[Avodah] Quantum of Halachic Time

[Akiva Miller]

.
I wrote:

> IN ANY CASE, we also have a unit of time called a "rega", defined by
Rambam
> Kiddush Hachodesh 10:1 as 1/76 of a chelek, which makes it MUCH smaller
> than any of the above.

R' Micha Berger responded:

> Except that I don't know of a din that relies on a rega. It
> may be useful for the Rambam's math, but our calendar ...

True, but the Rambam's math was not astronomy-oriented; it was indeed
halacha-oriented: In Kiddush Hachodesh 10:6, Rambam explains that the Beis
Din Hagadol used these more accurate calculations for figuring out when to
add a 13th month to the year. So while I will agree that the Rega is not
relevant to *us*, that doesn't mean it is devoid of halachic significance.

On a topic that is indeed relevant to us, I wrote:

> 1 mil = 2000 amos = 18 minutes = 1080 seconds
> 4 amos (1/500 mil) is therefore 2.16 seconds

To which RMB responded:

> Assuming people walk in shul at the same speed they walk
> to get places.

Thank you! If I understand you correctly, you are suggesting that people
might NOT walk 4 amos at the same speed as they walk a whole mil, so the
time it takes to walk those 4 amos might NOT be 1/500 of the time it takes
to walk a mil.

This brings us to a very fundamental question about the very definition of
"the time it takes to walk one mil". Yes, I do realize that I am changing
the subject, because we had previously been talking about four amos, but if
you can't trust the "one mil" calculation then there's no way to translate
it into shorter distances.

It hardly needs to be said (but I'll say it anyway) that "the time it takes
to walk one mil" is relevant to practical halacha in many varied
situations. It defines how long it takes dough to become chometz. It
defines the minimum time of salting meat for kashrus (if I remember
correctly). It defines how far one must travel for minyan, for netilas
yadayim, and other situations. (It MIGHT also be relevant for zmanim
calculations, but if I said that, it might confuse you in the next
paragraphs, so I'm NOT going to say it. :-) )

How long is this shiur, "the time it takes to walk one mil"? Most of us are
familiar with the answer "18 minutes", and many may know of the 22.5 and 24
minutes shitos. Where do these durations come from?

The Gemara Pesachim 93b-94a establishes that the average person walks 40
mil in a day. If one divides the 12 hours (720 minutes) of daytime into 40
units, it is simple to calculate that one walks each mil in an average of
18 minutes. Others hold that these 40 mil were not traversed from sunrise
to sunset, but from alos to tzeis. Therefore, if 4 mil are traversed during
the morning twilight, and another 4 in the evening, then he walked only 32
mil during the middle 720 minutes of sun, and each mil takes 22.5 minutes
to walk. A variant of this calculation reserves *five* mil for each
twilight, leaving 30 in the middle, and each mil ends up at 24 minutes.

Regardless which of those three calculations you prefer, we are forced to
say that there is a 1:40 ratio between the distance one covers in "the time
it takes to walk one mil" and the distance (40 mil) that one covers in a
full day (regardless of how you're going to define "day").

Except that when one walks for a full day, there will inevitably be breaks
for rest, for meals, for davening, and perhaps other purposes. This person
did NOT walk for "a full day"; he walked for some minutes- perhaps even a
couple of hours! - less than that. In order to accurately calculate the
walking speed, one needs an accurate measure of the time actually spent
walking.

If a person actually did cover 40 mil (80,000 amos) in a single day, then
in any typical 18/22.5/24 minute part of that day, he must have walked
somewhat more than 2000 amos. It is only by averaging the entire day
together that one concludes he walked 2000 amos per "keday hiluch mil".

To state it more plainly: In the time it takes an average person to walk
one single mil, he will actually walk MORE than a mil, presuming that he is
actually walking the whole time and not stopping for breaks. Again, it is
only by averaging the entire day together that one concludes he walked one
mil per keday hiluch mil.

(That is the point which I suspect RMB alluded to when he wrote "Assuming
people walk in shul at the same speed they walk to get places." Our
definition of "keday hiluch mil" seems to assume that the person who walks
40 amos in a day does so at the same speed for the whole day, even while
eating and praying.)

In some systems of measurement, time and distance are interchangeable. For
example, one unit of Planck time is how long it takes light to travel one
Planck length. Similarly, keday hiluch mil is, *by* *definition*, the time
it takes an average person to walk one mil.

But I seem to have disproven that.

I suppose it is possible that the Gemara in Pesachim was not bothered by
this calculation. The Mishna and Gemara there are trying to define "derech
rechoka" - how far must one be from Yerushalayim in order to qualify for
Pesach Sheni. The first answer given is the city of Modiin, 15 mil away. I
can easily imagine that for such a distance, Chazal were okay with the idea
that 3/8 of a day's travel *including* breaks was enough to qualify for
Pesach Sheni. But this does not mean that they would have been okay with
including breaks while scaling it down to a four-amos trip!

My guess is that the bottom line might be: How much precision did Chazal
expect from us in these things?

Akiva Miller
.
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