193939
939391
393919
939193
391939
and 919393
… are all prime.
Science & Math
Misc
- The Fall has had 66 members.
- Roundly defeated is squarely defeated.
- One pound of U.S. dimes, quarters, and half dollars, in any combination, is worth $20.
- Reverse the digits in any multiple of 11 and you’ll get another multiple of 11.
- Bertrand Russell’s recipe for longevity: “Choose your parents wisely.”
One for All?
Suppose that there’s a power outage in your neighborhood. If someone calls the electric company, they’ll send someone to fix the problem. This puts you in a dilemma: If someone else makes the call, then you’ll benefit without having to do anything. But if no one calls, then you’ll all remain in the dark, which is the worst outcome:
This is the “volunteer’s dilemma,” a counterpart to the famous prisoner’s dilemma in game theory. Each participant has a greater incentive for “free riding” than acting, but if no one acts, then everyone loses.
A more disturbing example is the murder of Kitty Genovese, who was stabbed to death outside her New York City apartment in 1964. According to urban lore, many neighbors who were aware of the attack chose not to contact the police, trusting that someone else would make the call but hoping to avoid “getting involved.” Genovese died of her wounds.
In a 1988 paper, game theorist Anatol Rapaport noted, “In the U.S. Infantry Manual published during World War II, the soldier was told what to do if a live grenade fell into the trench where he and others were sitting: to wrap himself around the grenade so as to at least save the others. (If no one ‘volunteered,’ all would be killed, and there were only a few seconds to decide who would be the hero.)”
The Guinness Book of World Records lists the Yaghan word mamihlapinatapai as the “most succinct word.” It’s defined as “a look shared by two people, each wishing that the other would initiate something that they both desire but which neither wants to begin.”
(From William Poundstone, Prisoner’s Dilemma, 1992.)
Kindling Trouble
Now, for something a bit more serious: I am starting a new religion. Care to join? As with the Catholic religion, my religion has an index of forbidden books. There is only one book that the index forbids. Can you guess which? You probably have! It is the index itself!
— Raymond Smullyan, “Self-Reference in All Its Glory!”, conference “Self-Reference,” Copenhagen, Oct. 31-Nov. 2, 2002
Podcast Episode 121: Starving for Science
During the siege of Leningrad in World War II, a heroic group of Russian botanists fought cold, hunger, and German attacks to keep alive a storehouse of crops that held the future of Soviet agriculture. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Vavilov Institute, whose scientists literally starved to death protecting tons of treasured food.
We’ll also follow a wayward sailor and puzzle over how to improve the safety of tanks.
A Cognitive Illusion
Given these premises, what can you infer?
- If there is a king in the hand then there is an ace, or if there isn’t a king in the hand then there is an ace, but not both.
- There is a king in the hand.
Practically everyone draws the conclusion “There is an ace in the hand.” But this is wrong: We’ve been told that one of the conditional assertions in the first premise is false, so it may be false that “If there is a king in the hand, then there is an ace.”
But almost no one sees this. Princeton psychologist Philip Johnson-Laird writes, “[Fabien] Savary and I, together with various colleagues, have observed it experimentally; we have observed it anecdotally — only one person among the many distinguished cognitive scientists to whom we have given the problem got the right answer; and we have observed it in public lectures — several hundred individuals from Stockholm to Seattle have drawn it, and no one has ever offered any other conclusion.” Johnson-Laird himself thought he’d made a programming error when he first discovered the illusion in 1995.
Why it happens is unclear; in puzzling out problems like this, we seem to focus on what’s true and neglect what might be false. Computers are much better at this than we are, which ironically might lead a competent computer to fail the Turing test. In order to pass as human, writes researcher Selmer Bringsjord, “the machine must be smart enough to appear dull.”
(Philip N. Johnson-Laird, “An End to the Controversy? A Reply to Rips,” Minds and Machines 7 [1997], 425-432.)
10/18/2016 UPDATE: Readers Andrew Patrick Turner and Jacob Bandes-Storch point out that if we take the first premise to mean material implication (and also allow double negation elimination), then not only can we not infer that there must be an ace, but we can in fact infer that there cannot be an ace in the hand — exactly the opposite of the conclusion that most people draw! Jacob offers this explanation (XOR means “or, but not both”, and ¬ means “not”):
I’ll use the shorthand “HasKing” to be a logical variable indicating whether there is a king in the hand.
Similarly, “HasAce” is a variable which indicates whether there is an ace in the hand.We’re given two statements:
#1: (HasKing → HasAce) XOR ((¬HasKing) → HasAce).
#2: HasKing.
#2 has just told us that our “HasKing” variable has the value “true”.
So, we can fill this in to #1, which becomes “(true → HasAce) XOR (false → HasAce)”.
I’ll call the sub-clauses of #1 “1a” & “1b”, so #1 is “1a XOR 1b”.
1a: “(true → HasAce)” is a logical expression that’s equivalent to just “HasAce”.
1b: “(false → HasAce)” is always true — because the antecedent, “false”, can never be satisfied, the consequent is effectively disregarded.
Recall what statement #1 told us: (1a XOR 1b). We now know 1b is true, so 1a must be false. Thus “HasAce” is false: there is not an ace in the hand.
Jacob also offered this demonstration in Prolog. Many thanks for Andrew and Jacob for their patience in explaining this to me.
Sky-High
A memory of Lewis Carroll by Lionel A. Tollemache:
He was, indeed, addicted to mathematical and sometimes to ethical paradoxes. The following specimen was propounded by him in my presence. Suppose that I toss up a coin on the condition that, if I throw heads once, I am to receive 1d.; if twice in succession, 2d.; if thrice, 4d.; and so on, doubling for each successful toss: what is the value of my prospects? The amazing reply is that it amounts to infinity; for, as the profit attached to each successful toss increases in exact proportion as the chance of success diminishes, the value (so to say) of each toss will be identical, being in fact, 1/2d.; so that the value of an infinite number of tosses is an infinite number of half-pence. Yet, in fact, would any one give me sixpence for my prospect? This, concluded Dodgson, shows how far our conduct is from being determined by logic.
Actually this curiosity was first noted by Nicholas Bernoulli; Carroll would have met it in his studies of probability. Tollemache wrote, “The only comment that I will offer on his astounding paradox is that, in order to bring out his result, we must suppose a somewhat monotonous eternity to be consumed in the tossing process.”
(Lionel A. Tollemache, “Reminiscences of ‘Lewis Carroll,'” Literature, Feb. 5, 1898.)
Fair Enough
In the index to Donald E. Knuth’s The Art of Computer Programming, the entries for Circular definition and Definition, circular point to each other.
Best Efforts
A portrait of a Civil War field hospital in 1863, written by a Union colonel wounded at Port Hudson:
I never wish to see another such time as the 27th of May. The surgeons used a large Cotton Press for the butchering room & when I was carried into the building and looked about I could not help comparing the surgeons to fiends. It was dark & the building lighted partially with candles: all around on the ground lay the wounded men; some of them were shrieking, some cursing & swearing & some praying; in the middle of the room was some 10 or 12 tables just large enough to lay a man on; these were used as dissecting tables & they were covered with blood; near & around the tables stood the surgeons with blood all over them & by the side of the tables was a heap of feet, legs & arms. On one of these tables I was laid & being known as a Col. the Chief Surgeon of the Department was called (Sanger) and he felt of my mouth and then wanted to give me cloriform: this I refused to take & he took a pair of scissors & cut out the pieces of bone in my mouth: then gave me a drink of whiskey & had me laid away.
In 1918, after a half-century of medical advances, one federal surgeon looked back on the war:
We operated in old blood-stained and often pus-stained coats, the veterans of a hundred fights. … We used undisinfected instruments from undisinfected plush-lined cases, and still worse, used marine sponges which had been used in prior pus cases and had been only washed in tap water. If a sponge or an instrument fell on the floor it was washed and squeezed in a basin of tap water and used as if it were clean. Our silk to tie blood vessels was undisinfected. … The silk with which we sewed up all wounds was undisinfected. If there was any difficulty in threading the needle we moistened it with … bacteria-laden saliva, and rolled it between bacteria-infected fingers. We dressed the wounds with clean but undisinfected sheets, shirts, tablecloths, or other old soft linen rescued from the family ragbag. We had no sterilized gauze dressing, no gauze sponges. … We knew nothing about antiseptics and therefore used none.
In The Life of Billy Yank, historian Bell I. Wiley writes, “Little wonder that gangrene, tetanus and other complication were so frequent and that slight wounds often proved mortal.”
In a Word
cacodoxy
n. wrong opinion or doctrine
agnition
n. a recognition, an acknowledgement
veriloquous
adj. speaking the truth
Chlorine was at first thought to be an oxide obtained from hydrochloric acid, then known as muriatic acid, and was hence called oxymuriatic acid.
In 1810 Sir Humphry Davy realized that it’s an element and proposed the name chlorine, meaning green-yellow. Swedish chemist Jacob Berzelius resisted this at first but revealed his change of heart unexpectedly one day, as overheard by his colleague Friedrich Wöhler:
One day Anna Sundström, who was cleaning a vessel at the tub, remarked that it smelt strongly of oxymuriatic acid. Wöhler’s earlier surprise sublimed into astonishment when he heard Berzelius correct her, in words that have since become historic: ‘Hark thou, Anna, thou mayest now speak no more of oxymuriatic acid; but must say chlorine: that is better.’
[Hör’ Anna, Du darfst nun nicht mehr sagen oxydirte Salzsäure, sondern musst sagen Chlor, das ist besser.]
In Humour and Humanism in Chemistry, John Read writes, “These words, issuing from the mouth of the great chemical lawgiver of the age, sealed the fate of oxymuriatic acid.”