Rabbinic Mathematics

יַּ֥עַשׂ אֶת־הַיָּ֖ם מוּצָ֑ק עֶ֣שֶׂר בָּ֠אַמָּה מִשְּׂפָת֨וֹ עַד־שְׂפָת֜וֹ עָגֹ֣ל׀ סָבִ֗יב וְחָמֵ֤שׁ בָּֽאַמָּה֙ קוֹמָת֔וֹ ׳וּקְוֵה׳ ״וְקָו֙״ שְׁלֹשִׁ֣ים בָּֽאַמָּ֔ה יָסֹ֥ב אֹת֖וֹ סָבִֽיב׃
מלכים א 7:23

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.
I Kings 7:23

This Hebrew Bible passage from I Kings—along with a similar one from II Chronicles—forms the biblical basis for Talmudic scholar Matityahu Hacohen Munk’s suggestion that “some of the geometrical rules did not hold in King Solomon’s temple,” a heavenly ‘‘world of truth’’ beyond our own, mathematical historians Tsaban and Garber write [1].

What’s so heavenly about the Molten Sea, a putative basin created by King Solomon in the ancient Temple of Jerusalem for ritual ablution? And why do the Rabbis Johanan and Papa discuss it extensively in the Babylonian Talmud, bickering in particular about its brim—“[as thin as] the flower of a lily… a handbreadth thick… wrought like the brim of a cup” [2, Eruvin 14a:29-31]?

The simple answer is that this particular snippet of the Word of God contains an oddity, asserting that this circular basin’s circumference is thrice its diameter—or that the geometrical constant π, rather than an irrational number, with an infinite and unpredictable decimal expansion, is in fact rational, and indeed an integer—the number 3, to be exact. Continue reading

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Med School Sees the Psychic

During our medical school orientation, a guest speaker came from the Business School, as a part of an Inter-School Collaborative Effort, to administer and explain the Meyers Briggs Type Indicator. I left the auditorium with nothing but a feeling of regret at time wasted. I had always been skeptical of the Meyers Briggs personality test. But now, I fully understand that the MBTI, without even the slightest glimmer of doubt, is worthless.

The MBTI test tells the test-taker where she stands on each of four spectra: from introversion to extroversion; from sensing to intuition; from thinking to feeling; and from judging to perceiving. After finishing the test, each test-taker has a type. One might be an INTJ, or an introverted intuition-using thinking judger; another might be an ESFP, or an extroverted sensing feeling perceiver.

Why didn’t the test just ask me which type I was, right off the bat? Are you an introvert, or an extrovert? the test could have asked. This would have saved me 90 minutes. Instead, the test asked 90 questions that were supposed to elucidate for me which type I am. But the questions were no more effective in elucidating my type than they would have been had they simply asked me my type. Make sense?

Take the thinking/feeling dichotomy, for example. Here are a few example questions.

6. Do you more often let

_ your heart rule your head, or

_ your head rule your heart?

Continue reading