Cardiology

In other words, this is the day on which those charming little missives, ycleped Valentines, cross and intercross each other at every street and turning. The weary and all for-spent twopenny postman sinks beneath a load of delicate embarrassments, not his own. It is scarcely credible to what an extent this ephemeral courtship is carried on in this loving town, to the great enrichment of porters, and detriment of knockers and bell-wires. In these little visual interpretations, no emblem is so common as the heart,–that little three-cornered exponent of all our hopes and fears,–the bestuck and bleeding heart; it is twisted and tortured into more allegories and affectations than an opera-hat. What authority we have in history or mythology for placing the head-quarters and metropolis of god Cupid in this anatomical seat rather than in any other, is not very clear; but we have got it, and it will serve as well as any other thing. Else we might easily imagine, upon some other system which might have prevailed for any thing which our pathology knows to the contrary, a lover addressing his mistress, in perfect simplicity of feeling, ‘Madam, my liver and fortune are entirely at your disposal;’ or putting a delicate question, ‘Amanda, have you a midriff to bestow?’ But custom has settled these things, and awarded the seat of sentiment to the aforesaid triangle, while its less fortunate neighbours wait at animal and anatomical distance.

— Charles Lamb, Essays of Elia, 1823

A mathematical valentine:

http://commons.wikimedia.org/wiki/File:Heart3D.png

Justice Confused

Suppose that a house is robbed and police find a strand of the burglar’s hair at the scene of the crime. A suspect is in custody, and tests show that the strand matches his hair. A forensic scientist testifies that the chance of a random person producing such a match is 1/2000. Does this mean that there’s a 1999/2000 chance that the suspect is guilty?

No, it doesn’t. In a city of 5 million there will be 1/2000 × 5,000,000 = 2,500 people who produce a match, so on the basis of this evidence alone the probability that the suspect is guilty is only 1/2500.

In a 1987 article, William Thomson and Edward Schumann dubbed this “prosecutor’s fallacy.” Unfortunately, it’s matched by the “defense attorney’s fallacy,” which holds that the hair-match evidence is worthless because it increases the likelihood of the suspect’s guilt by a negligible amount, 1/2500. In fact it drastically narrows the range of possible suspects, from 5 million to 2,500, while failing to exclude the defendant, hardly cause for confidence.

Worryingly, Thompson and Schumann found an experienced prosecutor who insisted that if a defendant and a perpetrator match on a blood type found in 10 percent of the population, then there’s a 10 percent chance that the defendant would have this blood type if he were innocent and hence a 90 percent chance that he’s guilty. “If a prosecutor falls victim to this error,” they write, “it is possible that jurors do as well.”

(William C. Thompson and Edward L. Schumann, “Interpretation of Statistical Evidence in Criminal Trials,” Law and Human Behavior, 11:3 [September 1987], 167-187)

Fixing Dates

In 1899, British statistician Moses B. Cotsworth noted that recordkeeping could be greatly simplified if each month contained a uniform number of whole weeks. He proposed an “international fixed calendar” containing 13 months of 28 days each:

international fixed calendar

This makes everything easier. The 26th of every month falls reliably on a Thursday, for example, and statistical comparisons between months are made more accurate, as each month contains four tidy weeks with four weekends. (Unfortunately for the superstitious, every one of the 13 months contains a Friday the 13th.) A new month, called Sol, would be wedged between June and July, and an extra day, “Year Day,” would be added at the end of the year, but it would be independent of any month (as would Leap Day).

In 1922 the League of Nations chose Cotsworth’s plan as the most promising of 130 proposed calendar reforms, but the public, as always, resisted the unfamiliar, and by 1937 the International Fixed Calendar League had closed its doors. It left one curious legacy, though: George Eastman, the founder of Eastman Kodak, was so pleased with Cotsworth’s scheme that he adopted it as his company’s official calendar — and it remained so until 1989.

Misc

  • Babe Ruth struck out 1,330 times.
  • EMBARGO spelled backward is O GRAB ME.
  • The numbers on a roulette wheel add to 666.
  • The fourth root of 2143/22 is nearly pi (3.14159265258).
  • “A prosperous fool is a grievous burden.” — Aeschylus

Six countries have names that begin with the letter K, and each has a different vowel as the second letter: Kazakhstan, Kenya, Kiribati, Kosovo, Kuwait, Kyrgyzstan.

(Thanks, Danny.)

The Ulysses Contract

http://commons.wikimedia.org/wiki/File:Ulysses_and_the_Sirens_by_H.J._Draper.jpg

In 1982, 24-year-old schizophrenic patient J.S. faced a difficult decision: The neuroleptic drug Prolixin relieved his psychotic symptoms, but it produced tardive dyskinesia, a progressive disorder that caused uncontrollable movements of his legs, arms, and tongue.

His therapist learned of an experimental program that might reduce this side effect, and J.S. signed consent forms to enter treatment. But the first step was to stop all medications, and without the Prolixin he descended again into psychosis and refused the experimental medication.

This produces an impossible dilemma: Does J.S.’ “sane” self have the right to overrule his “insane” self, if the two disagree? Can Dr. Jekyll bind Mr. Hyde? Such a directive is sometimes called a Ulysses contract, after the Greek hero who ordered his men to disregard his commands as they sailed past the sirens. If a patient directs his caregivers to ignore his own future requests, can the caregivers follow these orders?

In J.S.’ case, the answer was no. The research unit’s legal counsel decided that his earlier consent did not override his later refusal, and he was withdrawn from the program. When he resumed his antipsychotic medication and learned what had happened, he begged for another chance to try the experimental medication. Had they been wrong to refuse him?

(Morton E. Winston, Sally M. Winston, Paul S. Appelbaum, and Nancy K. Rhoden, “Can a Subject Consent to a ‘Ulysses Contract’?”, The Hastings Center Report 12:4 [August 1982], 26-28.)

Dog Tired

http://commons.wikimedia.org/wiki/File:Canal_de_Panam%C3%A1_Construcci%C3%B3n_003.jpg

Maybe figures can’t lie, but liars can certainly figure, and that is why statistics can be made to ‘prove’ almost anything. Consider a group of ten girls, nine of them virgins, one pregnant. On the ‘average’ each of the nine virgins is ten per cent pregnant, while the girl who is about to have a baby is ninety per cent a virgin. Or, assuming that a fox terrier two feet long, with a tail an inch and a half high, can dig a hole three feet deep in ten minutes, to dig the Panama Canal in a single year would require only one fox terrier fifteen miles long, with a tail a mile and a half high.

— Stuart Cloete, The Third Way, 1947

Never the Twain

proclus paradox

A paradox attributed to Proclus Lycaeus (412-485):

Consider two nonparallel lines, AQ and BP. BP is perpendicular to AB; AQ isn’t. Find the midpoint of AB and mark AC = BD = AB/2. Now if AQ and BP are going to intersect, it can’t happen on AC or BD; if it did, say at a point R, then that would give us a triangle ARB where the sum AR + RB < AB, which is impossible. But now we can connect CD and follow the same process: CE and DF can't intersect for the same reason. EG and FH are likewise ruled out, and so on up the line forever. This seems to mean that two nonparallel lines will never intersect. That can’t be right, but where is the error?

(From Alfred Posamentier, Magnificent Mistakes in Mathematics, 2013.)

Non-Fiction

http://www.sxc.hu/photo/440835

Sherlock Holmes is an honorary fellow of the Royal Society of Chemistry.

“Holmes did not exist, but he should have existed,” society chief David Giachardi said in bestowing the award in 2002. “That is how important he is to our culture. We contend that the Sherlock Holmes myth is now so deeply rooted in the national and international psyche through books, films, radio and television that he has almost transcended fictional boundaries.”