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
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.
Tippi Hedren, star of Alfred Hitchcock’s The Birds, shared her home with a 400-pound lion.
Sources for our feature on Nikolai Vavilov:
S.M. Alexanyan and V.I. Krivchenko, “Vavilov Institute Scientists Heroically Preserve World Plant Genetic Resources Collections During World War II Siege of Leningrad,” Diversity 7:4 (1991), 10-13.
James F. Crow, “N. I. Vavilov, Martyr to Genetic Truth,” Genetics 134:4 (May 1993).
Olga Elina, Susanne Heim, and Nils Roll-Hansen, “Plant Breeding on the Front: Imperialism, War, and Exploitation,” Osiris 20 (2005), 161-179.
Peter Pringle, The Murder of Nikolai Vavilov, 2008.
Boyce Rensberger, “Soviet Botanists Starved, Saving Seeds for Future,” Washington Post, May 12, 1992.
Michael Woods, “Soviet Union’s Fall Threatens ‘Gene Bank’ for Food Crops,” Pittsburgh Post-Gazette, April 26, 1993.
Joel I. Cohen and Igor G. Loskutov, “Exploring the Nature of Science Through Courage and Purpose,” SpringerPlus 5:1159 (2016).
Peter Nichols, A Voyage for Madmen, 2001.
Nicholas Tomalin and Ron Hall, The Strange Last Voyage of Donald Crowhurst, 1970.
Ed Caesar, “Drama on the Waves: The Life and Death of Donald Crowhurst,” Independent, Oct. 27, 2006.
This week’s lateral thinking puzzle was contributed by listener Tommy Honton, who cites this source (warning: this link spoils the puzzle).
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Many thanks to Doug Ross for the music in this episode.
If you have any questions or comments you can reach us at firstname.lastname@example.org. Thanks for listening!
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 , 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 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 the patience in explaining this to me.
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.)
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.
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.”
n. wrong opinion or doctrine
n. a recognition, an acknowledgement
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.”
In 1983, East Carolina University mathematicians Thomas Chenier and Cathy Vanderford programmed a computer to find the best strategies in playing Monopoly. The program kept track of each players’ assets and property, and subroutines managed the decisions whether to buy or mortgage property and the results of drawing of Chance and Community Chest cards. They auditioned four basic strategies (I think all of these were in simulated two-player games):
- Bargain Basement. Buy all the unowned property that you can afford, hoping to prevent your opponent from gaining a monopoly.
- Two Corners. Buy property between Pennsylvania Railroad and Go to Jail (orange, red, and yellow), hoping your opponent will be forced to land on one on each trip around the board.
- Controlled Growth. Buy property whenever you have $500 and the color group in question has not yet been split by the two players. Hopefully this will allow you to grow but retain enough capital to develop a monopoly once you’ve acquired one.
- Modified Two Corners. This is the same as Two Corners except that you also buy the Boardwalk-Park Place group.
After 200 simulated games, the winner was Controlled Growth, with 88 wins, 79 losses, and 33 draws. Bargain Basement players tended to lack money to build houses, and Two Corners gave the opponent too many opportunities to build a monopoly and was vulnerable to interference by the opponent, but Modified Two Corners succeeded fairly well. In Chenier and Vanderford’s calculations, Water Works was the most desirable property, followed by Electric Co. and three railroads — B&O, Reading, and Pennsylvania. Mediterranean Ave. was last. Of the property groups, orange was most valuable, dark purple least. And going first yields a significant advantage.
“In order for everyone here to become Monopoly Moguls, we offer the following suggestions: If your opponent offers you the chance to go first, take it. Buy around the board in a defensive manner (that is at least one property per group). When trading begins, trade for the Orange-Red corner as well as for the Lt. Blue properties. They are landed on most frequently and offer the best return. The railroads and utilities offer a good chance for the buyer to raise some cash with which he may later develop other properties. Finally, whenever your opponent has a hotel on Boardwalk, never, we repeat, never land on it.”
(Thomas Chenier and Cathy Vanderford, “An Analysis of Monopoly,” Pi Mu Epsilon Journal 7:9 [Fall 1983], 586-9.)
A driver is sitting in a pub planning his trip home. In order to get there he must take the highway and get off at the second exit. Unfortunately, the two exits look the same. If he mistakenly takes the first exit he’ll have to drive on a very hazardous road, and if he misses both exits then he’ll reach the end of the highway and have to spend the night at a hotel. Assign the payoff values shown above: 4 for getting home, 1 for reaching the hotel, and 0 for taking the first exit.
The man knows that he’s very absent-minded — when he reaches an intersection, he can’t tell whether it’s the first or the second intersection, and he can’t remember how many exits he’s passed. So he decides to make a plan now, in the pub, and follow it on the way home. This amounts to choosing between two policies: Exit when you reach an intersection, or continue. The exiting policy will lead him to the hazardous road, with a payoff of 0, and continuing will lead him to the hotel, with a payoff of 1, so he chooses the second policy.
This seems optimal. But then, on the road, he finds himself approaching an intersection and reflects: This is either the first or the second intersection, each with probability 1/2. If he were to exit now, the expected payoff would be
That’s twice the payoff of going straight! “There appear to be two contradictory optimal strategies, one at the planning stage and one at the action stage while driving,” writes Leonard M. Wapner in Unexpected Expectations. “At the pub, during the planning stage, it appears the driver should never exit. But once this plan is in place and he arrives at an exit, a recalculation with no new significant information shows that exiting yields twice the expectation of going straight.” What is the answer?
(Michele Piccione and Ariel Rubinstein, “On the Interpretation of Decision Problems with Imperfect Recall,” Games and Economic Behavior 20 , 3-24.)