How fast does time pass? We have no way to measure this. We can reply, helplessly, that it passes at one second per second, but this is not a rate of change — 1 second divided by 1 second is 1. Not 1 of anything, just 1.

“‘One’ can be an answer, right or wrong, to the questions ‘How many children had Lady Macbeth?’, ‘How many Gods are there?’, and ‘How many minutes do sixty seconds make?’,” writes Notre Dame philosopher Peter van Inwagen. “‘One’ can never be an answer, not even a wrong one, to any other sort of question — including those questions that ask ‘how fast?’ or ‘at what rate?’ Therefore, if time is moving, it is not moving at any rate or speed.”

(From his Metaphysics, 2002.)

This tiling pattern is sometimes referred to as Pythagorean because it can be construed to prove the Pythagorean theorem.

The red area is a right triangle. The square of its shorter side is equivalent to a green square, and the square of its longer side is equivalent to a yellow square.

One green and one yellow square can be cut up and reassembled to fit into one of the canted white squares, which is equivalent to the square of the red triangle’s hypotenuse. Hence a² + b² = c².

Imagine that I first walk through Divinity Avenue, and then imagine that the powers governing the universe annihilate ten minutes of time with all that it contained, and set me back at the door of this hall just as I was before the choice was made. Imagine then that, everything else being the same, I now make a different choice and traverse Oxford Street. You, as passive spectators, look on and see the two alternative universes,–one of them with me walking through Divinity Avenue in it, the other with the same me walking through Oxford Street. Now, if you are determinists you believe one of these universes to have been from eternity impossible: you believe it to have been impossible because of the intrinsic irrationality or accidentality somewhere involved in it. But looking outwardly at these universes, can you say which is the impossible and accidental one, and which the rational and necessary one? I doubt if the most ironclad determinist among you could have the slightest glimmer of light on this point. In other words, either universe after the fact and once there would, to our means of observation and understanding, appear just as rational as the other.

— William James, “The Will to Believe,” 1896

The statement “You will recover from this illness” is either true or false. If it’s true, then it has been true for all eternity, and you’ll recover whether you summon a doctor or not.

If the statement is false, then it has always been false, and you will not recover even with a doctor’s aid.

So there is no point in calling a doctor.

(From Cicero’s De Fato.)

The U.S. Customs Service received an odd bit of paperwork on July 24, 1969:

All three Apollo 11 astronauts signed the form, which was filed at the Honolulu airport on the day they splashed down.

“Yes, it’s authentic,” NASA spokesperson John Yembrick told Space.com. “It was a little joke at the time.”

See Business Trip and Space Bills.

(Thanks, Pablo.)

If you touch a gold ball, you touch its surface and you touch gold. It seems reasonable to conclude that the surface is made of gold. But University of Exeter computer scientist Antony Galton points out that the surface is two-dimensional; it can’t contain any quantity of gold.

What then is it? We can’t say it’s the outermost layer of gold atoms, for that’s a film with two surfaces. And we can’t say it’s an abstract boundary with no physical existence, for we can see it and touch it. So what is it?

J.L. Austin asked, “Where and what exactly is the surface of a cat?”

[Lewis Carroll] told me of a simple, too simple, rule by which, he thought, one could be almost sure of making something at a horse-race. He had on various occasions noted down the fractions which represented the supposed chances of the competing horses, and had observed that the sum of these chances amounted to more than unity. Hence he inferred that, even in the case of such hard-headed men as the backers, the wish is often father to the thought; so that they are apt to overrate the chances of their favourites. His plan, therefore, was to bet against all the horses, keeping his own stake the same in each case. He did not pretend to know much about horse-racing, and I probably know even less; but I understand that it would be impossible to adjust the hedging with sufficient exactitude — in fact, to get bets of the right amount taken by the backers.

— Lionel Arthur Tollemache, Old and Odd Memories, 1908