Science & Math


  • Newton was born the year that Galileo died.
  • Cole Porter’s summer home was called No Trespassing.
  • 66339 = (6 × 6)3 + 39
  • Could you have had different parents?
  • “A good conscience is a continual Christmas.” — Ben Franklin

UPDATE: The first item here is incorrect. The dates coincide only if one uses the Gregorian calendar to date Galileo’s death and the Julian to date Newton’s birth. The two events occurred 361 days apart, which puts them in separate years on both calendars. Apparently this is a very common error. (Thanks, Igor.)

Snappy New Year

In Insurmountable Simplicities (2006), Roberto Casati points out that a traveler flying east may miss midnight — by entering a new time zone, he may jump from the 11:00 hour into the 12:00 hour without passing through midnight:

Mathematics and geography tell us that during the flight it will happen more than once that we reach the stroke of the hour without leaving the time zone we are in. If our flight lasts eight hours and the time difference between New York and Paris is six hours, this will happen at least twice, and at most eight times. But there is no guarantee that the stroke of midnight will be among these cases.

Thus, if it’s New Year’s Eve, an eastbound traveler may get no champagne.

Frozen Fire

Lightning can fuse sand into curious rootlike tubes up to 5 meters long, called fulgurites. Because their shape records the path of the strike as it passes into the ground, they’re sometimes known as petrified lightning.

Lightning had a ruinous history before the introduction of Ben Franklin’s lightning rod. The campanile of St. Mark in Venice was destroyed three times over. In 1769, a bolt struck the tower of St. Nazaire in Brescia, whose magazine contained 100 tons of gunpowder. One-sixth of the town was destroyed, and 3,000 people died.

Compounding the harm was the disastrous belief that ringing bells during thunderstorms would allay lightning. In one 33-year period, lightning struck 386 church towers and killed 103 bell ringers.

Modern strikes are less dire. In 1919, Cleveland Indians pitcher Ray Caldwell was struck by lightning during a game against the Philadelphia Athletics. “It felt like a sandbag hit me,” he said. He refused to leave the game and pitched to Joe Dugan for the final out. The Indians won, 2-1.

Bites and Pieces

Properly speaking, can the top half of an apple exist without the whole?

What is it the top half of?


Any set of 10 positive integers smaller than 100 will always contains two subsets with the same sum.

In any such group, the number of possible subsets (excluding the empty set) is 210 – 1, or 1023. And the largest possible sum of any subset is 90 + 91 + … + 99 = 945. Hence, no matter which numbers are chosen, there will always be more subsets than possible sums, and some subsets (dozens, actually) must yield the same sum.

Squeeze Play

A rail one mile long is lying on the ground. If you push its ends closer together by a single foot, so that the distance between them is 5279 feet rather than 5280, how high an arc will the rail make?

Click for Answer

The Pizza Theorem

If you’re sharing a pizza with another person, there’s no need to cut it into precisely equal slices.

Make four cuts at equal angles through an arbitrary point and take alternate slices. You’ll both get the same amount of pizza.

Also: If a pizza has thickness a and radius z, then its volume is pi z z a.


  • Dorothy Parker named Alexander Woollcott’s apartment “Wit’s End.”
  • Can you look at something and imagine it at the same time?
  • 36850 = (36 + 8) × 50
  • AGNOSTIC is an anagram of COASTING.
  • “The errors of a man are what make him really lovable.” — Goethe

Skyline Trouble

In June 1978, a Princeton engineering student called structural engineer William LeMessurier with some worrying calculations. LeMessurier’s new Citicorp Tower, which had opened the previous year, was vulnerable to quartering winds — winds that blew from a 45-degree angle. On investigating, LeMessurier found also that the welded joints he had specified had been replaced with weaker bolted joints during construction. This meant that a strong wind could shear the bolts and topple a 59-story building into midtown Manhattan.

With hurricane season approaching, welders worked from 8 p.m. to 4 a.m. every night, reinforcing the building’s joints, and the Red Cross worked out an evacuation plan for the surrounding neighborhood. Because of a press strike at the time, many of these details came to light only 20 years later.

That year’s Hurricane Ella actually bore down on New York as the workers were finishing the job, but the storm veered out to sea before reaching the city. The welding was completed in October, and it’s now estimated that a storm strong enough to rock the tower will occur only once every 700 years.


How fast does time pass? We have no way to measure this. We can reply, helplessly, that it passes at one second per second, but this is not a rate of change — 1 second divided by 1 second is 1. Not 1 of anything, just 1.

“‘One’ can be an answer, right or wrong, to the questions ‘How many children had Lady Macbeth?’, ‘How many Gods are there?’, and ‘How many minutes do sixty seconds make?’,” writes Notre Dame philosopher Peter van Inwagen. “‘One’ can never be an answer, not even a wrong one, to any other sort of question — including those questions that ask ‘how fast?’ or ‘at what rate?’ Therefore, if time is moving, it is not moving at any rate or speed.”

Ceramic Geometry

pythagorean tiling

This tiling pattern is sometimes referred to as Pythagorean because it can be construed to prove the Pythagorean theorem.

The red area is a right triangle. The square of its shorter side is equivalent to a green square, and the square of its longer side is equivalent to a yellow square.

One green and one yellow square can be cut up and reassembled to fit into one of the canted white squares, which is equivalent to the square of the red triangle’s hypotenuse. Hence a2 + b2 = c2.

Keeping Things Interesting

Each year, when the last flight of the summer field season departs the U.S. research station at the South Pole, the remaining staff gather to watch The Thing.

The next flight won’t arrive for eight months.

Time and Again

Imagine that I first walk through Divinity Avenue, and then imagine that the powers governing the universe annihilate ten minutes of time with all that it contained, and set me back at the door of this hall just as I was before the choice was made. Imagine then that, everything else being the same, I now make a different choice and traverse Oxford Street. You, as passive spectators, look on and see the two alternative universes,–one of them with me walking through Divinity Avenue in it, the other with the same me walking through Oxford Street. Now, if you are determinists you believe one of these universes to have been from eternity impossible: you believe it to have been impossible because of the intrinsic irrationality or accidentality somewhere involved in it. But looking outwardly at these universes, can you say which is the impossible and accidental one, and which the rational and necessary one? I doubt if the most ironclad determinist among you could have the slightest glimmer of light on this point. In other words, either universe after the fact and once there would, to our means of observation and understanding, appear just as rational as the other.

— William James, “The Will to Believe,” 1896

Healthcare Reform

The statement “You will recover from this illness” is either true or false. If it’s true, then it has been true for all eternity, and you’ll recover whether you summon a doctor or not.

If the statement is false, then it has always been false, and you will not recover even with a doctor’s aid.

So there is no point in calling a doctor.

(From Cicero’s De Fato.)

A Good Man

Should other species be regarded as human? In 1779 Lord Monboddo proposed that orangutans should: They walk upright, use weapons, form societies, build shelters, and behave with “dignity and composure.” “If … such an Animal be not a Man, I should desire to know in what the essence of a Man consists, and what it is that distinguishes a Natural Man from the Man of Art?”

Thomas Love Peacock mocked this view in his 1817 novel Melincourt, in which a civilized orangutan (“Sir Oran Hout-ton”) is elected to Parliament. And an anonymous wag objected even to the satire:

The author of a novel lately written,
Entitled “Melincourt,”
(‘Tis very sweet and short),
Seems indeed by some wondrous madness bitten,
Thinking it good
To take his hero from the wood:
And though I own there’s nothing treasonable
In making ouran-outangs reasonable,
I really do not think he should
Go quite the length that he has done,
Whether for satire or for fun,
To make this creature an M.P.
As if mankind no wiser were than he.
However, those who’ve read it
Must give the author credit
For skill and ingenuity,
Although it have this monstrous incongruity.

But today Monboddo’s view is on the ascendancy. Harvard legal scholar Steven M. Wise argues that orangutans — as well as chimpanzees, bonobos, elephants, parrots, dolphins, and gorillas — deserve legal personhood. “Ancient philosophers claimed that all nonhuman animals had been designed and placed on this earth just for human beings,” he writes. “Ancient jurists declared that law had been created just for human beings. Although philosophy and science have long since recanted, the law has not.”

Heavenly Form

The U.S. Customs Service received an odd bit of paperwork on July 24, 1969:

apollo 11 customs form

All three Apollo 11 astronauts signed the form, which was filed at the Honolulu airport on the day they splashed down.

“Yes, it’s authentic,” NASA spokesperson John Yembrick told “It was a little joke at the time.”

See Business Trip and Space Bills.

Math Notes

math notes

(Thanks, Pablo.)

Surface Matters

If you touch a gold ball, you touch its surface and you touch gold. It seems reasonable to conclude that the surface is made of gold. But University of Exeter computer scientist Antony Galton points out that the surface is two-dimensional; it can’t contain any quantity of gold.

What then is it? We can’t say it’s the outermost layer of gold atoms, for that’s a film with two surfaces. And we can’t say it’s an abstract boundary with no physical existence, for we can see it and touch it. So what is it?

J.L. Austin asked, “Where and what exactly is the surface of a cat?”

Sure Thing

[Lewis Carroll] told me of a simple, too simple, rule by which, he thought, one could be almost sure of making something at a horse-race. He had on various occasions noted down the fractions which represented the supposed chances of the competing horses, and had observed that the sum of these chances amounted to more than unity. Hence he inferred that, even in the case of such hard-headed men as the backers, the wish is often father to the thought; so that they are apt to overrate the chances of their favourites. His plan, therefore, was to bet against all the horses, keeping his own stake the same in each case. He did not pretend to know much about horse-racing, and I probably know even less; but I understand that it would be impossible to adjust the hedging with sufficient exactitude — in fact, to get bets of the right amount taken by the backers.

— Lionel Arthur Tollemache, Old and Odd Memories, 1908

Pi Coincidences

The number 360 is centered across the 360th decimal place of π:

pi coincidences - 360

6998970 = 36 + 19 + 49 + 18 + 59 + 97 + 20

6998971 = 36 + 19 + 49 + 18 + 59 + 97 + 21

(Thanks, Pablo.)

pi coincidences - approximations

The 22nd, 7th, 355th, 113th, and 52163rd digits of π (counting from the 3) are 2s.

The 16604th digit, alas, is a 1 — but it’s flanked by 2s.

After You

At the end of your visit to an elderly, infirm relative who lives alone, the relative says, ‘I’m sorry but my arthritis won’t let me get up from this chair today. You’ll have to show yourself out.’ How can you show yourself out of someone’s house? If you know the way out, you can act as a guide to someone else. But how can you act as your own guide?

— T.S. Champlin, Reflexive Paradoxes, 1988

Johnson Circles

johnson circles

If three hula hoops cover a common point, then a fourth hoop will cover their remaining intersections.

Safe Passage

Mathematician G.H. Hardy had an ongoing feud with God. Once, after spending a summer vacation in Denmark with Harald Bohr, he found he’d have to take a small boat across the tempestuous North Sea to return to England. Before boarding, he sent Bohr a postcard that said “I have proved the Riemann hypothesis. — G.H. Hardy.”

When Bohr excitedly asked about this later, “Oh, that!” Hardy said. “That was just insurance. God would never let me drown if it meant I’d get undue credit.”


  • Connecticut didn’t ratify the Bill of Rights until 1939.
  • Can one pity a fictional character?
  • 64550 = (64 – 5) × 50
  • BILLOWY is in alphabetical order, WRONGED in reverse.
  • “The essence of chess is thinking about the essence of chess.” — David Bronstein