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According to the Mishna (Sotah 9:12), the Shamir wasn't extinct until the destruction of the second Beis Hamikdash. Incidentally, there is no mention of the Shamir in Rambam. Ever the rationalist, Rambam doesn't believe in demons (which were associated with the Shamir). He held that it was okay to quarry and cut the stones outside the Beis Hamikdash area, ...
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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