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.)
In 1987, a Palermo physicist named Stronzo Bestiale published major papers in the Journal of Statistical Physics, the Journal of Chemical Physics, and the proceedings of a meeting of the American Physical Society in Monterey.
Why is this remarkable? Stronzo bestiale is Italian for “total asshole.”
Italian journalist Vito Tartamella wrote to one of “Bestiale’s” co-authors, Lawrence Livermore physicist William G. Hoover, to get the story. Hoover had been developing a sophisticated new computational technique, non-equilibrium molecular dynamics, with Italian physicist Giovanni Ciccotti. He found that the journals he approached refused to publish his papers — the ideas they contained were too innovative. But:
While I was traveling on a flight to Paris, next to me were two Italian women who spoke among themselves, saying continually: ‘Che stronzo (what an asshole)!’, ‘Stronzo bestiale (total asshole)’. Those phrases had stuck in my mind. So, during a CECAM meeting, I asked Ciccotti what they meant. When he explained it to me, I thought that Stronzo Bestiale would have been the perfect co-author for a refused publication. So I decided to submit my papers again, simply by changing the title and adding the name of that author. And the researches were published.
Renato Angelo Ricci, president of the Italian Physical Society, called the joke “an offense to the entire Italian scientific community.” But Hoover had learned a lesson: He thanked “Bestiale” at the end of another 1987 paper, saying that discussions with him had been “particularly useful.”
A spelling net is the pattern made when one writes down one instance of each unique letter that appears in a word and then connects these letters with lines, spelling out the word. For instance, the spelling net for VIVID is made by writing down the letters V, I, and D and drawing a line from V to I, I to V, V to I, and I to D.
Different words produce different spelling nets, of course, but every spelling net is an example of a graph, a collection of points connected by lines. A graph is said to be non-planar if some of the lines must cross; in the case of the spelling net, this means that no matter how we arrange the letters on the page, when we connect them in order we find that at least two of the lines must cross.
A word with a non-planar spelling net is called an eodermdrome, an ungainly name that itself illustrates the idea. The unique letters in EODERMDROME are E, O, D, R, and M. Write these down and run a pen among them, spelling out the word. You’ll find that no matter how the letters are arranged, it’s never possible to complete the task without at least two of the lines crossing:
Ross Eckler sought all the eodermdromes in Webster’s second and third editions; another example he found is SUPERSATURATES:
Since spelling nets are graphs, they can be studied with the tools of graph theory, the mathematical study of such networks. One result from that discipline says that a graph is non-planar if and only if it can be reduced to one of the two patterns marked K5 and K(3, 3) above. Since both EODERMDROME and SUPERSATURATES contain these forbidden graphs, both are non-planar.
A good article describing recreational eodermdrome hunting, by computer scientists Gary S. Bloom, John W. Kennedy, and Peter J. Wexler, is here. One warning: They note that, with some linguistic flexibility, the word eodermdrome can be interpreted to mean “a course on which to go to be made miserable.”
The three corners of any triangle ABC define a circle that surrounds it, called its circumcircle. And for any point P on this circle, the three points closest to P on lines AB, AC, and BC are collinear.
The converse is also true: Given a point P and three lines no two of which are parallel, if the closest points to P on each of the lines are collinear, then P lies on the circumcircle of the triangle formed by the lines.
This discovery is named for Robert Simson, though, as often happens, it was first published by someone else — William Wallace in 1797.
In 1872 Francis Galton reflected that congregations throughout Britain pray every Sunday for the health of the British royal family. If prayer has tangible effects, he wondered, shouldn’t all this concentrated well-wishing result in greater health for its objects? He compared the longevity of royalty to clergy, lawyers, doctors, aristocracy and gentry, as well as other professions, and found that
[t]he sovereigns are literally the shortest lived of all who have the advantage of affluence. The prayer has therefore no efficacy, unless the very questionable hypothesis be raised, that the conditions of royal life may naturally be yet more fatal, and that their influence is partly, though incompletely, neutralized by the effects of public prayers.
He noted also that missionaries are not vouchsafed a long life, despite their pious purpose; that banks that open their proceedings with prayers don’t seem to receive any benefit from doing so; and that insurance companies don’t offer annuities at lower rates to the devout than to the profane. Certainly men may profess to commune in their hearts with God, he wrote, but “it is equally certain that similar benefits are not excluded from those who on conscientious grounds are sceptical as to the reality of a power of communion.”
(Francis Galton, “Statistical Inquiries Into the Efficacy of Prayer,” Fortnightly Review 12 , 125-35.)
In 2001 UC-San Diego sociologist David Phillips and his colleagues noted that deaths by heart disease seem to occur with unusual frequency among Chinese and Japanese patients on the 4th of the month. A study of death records revealed a 7 percent increase in cardiac deaths on that date, compared with the daily average for the rest of the week. And deaths from chronic heart disease were 13 percent higher.
One explanation is that the number 4 sounds like the word for “death” in Mandarin, Cantonese and Japanese, which causes discomfort and apprehension among some people. The effect is so strong that some Chinese and Japanese hospitals refrain from assigning the number 4 to floors or rooms. The psychological stress brought on by that date, the researchers suggest, may underlie the higher mortality.
They dubbed this the Baskerville effect, after the Arthur Conan Doyle novel in which a seemingly diabolical dog chases a man, who flees and suffers a fatal heart attack. “This Baskerville effect seems to exist in fact as well as in fiction,” they wrote in the British Medical Journal (PDF).
“Our findings are consistent with the scientific literature and with a famous, non-scientific story. The Baskerville effect exists both in fact and in fiction and suggests that Conan Doyle was not only a great writer but a remarkably intuitive physician as well.”