1 × 9 + 2 = 11
12 × 9 + 3 = 111
123 × 9 + 4 = 1111
1234 × 9 + 5 = 11111
12345 × 9 + 6 = 111111
123456 × 9 + 7 = 1111111
1234567 × 9 + 8 = 11111111
12345678 × 9 + 9 = 111111111
Science & Math
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?
Oops
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.)
Geometry Disproves Arithmetic
The first figure, measuring 5 by 5, can be reassembled to form the second, measuring 8 by 3. Thus 25 equals 24.
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
La Fornarina
When Raphael died in 1520, a portrait was found in his studio of a local baker’s daughter named Margherita. She is thought to have been his lover — on his deathbead he had bid her farewell and arranged for her care.
The portrait might reveal something else as well. Writing in The Lancet in 2002, Georgetown University medical professor Carlos Hugo Espinel suggests that “La Fornarina” might have had breast cancer:
There is a bulge in the [left] breast that, beginning inward from the axilla and curving horizontally to the right, slopes gently toward the nipple. This bulge seems to be a mass, oval in shape, puckering just above the tip of La Fornarina’s index finger.
After studying other artworks, Espinel has also concluded that Michelangelo had gout, that Rembrandt died of temporal arteritis, and that the Mona Lisa’s smile may have resulted from the partial paralysis of a facial muscle. Independent research has supported some of these diagnoses.
Loopy
You can measure a circle’s circumference by “unrolling” it along a line, like this:
But note that the smaller circle unrolls at the same time … and it gives the same length. Clearly we could do the same thing with circles of any size. Do all circles have the same circumference?
Perspective
Earth seen from 4 billion miles away, photographed by Voyager 1 on June 6, 1990.
Of the “pale blue dot,” astronomer Carl Sagan said, “That’s here. That’s home. That’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every ‘superstar,’ every ‘supreme leader,’ every saint and sinner in the history of our species lived there — on a mote of dust suspended in a sunbeam.”
Exception Paradox
If every rule has an exception, then there must be an exception to the rule that every rule has an exception.