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The Bavli, Shabas 31 amud 1, has two stories in which a gentile came to Shamay asking to be converted to Judaism, upon which Shamay "pushed him with the construction cubit in his hand". Rashi explains that a construction cubit was a cubit-long stick used in construction for measurement.

Why did Shamay have one in his hand?

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I heard once in a recording from R. Y.S. Schorr that Shamai represented a middas hadin, an exacting attitude of strict justice (as is evidenced by those very stories). His measuring stick was a display of just that point - everything had to be measured and exactly according to what was deserved.

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+1, and thanks. Is that the one at Or Sameach (Monsey)? – msh210 Jul 28 '14 at 5:16
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@msh210 Yessir. I bought the recording there, but you can find them at jhfweb.org/parsha_schorr.html. I think it was in either Parshas Korach or Pinchas. – Y ez Jul 28 '14 at 5:18

The Chassam Sofer seen here s.v. על רגל אחד says that Shammai besides being a Talmid Chacham was also a builder by trade, כי הוא היה תלמיד חכם וגם בנאי באמת הבנין.

The apikores thought that a person must choose between being a good person who interacts with other people kindly, or one can dedicate their life to Hashem as a religious recluse. Shammai wanted to show him that it is actually possible to serve Hashem in both regards, and proved this by chasing him with the tool of his trade and allowing the apikores to recognize he was both a talmid chacham and a builder (i.e. involved in a trade and interacting kindly with people).

Hillel's response was to say that you can 'learn on one foot', by which he meant to only involve yourself in kindness. However explains the Chassam Soffer, don't forget that the single foot of kindness includes kindness to Hashem, which means keeping His torah.

The Ben Yehoyada (in one explanation here), similarly, says he was a building-measurer by trade, and so carried a stick with him.

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Can,you source where? – sam Jul 28 '14 at 15:05
    
Its in the chidushim of Chassam Sofer on the sugya. – user6591 Jul 28 '14 at 21:37
    
i dont see it,where? – sam Jul 29 '14 at 0:47
    
I don't have one with me. Its the set that is collated all his chidushim that are on a given sugya. I actually have a picture of the vort in my phone but i dont know how to put it up here. – user6591 Jul 29 '14 at 0:57
    
Not just that he interacted with people. He earned himself an honest living in addition to being a scholar. What a Kiddush HaShem!! – Double AA Jan 7 at 19:34

The Maharsha there s.v. על רגל אחת explains that Shamai was, in the two accounts in which he was holding the construction cubit (as he was not reported to be holding it in the first account), showing the questioner some important element of his response.

The fellow who asked to be taught the entire Torah on one foot was being shown that just as a building cannot stand on one pillar, so too the Torah has many mitzvos which cannot be given one simple foundation.

The fellow who asked to be a kohen gadol was being shown that the Torah does not stand on the pillar of kehuna (priesthood) alone.

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I don't see how this answers the question. Okay, so if Shamay had a ruler, he pushed the fellow with it to show that the Torah is like a building. It doesn't explain why Shamay had a ruler, which was my question. (+1 on your other answer post, though, which does answer that question.) – msh210 Nov 2 '15 at 5:43
    
@msh210 Maharsha points out that the Talmud is not consistent about him having a ruler - he had it in two of the accounts but not in the third. He seems to have taken the ruler for the purpose of making the point. – Y ez Nov 2 '15 at 5:46
    
ah, I see. Thanks! – msh210 Nov 2 '15 at 5:48

in chovos halevavos gate 9 ch.5

Do so in your heart and mind if you are unable to free your body to matters of the next world due to being so fully engaged with providing for your livelihood and maintenance, as our Rabbis mentioned on many (great men), who would toil in matters of this world, while being separate from it (in heart and mind), such as Aba Chilkiya who would work hoeing the ground (Taanis 23a), Shammai in construction work, and Hillel who would earn his livelihood by chopping trees and selling the wood (Yoma 35b).

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+1 Very nice! Earliest source so far. – user6591 Jan 7 at 23:29

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