Science & Math

Misc

  • To frustrate eavesdroppers, Herbert Hoover and his wife used to converse in Chinese.
  • Asteroids 30439, 30440, 30441, and 30444 are named Moe, Larry, Curly, and Shemp.
  • COMMITTEES = COST ME TIME
  • 15618 = 1 + 56 – 1 × 8
  • How is it that time passes but space doesn’t?

Webster’s Third New International Dictionary gives no pronunciation for YHWH.

Anomalous Cancellation

anomalous cancellation

The Tippe Top

The tippe top is a round top that, when spun, tilts to one side and leaps up onto its stem. This is perplexing, as the toy appears to be gaining energy — its center of mass rises with the flip.

How is this possible? The geometrical center of the top is higher than its center of mass. As the toy begins to topple to one side, friction with the underlying surface produces a torque that kicks it up onto its stem. It does gain potential energy, but it loses kinetic energy — in fact, during the inversion it actually reverses its direction of rotation.

Entire treatises have been written on the underlying physics, and the toy has occupied at least two Nobel Prize winners — below, Wolfgang Pauli and Niels Bohr play with one at the inauguration of the Institute of Physics at Lund, Sweden, in July 1954.

http://en.wikiquote.org/wiki/File:Pauli_wolfgang_c4.jpg

Constellation

German astronomer Karl Reinmuth discovered and named more than 400 asteroids. Among them are these eight:

1227 Geranium
1228 Scabiosa
1229 Tilia
1230 Riceia
1231 Auricula
1232 Cortusa
1233 Kobresia
1234 Elyna

Their initials spell G. STRACKE, for Gustav Stracke, a fellow astronomer who had asked that no planet be named after him. In this way Reinmuth could honor his colleague without contradicting his wish.

Shorthand

University of Michigan mathematician Norman Anning offered this “non-commutative soliloquy of an introspective epistemologist” in Scripta Mathematica in 1948:

[(N + H)ow + (T + W)hat](I know).

Expand the expression and you get Now I know how I know that I know what I know.

Contraband

http://commons.wikimedia.org/wiki/File:Astronaut_John_Young_gemini_3.jpg

Astronaut John Young smuggled a corned beef sandwich into space. As Gemini 3 was circling Earth in March 1965, Young pulled the sandwich out of his pocket and offered it to Gus Grissom:

Grissom: What is it?

Young: Corned beef sandwich.

Grissom: Where did that come from?

Young: I brought it with me. Let’s see how it tastes. Smells, doesn’t it?

Grissom: Yes, it’s breaking up. I’m going to stick it in my pocket.

Young: Is it? It was a thought, anyway.

“Wally Schirra had the sandwich made up at a restaurant at Cocoa Beach a couple of days before, and I hid it in a pocket of my space suit,” Young explained later. “Gus had been bored by the official menus we’d practiced with in training, and it seemed like a fun idea at the time.”

Grissom wrote, “After the flight our superiors at NASA let us know in no uncertain terms that non-man-rated corned beef sandwiches were out for future space missions. But John’s deadpan offer of this strictly non-regulation goodie remains one of the highlights of our flight for me.”

Misc

  • Colombia is the only South American country that borders both the Atlantic and the Pacific.
  • GRAVITATIONAL LENS = STELLAR NAVIGATION
  • 28671 = (2 / 8)-6 × 7 – 1
  • Can a man released from prison be called a freeee?
  • “Nature uses as little as possible of anything.” — Johannes Kepler

Sergei Prokofiev died on the same day that Joseph Stalin’s death was announced. Moscow was so thronged with mourners that three days passed before the composer’s body could be removed for a funeral service.

(Thanks, Alina.)

The Indiana Pi Bill

In 1894, Indiana physician Edwin J. Goodwin published a one-page article in the American Mathematical Monthly claiming to have found a method of squaring the circle — that is, of constructing a square with the same area as a given circle using only a compass and straightedge, a task known to be impossible. He proposed a bill to state representative Taylor I. Record, laying out the “new mathematical truth” and offering it “as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the legislature of 1897.”

Apparently flummoxed, the House referred the bill to its Committee on Swamp Lands, which transferred it to the Committee on Education … which approved it. Whereupon the whole house passed it unanimously.

The bill, which the Indianapolis Journal was already calling “the strangest bill that has ever passed an Indiana Assembly,” moved on to the senate, which referred it the Committee on Temperance. (Chronicler Will E. Edington writes, “One wonders whether this was done intentionally, for certainly the bill could have been referred to no committee more appropriately named.”) Equally flummoxed, the committee recommended that it pass.

The bill might have achieved full passage had not Purdue mathematics professor C.A. Waldo happened to be visiting the House that day. “A member … showed the writer a copy of the bill just passed and asked him if he would like an introduction to the learned doctor,” Waldo later recalled in the Proceedings of the Indiana Academy of Science. “He declined the courtesy with thanks, remarking that he was acquainted with as many crazy people as he cared to know.”

That did it. “Representative Record’s mathematical bill legalizing a formula for squaring the circle was brought up and made fun of,” reported by Indianapolis News on Feb. 13. “The Senators made bad puns about it, ridiculed it and laughed over it. The fun lasted half an hour. Senator Hubbell said that it was not meet for the Senate, which was costing the State $250 a day, to waste its time in such frivolity.”

“Senator Hubbell characterized the bill as utter folly,” added the Indianapolis Journal. “The Senate might as well try to legislate water to run up hill as to establish mathematical truth by law.”

Round and Round

In describing a large water basin, 2 Chronicles 4:2 reads, “Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.” A similar verse appears at 1 Kings 7:23.

Critics point out that this implies that π is 3, and in 1983 about 100 professors and students at Emporia State University in Kansas founded an Institute of Pi Research to lobby (wryly) for adopting this new value in place of the awkward 3.14159 …

“To think that God in his infinite wisdom would create something as messy as this is a monstrous thought,” medieval historian Samuel Dicks told the Kansas City Times. “I think we deserve to be taken as seriously as the creationists.”

“If the Bible is right in biology, it’s right in math,” added economic historian Loren Pennington.

But writing in the Mathematical Gazette in 1985, M.D. Stern of Manchester Polytechnic noted (also wryly) that the word translated as line above is transliterated qwh but read qw. Further, the ancient Greeks and Jews used letters to denote numbers, with the letters q, w, and h taking the numerical values 100, 6, and 5.

“Thus the word translated line in its written form has numerical value 111 whereas as read the value is 106. If we take the ratio of these numbers as a correcting factor for the apparent value of π as 3 and calculate 3 × (111/106), we obtain 3.141509 to 7 significant figures. This differs from the true value of π by less than 10-4 which is remarkable. In view of this, it might be suggested that this peculiar spelling is of more significance than a cursory reading might have suggested.”

Conjuring

Remove any nine cards from an ordinary deck, shuffle them, and deal them face down into three piles. Choose any pile and note its bottom card. Then assemble the three piles into one, being sure to place the chosen pile on top.

Suppose the card you chose is the three of spades. Spell T-H-R-E-E, dealing one card face down onto the table with each letter. Place the remaining cards on top of these five and take up the whole packet. Now spell O-F, and again place the remaining cards on top of these two. Then spell S-P-A-D-E-S and place the remaining cards on top.

Now pick up the packet and spell M-A-G-I-C, dealing the final card face up. It’s the three of spades.

Remarkably, this trick will produce any card, from the 10-letter ace of clubs to the 15-letter queen of diamonds. It was invented by California magician Jim Steinmeyer and appears in his 2002 book Impuzzibilities (used by permission).

Misc

  • Mississippi didn’t ratify the 13th Amendment, abolishing slavery, until 2013.
  • To protect its ecosystem, the location of Hyperion, the world’s tallest living tree, is kept secret.
  • 34425 = 34 × 425
  • CIRCUMSTANTIAL EVIDENCE = ACTUAL CRIME ISN’T EVINCED
  • “Well, if I called the wrong number, why did you answer the phone?” — James Thurber

Surface Tension

Lewis Carroll on the perils of physics:

Suppose a solid held above the surface of a liquid and partially immersed: a portion of the liquid is displaced, and the level of the liquid rises. But, by this rise of level, a little bit more of the solid is of course immersed, and so there is a new displacement of a second portion of the liquid, and a consequent rise of level. Again, this second rise of level causes a yet further immersion, and by consequence another displacement of liquid and another rise. It is self-evident that this process must continue till the entire solid is immersed, and that the liquid will then begin to immerse whatever holds the solid, which, being connected with it, must for the time be considered a part of it. If you hold a stick, six feet long, with its end in a tumbler of water, and wait long enough, you must eventually be immersed. The question as to the source from which the water is supplied — which belongs to a high branch of mathematics, and is therefore beyond our present scope — does not apply to the sea. Let us therefore take the familiar instance of a man standing at the edge of the sea, at ebb-tide, with a solid in his hand, which he partially immerses: he remains steadfast and unmoved, and we all know that he must be drowned.

“The multitudes who daily perish in this manner to attest a philosophical truth, and whose bodies the unreasoning wave casts sullenly upon our thankless shores, have a truer claim to be called the martyrs of science than a Galileo or a Kepler.”

Round Trip

http://www.google.com/patents/US5678489

Frustrated in trying to describe higher topology abstractly to students, Xian Wang invented a model train that can hug either side of a track:

It is therefore a primary object of the present invention to provide an electrically-operated ornament travelling on a rail which can be used to explain the Mobius Theorem. … In general textbooks, this advanced mathematic rule is usually explained by demonstrating a body circularly moving on a front and a reverse side of a twisted two-ends-connected belt. Most people can not understand and imagine the theorem from such explanation and demonstration.

Of course, once you’ve built one you can put it to other uses:

http://www.google.com/patents/US5678489

Morphology

nabokov on kafka

This is the opening page of “The Metamorphosis,” from Vladimir Nabokov’s teaching copy. Kafka’s novella held a special interest for Nabokov, who was a trained entomologist. From his lecture notes at Cornell:

Now, what exactly is the ‘vermin’ into which poor Gregor, the seedy commercial traveler, is so suddenly transformed? It obviously belongs to the branch of ‘jointed leggers’ (Arthropoda), to which insects, and spiders, and centipedes, and crustaceans belong. … Next question: What insect? Commentators say cockroach, which of course does not make sense. A cockroach is an insect that is flat in shape with large legs, and Gregor is anything but flat: he is convex on both sides, belly and back, and his legs are small. He approaches a cockroach in only one respect: his coloration is brown. That is all. Apart from this he has a tremendous convex belly divided into segments and a hard rounded back suggestive of wing cases. In beetles these cases conceal flimsy little wings that can be expanded and then may carry the beetle for miles and miles in a blundering flight. … Further, he has strong mandibles. He uses these organs to turn the key in a lock while standing erect on his hind legs, on his third pair of legs (a strong little pair), and this gives us the length of his body, which is about three feet long. … In the original German text the old charwoman calls him Mistkafer, a ‘dung beetle.’ It is obvious that the good woman is adding the epithet only to be friendly. He is not, technically, a dung beetle. He is merely a big beetle.

“Curiously enough,” he added, “Gregor the beetle never found out that he had wings under the hard covering of his back. This is a very nice observation on my part to be treasured all your lives. Some Gregors, some Joes and Janes, do not know that they have wings.”

Square Deal

square deal - problem

A “coffin,” or killer problem, from the oral entrance exams to the math department of Moscow State University:

Construct (with ruler and compass) a square given one point from each side.

Click for Answer

The Shooting Room

You’re about to play a game. A single person enters a room and two dice are rolled. If the result is double sixes, he is shot. Otherwise he leaves the room and nine new players enter. Again the dice are rolled, and if the result is double sixes, all nine are shot. If not, they leave and 90 new players enter.

And so on, the number of players increasing tenfold with each round. The game continues until double sixes are rolled and a group is executed, which is certain to happen eventually. The room is infinitely large, and there’s an infinite supply of players.

If you’re selected to enter the room, how worried should you be? Not particularly: Your chance of dying is only 1 in 36.

Later your mother learns that you entered the room. How worried should she be? Extremely: About 90 percent of the people who played this game were shot.

What does your mother know that you don’t? Or vice versa?

(Paul Bartha and Christopher Hitchcock, “The Shooting Room Paradox and Conditionalizing on Measurably Challenged Sets,” Synthese, March 1999)

(Thanks, Zach.)

Pièce de Résistance

Take an ordinary magic square and replace its numbers with resistors of the same ohmic value. Now the set of resistors in each row, column, and diagonal will yield the same total resistance value when joined together end to end.

This paramagic square, by Lee Sallows, is similar — except that the resistors must be joined in parallel:

sallows paramagic square

The Problem of the Two Boys

A family has two children, and you know that at least one of them is a boy. What is the probability that both are boys? There are four possibilities altogether (boy-boy, boy-girl, girl-boy, and girl-girl), and we can eliminate the last, so it would seem that the answer is 1/3.

But now suppose you visit a family that you know has two children, and that a boy comes into the room. What is the probability that both children are boys? Of the two children, you know that this one is a boy, and there is a probability of 1/2 that the other is a boy. So it seems that there is a probability of 1/2 that both are boys.

How can this be? We seem to have the same amount of information in both cases. Why does it lead us to two different conclusions?

Din Minimum

In 1958, acoustician William MacLean of the Polytechnic Institute of Brooklyn answered a perennial question: How many guests can attend a cocktail party before it becomes too noisy for conversation? He declared that the answer, for a given room, is

cocktail party noise

where

N0 = the critical number of guests above which each speaker will try overcome the background noise by raising his voice
K = the average number of guests in each conversational group
a = the average sound absorption coefficient of the room
V = the room’s volume
h = a properly weighted mean free path of a ray of sound
d0 = the conventional minimum distance between speakers
Sm = the minimum signal-to-noise ratio for the listeners

When the critical guest N0 arrives, each speaker is forced to increase his acoustic power in small increments (“I really don’t know what she sees in him.” — “Beg your pardon?” — “I say, I REALLY DON’T KNOW WHY SHE GOES OUT WITH HIM”) until each group is forced to huddle uncomfortably close in order to continue the conversation.

“We see therefore that, once the critical number of guests is exceeded, the party suddenly becomes a loud one,” MacLean concluded, somewhat sadly. “The power of each talker rises exponentially to a practical maximum, after which each reduces his or her talking distance below the conventional distance and then maintains, servo fashion, just the proximity, tête à tête, required to attain a workable signal-to-noise ratio. Thanks to this phenomenon the party, although a loud one, can still be confined within one apartment.”

(William R. MacLean, “On the Acoustics of Cocktail Parties,” Journal of the Acoustical Society of America, January 1959, 79-80.)

Construction Set

From the ever-inventive Lee Sallows, a self-tiling tile set:

sallows self-tiling tiles

His article on such self-similar tilings appears in the December 2012 issue of Mathematics Magazine.

Vanishing Act

In 1913 mathematician P.E.B. Jourdain proposed a familiar paradox:

On one side of a blank strip of paper, write The statement on the other side of this paper is true.

On the other side, write The statement on the other side of this paper is false.

“The paradox in this form is quite vulnerable to an absolute refutation,” wrote Valdis Augstkalns in a 1970 letter to The Listener. “One takes the paper, gives it a half twist, and joins the ends to form a Möbius strip. The serious and philosophically legitimate question is transformed to ‘Eminent members of the panel, which is the other side of the paper?'”

Topsy Turvy

http://books.google.com/books?id=iUoXAAAAYAAJ

This reversible magic square comes from Henry Dudeney’s Canterbury Puzzles.

Each row, column, and diagonal in the square totals 179.

Thanks to some clever calligraphy, this remains true when the square is turned upside down.

Misc

  • A pound of dimes has the same value as a pound of quarters.
  • The French word hétérogénéité has five accents.
  • 32768 = (3 – 2 + 7)6 / 8
  • Can you deceive yourself deliberately?
  • “My country is the world, and my religion is to do good.” — Thomas Paine

In 2000, Guatemalan police asked Christmas revelers not to fire pistols into the air. “Lots of people die when bullets fall on their heads,” National Civilian Police spokesman Faustino Sanchez told Reuters. He said that five to ten Guatemalans are killed or injured each Christmas by falling bullets.

The Chosen Ones

http://commons.wikimedia.org/wiki/File:Hans_Hoffmann_nach_D%C3%BCrer_Hirschk%C3%A4fer.jpg

J.B.S. Haldane was once asked what his study of biology had taught him about God.

He said that the Creator, if he exists, has “an inordinate fondness for beetles.”