Mistaken Identity

Suppose a brave Officer to have been flogged when a boy at school, for robbing an orchard, to have taken a standard from the enemy in his first campaign, and to have been made a General in advanced life: Suppose also, which must be admitted to be possible, that when he took the standard, he was conscious of his having been flogged at school; and that, when made a General, he was conscious of his taking the standard, but had absolutely lost the consciousness of his flogging. These things being supposed, it follows from Mr. Locke’s doctrine, that he who was flogged at school is the same person who took the standard; and that he who took the standard is the same person who was made a General. Whence it follows, if there be any truth in logic, that the General is the same person with him who was flogged at school. But the General’s consciousness does not reach so far back as his flogging; therefore, according to Mr. Locke’s doctrine, he is not the person who was flogged. Therefore the General is, and at the same time is not, the same person with him who was flogged at school.

— Thomas Reid, Essays on the Intellectual Powers of Man, 1785

| Science & Math

A Canny Gambler

http://www.sxc.hu/photo/560246

In 1693, Samuel Pepys wrote to Isaac Newton with this question:

“Which is more likely, to throw at least 1 six with 6 dice, or at least 2 sixes with 12 dice, or at least 3 sixes with 18 dice?”

To Pepys’ surprise, Newton found that the first choice has the highest likelihood. The probabilities are 0.665, 0.619, and 0.597 (rounded to three places).

| Science & Math

The Mensa Diet

Finding himself hot and overweight at an Air Force base during World War II, Jerry Salny decided he could shed pounds by drinking scotch and soda. Here’s his reasoning:

  • It takes 1 calorie of heat to raise the temperature of 1 gram of water by 1° Celsius.
  • A glass holds about 200 cc of scotch, soda, and ice. Its temperature is 0° Celsius.
  • As he drinks the scotch and soda, his body must supply enough heat to raise 200 grams to body temperature, or 37°C.
  • That’s 200 grams × 37°C, or 7,400 calories.
  • “Since all the calorie books show scotch as having 100 calories per ounce, and none at all for the soda, we should be able to drink scotch and soda all day and lose weight like mad.”

“This has been tried,” Salny reported, “and although the experimenter hasn’t lost any weight in the process, he doesn’t worry about it much anymore.”

Why doesn’t it work?

Click for Answer
| Puzzles · Science & Math

The Two Cultures

Tennyson’s poem “The Vision of Sin” contains this couplet:

Every moment dies a man,
Every moment one is born.

When he published it in 1842, Charles Babbage sent him a note:

I need hardly point out to you that this calculation would tend to keep the sum total of the world’s population in a state of perpetual equipoise, whereas it is a well-known fact that the said sum total is constantly on the increase. I would therefore take the liberty of suggesting that, in the next edition of your excellent poem, the erroneous calculation to which I refer should be corrected as follows:–

Every moment dies a man,
And one and a sixteenth is born.

“I may add that the exact figures are 1.167,” he added, “but something must, of course, be conceded to the laws of metre.”

| Literature · Poems · Science & Math

Dark Science

http://commons.wikimedia.org/wiki/Image:Tickling_the_Dragons_Tail.jpg

On Aug. 21, 1945, physicist Harry Daghlian accidentally dropped a brick of tungsten carbide into a plutonium bomb core at the Los Alamos National Laboratory. The mass went critical, and Daghlian died of radiation sickness.

Exactly nine months later, physicist Louis Slotin was conducting an experiment on the same mass of plutonium when his screwdriver slipped and the mass again went critical. He too died of radiation sickness.

The mass became known as “the demon core.”

| Oddities · Science & Math

The Vanishing Debtor

Alpha approaches Beta, asking for payment of a debt.

Beta: If you had an odd number of pebbles — or for that matter an even one — and then chose to add or subtract a pebble, do you think you would have the same number?

Alpha: No.

Beta: If you had a measure of one cubit and chose to add or cut off some length of it, that measure would no longer exist, would it?

Alpha: No.

Beta: Well now, think of a human in the same way: one human is growing and another is diminishing. All are constantly in the process of change. But what by its nature changes and never stays put must already be different from what it changed from. You and I are different from who we were yesterday, and by the same argument will be different again tomorrow.

Exasperated, Alpha strikes Beta.

Beta: Why are you angry with me?

Alpha: As someone nearby just demonstrated, it was not I who hit you, not I at all, but someone else altogether.

(From a fragment by Epicharmus.)

| Science & Math

Newcomb’s Paradox

Flamdor McSqueem is a superintelligent wombat from the planet Zortag. He shows you two boxes. You can choose to take the contents of Box A or the contents of both boxes. He has privately predicted what you will do.

If Flamdor predicted you would choose Box A only, then Box A contains $1 million. If he predicted you’d choose both boxes, then Box A contains nothing. Either way, Box B contains $1,000. What should you do?

Some people reason that Flamdor is very intelligent and his predictions are usually accurate, so it would seem best to choose Box A. Others note that Flamdor has already made his prediction and can’t change the contents of the boxes now, so it seems best to take both boxes.

There’s no correct answer — decision theorists are still arguing about it. What would you do?

| Science & Math