Futility Closet

If three hula hoops cover a common point, then a fourth hoop will cover their remaining intersections.

Mathematician G.H. Hardy had an ongoing feud with God. Once, after spending a summer vacation in Denmark with Harald Bohr, he found he’d have to take a small boat across the tempestuous North Sea to return to England. Before boarding, he sent Bohr a postcard that said “I have proved the Riemann hypothesis. — G.H. Hardy.”

When Bohr excitedly asked about this later, “Oh, that!” Hardy said. “That was just insurance. God would never let me drown if it meant I’d get undue credit.”

• Connecticut didn’t ratify the Bill of Rights until 1939.
• Can one pity a fictional character?
• 64550 = (6⁴ – 5) × 50
• BILLOWY is in alphabetical order, WRONGED in reverse.
• “The essence of chess is thinking about the essence of chess.” — David Bronstein

Peter believes that politicians never have musical talent. He knows of Paderewski, the great pianist and composer, and he has heard of Paderewski the Polish statesman, but he does not know that they are the same person.

Does Peter believe that Paderewski had musical talent?

(From Saul Kripke.)

From Samuel Isaac Jones, Mathematical Wrinkles (1929), a magic square with a twist:

“It will be observed that this square when turned upside down is still magic.”

From Roberto Casati:

All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
…

This array manages to be paradoxical without being circular. The statements can’t all be false, because that would make the first one true, a contradiction. But neither can any one of them be true, as a true statement would have to be followed by an infinity of false statements, and the falsity of any one of them implies the truth of some that follow. “A paradox — but a rectilinear one.”

Discovered by J.A.H. Hunter.

A line that bisects the right angle in a right triangle also bisects a square erected on the hypotenuse.

Proof:

If a second is defined by reference to the rotation of the earth on its axis, i.e. as 1/60 of 1/60 of 1/24 of the time between 2 identical positions of the Greenwich meridian relatively to the fixed stars, then, if the earth rotated 10 times more slowly than it does now, it would be possible to run 10 yds. in a second, instead of only a yard as now, and a second would be 10 times longer than it is now; but if cinema machines still moved as fast as they do now, it would still be quite impossible for any one to see a succession of static pictures instead of a moving one. Don’t we mean by a second the length of time which is now 1/60 of 1/60 of 1/24 of the time between etc.?

– G.E. Moore, Commonplace Book, 1962

On Jan. 18, 1897, California farmer George Jones bought a quantity of livestock feed from Henry B. Stuart of San Jose. As security he signed a $100 promissory note that bore 10 percent interest per month, compounded monthly.

They had agreed that Jones would pay the debt in three months, but the note had run for almost 25 years when Stuart got tired of waiting and told his lawyer to sue. Judge J.R. Welch of the Superior Court of Santa Clara entered this judgment on March 6, 1922:

“Wherefore, by virtue of the law and the facts, it is Ordered, Adjudged and Decreed that said Plaintiff have and recover from said Defendant the sum of $304,840,332,912,685.16 with interest thereon at the rate of 7% per annum until paid, together with the further sum of $50.00 Plaintiff’s attorney’s fees herein with interest thereon at the rate of 7% per annum until paid.”

That’s $304 trillion, “more money than there is in the world, outside of Russia,” the New York Tribune reported drily. Jones paid $19.69 and filed for bankruptcy.