- Dorothy Parker left her entire estate to Martin Luther King Jr.
- SOUTH CAMBRIDGE, NY contains 16 different letters.
- 45927 = ((4 + 5) × 9)2 × 7
- STONE AGE = STAGE ONE
- “You cannot be both fashionable and first-rate.” — Logan Pearsall Smith
Science & Math
Upstanding
You can distinguish a raw egg from a hard-boiled one by spinning it.
The reason for this was puzzled out only in 2002 by mathematicians Keith Moffat of Cambridge University and Yatuka Shimomura of Keio University. Friction between the egg and the table produces a gyroscopic effect, and the egg trades some kinetic energy for potential energy, raising its center of gravity. The raw egg can’t do this because its runny interior lags behind the shell. Moffat wrote:
Place a hard-boiled egg on a table,
And spin it as fast as you’re able;
It will stand on one end
With vectorial blend
Of precession and spin that’s quite stable.
Math Notes
Right and Wrong
Can objects have preferences? The rattleback is a top that seems to prefer spinning in a certain direction — when spun clockwise, this one arrests its motion, shakes itself peevishly, and then sweeps grandly counterclockwise as if forgiving an insult.
There’s no trick here — the reversal arises due to a coupling of instabilities in the top’s other axes of rotation — but prehistoric peoples have attributed it to magic.
See Right Side Up.
Some Coincidences
There are almost exactly 500 million inches in the pole-to-pole diameter of the earth.
The speed of light is within 0.1% of 300,000 kilometers per second.
A cube with a side of 1 mile has nearly the same volume as a sphere with a radius of 1 kilometer.
See Applied Math.
(Thanks, Ben.)
High Hopes
A worm crawls along an elastic band that’s 1 meter long. It starts at one end and covers 1 centimeter per minute. Unfortunately, at the end of each minute the band is instantly and uniformly stretched by an additional meter. Heroically, the worm keeps its grip and continues crawling. Will it ever reach the far end?
Heads and Tails
Let’s play a coin-flipping game. At stake is half the money in my pocket. If the coin comes up heads, you pay me that amount; if it comes up tails, I pay you.
Initially this looks like a bad deal for me. If the coin is fair, then on average we should expect equal numbers of heads and tails, and I’ll lose money steadily. Suppose I start with $100. If we flip heads and then tails, my bankroll will rise to $150 but then drop to $75. If we flip tails and then heads, then it will drop to $50 and then rise to $75. Either way, I’ve lost a quarter of my money after the first two flips.
Strangely, though, the game is fair: In the long run my winnings will exactly offset my losses. How can this be?
Rules of Thumb
“If an elderly but distinguished scientist says that something is possible he is almost certainly right, but if he says that it is impossible he is very probably wrong.” — Arthur C. Clarke
“When, however, the lay public rallies around an idea that is denounced by distinguished but elderly scientists and supports that idea with great fervor and emotion — the distinguished but elderly scientists are then, after all, probably right.” — Isaac Asimov
Midair
A “curious puzzle” from Raymond Smullyan:
Imagine a plane table of infinite extent. Attached perpendicularly to the table is a rod of finite length, and above that, attached by a hinge, is a second vertical rod, this one infinitely long.
Operate the hinge. What happens? The infinite rod descends freely through the first 90 degrees, until it’s parallel to the tabletop. But it can’t go beyond this, because then at some point the solid rod would intersect the solid table.
Thus it’s impossible to “rest” an infinite rod on an infinite plane. “And so, you have the curious phenomenon of the hinged rod being supported at only one end!”
Teamwork
LOGIC, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion–thus:
Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.
Minor Premise: One man can dig a posthole in sixty seconds; therefore–
Conclusion: Sixty men can dig a posthole in one second.
This may be called the syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.
— Ambrose Bierce, The Devil’s Dictionary, 1911