameses, and made camp at Succoth. The time they spent in Egypt amounted to four hundred and thirty years.” [18] Clearly the employment of hyperbolic language was lost on the early Church and yet modern apologists seem to be the recipients of this renewed knowledge. Modern apologists seem to have been able to figure out the literary intentions of the ancient writers which went unnoticed for generations of pious scholars. How do modern apologists recognize the hyperbolic language of the text when ancient authors such as St. Ephrem the Syrian did not? Some may claim that today’s scholarship is the beneficiary of multidisciplined research. Literary scholarship is supplemented and informed by studies in anthropology, archaeology, ethnology and other relevant fields. These various academic disciplines combine to create a more complete study of the text that was unknown to early students of the biblical text. While true, this explanation begs the question posed earlier with slight modifications given the current argument: If Yahweh could not protect the transmittal integrity of the Bible, how could he protect anything he says? Are subsequent generations –those following the generation of those who heard or read the word in its “original” form—simply to rely upon the assumptions of apologists who, like the pious but mistaken students of the text from centuries ago, have no real idea what was intended in the original copies? It seems impossible that modern apologists are insightful enough via the Holy Spirit to see into the past and reconstruct the “original” intention of the text, even if it is claimed that this is done under approved academic disciplines, while such academic gymnastics could have been avoided by the omniscient deity via a plain inspiration of the text, free of culturally and temporally bound literary conventions in the first place.

Let me stress that this explanation of hyperbolic exaggeration for the text is completely in harmony with a non-theistic study of the text. A person who does not subscribe to biblical inerrancy, much less a text inspired by a divine entity, will be perfectly happy with the notion that the exodus figures in Exodus and Numbers are built upon hyperbolic exaggerations. They have no vested interest in a god which apparently seemed bound by ancient literary conventions and seemed unable or unwilling to inspire a text which plainly stated the historical facts. For a non-theistic reader of the text, the biblical narrative really is a product of a certain culture and a certain time and was never intended to transcend (much less foresee) its own cultural/temporal boundaries. But the argument for hyperbolic exaggeration of the exodus numbers seems to imply that Yahweh was somehow held captive by this ancient literary device when inspiring his authors to write his text. It seems as though it was not possible for the deity to inspire his authors to not only write plainly for an ancient audience but also in anticipation for an audience that would appear after the Enlightenment.

As Darwin is said to have noted when he read the rationalizations of men who tried to reconcile the obviously poor designs of nature with the belief that God created all living things: “What bosch!! The designs of an omnipotent creator, exhausted and abandoned. Such is Man's philosophy, when he argues about his Creator!” Something similar could be said here: What bosch!! The intentions of an omnipotent and omniscient author, held captive or unable to break the literary constraints of a long dead generation. Such is Man’s apologet