When German physicist Walther Nernst learned that his cowshed was warm because of the cows’ metabolic activity, he resolved to sell them and invest in carp.
A thinking man, he said, cultivates animals that are in thermodynamic equilibrium with their surroundings and does not waste his money in heating the universe.
‘Twas Euclid, and the theorem pi
Did plane and solid in the text,
All parallel were the radii,
And the ang-gulls convex’d.
“Beware the Wentworth-Smith, my son,
And the Loci that vacillate;
Beware the Axiom, and shun
The faithless Postulate.”
He took his Waterman in hand;
Long time the proper proof he sought;
Then rested he by the XYZ
And sat awhile in thought.
And as in inverse thought he sat
A brilliant proof, in lines of flame,
All neat and trim, it came to him,
Tangenting as it came.
“AB, CD,” reflected he–
The Waterman went snicker-snack–
He Q.E.D.-ed, and, proud indeed,
He trapezoided back.
“And hast thou proved the 29th?
Come to my arms, my radius boy!
O good for you! O one point two!”
He rhombused in his joy.
‘Twas Euclid, and the theorem pi
Did plane and solid in the text;
All parallel were the radii,
And the ang-gulls convex’d.
— Emma Rounds
Socrates likes company. He wants to eat only if Plato wants to eat.
But Plato is angry at Socrates. He wants to eat only if Socrates does not want to eat.
Does Socrates want to eat?
(From Buridan’s Sophismata.)
Suppose there were an experience machine that would give you any experience you desired. Superduper neuropsychologists could stimulate your brain so that you would think and feel you were writing a great novel, or making a friend, or reading an interesting book. All the time you would be floating in a tank, with electrodes attached to your brain. Should you plug into this machine for life, preprogramming your life’s experiences? If you are worried about missing out on desirable experiences, we can suppose that business enterprises have researched thoroughly the lives of many others. You can pick and choose from their large library or smorgasbord of such experiences, selecting your life’s experiences for, say, the next two years. After two years have passed, you will have ten minutes or ten hours out of the tank, to select the experiences of your next two years. Of course, while in the tank you won’t know that you’re there; you’ll think it’s all actually happening. … Would you plug in?
— Robert Nozick, Anarchy, State, and Utopia, 1974
10102323454577 is the smallest 14-digit prime number that follows the rhyme scheme of a Shakespearean sonnet (ababcdcdefefgg).
(Discovered by Jud McCranie.)
Eric Chandler offered this perpetual-motion scheme for Edward Barbeau’s “Fallacies, Flaws and Flimflam” column in the College Mathematical Journal. Points A and B are at the same height, and C is halfway between them. The ramp AC is a segment of a cycloid, a curve designed to produce the fastest descent under gravity.
A ball released at A rolls down the ramp AC to C covering a greater distance in a shorter time than it would have had it rolled down BC to C. The relation Velocity = Distance/Time thus implies that the ball arrives at C with greater velocity than it would have had it rolled down BC. This added velocity enables the ball to roll from C up to and past B to a point D a little farther along. It then returns to A along the inclined ramp DA to repeat the cycle endlessly.
Where is the error?
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999989999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999 is prime.
In probability theory, the formula for the Poisson distribution is
Pm(n) = mne–m/n!
Pleasingly, the mnemonic for this is mnemonic: “m to the n, e to the –m over n factorial.” Arguably the factorial sign even resembles an inverted i.
Now we just need a way to remember that …
(From M.H. Greenblatt, Mathematical Entertainments, 1965.)
There was Diodorus Chronos, a most acute and subtle reasoner. He proved there was no such thing as motion. A body must move either in the place where it is or in the place where it is not. Now, a body cannot be in motion in the place where it is stationary, and cannot be in motion in the place where it is not. Therefore, it cannot move at all. …
Diodorus was brought up roundly by another densely practical intelligence. Having dislocated his shoulder, he sent for a surgeon to set it. ‘Nay,’ said the practitioner, doubtful, perhaps, whether so subtle an intelligence might not euchre him out of his fee by some logical ingenuity, ‘your shoulder cannot possibly be put out at all, since it cannot be put out in the place in which it is, nor yet in the place in which it is not.’
— “Some Famous Paradoxes,” The Illustrated American, Nov. 1, 1890