“The only way to keep ahead of the procession is to experiment. If you don’t, the other fellow will. When there’s no experimenting there’s no progress. Stop experimenting and you go backward. If anything goes wrong, experiment until you get to the very bottom of the trouble.” — Thomas Edison

Finger Numerals


Writing in the north of England in the early 8th century, the Venerable Bede described a Roman system of finger counting:

1 = the little finger bent at the middle joint
2 = the ring and little fingers bent at the middle joints
3 = the middle, ring, and little fingers bent at the middle joints
4 = the middle and ring fingers bent at the middle joints
5 = the middle finger only bent at the middle joint
6 = the ring finger bent at the middle joint
7 = the little finger closed on the palm
8 = the ring and little fingers closed on the palm
9 = the middle, ring, and little fingers closed on the palm
10 = the tip of the index finger touching the middle joint of the thumb
11 to 19 = the actions denoting each numeral from 1 to 9 plus that of 10
20 = the thumb tucked between the index and middle fingers, so that the thumbnail touches the middle joint of the index finger
21 to 29 = the actions denoting each numeral from 1 to 9 plus that of 20
30 = the tips of the thumb and index finger touching and forming a circle or ring
40 = the thumb and index finger standing erect and close together
50 = the thumb bent at both joints and held against the palm
60 = the index finger closed over the thumb
70 = the first joint of the index finger resting over the first joint of the thumb, which is held nearly straight
80 = the tip of the index finger resting on the first joint of the thumb
90 = the thumb bent over the first joint of the index finger

The signs for 100, 200, 300, and so on are the same as 10, 20, 30, but made by the right hand; and the signs for 1,000, 2,000, 3,000 and so on are the same as 1, 2, 3 but made by the right hand. “To add two numbers, one simply signed the first, then made the mental arithmetical calculation and reproduced the gesture corresponding with the correct sum,” writes Angus Trumble in The Finger: A Handbook (2010). “The process was cumulative; to add a further number to the sum of the first two, you proceeded to represent the gesture corresponding with the new total, and so on. Likewise, the task of subtraction merely threw the whole system into reverse. It was perfectly clear to anyone observing you carry out these separate procedures whether the job in hand was one of addition or subtraction.”

Trumble says that at the end of the 19th century Wallachian peasants were discovered to have preserved a few methods of digital multiplication and division that had been preserved throughout the Roman empire. Here’s one.

The Georgia Guidestones

Image: Wikimedia Commons

In Elbert County, Georgia, stands a granite monument bearing 10 guidelines inscribed in eight languages:

  1. Maintain humanity under 500,000,000 in perpetual balance with nature.
  2. Guide reproduction wisely — improving fitness and diversity.
  3. Unite humanity with a living new language.
  4. Rule passion — faith — tradition — and all things with tempered reason.
  5. Protect people and nations with fair laws and just courts.
  6. Let all nations rule internally resolving external disputes in a world court.
  7. Avoid petty laws and useless officials.
  8. Balance personal rights with social duties.
  9. Prize truth — beauty — love — seeking harmony with the infinite.
  10. Be not a cancer on the earth — Leave room for nature — Leave room for nature.

It was commissioned in 1979 by a man using the pseudonym Robert C. Christian, who seemed to have considerable resources. A ledger nearby explains that the structure operates as an astronomical calendar and that a time capsule lies 6 feet beneath.

It’s thought that the inscription lists the principles that will be needed to rebuild a devastated civilization. A tablet reads, “Let these be guidestones to an Age of Reason.”

“Settling a Bill”

Four sharpers having treated themselves to a sumptuous dinner at the Hotel Montreuil, were at a loss how to settle for it, and hit on the following plan: They called for the waiter and asked for the bill. One thrust his hand into his pocket as if to draw his purse; the second prevented him, declaring he would pay; the third did the same. The fourth forbade the waiter from taking any money from either of them, but all three persisted. At last one said: ‘The best way to decide is to blindfold the waiter, and whoever he first catches shall settle the bill.’ This proposal was accepted, and while the waiter was groping his way around the room they slipped out of the house one after another.

Western Literary Messenger, May 1854



Choose one of these cards and fix it clearly in your mind. Then open the answer box.

Click for Answer

Our System


“If x is the population of the United States and y is the degree of imbecility of the average American, then democracy is the theory that x × y is less than y.” — H.L. Mencken, A Mencken Chrestomathy, 1949

The Precarious Picture

Suppose you want to hang a picture by a string that’s attached at two points on the back of the frame. How can you arrange the string on two nails such that the picture will fall if either nail is removed?

One solution is above. I don’t know who first asked the question; I first saw it in Mathematical Mind-Benders, by Peter Winkler, who got it from Giulio Genovese, a mathematical graduate student at Dartmouth, who’d seen it in more than one source in Europe.

But it opens up a surprisingly rich discussion — see the paper below for some entertainingly complex variants.

(Erik D. Demaine et al., “Picture-Hanging Puzzles,” Theory of Computing Systems 54:4 [2014], 531-550.)

A Near Thing

British infantryman Charlie “Ginger” Byrne was advancing on the German-held village of Beaumont-Hamel on July 1, 1916, when the other members of his gun crew were hit and he was forced to take refuge in a shallow shell hole. He lay there among the ammunition boxes he’d been carrying with only four inches of earth above his head.

I lay as I fell because I daren’t move. I had my legs folded under me and my bloomin’ bayonet was on my left-hand side. I was dying to move that bayonet out of the way so I could get my hip down lower. But that Jerry decided he hadn’t anything better to do than play his gun across my shell-hole. He knew I wasn’t hit. I knew what he was doing. I was a machine gunner myself, wasn’t I? He’d be holding the two handles of his gun, then he’d tap, tap so it played right across the top of the hole; then he’d turn the wheel at the bottom to lower the barrel and then he’d tap, tap the other side to bring it back again. He was hitting the dust just above my head and he smashed the bloomin’ boxes. Bits of ammo flew about everywhere. In a queer sort of way I was lying there almost admiring what he was doing, as though it wasn’t me he was aiming at. He was a fellow machine-gunner, wasn’t he? And he certainly knew his job. But he just couldn’t get that trajectory low enough.

Byrne waited 14 hours through the interminable summer day with the German gunner “nagging away,” firing just over the hole. “Sometimes he’d stop for a bit and turn the gun on someone else; but he’d got right fond of me. Wasted a lot of ammo on me that Jerry did.” When darkness finally came he crawled and then ran across no-man’s-land and escaped, entirely uninjured.

(From Richard van Emden, Meeting the Enemy: The Human Face of the Great War, 2013.)

Eye to Eye

One other interesting detail from In Your Face, psychologist David Perrett’s 2010 exploration of human attraction. Perrett’s Perception Lab recruited 300 men and 400 women, all of whom had heterosexual partners and had been raised by two parents. They learned that romantic partners tend to look alike — the participants and their partners tended to have similar hair color and similar eye color.

This might be explained by a self-similar preference or narcissism, but on looking deeper into the data Perrett’s team found that the single best predictor of one’s partner’s eye color was the eye color of one’s parent of the opposite sex. If a woman’s mother had blue eyes and her father had brown eyes, she would most likely be partnered with a brown-eyed man. If a man’s mother had blue eyes and his father had brown eyes, his partner most likely had blue eyes. Similarly, the hair color of a man’s mother was the single best predictor of his partner’s hair color. “These results indicate that individuals choose partners who resemble their opposite-sex parent both in eye and hair color.”

(Anthony C. Little et al., “Investigating an Imprinting-Like Phenomenon in Humans: Partners and Opposite-Sex Parents Have Similar Hair and Eye Colour,” Evolution and Human Behavior 24:1 [2003], 43-51.)