You’re Welcome

You’d pay $1,000 to witness my mastery of the black arts, wouldn’t you? Of course you would.

  1. Buy a brand-new deck of cards.
  2. Discard the jokers, cut the deck 13 times, and deal it into 13 piles.
  3. Now stand back … Ph’nglui mglw’nafh C’thulhu R’lyeh wgah’nagl fhtagn!
  4. Look at the cards. Presto! They have magically grouped themselves by value — all the aces are in one pile, kings in another, etc.

You owe me $1,000.

Finders’ Fees

Donald Knuth is so revered among computer scientists that they won’t cash his checks.

Knuth offers a standard reward of $2.56 (one “hexadecimal dollar”) to the first finder of each error in his published books. Since 1981 he has written more than $20,000 in checks, but most of the recipients have simply framed them as points of pride.

“There’s one man who lives near Frankfurt who would probably have more than $1,000 if he cashed all the checks I’ve sent him,” Knuth said in an October 2001 lecture. “Even if everybody cashed their checks, it would still be more than worth it to me to know that my books are getting better.”

Epimenides Soused

Somebody had told me of a dealer in gin who, having had his attention roused to the enormous waste of liquor caused by the unsteady hands of drunkards, invented a counter which, through a simple set of contrivances, gathered into a common reservoir all the spillings that previously had run to waste. … It struck me, therefore, on reviewing this case, that the more the people drank, the more they would titubate, by which word it was that I expressed the reeling and stumbling of intoxication. … [T]he more they titubated, the more they would spill; and the more they spilt, the more, it is clear, they did not drink. … Yet, again, if they drank nothing worth speaking of, how could they titubate? Clearly they could not; and, not titubating, they could have had no reason for spilling, in which case they must have drunk the whole–that is, they must have drunk to the whole excess imputed, which doing, they were dead drunk, and must have titubated to extremity, which doing, they must have spilt nearly the whole. … ‘And so round again,’ as my lord the bishop pleasantly expresses it, in secula seculorum.

— Thomas de Quincey, Essays on Philosophical Writers, 1856

Hands Up?

Beginning poker players are often shown a table like this:

"poker frequencies - no wild cards

It’s straightforward enough, assigning a hierarchy to the hands based on the likelihood of their appearance. But a strange thing happens when wild cards are introduced. Suppose we add one wild joker:

poker frequencies - one wild joker

Now three of a kind is more likely (and thus less valuable) than two pair. Well, can we just reverse their places in the table? No, we can’t, because the wild card permits some players to reinterpret their hands. If you’re holding 6♠ 6♥ 7♣ 10♦ plus the joker, and we change the table, you’ll simply decide you’re holding two pair rather than three of a kind. So will everyone in your position. In fact, if we recalculate the odds with this expectation, we find that two pair has again become the more likely hand (13:1 vs. 34:1).

This can go on all day. Whenever a hand is declared “rare” it becomes popular — and thus not rare. The bottom line is that when wild cards are allowed, it becomes impossible to rank hands based on frequency.

From Julian Havil, Impossible?, 2008.

Numbers Game

On June 18, 1964, an elderly woman was walking through a Los Angeles alley when a blond woman with a ponytail pushed her to the ground and stole her purse. The blond woman escaped in a yellow car driven by a bearded black man.

Police arrested Janet Collins, a ponytailed blond woman whose bearded black husband drove a yellow Lincoln. At trial, a local mathematics instructor testified that there was 1 chance in 12 million that another couple would meet this description, and the jury convicted the Collinses of second-degree robbery. Sound reasonable?

Well, no. The California Supreme Court reversed the conviction, noting that the prosecution had offered no statistical evidence and that the mathematician had simply invented estimates for each of the six factors and multiplied them together, without adjusting for dependence or the possibility of mistake.

“The testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules,” wrote justice Raymond Sullivan. “Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him.”

Sound Reasoning

Wintering in the Canadian Arctic in 1822, Capt. W.E. Parry made a series of experiments to see whether cold affects the velocity of sound. He marked a line of 5,645 feet on the sea ice, put a six-pounder gun at one end, and stood with a second observer at the other end. The gun fired 15 blank charges, and the observers timed the interval between each flash and its report. Generally they got good results, giving a mean velocity of 1,023 feet per second. But, writes Mr. Fisher:

The Experiments on the 9th February, 1822, were attended with a singular circumstance, which was–the officers’ word of command ‘fire,’ was several times distinctly heard both by Captain Parry and myself, about one beat of the chronometer [half a second] after the report of the gun; from which it would appear, that the velocity of sound depended in some measure upon its intensity.

“The word ‘fire’ was never heard during any of the other experiments; upon this occasion the night was calm and clear, the thermometer 25° below zero, the barometer 28.84 inches, which was lower than it had ever been observed before at Winter Island.” The phenomenon, whatever it was, has never been observed elsewhere, but Parry noted another acoustic oddity on his next voyage.