Here I try to explore the various options for a logically feasible Exodus.
The traditional Exodus has some 2-3 million Israelites leaving Egypt. Unsurprisingly, I propose changes to these numbers. The story carries many elements one would expect in a micro-revolution like that: hardship, doubt, dissent, trials, failure and success both from inside (God's displeasure) and out (diseases, enemies).
Numbers and names are the first to be mutilated in textual transmission down the ages. So commonly that the 13th century monk, Caesarius of Heisterbach, attributed them to a demon who caused typographical errors in the work of scribes. With a large number of copies close to the source the errors can be easily detected. But for the Old Testament, such small variations can in some cases no longer be detected.
This happens especially when the language changes, and it's not something peculiar to the Bible. Vercingetorix, the Gaulish chief who fought Caesar at Alesia, is rendered as "Vergentorix" by Plutarch (Life of Caesar 25.3). David's name originates from the Phoenician "Dido." There were several different names for the kingdom of Mitanni depending on which nation around them you asked. Sometimes these changes are intentional. For example, some later copies of Acts omit the name of the magician at Paulus' court (Acts 13:6), bar-Jesus, because it is the "holy" name.
Numbers are even easier to lose because they are letter characters of the alphabet and can closely resemble each other. For example the well-known number of Solomon's stables 4,000 (2 Chron. 9:25) vs 40,000 (1 Ki 4:26) stalls.
Through archaeology, the Israelite population in the highlands in the 11th century BC is known to have been something like 40,000 at most. The cities would've had maybe more, but we could probably round the total to around 50,000. It took about 200 years for this number to double from 20,000 in the 12th century. Apparently there were enough Israelites to cause them to be mentioned as a major enemy by Merneptah in 1209 BC, so they must've numbered in the thousands by the late 13th century. If we take a 13th century BC Exodus, which I do not argue, then the number of Israelites leaving Egypt must've been at least 5,000-10,000. A 15th century BC exodus would essentially reduce this number in half and have around 2500-5000 leave Egypt; probably the lower value. This I think is the closer number, which explains many of the logistical problems of millions leaving, and also why the Egyptians did not bother recording (or explaining away!) their defeat. Thousands of slaves leaving Egypt and, as the Egyptians saw it, plundering the countryside would've certainly raised the attention of the Pharaoh. But in the long run, it would've been seen as a band of brigands who simply pillaged and left after annoying the king with a few lucky victories of escape.
This has to be put into perspective, though. At the time, the Canaanites numbered no more than 100,000. And so 5000-10,000 would've been a significant number; the Israelites didn't reach everywhere anyway (undoubtedly because of this). And it explains why the Egyptians are such a non-issue after the Exodus, whereas everyone in Jericho and beyond hears of what happens: the population of Egypt was in the millions! (Moreover, Jericho couldn't have numbered more than 3000 people at the time (comparable to Midian?)) The censuses and animals are later additions (like the legends of the names of the thieves on the cross: Desmas and Gismas - out of curiosity's sake); the captains of 10,000 (and judges) are also later additions (proof/reasoning?). So also most battle numbers. 40,000 by 1000 BC is an impressively high number and implies a dominance that must've included military victories for such a continuous suppression (for what reason?) of Canaanite culture (parallels?).
II. How Many Israelites?
If we take the numbers given in the various censuses in the Old Testament at face value, we come up with millions of Israelites. There are three countings: Exodus 12:37, Numbers 1:46, and Numbers 26:51, each of which give 600,000 foot soldiers, ages 20-50, colloquially called "all Israel" (Num. 1:49, 52-53; 26:51, 62-64). The number of people over 50 wouldn't have been that many. The number of men and children ages 1-20 would've bumped the total to at least 1 million males; 2+ million people total.
Alternate Theory 1: Eleph means "family" not "thousand"
The most popular alternative has the Hebrew word eleph, usually translated as "1000" to be translated as "family". So instead of 600,000 people, we have 600 families, which would be something like 5000-10,000 people (adding slaves and others who might have taken the opportunity to leave with them). Perhaps more, depending on what constituted a "family". If "head of household" was meant, this would be more people. Abraham, for example, could muster 318 soldiers against the Mesopotamian kings in Genesis 14, for a total of maybe 1000 people or more in his house. This theory, by itself, has numerous unsolvable problems, including the fact that the detailed breakdowns of each tribe in Numbers 1 and 26 makes the addition illogical with families, but mathematically sound as "thousands."
Alternate Theory 2: Unconventional Counting Methods
Perhaps we can't assume how or what the author was counting. Maybe the same people were counted more than once if they had different jobs. If a family has a father, a mother, a husband, a wife, and a child this is still a family of three and not five, right? A similar inflation can perhaps be suggested for Herodotus' count of Xerxes' Persian army. Each soldier had a helper/armor-bearer. Herodotus, perhaps knowing this, doubled his source's ~850,000 to ~1.7 million. Imagine if his source did the same and the actual number of soldiers was half of the 850,000 - ~425,000. This is still an unrealistic number, and it's technically an error, but the point behind the counting remains. It's possible someone was counting the entire Persian army and not necessarily that all of it was being deployed, and by the time Herodotus was writing the story transformed into a Persian invasion of millions. If something like this was our case here, we are still left with the task of discovering how many Israelites there were/could have been, and how we got the numbers in the text.
This website makes the interesting suggestion that Moses was counting all Israelite ancestors. So the number 600,000 in Exodus 12:37, Numbers 1:46, and Numbers 26:51 refers to the total number of Israelite men ever, dead or alive.
Genesis 46:15, 27 doesn't do this with Jacob's 70, but Numbers' theological reasons might be the difference. Num. 26:63-65 explicitly mentions that it did not count the previous generation. That the number of Israelites is actually fewer than in Numbers 1:46 could suggest that there were ~22,000 (actually more since the current generation is counted, fewer now due to the inhospitable climate), which is quite reasonable given the numbers Herodotus gives for expatriated groups from Egypt. The number of firstborns being 23,000 in Numbers 1 has long been recognized as too low for several million (not necessarily true with a high birthrate and infant mortality, meaning fewer firstborns survive the first month - why the Romans waited until day 9 to name their child). But 23,000 firstborns would still be too high for anything smaller than in the hundreds of thousands.
There is perhaps some merit in this suggestion. These are the kind of logical suggestions we must always remember are possible. In medieval chronicles, the opposite happened: the number of participants in a battle was usually based on how many knights there were, yet each knight usually brought with him 3-4 footsoldier commoners. So if a writer said a certain battle had 300 on each side, one could actually consider the total to have been 300 knights + 900-1200 men-at-arms for a total of 1200-1500 (Agincourt; two sources give both the lower and actual numbers).
Alternate Theory 3: Copyist Errors due to Glosses and Other Such
Another possibility, and I think this was somewhat the case with our Exodus numbers, is copyist errors due to glosses. A gloss is a comment regarding a certain passage that a commentator makes. When someone copies, these were sometimes mistakenly added into the text as if the original author wrote them. For example, famously the Johannine Comma in 1 John 5:7-8 was originally a gloss, perhaps by the ancient heretic Priscillian, which made its way into the Textus Receptus (the source for the KJV).
It's possible that some scribe decided to record the population of Israel by clan in his day, juxtaposing his numbers over the ones in Numbers 1. Perhaps sometime later the same person or someone else did this in Numbers 26. Or decided to "correct" the lower values. This was later misinterpreted by someone else who deleted the original numbers. Exodus 12:37 is an easily possible gloss, in the numbers, if not in its entirety - it appears randomly being so specific, but would be of interest to later readers in such a spot, and is completely rounded.
In David's day, the number of men of military age were ~1 million (1 Sam; 1 Chron). But this was after he'd taken large territories, which would have added to him many people. It took centuries to double in those days. One can speculate that the poor conditions of oppression after the Exodus until around Saul's days made the population grow very slow (in the Numbers 26 census the Israelites are actually fewer than when they leave Egypt in Numbers 1, supporting this; slightly more with the plague that killed 24,000 earlier). But archaeology has found that this is an unsustainable number. The Israelite settlements uncovered from the period of the Judges supported around 400 people each, and there have been 300 found all over the biblical area described in the Bible (supporting an Exodus, Conquest, and non-Canaanite origin for Israel and such (against Finkelstein)). Perhaps there are more to be found, but this means the population around 1200 BC was hardly more than 200,000-300,000. This number makes it possible for David, 200 years later with his many non-Israelite territories he conquered, to bring it to around 1 million for a total population of 2-3 million.
More proof is that the number of soldiers from Reuben, Gad, and Manasseh (it says every one of whom gathered) in Joshua 4:13 is 40,000, yet the censuses in both Numbers 1 and 26 give three times as many men. It's not that the population count in Numbers 26 is the total males or people (v.52) - as we noted that means all Israel 20 and up (v.2). For a reduction of the population by 1/3 from the Exodus to the Conquest 40 years later, it would mean that in the course of a generation some 1-1.5 million people died prematurely. Even if we take into account that semi-nomadism could've reduced and restrains population size/growth, this is unlikely to be unmentioned if it happened.
We can suppose that the value of 40,000 was something like "all veterans," or "volunteers," but at some point all these explanations start to sound like excuses when we look at all of our data. For example, the Israelites muster only 12,000 soldiers against five Midianite cities, whose population must have been more than this, but not by much. Individually, the divide and conquer strategy can successfully take each city without losing "even one man" - Jericho was a small city which is why two spies could be chased so (near) successfully. But the loot includes cattle that numbers half that of the Israelites' when they leave Egypt, which is not only suspiciously round (1/2 exactly), but also indicates that the Israelites themselves couldn't have numbered much more than ~30,000 people total at the time of the Exodus. In addition, there are numerous places where X value is said to be given partly to the Temple, the Tabernacle, the troops, and the people with the values written out, which would reflect more the original account, as it makes more sense for an eyewitness to "spell it out" for the people and himself for his own purposes, than for a later scribe to do this; but he changed the numbers.
Returning to the way the values changed, if we throw the first two theories in the mix here, we can suppose that the original values were something like X number of families, with various different ways of counting things, and a bold scribe decided to do the math to get solid answers and came up with what we have in the present text. This would explain why all the numbers are in the thousands in all three places, and eliminates the need to suppose someone was dumb enough to have so many unintentional glosses.
Writing in the 5th century BC, Herodotus notes that there were many groups of tens of thousands going in and out of Egypt, particularly the Nile Delta; though how accurate his information is on the numbers can be questionable. Certainly the Egyptians moved many tribes (Shasu) out of Egypt and into Canaan/Midian in the 13th and 12th centuries BC, though their numbers are speculative. Perhaps they learned from the Israelites and preferred this more ameliatory policy rather than to have to deal with more semi-nomadic uncontrollable elements, much like, for example, the Berbers of North Africa who were never really in full submission to the Fatimids (Jean of Joinville - they even followed their own sect of Islam, like other outlaws).
Whatever the case, we know that copying scribes made mistakes (4,000 or 40,000 chariots?), and sometimes even as a tool to reconcile perceived inconsistencies, such as the Greek and other texts of the reign lengths and correlations of the kings of Israel and Judah (Edwin R. Thiele gives a chart in his The Mysterious Numbers of the Hebrew Kings (3rd ed., 1983), pp.209-210).
III. Population Growth
If we suppose 70 people grew to 2-3 million in 430 years, the math could theoretically work. The ideal growth rate, with unlimited resources and land, doubles a population roughly every 25 years; even in their tens of thousands. The 70 are the men only, which means there were another ~70 women, for a total of around 150 Israelites (kids included as the 70 count does). Despite having wives, the Israelites could've taken extra wives from the locals, likely Western Semites like themselves who existed in large enough numbers by then. The women could've married servants, even Egyptian ones, without removing themselves from the Hebrew population (certainly not at such an early, close-knit to their family point) - e.g. 1 Chronicles 2:34 and Sheshan's daughter.
So we can suppose the 150 Israelites roughly doubled to 300 Hebrews within a few years. If we start doubling this number every 25-35 years we could obtain millions by the 430th year, even accounting for the persecution which still had the average Hebrew household have 3-4 children reach adulthood (Jochebed and Amram - two boys and a girl; Aaron - four sons and who knows how many daughters, as Miriam is noted only because of her connections to Moses).
And this is all without taking into account the biggest factor in population growth: immigration (Ex. 12:38; also servants). Populations from Canaan continuously emigrated to Egypt since at least 1800 BC at an ever-increasing rate, to the point that they established their own dynasties in Egypt (the Hyksos)! Even in Herodotus' day a thousand years later this was occurring in the hundreds. So even if we take an alternative interpretation of Exodus 12:40 (Gal. 3:17) and subtract the years in Canaan, leaving us 210-215 years, we have no problem. And the Kenite incorporation shows that the Israelites were never xenophobic enough to exclude anyone (reflected not only by the fact that the Kenites were Midianites, but by the foreigner-friendly laws in the Pentateuch). The rejections of Moabites and Ammonites from the Assembly of the Lord probably had exceptions (e.g. Ruth), or wasn't encompassing much (e.g. citizenship or to be a ruler; maybe some marriage regulations or perhaps, as usual, relating to money and taxes). Before that curse, there was no such ban on anyone (Numbers 15:15-16). It's completely possible many came under the Israelite fold, since they became the rulers of the Goshen. Settlers there would have easily assimilated, already being Western Semites like the Israelites, having the same language, culture, and currency.
This way, within 50 years Jacob's 70 can easily become tens of thousands. They are still few enough at Jacob's death 17 years later for all the Israelite adults to go on a pilgrimage to Canaan for the patriarch's burial, leaving the children and animals behind only (Genesis 50:7-8). Assuming the women went up with Joseph, leaving servants to take care of the children, this is still not more than a few hundred people as we estimated.
If we suppose the Israelites were 2+ million and stayed in Egypt 200-400 years, we can make the math work. But it needs an unrealistically idealistic framework as we'll show below (centuries of unhindered ideal birthrates despite oppression, space, etc), and hardly conforms with either the historical record or any kind of precedent.
IV. Data Supporting an Alternate Hypothesis
• Number of Midwives
For there to have only been two Hebrew midwives (Exodus 1:15), who weren't on a shift or changed for so long that their names became remembered, the population of Israel couldn't have been more than 50,000 at Moses' birth. Let's imagine there were 2.4 million Israelites at the Exodus. Under ideal conditions, the population would've tripled over 80 years. This means there would have been c.800,000 Israelites at Moses' birth (80 years earlier). But the Israelites were oppressed, which meant their growth rate would've easily been twice as slow, meaning one would've needed a lot more (over 1 million).
Let's assume the only "realistic" value of 800,000. The birthrate under ideal conditions is 60/1,000 (Robert Sallares, The Ecology of the Ancient Greek World (CUP: 1991), p.90), which is what we need here to get 2.4 million by the time of the Exodus.
This gives us a value of 48,000 pregnancies a year or 160 per day. Split between two midwives equals 80 births per woman per day, every single day! The midwives do imply that they couldn't be present at absolutely every one of them (Ex. 1:19 - perhaps also that they go around from house to house and help with numerous births per day). But for the Pharaoh (and implicitly the biblical narrative) to have believed they could've supervised enough of them to reasonably help with his genocide, they must've been responsible for a large percentage.
Even if we reduce the fertility rate to a low 20/1,000 and the Hebrew population to 400,000 (impossible for a 600% growth over 80 years), we get over 10 pregnancies per midwife per day. What does make sense is a somewhat high birthrate with a very high deathrate (a 3.5% (total) growth is implied by the census at the beginning of the 40 years of Wandering [Numbers 1:46], compared with a census at the end [Numbers 26:51], not forgetting the 24,000 who died in the plague (625,000-601,000/603,000); but otherwise with the disease, it's actually a negative growth rate of -0.3% for the whole period). A birthrate of 30/1,000 for 40,000 people gives us around 1-2 births per midwife per day, some of which they could reasonably skip and still be in charge of most of the Israelite community's new/repeat mothers. But then we cannot get the ending number to be 2+ million (40,000 people with a growth rate of 3% per year gives us 425,000 in 80 years; and this is assuming all of the babies survive to have kids, whereas we know from ancient Near Eastern graves that half or more probably wouldn't, so we'd reduce that 3% to 1.5% giving us 130,000 after 80 years).
The narrative implies these were the only two midwives responsible for the main number of Israelite births, since they are relevant enough to be named (Ex. 1:15). These must've been there for some time, but even if they were the only midwives for a short period of time, why would there only be two for anything more than a week? Certainly they were there long enough for the Pharaoh to request their help and to see a rejection by inaction. To suppose they were the head of some "midwivery" is a stretch and is implicitly contradicted by the fact that they personally seem to go around performing the business of a midwife (Ex. 1:19). So they are not replacable on shifts either. This isn't a beaurocratic state of Israelites in Egypt - these are peasants (what is a "midwife school" anyway?).
• The Number of Levites in Each Clan
In Numbers 3:17-39 we're given a count of the number of Levites by clan. The problem is that there isn't enough time for these three men, who enter Egypt childless, to have thousands of descendants by the time the Exodus happens!
There are three lineages: Gershon, Kohath, and Merari - the three sons of Levi. Since these were direct sons of Levi (Gen. 46:11), and since Moses' father, Amram, is a direct son of one of these (Kohath - Exodus 6:18), there is a period of no more than Kohath's lifespan (133 years - Ex. 6:18) + Amram's lifespan (137 years - Ex. 6:20) + Moses' age at the Exodus (80 years). This gives us 350 maximum years for the Israelites in Egypt. But we will show that this maximum number is far from what's possible.
- There couldn't have been any "skipped" generations, because the text states Moses' mother, Jochebed, was a direct daughter of Levi's (Ex. 6:20; Num 26:59).
- 1 Chr. 2:24 says Caleb, Hezron's son, married his father's widow (step-mother/concubine). The text is clear that Caleb is a direct son by this very reference. This is presumably the daughter of Machir Hezron marries at 60 (v.21). Caleb was 38 when the Exodus happened (Josh. 14:10). Can the entire stay in Egypt be any longer than ~150 years, assuming Hezron was around 100 when he had Caleb? Realistically, it's probably closer to 100 as the text implies Hezron took a wife in his advanced age and died shortly thereafter for Caleb to marry her. The text wouldn't mention his age if this wasn't so, a strange occurrence as well. But 1 Chr. 4:4 says Asshur was her firstborn, so perhaps this is a different wife, and theoretically could've been a later one. Either way, a 400+ or even a 215 year Exodus is highly implausible.
- Kohath had no male progeny prior to Jacob's Entry in Egypt, or they would've been listed in Genesis 46, so we can't extend his lineage prior to the 350 years.
The reason for this much shorter Egyptian Stay is explained in the Old Testament Chronology article.
Jochebed herself couldn't have been a lot older than 25 when Moses was born. Her older daughter Miriam is old enough to supervise the basket, so Miriam must've been at least ~10. Women in those days (until relatively recently) had children around 12-15, so we can't suppose Jochebed was much older than 25 when she had Moses. Thirty was the average lifespan of peasant women (and men as grave excavations show) anyway, and she was alive to raise Moses until he was given to the Egyptian princess (Ex. 2:10).
All of the above gives us 110-120 years. Kohath had no children when he came to Egypt. He has four sons, of whom only three have children (Ex. 6:18,20-22; 1 Chron. 6:16-30). These three children have eight sons (Aaron, Moses, and Korah among them). We can already see that the average number of surviving males per family around 2-4 (Aaron and Moses have two sons who live to have children, while Korah has three). Abraham's father, Terah, has three sons. So we can multiply the number of Kohathites by 1.5-2 (3-4 children replacing 2 parents) every 20 years (6 times - 120 years). Even with such generous estimates, we only get at most about 2,100 Kohathites after 120 years. We have to suppose the other 5 grandsons of Kohath had 4 surviving sons each, and so did each subsequent descendant of theirs to get ~8,000 Kohathites (which is close enough; perhaps the rest were servants or followers of some kind [Ex. 12:38]?). This just doesn't seem very likely to me (for example Aaron's son Eleazar seems to have had only one son - Phinehas).
The same can be shown for other tribes' descendants. For example, in 1 Chronicles 7:14-15 we are told that Zelophehad is a son of Manasseh. His daughters pleaded with Moses near the end of the 40 years of Wandering to have some of their father's inheritance as he had no male children (Num. 27:1-11). This means Zelophehad had recently passed away. He couldn't have been much older than 40, the average age of the servant class in Egypt. Since he's the second son of Manasseh, Manasseh would've been no more than 25-30. Joseph is around the same age when he has Manasseh, so again we confirm our alternate hypothesis of a 50-60 year gap between Jacob's Entry and Moses' birth. Overall, this suggests that the number of Israelites was originally far fewer in Scripture.
I won't mention that the lack of stratigraphical and archaeological data speaks against a 2-3 million man Exodus. Even if Kadesh Barnea does not indicate millions having ever lived at that time, similar semi-nomad settlements quickly disappear. However, every archaeologist can confidently say that the desert cannot support such a large population. True, God provided the Israelites with manna for food throughout all 40 years of the Wilderness Wandering. But even with that, such a huge population would've left many marks in the environment (digging for example), and contact with the locals would've left something behind (homemade altars?) even if we extend God's providing for the Hebrews' clothes not to tear to such things as pots, house roofs, and soccer balls.
Also some things used natural resources. The water for flocks and humans was frequently depleted. Overgrazing would've been a huge issue (perhaps God regrew the grass quickly? But even then, like Greece's coasts, the landscape changes). In addition to this, it's noted that they went to the lavatory outside the camp. Aside from evidence that would've been left behind such as countless dug holes, this would've been quite a walk for those near the middle (a good 20+ miles). Perhaps each clan from each tribe had its own perimeters. But the narrative seems to suggest the entire camp is meant. One could suppose it is generalizing for brevity's sake, as it does in some places versus others. If they weren't arranged in a circle, but a very long rectangle, or a diagonal of rectangles for each tribe/clan this could perhaps work. But this would stretch even longer than 20 miles, and I don't think is very realistic as a layout.
Interestingly, the Moabite fears in Numbers 22:4 say: "This horde is going to lick up everything around us, as an ox licks up the grass of the field." In Herodotus' description of the millions Xerxes brought on his expedition against Greece (Histories 7.21.1; 187.1), these drank up entire rivers and lakes! But the case doesn't seem so advanced with the Israelites (perhaps pointing away from millions); even a group of 10,000 people can be accused of the Moabite fears.
A joke has it that if the number of Israelites were lined up, the line would stretch over 100 miles! The math is quite true on this one: if we give about 3 feet of legroom, estimate that around 25% would've been too young to walk so would be carried, we have 1.8 million Israelites stretching to 5.4 million feet (1000 miles)! Even if we made the line 10 rows deep, this is still 100 miles. Add to this cattle and whatever equipment they would've carried such as tents, and the Pharaoh would've not only caught up with them at the Red Sea - he would've been stuck in traffic with the Hebrews!
But this isn't a serious argument. The biblical data tells us that each tribe encamped and moved in a round group. If we took the 2.4 million and placed them in a circle, giving each family (5 people) a tent with a radius of 10 feet (the tent plus space around it for livestock, movement, etc) gives us an area of 100pi feet. This means we have 48 billion pi square feet for the entire 2.4 million. Taking the square root of 48 billion, we get a camp with a diameter of a little over 40 miles. That doesn't feel possible, especially in the Sinai, and even if it's supposed the tribes were scattered with some form of swift communication, it just doesn't feel like it conforms with the biblical narrative or to be very realistic.
If there are dozens of 10-man deep lines, with some leadership in the front, 100 miles become only a few. But many of the trails would've been singular chokepoints, unable to be followed by more than a few people. One of the Egyptian pharaohs of an army of only tens of thousands took the better part of a day to squeeze through a spot that was "three men" deep, where a chariot could barely pass. Millions would've taken years - perhaps why the Wilderness Wandering took 40 years!
This last point is especially pertinent to the Red Sea crossing. The Pharaoh, who would've been way better organized and had to mobilize much fewer men and resources, was unable to catch up to the Israelites. These could have hardly gathered fast enough to cross the Red Sea within time, especially since they were mostly on foot (or slow donkeys due to the giant population and materiel they had to carry), while the Pharaoh had horsemen (Ex. 14:9). Exodus 14:9 says they were overtaken at any rate, so the Egyptians were very close to them before they'd crossed. Let's we assume a Dunkirk-like situation, where for some reason the Pharaoh waited several days. We have to figure out how wide the gap would've been. We know that God used semi-miraculous means to create the dry land: an east wind. The Israelites must have crossed at the legs of the Red Sea, which left leg can be as narrow as 30 miles. If we suppose a 100-man deep line went through, this would require a width of maybe 1/4 of a mile. For such a violent wind, all the Israelites would've been blown back to Egypt and Pharaoh's army with them. We have to remember the Red Sea has two slopes going down a mile on each side, which would've taken more wind to blow away, as well as additional time to climb. The shallowness of a body of water does not matter regarding drowning a soldier with full armor - as long as it was over 10 feet (for the horsemen), this would be enough. Jean of Joinville tells us how a knight tried to drop in a longboat which he missed near the shore of the harbor-less Damietta, and drowned. While trying to cross one of the branches of the Nile at the delta, numerous mounted knights drowned when their horses slipped from under them. We already calculated that a 10-man deep line would stretch over 100 miles. A 100-man deep line is too wide, and this would have stretched 10 miles. Simply put, 2.4 million men crossing anything would've taken weeks if not months. Perhaps the Pharaoh was hampered by the terrain and supply lines and couldn't subjugate the Israelites - this certainly would've been why he "got to them" but didn't really get them. But for months to pass, this couldn't have stayed that way.
During the Second Punic War, when Hannibal's brother, Hasdrubal, was in Italy in 207 BC trying to reach the infamous Carthaginian general with reinforcements, he was surprised by a Roman army of 50,000, and having himself something like 45,000 soldiers decided to bolt. Getting lost in the dark after his guides deserted him, the Romans caught up to him and harrassed his rear, forcing him to make a pitched battle with them which he lost and died at in the process, charging as the ancient writers tell us, "with sword in hand when all seemed lost". Moses encountered a similar situation with the Amalekites who flipped on their agreement for Hebrew passage through their land. They picked off stragglers at the Israelite rear. They obviously wanted a pitched battle too, which they got. It's hard to imagine they found it so difficult, like the Romans, to catch up when they probably wanted loot (like the Gauls who harrassed Hannibal's army during his pass through the Alps), and it's not like they would've taken long to change their mind even if they started to be wary of a huge foreign presence that could disrupt pastures/towns (why let them pass through in the first place if genuinely letting them? How could anyone (Edomites) actually think letting millions pass through your pastureland could result in anything other than a catastrophe? (Num. 22:4)). And the Amalekites believed they could fight off millions?!
• Military Engagements
For a 600,000 man army to be afraid of anyone, it's a little hard to believe. They could've tried to even take Egypt with that. Fewer numbers of migrating, equally untrained Gauls tried this against Rome and Greece in the 4th/3rd centuries BC and again in the 3rd century AD. Though 250,000 Gauls were no match for Caesar's 40,000 legionnaires. But these latter proved to be highly disciplined, skilled, and well-equipped. It is true that professional soldiers can, with the right equipment, training, and leadership handle hundreds and even thousands of poorly armed and ill-trained militia, such as the dozen or so French knights who fend off 7000 peasants at a castle during the Jacquerie as Froissart tells us. But the sheer amount of numbers gives the larger crowd such a morale that no one considers defeat possible; and sometimes they win against the sedentary society, as we've shown.
The Pharaoh takes only 600 elite chariots with him, and although other units are mentioned, it doesn't seem to be a pursuit of millions or even hundreds of thousands. The fact that the Pharaoh was able to have most of his army wiped out by the Red Sea could suggest it wasn't a big army, or else many of the horsemen would've been able to get to the other side, especially as it would've taken some time to assemble everyone to get to the Red Sea, and to start going through it. The chariots broke down due to the wind, but like the Israelites and their livestock, the wind could've been overcome by horsemen.
But a population of some 10,000-20,000 Israelites with an untrained militia of ~5,000 makes the fear of Egyptians, Philistines, and Canaanites not only understandable, but magnifies God's miracles of military victories and explains God's anger and incredulity at their disobedience. One can easily hear something similar to the prophet that warned Amaziah from taking the Edomite idols (2 Chr. 25:14-16).
With 600,000 soldiers, it's hard to understand how the Israelites were losing without Moses' hands being lifted (Ex. 17; Num. 14:39-45, etc). Perhaps the age restriction of 20-40 could've made sense in Moses' day. The leadership of the east side by Judah (Num. 2) cannot be taken to mean a later projection of the kingdom of Judah. True, verse 9 says Joshua (perhaps inexperienced) chose some men. I suppose it's possible, especially if God wanted to prove a point, but it seems like this point had a real basis in their military weakness (cf. 1 Sam. 5-6 where the Philistines use their earthly military might for which God chastises them). These soldiers were perhaps learning, but the generation after them has little problem subduing Canaan under Joshua, and they hadn't really had any experience (starting with Og and Sihon). The fact that in Numbers 31 only 12,000 soldiers are used, whereas in the assault on Jericho, 40,000 are used, where Jericho is one city of no more than 3,000-4,000 people (1500-2000 people who could fight), shows that these weren't mighty warriors in Joshua's day, and that perhaps the number of people is a later gloss, considering the relatively low battle numbers and casualties (100,000 Israelite militia kill only 3000 men in Judah - 2 Chr. 25:6, 13 - although the area wasn't that large).
• The Firstborn Redemption
The rounding of the number of non-firstborn Levites (22,000) as opposed to the firstborn ones (273) suggests the former number isn't from Moses and possibly shows a later person. Similar such rounding due to a distance from the source (which would not be the case for Moses) is found in many other places. Occasionally this could be a coincidence (e.g. Jer. 52:28-30). But to suppose that the 273 firstborn Levites are contrasted with the even 22,000 non-firstborn, is a little too unlikely. One can say that the non-firstborns were unimportant enough and could be rounded, but if Numbers 4 rounds the Levites 30-50 years old to the nearest 10, it's extremely strange to round the total Levites a month and older to the nearest hundred or thousand, but then specific enough regarding the 273 leftover Israelite firstborns to pay 5 shekels each, giving exactly 1365 shekels.
V. Neutral Data
• Number of Firstborns
Numbers 1 and 26 give ~23,000 firstborns, one month and older. Ancient Near Eastern graves consisted of: 0-5 year-olds: 35%; 5-18 year-olds: 15% [Corrine L. Carvalho, Encountering Ancient Voices: A Guide to Reading the Old Testament (Saint Mary's Press: 2006), p.345]. We can round this statistic to 0-20 at 50% for convenience.
This number is confirmed by the number of Levites: the total a month and older is 22,000 (or 22,300) (Num. 3:39), and the number of Levites 30-50 years old was 8,580 (Num. 4:48), which would be close to half if we made it 20-50 years. In comparing the censuses in Numbers 1:46 and 26:52 over 40 years, the Israelite population growth rate was basically 0% (~0.09%/annum if we count the 24,000 dead in the plague in Num. 25). But we can calculate the number of firstborns at 2%. Therefore, the amount of Israelites 20 and younger was around the same amount as those over 20, giving us a total of ~2.4 million Israelites at the time of the Exodus.
This would make the number of male firstborns 2% of the male population. Did a firstborn female disqualify the first male born after her in the family? Romulus' purported saying cited by Dionysius of Halicarnassus says: "Romulus demanded that all the city’s residents should raise all their male children and the first born of the girls and not kill any child under three unless the child was disabled." The special treatment of the firstborn girls would seem to imply the firstborn males counted in Numbers 1 and 26 were the eldest male children of any given family.
With a plausible 46/1,000 births per year, 25/1,000 death rate per year, yielding a 2% annual growthrate from parallel statistics where the average lifespan was almost 40 (Madagascar in 1966 - [Robert Sallares, The Ecology of the Ancient Greek World (CUP: 1991), p.90]). This means there must have been no fewer than 500,000 Israelites when Moses was born.
In ancient Rome it was customary to wait a little over a week before naming a child - that's how high the infant mortality rate was. To avoid death before baptism, in medieval and pre-modern England baptisms quickly took place on the third day for this same reason (presumably one had to wait "in line" and couldn't do it right away). This is probably why only infants 1 month and older are counted in the Numbers 1 census. We can therefore suppose that ~20% of children died under one month.
The average family would've had up to 6-7 kids, of whom around half would've survived to having children of their own. For example, Moses' parents had three surviving kids: Miriam, Aaron, and Moses. Aaron had 4 sons, two of whom died without children. Zelophehad had 5 daughters and no sons. The genealogies in Exodus 6:14-25 also confirms this. Being semi-nomads, they needed a large number of children. The deathrate for children was even higher than that of adults. This probably reflects the information of whatever later author put this information, though it's maybe strange as to how he obtained the information regarding firstborns (which could be easier under Moses, and would make more sense). I don't think like some other commentators that this "low" amount of firstborns indicates a smaller Israelite population.
The more children each family had, the lower the number of firstborns, logically; and we need a very low number (1.5%-2%). But even with 6 surviving children who have children of their own, utilizing the above ancient deathrate statistics, the number of firstborns in a given population would be 6%-7% (reducing the actual number by 50% because some would be firstborn females, some males).
One could suppose that the firstborns, being older, were worked to death for more years and on harsher projects than the younger. Regardless, these numbers could've been written by Moses or a scribe, or it could've been a later author's glosses, reflecting firstborns from an earlier era when the Israelite population was 700,000 men, women, and children (if the 22,273 firstborns are 6.5% as we calculated), and not 2.4 million as in his day. Such censuses wouldn't have taken place until Saul's day, or perhaps in one of the later judges such as Samuel when things were more stable, and those numbers reflect this.
• Number of Animals
The number of animals can be a good indicator of how many people there are. However, even if the Bible had specified how much livestock they had with them on the Exodus, this data would be irrelevant because much of it was plundered from the Egyptians in addition to what others brought who joined them (Ex. 12:36, 38).
The one place we do have some numbers - the loot taken from the Midianites in Numbers 31 - doesn't really tell us anything other than the size of the population they attacked. Among other livestock, the Israelites find 675,000 sheep (Num. 31:32). Knowing that nomadic pastoralism requires 36 sheep per person (P. Nick Kardulias, The Ecology of Pastoralism (UPC: 2015), Ch.3 (p.16 of it)), this means the total Midianite population was something like 20,000 with 6,000 able bodied soldiers. Probably, like the Mongols and others (e.g. Kamose's reconquest of part of Lower Egypt), at least one city surrendered, especially after the extermination of the first city, to receive mercy that never came, like the Mongols at the Battle of the Kalka River (1223). Maybe all could've surrendered if the 12,000 men were divided to obtain the other four cities' surrender simultaneously in exchange for mercy. That there was no great battle is suggested by the fact that most of the population was taken (with 16,000 captives - v.46). Perhaps the plague, maybe some kind of venereal disease, eradicated or crippled many of them (similar to the pain of circumcision in Shechem, allowing two of Dinah's brothers to slaughter the entire male population). These were divided into 5 cities/regions (5 kings), so they were outnumbered by the Israelites, who could have easily employed guerrilla tactics (Froissart; similar tactics against Jericho in Joshua 6), resulting in zero Israelite casualties (Num. 31:49). If the Midianites weren't united, this would've been infinitely easier for Moses - similar divisions amongst the Seljuks was largely responsible for the First Crusade's success. Each Israelite tribe gave 1,000 units, which doesn't tell us a lot. They used 40,000 troops to attack Jericho (Josh. 4:13), showing that the Israelites had no standing army or warrior "caste". Kathleen Kenyon says that, owing to the size of Jericho, it could've had at most ~3000 people. This would mean something like 2000 men and women who could fight (cf. Judges 9:51, 53). Perhaps this number could've been swollen by people flocking in from the countryside due to the Israelite advance, but not by much (again owing to the size). It would explain why Rahab had to lie to only one group of guards, who would've taken a lot of time to look amongst the population, yet small enough to only have one such group looking, who were the only ones who spotted them (the only ones looking), reaching Rahab quickly; though the Hebrew spies left soon after. And only two spies are sent. The fact that only 12 spies are sent to reconnoitre Canaan also says something about the size of the operations and Israelite population. The size of the fruit they bring back also shows that the Israelites must've been very small in stature as we've noted before, and for this and other reasons, were also probably not very formidable warriors (and couldn't have eaten much, making the amount of food they needed smaller, but not small enough); explains how they found giants in Canaan too. Much of the 40,000 Israelite soldiers could've been armor-bearers and squires - like David in Saul's army. Many were probably in reserve. If we are to judge from the fact that Jericho never had more than 3,000 people (=1,000 militia soldiers) and Israel mustered 40,000 troops, then the number of Midianites could've easily been three times smaller - i.e. 7,000 people with around 2000 soldiers, divided amongst 5 cities (400 soldiers per city). Especially if a lot of the livestock belonged to the king/nobles.
The number of Midiniate persons can be calculated another way. The amount of money the army takes from them is 16,750 gold shekels (Num. 31:52). This would've equated to no more than ten times that number in silver shekels (poor societies had a very low gold-to-silver ratio). Again, a lot of this would've belonged to the 5 kings. If we calculate that each noble gave something in the vicinity of 25-50 (silver) shekels, following the tribute Menahem extracted from his nobles in 8th century BC Israel, we calculate around 3500-7000 nobles. Probably this was closer to 1000-2000 because the kings would've given most of it (similarly to the amounts the Conquistadors obtained from Native American chiefs who didn't even really value the scarce gold all that much, yet were still able to give tens of thousands of pounds [De Las Casas]). The egalitarian nature of pastoral peoples means that possibly there were no more than a few commoners per "noble" (although a bit different, in medieval Europe the average knight had around 3-4 men-at-arms with him; more important lords such as Jean of Joinville had 20 knights; the king was frequently surrounded by only 8 knights as his personal bodyguard of valiant knights). This means that the total population of all 5 cities would've hardly exceeded 4000-5000 people for all 5 cities. The Midianites seem to have had elders (Num. 22:4), but also kings, like the Moabites who had both (Num. 22:4, 7), so these were eminent messengers.
Looking at the 32,000 females under the age of 15 (v.35; the rest were killed - v.17-18), this would mean the total population of females was ~75,000, or 150,000 with the men. This isn't impossible for even 5,000 soldiers to accomplish. Most of these people were probably taken from surrounding villages, and the cities themselves would've had probably no more than a few thousand people. This could easily have resulted in zero Israelite casualties (unlike Jericho?) and with guerilla warfare, a protracted siege isn't necessary (Froissart - a group of 50 Englishmen during the Hundred Years' War sneak into a castle and take it with zero casualties on both sides; perhaps small towns for the 5 Midianite kings). It seems that in later times, for whatever reason, the rule of sparing young virgins wasn't given or, less likely, it's unstated. [Interpolational glosses of later campaigns - Sennacherib records taking 200,150 captives from his campaign in Judah in 701 BC, 46 walled cities + "innumerable towns and villages". A typical city gave 800 prisoners, which would mean the countryside had four times as many people as the city. But this is a proof of a gloss of later numbers].
Incursions such as this into Palestine by nomadic tribes have many historical parallels. The Byzantines and Sassanids frequently faced Arabian coalitions during temporary tribal unity even before the permanent Muslim takeover. The Gauls under Brennus sack Rome in 390 BC. Another group of Gauls invade Greece in 280-279 BC. Yet again, Aurelian has to expel these in 268 AD. The Israelite army received half of the loot, which has historical parallels (80% for soldiers in the Qur'an; two thirds during the Crusades [Jean of Joinville, Penguin Classics, p.207]; though unlike with Israel, the remainder of Muslim/Crusader loot went to the king/government, not the people (with 2% of the people's share and 0.2% of the soldiers' loot going to the Tabernacle, while Moses himself presumably got the same as the average person)). This doesn't make the Arabic/Crusader invasions more egalitarian because these didn't fight, like Prussia, like an army with a nation on its back, but launched campaigns where there was only the leader and the soldiers. Why should anyone else who didn't risk a fight get anything? So if anything, we've given some more support to the historicity of the Exodus by showing it to be genuinely egalitarian like a tribe on the move.
• Hebrews were More Numerous
In Exodus 1:9, the Pharaoh's rationale for oppressing the Israelites is that, "Behold, the people of the children of Israel are more and mightier than we" (KJV). This is clearly an exaggeration that even the Pharaoh's audience was supposed to know as such, because in verse 10, the Pharaoh continues by saying, "let us deal wisely with them; lest they multiply...when there falleth out any war, they join also unto our enemies, and fight against us..." To stress a fear of multiplying doesn't really make sense if the Egyptians were already technically outnumbered. This is why other translations such as the ESV correctly render the expression as, "Behold, the people of Israel are too many and too mighty for us."
Even with a population of 2-3 million, the Israelites wouldn't have outnumbered the Egyptians who at this point in history numbered around 3-4 million; unless one wants to suppose the Israelite population was included in this number, which would've been recorded by history (and economic catastrophe), whereas the Egyptians continued to themselves multiply and were 5-7.5 million in Roman times.
So we can't really use this verse to suggest that the Israelites must've been in the hundreds of thousands, if not millions. How the Pharaoh expected to control hundreds of thousands, whereas previously he or his predecessors were unconcerned is a mystery. On the other hand, even thousands of slaves can create havoc. Eunus took several Sicilian cities from the Romans in the First Servile War with only tens of thousands of slave-bandit followers (compare with Moses' killing of the Egyptian), and it took the Romans years and five large armies before they could quell the rebellion. The Goshen region was similarly largely a Semitic, non-Egyptian sector where enemies could come to enlist help (much like how easily Syrians and Egyptians helped both the Sassanids and Arabs against Byzantine authority which had carried out religious persecution for decades). The fact that the genocidal order fails to be carried out, with seeming subsequent abandonment of the plan as well as an absence of military action by the Egyptians also seems to suggest low numbers (lower than hundreds of thousands at least).
• The Size of Pharaoh's Army
The Pharaoh mobilizes 600 elite chariots + "other" chariots (Ex. 14:7) and horsemen/soldiers (Ex. 14:9). It took Jabin, some 200 years later, 900 iron chariots to oppress all of Israel, which certainly numbered at least a good 100,000-200,000 by then; probably more considering pastoral people can leave no trace of their existence in the archaeological record.
VII. Unconvincing Arguments
• Moses and the Judges
We are told by Numbers that the Midianite priest and father-in-law to Moses, Jethro, introduced the idea of judges that substituted Moses' hard and near-impossible task of judging each Israelite case individually. He suggests Moses set up representatives "over the people as chiefs of thousands, of hundreds, of fifties, and of tens. And let them judge the people at all times. Every great matter they shall bring to you, but any small matter they shall decide themselves. So it will be easier for you, and they will bear the burden with you." (Ex. 18:21b-22, ESV). Very similar to the Oval Office, this was a seriously needed, major organizational upgrade.
The objection is that, since Moses judges the people all day and this had been going on for years (he has two sons), he couldn't have judged the cases of hundreds of thousands individually. No one would've been excluded (all Israel), and they crowded around him out of need. Jethro suggests chiefs of 10, 50, 100, and 1,000. But not 10,000 or more. True, each tribe had no more than 50,000 people on average. However, this would still mean there were over 50 chiefs of 1,000 just for one tribe, and six of them had over 50,000 men only. This would've still been a burden for Moses, especially if Jethro suggests chiefs over 10 and 50! And the total would've added up to 600 chiefs just for the men (600,000 divided by 1,000). Yet for the census, Moses and Aaron enlist the help of 12 chiefs, one for each tribe (Num. 1:44; 4:34,46). It doesn't matter that each tribe had no more than 50,000-100,000 men: the people would flock to Moses regardless of tribal affiliation. Herodotus (Histories 7.60.1) does mention how Xerxes counted his army of several million: by placing people in a space designed for 10,000. But this was for the express purpose of counting everyone at the same time. And to assume there should've been not only chiefs of 10,000, but also of 100,000 is to suggest that everyone had an issue basically every day that required Moses. Out of 1.2 million or so adults, the numbers would've piled up pretty quickly, but maybe not more than in the thousands. For a case to have to reach Moses, it must've been a pretty serious matter anyway - there must've been other people (family heads, tribal chieftains) that the people would've tried going to first.
One can also say that Jethro wasn't being exhaustive (i.e. outside the text, he also suggested chiefs of 10,000 and 100,000), but as we saw this isn't necessary. Would Jethro have known the amount of Israelites? He can see and be told of an enormous multitude, but millions? After all, God tells Abraham that his descendants would be as innumerable as the stars, but only around 10,000 or so stars are visible to the naked eye (per Ptolemy's count anyway). It's hard to believe Moses would've omitted relating to Jethro the size of the Israelite population (Ex. 18:8-9), and Moses must've known its exact dimensions as soon as the Exodus happened for logistical considerations. But as mentioned, the possibilities are numerous. Perhaps forgetful or somewhat incredulous of millions, Jethro could've suggested his system as an example, which could easily be expanded as needed. Maybe the Midianite system he was familiar with went up only to 1,000. Most likely there just weren't that many cases going to Moses: enough to overwhelm one man, but even 50 a day can do this and it was not a number exceeding the thousands.
On a related note, Num. 31:48 speaks only of military commanders over 1,000 and 100, but in that specific case each tribe went out with only 1,000 soldiers.
• Balaam could see Israel from the mountain
That Balaam was able to see Israel from the mountain top doesn't prove much. One can see very far from a high enough mountain, presumably far enough from the "enemy" for Balak, the Moabite king, himself to be there in the last meeting. And Num. 22:41 tells us they could see the outskirts of the Israelite camp, so it must've been quite far, but close enough for the sympathetic magic to work in Balak's mind. And Balaam didn't have to have been in full view of absolutely everyone; this is actually implied as much by Num. 22:41. If anything this could now become an argument for a large number, but the statement is too general and seeing merely the outskirts of the Israelite camp can mean anything about its layout, the distance from Balak and Balaam, and the height from which they observed. Even a camp of 10,000 can be broad enough to be described by such terms.