Censuses and Numbers in the Old Testament
Is it possible to make consistent sense of the censuses and other mustering counts recorded in the Old Testament? English translations of the Old Testament record some six hundred thousand men plus dependants leaving Egypt during the Exodus, and the mustering of even larger numbers during later periods, culminating with a figure of 1.3 million fighting men reported by Joab when David ordered him to conduct a census (1 Sam 24:9). Many scholars have cast doubts on these numbers, some regarding them as fiction, with others considering them to have been misunderstood during the transmission process.
I suggest that a number of internal pointers exist within the Old Testament to indicate that these counts of fighting men are real counts, but are not to be understood as pure numbers. Firstly, let me introduce two very clear indications of this, before presenting more circumstantial evidence.
Joshua's Assault on Ai
The Old Testament records Joshua's strategy to capture the walled city of Ai in some detail, after the Israelites initial failure to do so due to Achan's theft of devoted plunder. We first read that 'Joshua chose thirty thousand of his best men' and sent them out at night to set an ambush to the west of Ai, whilst Joshua remained in the camp (Josh 8:3-9). The next morning Joshua mustered more soldiers and made a frontal approach to Ai, camping to the north of it. The text then mentions the pre-set ambush again, but this time describes Joshua as having 'taken about five thousand men' and having set them in ambush to the west of Ai (v.12). Same ambush, different numbers. The critical difference is the use of the prefixed preposition k in the second case to indicate an estimate of an actual headcount, whereas in the former case the figure should be read as an exact tally: 'thirty battalions' or similar. Thus we have here a single data point showing a ratio of 6:1 between nominal and actual military strength.
The Census Numbers
The Book of Numbers is so named for the two censuses it details, the former near the beginning of the Exodus wandering (Num 1) and the latter just before crossing the Jordan into the Promised Land (Num 26). The numbers at first look relatively consistent between the censuses (only Simeon records a dramatic fall in numbers, possibly related to the plague subsequent to the Moabite seduction, which centred round a Simeonite, Num 25:14). Moreover the numbers seem plausible between tribes, some flourishing rather more than others. However if we consider them to be actual counts, then the numbers themselves can be shown to be counterfeit!
Let's look at the units of a hundred1. In natural numbers of this size (tens of thousands) we would expect the hundreds to be more or less random, and drawn from a uniform distribution (if they were forged we would expect them to be too uniform). However, when we look at them we discover that they are strongly clustered. None of the tribal counts have zero, one, eight or nine 'hundreds'. There are two each of 200 and 300, three each of 600 and 700, and seven each of 400 and 500, leading to a pyramidal shape cluster of counts centred near 500. The observed data distribution for each census has a probability of less than 0.01 of occurring by chance, that for the combined data much less. We can also look for a correlation between the total thousands count and the hundreds count for each tribe (i.e. 46 versus 5 for Reuben in the first census). The departure from randomness is not as stark as with the previous statistic, but if we combine the two censuses, the probability that the observed positive correlation is just random is about 0.01.
Thus this forensic accounting-style treatment of the numbers indicates two things: firstly, the numbers are not natural numbers, and secondly, the number of 'hundreds' is almost certainly connected in some way to the number of 'thousands'.
Other Oddities
We have established that troop counts at least in some instances are not actual head counts. Before I suggest what they do represent, lets round up some more numerical oddities in the Old Testament. Of course we are working from a text with some corrupt numbers, and this will always limit the certainty of our conclusions. For example the Hebrew text describes Saul as 'son of a year when he began to reign, and he reigned for two years' (1 Sam 13:1), leading most English translations to follow the Septuagint figures instead. Moreover 1 Sam 6:19 abandons proper syntax to describe 'seventy men fifty thousand men' being put to death for looking in the ark.
Prominent among these oddities, or discrepancies, is the Levite count. There were 22,000 male Levites at least a month old (Num 3:39), and 8,580 between thirty and fifty years of age (Num 4:48), suggesting about 12,000 aged twenty years plus, for comparison with the census figures for the other tribes. Excluding the low second census count for Simeon (see above), this is scarcely one-third of the size of the next smallest count of 32,000 for Manasseh. The Levites seem to have flourished (particularly the priests, who number over 4,000 after the exile, Neh 7:39-42!), so one would expect them to be among the larger tribes, as indeed they would be if a tribal 'thousand' actually represents a much smaller head count.
Further indirect confirmation of this comes from the account of the troops of Reuben, Gad and the half-tribe of Manasseh preceding the Israelites across the Jordan. These numbered 'about forty thousand' (Josh 4:12-13), or more specifically, 44,760 (1 Chr 5:18); the second census (Num 26) equates this to 43,700 Reubenites, 40,000 Gadites and, say, 16,000 from half of Manasseh, i.e. 100,000 total, this time a ratio of about 2.5:1.
The count of the firstborn (22,273, a real number, Num 3:43) also suggests that a unit of a 'thousand' contains less than a thousand persons. From the account of Egyptian deaths resulting from the plague on the firstborn (Exod 12:29), it is clear that the eldest sons of living Egyptians died, and (v.30) that every household was affected. What is not clear is whether say, an eldest son was classified as 'firstborn' if his parents were already dead, nor whether an eldest son who already had children of his own was still 'firstborn' and subject to death from plague. Now 22,273 firstborn among 603,350 males of twenty years of age and older, gives a ratio of nearly 30:1. Adding women and children and assuming only one 'firstborn' per household, the strictest criterion possible, this yields a household size of around one hundred individuals. This seems implausible, unless most households were based around great-grandfathers! If the 6:1 ratio between nominal size and actual headcount that we found for the assault on Ai (see above) holds true, or the 2.5:1 ratio for the Transjordan tribes, this would give a more plausible household size of fifteen to forty people.
One final oddity occurs with David's census of the fighting men (2 Sam 24:9, 1 Chr 21:5). David forces a protesting Joab to carry out a census, but is guilt-stricken when Joab makes his report, as these are numbers he is not permitted to know. However both the authors of 2 Samuel and 1 Chronicles happily announce the numbers for posterity! It is clear that the act of individual numbering somehow requires an offering to be made in atonement for each life (see particularly Num 31:49-50). David, as commander-in-chief, had a right to know how many thousands (i.e. battalions or whatever, based on family clans) were at his disposal, in order to plan his military strategy. But he had no right to know his military strength in terms of individuals, as that is God's prerogative, to make Israel flourish or diminish as He pleases. Hence the numbers in 2 Samuel (800,000 Israelites, 500,000 Judahites) and the somewhat different figures in 1 Chronicles (630,000 Israelites, 470,000 Judahites) should be understood as examples of the former, which it was permissible to record.
Thousands, Hundreds, Fifties and Tens
We have seen that the 'thousands' and 'hundreds' that make up the census tallies are not to be understood as actual counts, but presumably relate to the hierarchical judicial, and subsequently military structure, instituted by Moses (Exod 18:21,25; Deut 1:15). Whilst one might assume 'hundreds' to be lower-ranking (and indeed subsets) of 'thousands', there are hints that this may not be the case. National conferences and ceremonies that mention 'commanders of thousands' almost always also mention 'commanders of hundreds'. Mentioned along with them are other top-level bureaucrats, e.g. tribal and royal officials (1 Chr 28:1), and judges and tribal leaders (2 Chr 1:2), suggesting they are of equal top-level status. Samuel's warning about kingship includes the curious combination 'commanders of thousands and commanders of fifties', where perhaps the two primary levels of hierarchy are being listed, with 'commanders of hundreds' to be understood implicitly as on a par with and subsumed under 'commanders of thousands'. As to the difference between them, it is possible that 'thousands' were standard battle-line military units, whereas 'hundreds' had other duties, such as reconnaissance; or even that 'thousands' contained native-born Israelites, whereas 'hundreds' were composed of non-Israelites affiliated with each tribe.
There are however two pieces of evidence which seem to tell against such an interpretation of the census numbers. The first is that totals are given for all the tribes (and for each camp composed of subsets of three tribes), with the totals further confirmed by the half-shekel atonement payments used for the tabernacle (Exod 38:25-28). The totals, however, have the appearance of scribal checksums (a wise addition considering frequent errors in the recording of other numbers!), added by editors unaware of the significance of 'thousands' and 'hundreds'. Alternatively, the checksums could be original, e.g. '598 thousands and 55 hundreds and fifty' for the first census, subsequently 'corrected' by an overzealous editor. The half-shekel atonement payments would then be a symbolic offering representing the desired unit strength, rather than for the actual headcount at the time.
The other slight fly in the ointment is that Exod 12:37 records 'about six hundred thousand men on foot went up from Egypt, besides dependants'. The 'about' usually indicates an estimate of a real number, but it is possible that here, prior to the census, it is an estimate of the (real) number of 'thousands' departing Egypt.
Thus, there remain many unanswered (and probably unanswerable) questions about the censuses and large numbers in the Old Testament. However I think the data presented above provide strong evidence that the census numbers were never intended to be taken as headcounts, but instead indicate counts of subdivisions termed 'thousands' and 'hundreds'.
1Curiously only one tribe in each census has a non-zero tens unit: five for Gad in the first census and three for Reuben in the second census. These are, quite frankly, baffling, though perhaps it is not a coincidence that the two numbers that do occur are ḥᵃmiššīm, 'fifty', which could represent a unit of veterans, fifty being the retirement age, at least for priests; and šᵊlōšīm, 'thirty', which is potentially the plural form of the word for 'adjutant', literally 'third man (in a chariot)'.
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