Toni Lassila wrote: > On 27 Jul 2006 09:34:28 -0700, "Craig Feinstein" <firstname.lastname@example.org> > wrote: > > >If you look at Jewish Talmudic sources, you'll see that rigorous and > >sophisticated mathematics was never really so high on the list of > >priorities for the rabbis. > > This claim, like many by Craig Feinstein, is dubious: > > http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJ3-4CYGBRF-MG&_user=10&_coverDate=08%2F31%2F1985&_rdoc=1&_fmt=summary&_orig=browse&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=320a9584cc080f579d37232f48d8bac6 > > Game theoretic analysis of a bankruptcy problem from the Talmud > > Robert J. Aumann and Michael Maschler > > The Hebrew University, 91904, Jerusalem, Israel > > Abstract > > For three different bankruptcy problems, the 2000-year old Babylonian > Talmud prescribes solutions that equal precisely the nucleoli of the > corresponding coalitional games. A rationale for these solutions that > is independent of game theory is given in terms of the Talmudic > principle of equal division of the contested amount; this rationale > leads to a unique solution for all bankruptcy problems, which always > coincides with the nucleolus. Two other rationales for the same rule > are suggested, in terms of other Talmudic principles. (Needless to > say, the rule in question is not proportional division).
I repeat, "rigorous and sophisticated mathematics was never really so high on the list of priorities for the rabbis". Basically, the math they did was simply the application of grade-school math and some basic geometry to Jewish Law. You have to go to a university, in this case "The Hebrew University" (which is really built on Greek, not Jewish ideals, despite its name) in order to get a game-theoretic analysis of this particular Mishnah in the Talmud. The Talmud isn't concerned with the game-theoretic properties of this solution to the bankruptcy problem. (This is something that the Ancient Greeks would have been interested in.) The Talmud just discusses the application of the particular solution given in the Mishnah to Jewish Law. Average Jewish children can and do learn this passage in the Talmud without any background in higher level mathematics.