# 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

# Russia’s Twisted Optimism

When the impoverished Tess – the main character of Thomas Hardy’s 1891 British novel, Tess of the D’Urbervilles – sets off to make her fortune, her fate progresses from tragic to downright calamitous. “Where was Tess’s guardian angel?” the narrator asks, as Tess is raped by the profligate son of the old widow for whom she has been forced to work. “Where was the providence of her simple faith? Perhaps… he was talking, or he was pursuing, or he was in a journey, or he was sleeping and not to be awaked.” [1] Tess’s story ends tragically.

Emma Bovary, of Gustav Flaubert’s 1856 French masterwork Madame Bovary, doesn’t fare much better. After a string of unsatisfying romantic encounters, Emma ends up deeply in depression and debt. “It seemed to her that Providence pursued her implacably,” the narrator observes. “She would have liked to strike all men, to spit in their faces, to crush them.” [2] Emma, too, is ultimately doomed to misery.

Why, then, did the Russian literature of the nineteenth century – while that of England and France was gothic and fatalistic – persistently insist on a peculiar twisted optimism in the face of despair? These Russian writers, indeed, repeatedly depicted characters who – despite unimaginable misfortune – experience soft joy, eternal joy, and joy from the simply unexplainable. Continue reading

# The Appropriate Practice Scope of Chiropractic May Be a Political Question, Not a Scientific One

1. Ground Control to Major Reform
2. Hospital Salaries Could Cut Care Costs
3. The Appropriate Practice Scope of Chiropractic May Be a Political Question, Not a Scientific One

Chiropractic isn’t the only legal business with questionable scientific underpinnings

A Colorful History

At the turn of the 20th century, medicine was at a turning point. Unscientific practices like bloodletting, bonesetting, and magnetic healing still pervaded medical practice. On the other hand, trust in the scientific method was mounting. Darwin’s controversial Origin of Species, published several decades earlier, was gaining acceptance. Louis Pasteur proved that life, including bacteria, can’t generate itself spontaneously, and Robert Koch developed a testable set of postulates for determining whether a particular bacteria was the cause of an illness. A future of medicine could be envisioned in which medical intervention was chosen from the pages of science alone, rather than from the pages of history.

D.D. Palmer was, then, what one might call a conservative. Continue reading

# The American

1. Mikhail Tal: The Deep Dark Forest
2. Bobby Fischer: The American
3. Tigran Petrosian: The Iron Fortress
4. Mikhail Botvinnik: The Research Player

Chess’s greatest player can tell us a lot about the game, the mind, and man in general.

The Soviets dominated world chess through the 20th century.  Why? Because the state subsidized the game.  Soon after the 1917 Bolshevik revolution, the Lenin regime officially introduced chess to the USSR as a means to gain international dominance on the mental battlefield.  (2) The government organized state-run tournaments and chess clubs.  It established official chess columns and publications. Most effective of all: a chess requirement was established for all Soviet schools.  Students began in elementary school; the students who showed the most promise were chosen for more advanced lessons; those students who showed the most promise were again moved to even more advanced teaching, and so on.  The plan worked; the USSR became a veritable grandmaster factory, churning out greats such as Alekhine, Botvinnik, Tal, Petrossian, and many more.  Suddenly, though, an unknown American player exploded onto the international scene, effectively turning the chess world upside down.

# Who Was Martin Guerre?

Martin Guerre was a peasant in 16th century France.  He left for the war, and was gone for many years—so long, in fact, that his family was certain he’d passed away.  Then, one summer evening, an exhausted man in tattered clothes stumbled into his dusty southern France village.  Guerre had returned!  His four sisters rejoiced, as did his wife Bertrande, who had remained faithful all these years.  The whole village welcomed the advent of its long-lost traveler.  The whole village, that is—except for one man.

Come home, Martin Guerre!

# The Pillars of Russian Mathematics

This fall, I’ll spend the semester studying math in Russia. (I can hardly contain my excitement.) I’ll be in Moscow, to be precise, studying with the “Math in Moscow” program; this program invites North American undergraduates for a semester of study at the small, elite “Independent University of Moscow”. The Independent University offers advanced, research-oriented coursework in the Russian pedagogical tradition. Interesting in their own right, however, are the mathematicians behind the University – Russian mathematical greats with fascinating histories and overflowing personalities.

Ya. Sinai (L) and V. Arnold (R), 1963

# Évariste Galois: Mathematician, Champion

Évariste Galois was a prolific mathematician at a young age: at 17 he proved that no equation can exist which would solve 5th degree polynomials (the “quintic formula”). By 18, he was expelled from school: a rising leader in France’s 1830 July Revolution, Galois wrote a letter to his headmaster condemning the institution’s ban on students’ participation in the movement – and signed it, confidently, with his full name. By 19, he was in jail: at a banquet attended by the entirety of France’s political elite, Galois offered an ardent toast to the king – while, in a thinly veiled threat, holding a dagger above his cup! In prison, Galois submitted his groundbreaking mathematical work (on an early form of modern “group theory”) to France’s preeminent journal – only for it to be rejected as “incomprehensible”. By 20, Galois was dead, from wounds incurred in a duel fought regarding a mysterious “Stéphanie-Félicie Poterin”. Throughout the entirety of the night before the duel, anticipating his demise and working by candle-light, Galois compiled his final paper; eminent mathematician Hermann Weyl would one day argue that the “novelty and profundity” of Galois’s final work make it “perhaps the most substantial piece of writing in the whole literature of mankind.”