Who knows sixty-four?
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If 64 units comprise the psychological volume of a Torah scholar, one of those -- no more no less -- should be pride.
(This is technically 1:63 ["one to sixty-three"], which is the same as 1/64 ["one in sixty-four"]. But 63 was already well-covered. By the way, Bitul b'shishim requires sixty to one.)
Talmud Bavli, Sotah 5a:
א"ר חייא בר אשי אמר רב ת"ח צריך שיהא בו אחד משמונה בשמינית א"ר הונא בריה דרב יהושע ומעטרא ליה כי סאסא לשבולתא אמר רבא בשמתא דאית ביה ובשמתא דלית ביה א"ר נחמן בר יצחק ל*א מינה ולא מקצתה*
In the course of a lengthy discussion on the evils of "gayva"/pride/arrogance/hubris, we get the statement that in fact a Torah scholar should have just a drop of it ("but it's batel b'shishim"); Rashi explains that a leader can't let people walk all over him, and has to assert his authority on occasion.
The next two views in the Talmud are: "darned if you do, darned if you don't" when it comes to having arrogance; and "it's too dangerous, just aim for zero."
The many ways of interpreting these statements -- and which ones we value more than others -- help explain the wide variety of personal leadership styles among Torah scholars.
64 are the verses in the Torah portion of Kedoshim.
This portion also contains 51 mitzvos (according to the reckoning of the Chinuch, and of R' Moshe Chagiz). So Kedoshim has, as far as I know, the highest verses-to-mitzvos ratio of any parshah.
1) The Mizbeyach and its ramp measured 32 amos apiece, for a total of 64 amos. The combined length was only 62 amos, however, due to the overlap on the ledges of the Yesod and Soveiv. (Zevachim 62b - cool mnemonic there!)
2) It is said in the name of the Gra that if one wanted to fulfill all of the various opinions with regard to the placement of the parshiyos in tefillin (Rashi, Rabbeinu Tam, plus others), he would need to wear 64 pairs in order to satisfy the various permutations. (For everything you ever wanted to know about this topic - see this chapter by Rav Moshe Shternbuch.)
3) There are 64 kortov in a log.