Is there any significance in the absence of the number 8 in the individual census of the 12 tribes taken in Chapter 1 of Bamidbar?

Reuben: 46,500

Simeon: 59,300

Gad: 45,650

Judah: 74,600

Issachar: 54,400

Zebulun: 57,400

Ephraim: 40,500

Manasseh: 32,200

Benjamin: 35,400

Dan: 62,700

Asher: 41,500

Naphtali: 53,400

The 8 only appears in the separate census of K’hos (8,600 - Chap. 3:28) and the total of Levi’im aged 30-50 years old where the number 8 appears twice (4:48) namely 8,580.

Do the esoteric properties of the number 8 have any significance here, especially relating to the special and privileged role of the  Family of K’hos.

  • 2
    I also only see one 9. Probably this is some application of Bedford's law. – Double AA Jun 12 at 20:34
  • @DoubleAA I think that's only for the first digit [/has generalizations for later digits but they show less of a trend - you can just use Benford's law in base 100 and then sum over the possible first digits], but I agree that this question would be much more interesting with a statistical analysis. – Heshy Jun 12 at 20:50
  • 1
    Because that's how many Jews there were, and how many people in the tribe of Kehas... – רבות מחשבות Jun 12 at 20:59
  • 1
    @DoubleAA Actually no, this isn't Benford's law because none of the numbers start with 1. You'd have to have the population probability distribution, which I don't see how it's possible to get based on odd features like sextuplets and judaism.stackexchange.com/q/13815/11532. What you could do is ignore the first digits (which aren't that relevant to this question anyway because Yehuda is an outlier and the probability of someone being in the 80s is small) and Gad's 50, assume the 2nd and 3rd digits have a uniform distribution, and then plug into Poissons and compare to Monte Carlo. – Heshy Jun 12 at 21:00
  • Nobody's perfect? – Al Berko Jun 12 at 21:26

Remez is much more interesting when you can find a feature that has a low probability of happening by chance. Before asking for the significance, you should look at the probability that this would happen in a random similar text. In other words, we want to define what you find to be "interesting", generate random data similar to what we find in the Chumash, and see if we find similar results. If we do, the remez becomes less compelling, because we would have expected something similar to happen in any case.

How can we generate lists of numbers similar to these? To start with, we don't have to worry about the last digit, which is always 0. The second to last digit is also 0 for everybody except Gad, so let's exclude that as well. Generating lists of numbers for the first digit would be very hard because it would have to involve data about the population growth and size, which was far from natural due to sextuplets, What happened to the bechorim (first-borns)?, and other things. In any case they're not so relevant to this question, because Yehuda, who had unusually large population, still fell short of 80,000 people.

We can approximate that in populations of people of around this size, the second and third digits would be randomly distributed. There are 24 numbers in these positions - two from each shevet. So, we can generate lists of 24 random digits and see how likely it is that there's a digit that doesn't appear.

Running this code in python:

import numpy as np
from collections import Counter
from scipy.stats import poisson

simple = True

def probability(ints):
  ctr = Counter(ints)
  counts = [ctr[_] for _ in range(10)]
  if simple:
    return 0 in counts
    return np.prod([poisson(2.4).pmf(_) for _ in counts])

for i in range(20):
  print(probability(np.random.randint(0, 10, size=24)))


I first simulate 20 lists of 24 numbers and print whether or not there's a digit that doesn't appear. I get about half True and half False. Then I print whether there's a digit that doesn't appear in the real numbers, and of course I get True.

For a more complicated analysis, you can set simple = False. Then it will print the probability of getting the counts, using a Poisson distribution with a mean of 2.4 for each digit. The probability for the real numbers is about 4e-09, which is on the low end but within the range I find for the simulated numbers.

Obviously, Hashem gave us these numbers for a reason, but I don't think the absence of 8 is that reason.

  • How do I get the code to syntax highlight? – Heshy Jun 12 at 21:40
  • I am sorry but I don't understand – kouty Jun 13 at 5:48
  • @Heshy 1) is this an answer? 2) can you paraphrase it in plain language please? – Avrohom Yitzchok Jun 13 at 11:48
  • I think there might be a flaw here. You can't ignore the first digit because everyone "fell short of 80,000" and then check against your simulations to see if "there's a digit that doesn't appear". Digits other than 0,1,2,8 and 9 do appear as first digits and therefore it isn't fair to count them if they don't appear at all in the second or third digits. – Silver Jun 14 at 17:03
  • @Silver I see your point, hadn't thought of it that way. It's essentially a factor of 2 effect, so it doesn't change the overall picture. I'll try to edit when I get a chance. – Heshy Jun 14 at 17:55

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