In 1894 Francis Galton experimented with conducting addition and subtraction by smell. He designed an apparatus that would produce whiffs of scented air and then memorized their combinations: “I taught myself to associate two whiffs of peppermint with one whiff of camphor; three of peppermint with one of carbolic acid, and so on.”

After practicing sums using the scents themselves, he moved on to doing them entirely in his imagination. “There was not the slightest difficulty in banishing all visual and auditory images from the mind, leaving nothing in the consciousness besides real or imaginary scents. In this way, without, it is true, becoming very apt at the process, I convinced myself of the possibility of doing sums in simple addition with considerable speed and accuracy solely by means of imaginary scents.”

He had similar success with subtraction, but didn’t try multiplication. And some further experiments seemed to show that “arithmetic by taste was as feasible as arithmetic by smell.”

(Francis Galton, “Arithmetic by Smell,” Psychological Review 1:1 [January 1894], 61-62.)

If a tetrahedron is constructed on a base with side lengths 125, 244, 267, then the remaining sides can take the shapes of three right triangles: (44, 240, 244), (44, 117, 125), (117, 240, 267).

And now the sum of the squares of the lengths of each pair of opposite sides in the tetrahedron is the same:

117² + 244² = 125² + 240² = 44² + 267² = 73225

(From Edward Barbeau, Power Play, 1997.)

In 1728 English surgeon William Cheselden removed the cataracts from a 13-year-old boy, producing the first known case of full recovery from blindness:

Having often forgot which was the cat, and which the dog, he was ashamed to ask; but catching the cat, which he knew by feeling, he was observed to look at her steadfastly and then, setting her down said, ‘So, puss, I shall know you another time.’ He was very much surprised, that those things which he had liked best, did not appear most agreeable to his eyes, expecting those persons would appear to be most beautiful that he loved most, and such things to be most agreeable to his sight, that were so to his taste.

Also: “Being shewn his father’s picture in a locket at his mother’s watch, and told what it was, he acknowledged the likeness, but was vastly surprised; asking, how it could be, that a large face could be expressed in so little room, saying, it should have seemed as impossible for him, as to put a bushel of anything into a pint.” A fuller account is here. See also Molyneaux’s Problem.

The smokestack of the local power plant in Turku, Finland, bears the first ten numbers of the Fibonacci sequence in glowing letters seven feet high.

The artist, Mario Merz, had been obsessed with the sequence for nearly 30 years when he added the numbers in 1995; he’d already added them to a chapel in Paris and a spire in Turin.

“It is entirely by accident that the sequence reflects two of the major research fields of the University of Turku, namely, number theory and mathematical biology,” write mathematicians Mats Gyllenberg and Karl Sigmund. “As is well known, Fibonacci introduced the sequence at around AD 1200 to model the growth of a rabbit population.”

(Mats Gyllenberg and Karl Sigmund, “The Fibonacci Chimney,” Mathematical Intelligencer 22:4 [2000], 46.)

The population on the left has equal numbers of blue and red individuals. But if it colonized a new area using a very small number of individuals, one color or the other might predominate, with sometimes dramatic effects.

The Afrikaner population of South Africa is descended primarily from one shipload of immigrants that landed in 1652. One of these colonists carried the gene for Huntington’s disease, an autosomal dominant disease that causes a fatal breakdown of nerve cells in the brain. Most cases of the disease in the modern Afrikaner population can be traced to that individual.

Another condition, lipoid proteinosis, has been traced to Jacob Cloete, a German immigrant to the Cape in 1652. His great-grandson, Gerrit Cloete, migrated to Namaqualand in 1742. The area is somewhat isolated, so intermarriages were relatively common, compounding the effect.

(Thanks, Matt.)

The University of Oxford has a bell that’s been ringing almost continuously since 1840. A little 4-millimeter clapper oscillates between two bells, each of which is positioned beneath a dry pile, an early battery. Due to the electrostatic force, the clapper is first attracted to and then repelled by each bell in turn, so it’s been ringing them alternately for 179 years. The operation conveys only a tiny amount of charge between the bells, which explains why it’s managed to run so long. The whole apparatus is kept under two layers of glass, but the ringing is so faint that it would be inaudible in any case.

It’s estimated that the bell has produced 10 billion rings so far — it holds the Guinness World Record as “the world’s most durable battery [delivering] ceaseless tintinnabulation.”