[Avodah] Chazal are Infallible

[Kohn, Shalom]

As I anticipated, various posters defended Chazal as to geometric
relationships on the ground (a) they were using approximations; (b) they
were writing for the "hamon am" (R. MYG). [Does anyone really think
tosafot was writing for the Hamon Am, as R. MYG says? And if tosafot did
so intend, would it have been a problem for tosafot to say, "we know the
relationship is as follows, and here how one can prove it?  This is to
R. Aryeh Folger's point that the tosafot is used in Israel to teach
geometry.  How much better would that lesson be if tosafot had declared
the mathematical relationship, and THEN brought the proof?)

Let me just say that I commend the gemara in Sukka to the list's
attention, and you will see that chazal, rashi and tosafot are
struggling with the relationships in a way that an elementary school
child today would not.  Further, the gemara reflects a desire for
precision (to establish shiurim for a kosher sukkah) which is belied by
the suggestion of our posters that the "rules" were only intended as
approximations.  
 
And of course, my comment about nishtaneh hatevah was, shall we say,
ironic.

More specifically, R. MYG wrote:

> Indeed, we find that Rishonim and Acharonim were familiar
with advanced geometry and trigonometry, e.g. the Rambam and the Vilna
Gaon.

I know the Vilna Gaon wrote a math book (which some posters have
suggested was not written by him because of the bitul torah involved,
and others -- incredibly -- suggested the Gaon wrote in the bathroom!!)
but exactly where in the Rambam do we see him discuss equations of pi,
x-squared, and the Pythagorean theorem?

R. Chaim Manaster wrote:

>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. 

Why do we assume Chazal had a good "secular" education, and more
particularly, since we are dealing with shiurim to be yotzeh according
to halacha, why would chazal NOT be as precise as possible?  Again, see
the gemara I cited.


Eh, regarding the Rishonim, let me clearly state the opposite. There are

elements in the Israeli education scene that want to make Tosafot's
proof 
(which is actually from an earlier Jewish source, I believe) standard in

teaching geometry, because students can more readily grasp it than the
usualy 
calculations. That this beautiful and simple proof comes from our
masters, 
the Rishonim, is of course an important benefit. The secular Israeli
teenager 
will be somewhat exposed to their greatness through a subject matter he 
understands.

I would restate your speculation, saying that 'Hazal were interested in 
stating things in such a way that a non-scientifically trained person
could 
apply halakhah. RMB stated the same thing regarding the height of the
sukkah, 
IIRC.

It is only nowadays, when many people have the benefit of a science
education, 
that we look at these statements askance, because we cannot remember
that 
almost nobody among the common folk would have know how to apply the 
halakhah, had the gemeara stated that "sukkah 'agulah, midatah ``pi''
Yevanit 
pe'am shoresh shel shetayim kaful arba' amot." Come to think of it, even

nowadays most people wouldn't know what to do with this, once they are
out of 
high school.

Kol tuv,

Arie Folger


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