Syllogismus Crocodilus

http://commons.wikimedia.org/wiki/File:Brockhaus_and_Efron_Encyclopedic_Dictionary_107.jpg

Here is a curious old story that is something like a puzzle: A crocodile stole a baby, ‘in the days when animals could talk,’ and was about to make a dinner of it. The poor mother begged piteously for her child. ‘Tell me one truth,’ said the crocodile, ‘and you shall have your baby again.’ The mother thought it over, and at last said: ‘You will not give it back.’ ‘Is that the truth you mean to tell?’ asked the crocodile. ‘Yes,’ replied the mother. ‘Then by our agreement I keep him,’ added the crocodile; ‘for if you told the truth I am not going to give him back, and if it is a falsehood, then I have also won.’ Said she: ‘No, you are wrong. If I told the truth you are bound by your promise; and, if a falsehood, it is not a falsehood, until after you have given me my child.’ Now, the question is, who won?

— Pennsylvania School Journal, March 1887

| Science & Math

Self-Expression

The first few powers of 5 share a curious property — their digits can be rearranged to express their value:

25 = 52
125 = 51 + 2
625 = 56 – 2
3125 = (3 + (1 × 2))5
15625 = 56 × 125
78125 = 57 × 182

It’s conjectured that all powers of 5 have this property. But no one’s proved it yet.

| Science & Math

A Canceled Debt

Suppose you borrowed $10 from Tom and $10 from Bob. On your way to repaying them you are robbed of everything but the $10 you had hidden in your shirt pocket. By no fault of your own, you now face the following paradoxical dilemma:

(1) You are obligated to repay Tom and Bob.
(2) If you pay Tom you cannot repay Bob.
(3) If you repay Bob you cannot repay Tom.
(4) You cannot honor all your obligations: in the circumstances this is impossible for you. (By (1)-(3).)
(5) You are (morally) required to honor all your obligations.
(6) You are not (morally) required to do something you cannot possibly do (ultra posse nemo obligatur).

— Nicholas Rescher, Paradoxes, 2001

| Science & Math

Scale Degrees

Suppose that in one night all the dimensions of the universe became a thousand times larger. The world will remain similar to itself, if we give the word similitude the meaning it has in the third book of Euclid. Only, what was formerly a meter long will now measure a kilometer, and what was a millimeter long will become a meter. The bed in which I went to sleep and my body itself will have grown in the same proportion. When I wake in the morning what will be my feeling in face of such an astonishing transformation? Well, I shall not notice anything at all. The most exact measures will be incapable of revealing anything of this tremendous change, since the yard-measures I shall use will have varied in exactly the same proportions as the objects I shall attempt to measure.

— Henri Poincaré, Science and Method, 1908

| Science & Math

Asking Directions

http://www.sxc.hu/photo/1084981

If we take a cube and label one side top, another bottom, a third front, and a fourth back, there remains no form of words by which we can describe to another person which of the remaining sides is right and which left. We can only point and say here is right and there is left, just as we should say this is red and that blue.

— William James, The Principles of Psychology, 1890

| Science & Math

Hose and Cons

Sir John Cutler had pair of silk stockings, which his housekeeper, Dolly, darned for a long term of years with worsted; at the end of which time, the last gleam of silk had vanished, and Sir John’s silk stockings were found to have degenerated into worsted. Now, upon this, a question arose amongst the metaphysicians, whether Sir John’s stockings retained (or, if not, at what precise period they lost) their personal identity. The moralists again were anxious to know, whether Sir John’s stockings could be considered the same ‘accountable’ stockings from first to last. The lawyers put the same question in another shape, by demanding whether any felony which Sir John’s stockings could be supposed to have committed in youth, might legally be the subject of indictment against the same stockings when superannuated; whether a legacy left to the stockings in their first year, could be claimed by them in their last; and whether the worsted stockings could be sued for the debts of the silk stockings.

— Thomas de Quincey, “Autobiography of an English Opium-Eater,” from Tait’s Edinburgh Magazine, September 1838

| Literature · Science & Math

Moonlighting

http://commons.wikimedia.org/wiki/File:James_Joseph_Sylvester.jpg

J.J. Sylvester was a brilliant mathematician but, by all accounts, a lousy poet. The Dictionary of American Biography opines delicately that “Most of Sylvester’s original verse showed more ingenuity than poetic feeling.”

What it lacked, really, was variety. His privately printed book Spring’s Debut: A Town Idyll contains 113 lines, every one of which rhymes with in.

Even worse is “Rosalind,” a poem of 400 lines all of which rhyme with the title character’s name. In his History of Mathematics, Florian Cajori reports that Sylvester once recited “Rosalind” at Baltimore’s Peabody Institute. He began by reading all the explanatory footnotes, so as not to interrupt the poem, and realized too late that this had taken an hour and a half.

“Then he read the poem itself to the remnant of his audience.”

See Poetry in Motion.

| Literature · Science & Math