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

Good Enough

The opening of Edward Bulwer-Lytton’s 1830 novel Paul Clifford, “It was a dark and stormy night,” has been held up as a model of bad writing for nearly two centuries. But it’s also the opening sentence of Madeleine L’Engle’s award-winning 1962 young adult science fantasy novel A Wrinkle in Time.

Apparently this was deliberate. L’Engle biographer Leonard Marcus writes, “With a wink to the reader, she chose for the opening line of A Wrinkle in Time, her most audaciously original work of fiction, that hoariest of clichés … L’Engle herself was certainly aware of the old warhorse’s literary provenance as … Edward Bulwer-Lytton’s much-maligned, much-parodied repository of Victorian purple prose, Paul Clifford.”

| Literature

“Scripture Cake”

Contributed by Mrs. M.L. Dow to a cookbook compiled by the Ladies of Trinity Church, Claremont, N.H., 1899:

4 1/2 cups 1st Kings 4:22
1 1/2 cups Judges 5:25
2 cups Jeremiah 6:20
2 cups 1st Samuel 30:12
2 cups Nahum 3:12
1 cup Numbers 17:8
1/2 cup Judges 4:19
2 tablespoons of 1st Samuel 14:25
1 pinch of Leviticus 2:13
2 teaspoons of Amos 4:5
6 teaspoons Jeremiah 17:11

The first line calls for 4 1/2 cups of flour, because 1 Kings 4:22 reads “And Solomon’s provision for one day was thirty measures of fine flour, and threescore measures of meal.” In the same way, the rest refer respectively to butter, sugar, raisins, figs, almonds, milk, honey, salt, leaven, and eggs. No baking instructions are given.

| Religion

CyberChance

A puzzle by National Security Agency applied research mathematician Nicholas R., from the agency’s October 2016 Puzzle Periodical:

Eddie, Layne, Kurt, and Chris are locked in a heated game of CyberChance which only one of them will win. Their fans are on the edge of their seats: everyone knows that in CyberChance, things can change at any moment. One fan, who prefers Kurt or Chris, is feeling worried since there is only a 4-in-10 chance that one of them will win. An Eddie fan brags that Eddie is twice as likely as Layne to come out on top. Another Eddie fan concurs, and adds the following observation: Chris is Eddie’s main competition. He figures that, given that Chris doesn’t win, Eddie has a 4-in-7 chance of winning. A Kurt fan has been quietly standing in the corner, listening to all the other fans, and wonders: What chance does Kurt have of winning CyberChance?

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| Puzzles

Polchinski’s Paradox

https://commons.wikimedia.org/wiki/File:Grandfather_paradox_billiard_ball.svg
Image: Wikimedia Commons

In 1990, physicist Joseph Polchinski described a puzzling situation: Suppose a billiard ball were sent through a traversable wormhole into the past, where it knocked its earlier self off course, away from the wormhole. This is a version of the famous grandfather paradox: How can we explain the ball’s presence where it seems to have prevented its own arrival?

Fortunately, Caltech students Fernando Echeverria and Gunnar Klinkhammer found that self-consistent solutions exist in which the older ball imparts only a glancing blow to its younger self, one that sends it through the hole at just the right angle to deliver a similarly glancing blow to its own forebear, and so on, sparing us from the paradox. (In 1991 the students and Kip Thorne reported that they’d failed to find any initial conditions in which such self-consistent solutions were unavailable, so it’s plausible that they exist for every possible initial trajectory. But this hasn’t been proven.)

Another pleasing possibility is that the older ball knocks the younger out of the way and itself enters the wormhole again. This creates an infinite loop, and some existential bewilderment, but no paradox.

| Oddities · Science & Math

Tile Swap

You’re tiling a floor with 4×1 and 2×2 tiles when you accidentally break one. A tile of the other shape is available. Show that it’s not possible to cover the floor by rearranging the tiles.

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| Puzzles