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.


You can measure a circle’s circumference by “unrolling” it along a line, like this:

circumference fallacy

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?


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.”


Seeing a red apple should increase your confidence that all ravens are black.

Why? Because the statement “All ravens are black” is logically equivalent to “All non-black things are non-ravens.” And seeing a red apple (or green grass) confirms this belief.

This is logically inescapable, even if it’s counterintuitive. It’s known as Hempel’s paradox.

Oral Exam,M1

Math prodigy George Bidder was born to a Devonshire stonemason in 1806. In a public appearance at age 11, he answered each of these questions in less than a minute:

  • What is the cube root of 673,373,097,125? “Answer, 8,765.”
  • If a mouse can draw one ounce and a half, how many mice can draw 50,000 tons? “Answer, 1,194,666,666, and one ounce over.”
  • If a coach travels from Exeter to Plymouth, 44 miles, every day in a year, how often does a wheel turn round that is 2 feet 9 inches? “Answer, 30,835,200.”
  • If a fan of a windmill goes round 15 times in a minute, how many times will it go round in 7 years, 4 months, 1 week, 2 hours, 3 minutes — 365 days 6 hours to the year, and 28 days to the month? “Answer, 57,897,245.”
  • If the ministers have taken of the income tax 12 millions of money in 1-pound notes, how many miles would they cover a road 30 feet wide, each note being 8 inches by 4 and a half? “He directly answered, 18 miles, 1,653 yards, and one foot.”
  • Suppose the earth to consist of 971 million of inhabitants, and suppose they die in 33 years and four months, how many have returned to dust since the time of Adam, computing it to be 5,850 years? “Answer, 170,410,500,000.” Multiply it again by 99. “Answer, 16,870,639,500,000.”

(Reported in Kirby’s Wonderful and Scientific Museum, 1820)


Sorry about the photo. It’s a dog’s head, kept alive in the 1940s by an experimental Soviet device called an autojector, which pumped oxygenated blood through it. Reportedly this kept the head alive for hours — it would cock its ears at sounds and lick its chops when citric acid was smeared on them.

That ain’t all. If you believe the 1940 film Experiments in the Revival of Organisms, Soviet scientist Sergei S. Bryukhonenko drained the blood from a dog until it reached clinical death, left it in that state for 15 minutes, then connected it to the autojector. In the film, the heart and lungs resume functioning, and 12 hours later the dog is reported to be on its feet, barking and wagging its tail.

Is all this for real? The film’s authenticity is debated — some say it may show re-enactments rather than authentic experiments — but the research itself was well documented, leading eventually to modern heart-lung machines and a posthumous Lenin Prize for Bryukhonenko.

Seeing Double

More proof (if any were needed) that 2 equals 1:

s = 1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 + 1/7 – 1/8 + 1/9 – 1/10 + 1/11 – 1/12 …

2s = 2 – 2/2 + 2/3 – 2/4 + 2/5 – 2/6 + 2/7 – 2/8 + 2/9 – 2/10 + 2/11 – 2/12 …

Rearrange terms:

2s = (2 – 2/2) – (2/4) + (2/3 – 2/6) – (2/8) + (2/5 – 2/10) – (2/12) …

2s = 1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 …

But that’s just s again. So 2s = s, and therefore 2 = 1.

(Thanks, Gonzalo!)