[Avodah] The census numbers in bamidbar

[Akiva Miller]

.
R' Marty Bluke asks two distinct questions, but both concern whether (and
to what extent) the census numbers were rounded.

His first question focuses on *all* the shevatim. Most of them seem to be
rounded to the nearest hundred, while one lone shevet seems to be rounded
to the nearest fifty. It is puzzling why this should be so, and for a long
time I thought it might be evidence that all of them are, in fact, exact
numbers.

But I recently considered another idea, that they are all in fact rounded
to the nearest hundred, but the Torah's rules for rounding differ from
ours. Our rules for rounding state that 1-49 are rounded down, and 50-99
are rounded up, and that sounds fine until you realize that you're rounding
up slightly more often than down, which will eventually make your work
slightly inaccurate, Perhaps the Torah's rule for rounding is: "Numbers
ending 01-49 are rounded down to the lower hundred. Numbers ending 51-99
get rounded up to the next hundred. Numbers ending 00 or 50 are left alone
and are not rounded."

His second question is even more powerful. We have 22273 bechorim, which is
obviously an exact number, and we compare it to the 22000 leviim, which
certainly *appears* to have been rounded. The difference between the two
appears to be an exact number, and the Torah even underscores the precision
by telling us the result of multiplying that number of people by 5 shekalim
each. In my mind, this is very powerful evidence that the 22000 is indeed
an exact count, not rounded in any way.

Unfortunately, even if one accepts this proof that the 22000 is exact, we
have no real evidence whether it is an exception to the rule (and the other
numbers are actually rounded) or whether it is an illustration of the rule
(and all the other numbers are also exact).

This led me to think of another case where one can argue about rounding.
The number 600,000 is quite famous to students of Torah, but is it exact or
not? In Shemos 12:37 the word "shesh" has a Kaf prefix, explicitly telling
us "around 600,000". But this number also appears in B'midbar 11:21 without
the kaf, suggesting that it is *not* an approximation. On the other hand,
the number 603,550 is given in Shemos 38:26. and B'midbar 1:46 and 2:32,
while 601,730 is in B'midbar 26:51.

Now here's my question: Suppose we would find that exactly 600,900 people
travel through a certain area daily. Would this be a vadai
reshus harabim because it is more than 600,000 people? Or would it still be
a safek because the threshold is actually 601,730? What if exactly 602,000
people were there (which is less than 603,550)? Do any of Chazal raise this
question? Does anyone offer an opinion on which of these three numbers to
use? Yes, the cutoff point is always *reported* as "600,000", but I'm not
convinced that their intention is for that particular number, ruling
against the other two.

Some might consider this to be a "klutz kashya", because how can we
possibly be confident that the population is definitely more than 600,000,
and also definitely less than 601,730. Once the Traffic Department's
numbers get that high, they are inherently estimates, right? My response is
that if Chazal can ask how to deal with an unsolved murder victim who lies
*exactly* in the middle between two cities (their answer is to measure the
distance to his navel, if I remember correctly), then I can ask about
600,900 people.

(BTW, this question is totally separate from the fact that those three
numbers all focus specifically on adult men of a certain age, whereas
traffic counts seem to count everyone, regardless of gender or age. We can
discuss that part some other time.)

To sum up: If someone can show me a discussion in Chazal about which of
these 3 shiurim to use for the definition of Reshus Harabim, that
discussion might shed light on the roundedness of the census of the
shevatim. But if this question never came up, then perhaps Chazal were
signaling something to us, perhaps that the distinction between "exact" and
"rounded" is less important than we are tempted to think.

Akiva Miller
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