[Avodah] Chazal are Infallible

[hankman]

RSLK wrote:
Should we lose our respect for the gemara, Rashi and tosafot because their understanding of geometry was so unsophisticated? 

CM responds:
Of course not. A common response is that they knew that these values were not exact, but only approximations. They used these values because in halacha these approximations are sufficient. I am not sure if this answer can be used for all the later meforshim as well as it may be hard to fit into  some of their discussions.

RSLK:
 Or do we assume that "nishtaneh ha-tevah" and that the geometric relationships of circles and squares has changed?  

CM:
Again, of course not. There is no need for nishtaneh hatevah as they knew these were only approximations. Besides how do you apply this to a mathematical concept as opposed to a physical reality?

RSLK:
Or rather (my view) that it is perfectly fine for chazal to have dealt with the level of knowledge at the time, and we need not hold them to account on areas outside the purview of torah? 

CM:
Actual the Babylonians and Greeks had better values than the ones used in shas. It is safe to assume that chazal knew these values that well preceded the time of the mishna and gemara even if you choose to assume that chazal only knew what the intelligencia of their day knew in science. They chose to use these rounded values since these approx. were sufficient halachakly and easier for the less sophisticated hamon am to use. By the time of Archimedes, who preceded mishna by several centuries,  one could (theoretically) use the circumference of an 2n sided polygon to approx. a circle. As n grows large this converges (slowly and tediously) to pi. So they were able to calculate pi to great accuracy if they so desired.

BTW there is a well known remez to a better value in the pasuk about the yam shel Shlomo that ostensibly is the source for the value of 3 for pi. there is a kri and a ksiv for the word kav with and without the 'heh.' The ratio of 111/106 (ksiv over kri) when used as a correction for the approx. value of pi of 3 used in the pasuk gives 3.1415, a much better value, although not the infinite digits of the real decimal value. This value is the correct one (infinite places) truncated to 4 decimal places.

KVT

Chaim Manaster
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