Counting the Days

Thomas Fuller, known as the Virginia Calculator, was stolen from his native Africa at the age of fourteen and sold to a planter. When he was about seventy years old, two gentlemen, natives of Pennsylvania, viz., William Hartshorne and Samuel Coates, men of probity and respectable characters, having heard, in travelling through the neighborhood in which the slave lived, of his extraordinary powers in arithmetic, sent for him and had their curiosity sufficiently gratified by the answers which he gave to the following questions: First, upon being asked how many seconds there were in a year and a half, he answered in about two minutes, 47,304,000. Second: On being asked how many seconds a man has lived who is 70 years, 17 days and 12 hours old, he answered in a minute and a half 2,210,500,800. One of the gentlemen who employed himself with his pen in making these calculations told him he was wrong, and the sum was not so great as he had said — upon which the old man hastily replied: stop, master, you forget the leap year. On adding the amount of the seconds of the leap years the amount of the whole in both their sums agreed exactly.

— E.W. Scripture, “Arithmetical Prodigies,” American Journal of Psychology, 1891

Three Strikes

Predictions by Scottish mathematician and physicist Lord Kelvin, president of the Royal Society:

  • “X-rays will prove to be a hoax.” (1883)
  • “Heavier-than-air flying machines are impossible.” (1895)
  • “Radio has no future.” (1897)

Speaking to the British Association for the Advancement of Science in 1900, he said, “There is nothing new to be discovered in physics now; all that remains is more and more precise measurement.” Einstein’s annus mirabilis came five years later.

Alcohol Problem

Fill one glass with wine and another with water. Transfer a teaspoonful of wine from the first glass into the second. Then transfer a teaspoonful of that mixture back into the first glass. Now, is there more wine in the water or water in the wine?

Most people will predict it’s the former, but in fact the two quantities will always be the same. Can you see why?


In 1890, a well-intentioned New Yorker named Eugene Schieffelin released 80 starlings in Central Park. He wanted to introduce every bird mentioned the works of William Shakespeare into the United States. (In The First Part of King Henry the Fourth, Hotspur says, “Nay, I’ll have a starling shall be taught to speak nothing but ‘Mortimer.'”)

He should have reconsidered. Scientists estimate that those birds have multiplied into more than 200 million in North America, where the starling has become a major pest, outcompeting other birds for nest holes. Opponents of genetically modified organisms still point to Schieffelin’s act to warn of the dangers of invasive species.

04/12/2022 UPDATE: Not true, according to John MacNeill Miller of Allegheny College. (Thanks, Sharon.)

The Fermi Paradox

Purported UFO, Passoria, N.J., 1952. Enthusiasts point out that with 250 billion stars in the Milky Way and 70 sextillion in the visible universe, it’s overwhelmingly likely that there are other intelligent, communicating beings out there.

But over a lunch discussion in 1950, physicist Enrico Fermi asked a telling question: “Where are they?” The universe is 13 billion years old, and it’s been estimated that an advanced civilization could colonize our whole galaxy in 5 million years. That’s a flash, as cosmologists reckon time — even if the aliens themselves couldn’t survive an interstellar journey, surely they could design a self-replicating spacecraft that could.

So how come we haven’t met our galactic neighbors? Opinions vary. Maybe we’re in a zoo. Maybe they’re so alien that even detecting them is impossible. Or maybe they don’t believe in us.

A Clever Landlord

At an humble inn where there were only six rooms, seven travellers applied for lodging, each insisting on having a room to himself. The landlord put the first man in room No. 1 and asked one of the other men to stay there also for a few minutes. He then put the third man in room number two, the fourth man in room No. 3, the fifth man in room No. 4, and the sixth man in room No. 5. Then returning to room No. 1 he took the seventh man and put him in room No. 6. Thus each man had his own room!

— H.E. Licks, Recreations in Mathematics, 1917