• If the number is even, divide it by two.
• If the number is odd, triple it and add one.

If you apply these rules repeatedly, will you always reach 1? Surprisingly, no one knows.

Paul Erdos said, “Mathematics is not yet ready for such confusing, troubling, and hard problems.”

Karl Selim Lemström worked a quiet miracle in 1882: He strung conducting wire over the summit of a Lapland mountain and watched it draw down a shaft of light from the night sky — poetic proof that the aurora borealis is an electrical discharge from the upper atmosphere.

See Charged Words.

Here’s a sugar alcohol derived from the North Atlantic seaweed Fucus vesiculosus. It’s called fucitol.

And its optical isomers are called D-fuc-ol and L-fuc-ol.

The glycoprotein that vampire bats use to prevent their victims’ blood from clotting is called draculin.

And diethyl azodicarboxylate is explosive, shock-sensitive, carcinogenic, and an eye, skin, and respiratory irritant, which helps to justify its acronym: DEAD.

See Juvenile Chemistry.

Take of common polypody dried and powdered, of moss growing from the skull of a man who died by violent means (criminals preferred), of nail-filings from human hands and feet, two drachms each; piony root half an ounce, and of fresh misletoe half an ounce. Boil them together as the moon wanes; cool, strain, and administer in small doses.

Cited in Charles White, Three Years in Constantinople, 1846.

See Well, Hey!

In The Hunting of the Snark, the Butcher confirms for the Beaver that Two and One are Three:

Taking Three as the subject to reason about–
A convenient number to state–
We add Seven, and Ten, and then multiply out
By One Thousand diminished by Eight.

The result we proceed to divide, as you see,
By Nine Hundred and Ninety and Two:
Then subtract Seventeen, and the answer must be
Exactly and perfectly true.

Fittingly for Carroll, the math works:

If Martians are observing us, how can we show them we’re intelligent?

Carl Friedrich Gauss proposed marking a huge right triangle on the Siberian plain; Austrian astronomer Joseph von Littrow suggested carving a perfect circle in the Sahara and filling it with burning kerosene.

Joseph Pulitzer favored a more direct approach: He wanted to build a huge billboard in New Jersey recommending his newspaper to inquiring Martians.

He pressed the idea until an assistant asked, “What language shall we print it in?”

If N > 1 then N² > N, which breaks our definition of N as the largest integer. Therefore N = 1.

“The implications of this paradox are devastating,” writes Laurence Chisholm Young. “In seeking the solution to a problem, we can no longer assume that this solution exists. Yet this assumption has been made from time immemorial, right back in the beginnings of elementary algebra, where problems are solved by starting off with the phrase: ‘Let x be the desired quantity.’”

The disciples of Descartes made a perfect anagram upon the Latinised name of their master, ‘Renatus Cartesius,’ one which not only takes up every letter, but which also expresses their opinion of that master’s speciality–’Tu scis res naturae’ (Thou knowest the things of nature).

– William T. Dobson, Poetical Ingenuities and Eccentricities, 1882