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There are generally two types of Shiurim, the "classic" type (R' Avrohom Chaim Noeh) which says that when we measure an Amah nowadays it is roughly the size of an Amah in the time of the Beis Hamikdash (so an Amah is 48 cm) while the Nodah Be'Yehuda (and the Chazon Ish) say that the hands in the time of the Beis Hamikdash were bigger than the ones nowadays so an Amah is roughly 57cm.

Moreover, there are other opinions in between these two. (For example, R' Moshe Feinstein held that an Amah is around 54cm.)

What is the source of these two opinions? Did R' Avrohom Chaim Noeh measure arm lengths and average them, and how did the Noda Be'Yehuda know that the sizes were bigger in those days?

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this may be useful. From here: lookstein.org/links/orthodoxy.htm#_ednref9 --- "Around the year 1940, R. Yeshayahu Karelitz, the Hazon Ish, published an essay in which he vigorously questioned whether scholars had not, in effect, seriously underestimated the size of an olive in Talmudic times. He then insisted on a minimal standard about twice the size of the commonly accepted one." -- The essay is now readily available in Hazon Ish, Orah Hayyim, Mo'ed (Bnei Brak: n.p., 1957), sec. 39 (Kuntras ha-Shi'urim) –  Menachem Feb 29 '12 at 21:19
    
related: judaism.stackexchange.com/questions/6234/… –  Menachem Feb 29 '12 at 21:23
    
possible relevant: rationalistjudaism.com/2010/03/evolution-of-olive.html –  josh waxman Feb 29 '12 at 21:40
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IIRC R Naeh measured the coin known as a Drahm and there was a longstanding tradition regarding converting from Drahms to biblical. He just finalized the Drahm measurement into metric. –  Double AA Feb 29 '12 at 21:54
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@DoubleAA, that, but also he quotes She'eiris Yehudah (by the Baal Hatanya's brother R. Yehudah Leib) who reports some experiments that the Baal Hatanya performed to verify Rambam's figure of 7 barleycorn widths equaling one thumb. –  Alex Mar 1 '12 at 1:49
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1 Answer 1

Responsum of R' S.R. Hirsch Shemesh Marpei, Orah Hayim, Siman 23 Translated from Hebrew by yitznewton; emphasis added

Tuesday of Ki Savo, 5644 (September 2, 1884) [In response to R' Pinchas Elchanan Wechsler of Schwabach, regarding how to render Torah measurements in centimeters]

[R' Hirsch first apologizes that he was forced to limit his research and response due to the state of his health]

[...] In my humble opinion there is no doubt that you have done according to Torah law in seeking a mean fingerbreadth between the largest and smallest man's [finger] found among you. If you establish this value to calculate the practical Torah measurements that you come upon [including] the size of the lechi of your city's eruv, there is no doubt that you have discharged your obligation, for you will have done that which is incumbent on you in Torah law. There is also no doubt, in my humble opinion, that you should not be surprised if other Rabbis elsewhere will not [have the same value as] yours, with one rather being less and another greater than your measurement. For to my limited knowledge, it is totally impossible to definitively establish a single universal value for the measurements of the Torah's laws, and the Blessed Giver of our Torah did not have this in mind at all. Are not all the Torah's measurements in essence the dimensions of fruits and parts of the body (olive, pomegranate, barley-corn, kotevet, egg, fingerbreadth, handbreadth, cubit, etc.), and is it not so that the size of fruits and the stature of people, on which these measurements are based, differ in every place and generation? So perforce there will be varying values for the measurements of the Torah. In my humble opinion this does not reduce the truth of the Torah but rather increases it, for the goal of all of the Torah's laws is only to orient human affairs. The basis for all their measurements as given to us is, in my humble opinion, בערך מה אל ענין א' מעניני בני אדם. For example, in my humble opinion it is quite likely that the measurement given for the height of a mehitzah, whose purpose is to delineate human domains, will be larger or smaller according to the the height of the average person in a given time and place. I cannot elaborate, and anyway there is no need for an understanding person such as yourself. Also, even in a single time and place, fruits and people are not identical in size, and it is all but impossible that all who measure will find precisely the same average. [...]

[R' Hirsch goes on to recall a history of having local official shiurim, and advocates this]

(I didn't understand the bit I quoted in Hebrew; cheers to anyone who does and can translate it)

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Although I agree with his theory, I don't think this really answers the question. –  Double AA Feb 29 '12 at 22:20
    
@DoubleAA it answers that some held that one may just rely on survey of the average arm length. –  Shmuel Brin Feb 29 '12 at 22:46
    
@ShmuelBrill But wasn't your question about the sources for R Chaim Naeh, Chazon Ish and RMF and how they calculated and got to their numbers? This is giving a general principle about how you or I would do it, not what they did. –  Double AA Feb 29 '12 at 22:51
    
I hope this shows precedent for the Noeh position as presented in the question. Is that not part of what was asked? –  yitznewton Feb 29 '12 at 23:15
    
@yitznewton What did the question claim about how R Naeh got his opinion? All it said was that his opinion ends up being closer to what was probably the case then assuming people are about the same. That's an empirical observation not a methodological claim. (I may be just misreading the question.) –  Double AA Mar 1 '12 at 1:55
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