O Loving Hate!

In 1988, Harvard mathematician Steven Strogatz hit on a new way to teach differential equations. Juliet loves Romeo, but Romeo is fickle: The more she warms to him, the colder he becomes, but when her interest wanes his feelings grow. She, on the other hand, tends to echo his feeling for her, returning love for love and hate for hate:

dr/dt = –aj, dj/dt = br,

where

r(t) = Romeo’s love/hate for Juliet at time t
j(t) = Juliet’s love/hate for Romeo at time t.

Positive values of r, j signify love, negative values signify hate, and the parameters a, b are positive, to be consistent with the story.

“The sad outcome of their affair is, of course, a neverending cycle of love and hate; their governing equations are those of a simple harmonic oscillator. At least they manage to achieve simultaneous love one-quarter of the time.”

The same idea can be pursued in other variations. He adds, “the term ‘many-body problem’ takes on new meaning in this context.”

(Steven H. Strogatz, “Love Affairs and Differential Equations,” Mathematics Magazine 61:1 [February 1988], 35.)

| Literature · Science & Math

Checkmate

A puzzle by A. Savin, from the July-August 1996 issue of Quantum:

A mother, her brother, her daughter, and her son take part in a family chess tournament. Two of the four are twins. At the end of the tournament, the winner and the “loser” (the player in last place) are found to be the same age, and the winner is the opposite gender to the loser’s twin. Who won the tournament?

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| Puzzles

End to End

Read word by word, this sentence is a palindrome:

Girl, bathing on Bikini, eyeing boy, finds boy eyeing bikini on bathing girl.

From a New Statesman competition:

Women understand men; few men understand women.
God knows man. What is doubtful is what man knows God.
Does milk machinery milk does?
Bores are people that say that people are bores.

A few more.

| Language

Having Words

It’s said that Samuel Johnson resorted to unconventional methods to win a debate with a Billingsgate fishwife:

He called her a noun, a pronoun, an adverb, and she hesitated. He vigorously charged her with being conjunction and preposition. She wavered. And when at length with stentorian voice he accused her to her face of being a parallelopipedon, she broke in disorder and fled in the utmost confusion.

(Frederic Coudert, “Lying as a Fine Art,” 1873.)

| Language · Society

Dry

https://commons.wikimedia.org/wiki/File:Bertrand_Russell_transparent_bg.png

It has been claimed that only three people read the three volumes of Russell and Whitehead’s monumental Principia Mathematica in its entirety, namely Russell, Whitehead, and the proofreader. There has been some scepticism, however, about Russell and Whitehead belonging to the list.

— Leo Moser, quoted in Howard Eves, Mathematical Circles Adieu, 1977

| Science & Math

Bhartrhari’s Paradox

There are some things that are unnameable. But it seems impossible to verify this by giving positive instances, because this would require us to name that which we have declared to be unnameable.

From an observation by the fifth-century Indian grammarian and philosopher Bhartrhari. “[E]very argument advanced to support any instance of the unnameability thesis drives one still more firmly into the paradox,” note philosophers Hans and Radhika Herzberger, “for they naturally tend to involve repeated reference to the very things whose unnameability they undertake to establish.”

(Hans G. Herzberger and Radhika Herzberger, “Bhartrhari’s Paradox,” Journal of Indian Philosophy 9:1 [March 1981], 1-17.)

| Oddities

Taking Pause

‘Theft’ is a concept that logically and genetically depends on the antecedent concept of ‘rightfully owned property’ — and refers to the act of taking that property without the owner’s consent. If no property is rightfully owned, that is, if nothing is property, there can be no such concept as ‘theft.’ Thus, the statement ‘All property is theft’ has an internal contradiction: to use the concept ‘theft’ while denying the validity of the concept of ‘property,’ is to use ‘theft’ as a concept to which one has no logical right — that is, as a stolen concept.

— Nathaniel Branden, “The Stolen Concept,” The Objectivist Newsletter, January 1963

| Oddities · Society

Around the World

A brainteaser from the British intelligence agency GCHQ:

Explain the following: falkun, home de guerra, kick, lavoro, moed, mosca, raccordement, schafer, stobhach, tre, zevk.

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| Language · Puzzles