The symptoms of a typical attack
A clearly ordered sequence seldom lack;
The first complaint is epigastric pain
Then vomiting will follow in its train,
After a while the first sharp pain recedes
And in its place right iliac pain succeeds,
With local tenderness which thus supplies
The evidence of where the trouble lies.
Then only — and to this I pray be wise —
Then only will the temperature rise,
And as a rule the fever is but slight,
Hundred and one or some such moderate height.
‘Tis only then you get leucocytosis
Which if you like will clinch the diagnosis,
Though in my own experience I confess
I find this necessary less and less.
From Zachary Cope, The Diagnosis of the Acute Abdomen in Rhyme, 1947.
Further to my March post “A Lucrative Loop,” reader Snehal Shekatkar of S.P. Pune University notes a similar discovery of iterates leading to strange cycles among natural numbers.
Here is a simple example. Take a natural number and factorize it (12 = 2 * 2 * 3), then add all the prime factors (2 + 2 + 3 = 7). If the answer is prime, add 1 and then factorize again (7 + 1 = 8 = 2 * 2 * 2) and repeat (2 + 2 + 2 = 6). Eventually ALL the natural numbers greater than 4 eventually get trapped in cycle (5 -> 6 -> 5). Instead of adding 1 after hitting a prime, if you add some other natural number A, then depending upon A, numbers may get trapped in a different cycle. For example, for A = 19, they eventually get trapped in cycle (5 -> 24 -> 9 -> 6 -> 5).
For some values of A, several cycles exist. For example, when A = 3, some numbers get trapped in cycle (5 -> 8 -> 6 -> 5) while others get trapped in the cycle (7 -> 10 -> 7).
(Made with Tian An Wong of Michigan University.) (Thanks, Snehal.)
In the 1890s, Waldemar Haffkine worked valiantly to develop vaccines against both cholera and bubonic plague. Then an unjust accusation derailed his career. In this week’s episode of the Futility Closet podcast we’ll describe Haffkine’s momentous work in India, which has been largely overlooked by history.
We’ll also consider some museum cats and puzzle over an endlessly energetic vehicle.
It is a traditional axiom of medicine that health is the absence of disease. What is a disease? Anything that is inconsistent with health. If the axiom has any content, a better answer can be given. The most fundamental problem in the philosophy of medicine is, I think, to break the circle with a substantive analysis of either health or disease.
In 1938, Italian physicist Ettore Majorana vanished after taking a sudden sea journey. At first it was feared that he’d ended his life, but the perplexing circumstances left the truth uncertain. In this week’s episode of the Futility Closet podcast we’ll review the facts of Majorana’s disappearance, its meaning for physics, and a surprising modern postscript.
We’ll also dither over pronunciation and puzzle over why it will take three days to catch a murderer.
Statistics textbooks sometimes ask: Suppose you’re driving on the highway and adjust your speed so that the number of cars you pass is equal to the number that pass you. Is your speed the median or the mean speed of the cars on the highway?
The expected answer is that it’s the median speed, since the number of cars traveling more slowly than you is equal to the number traveling faster. But California State University mathematician Larry Clevenson and his colleagues wrote in 2001, “This certainly is true of the cars that you see, but that isn’t what the problem asks, and it isn’t the correct answer.”
Surprisingly, they found that the correct answer is the mean. “If you adjust your speed so that as many cars pass you as you pass, then your speed is the mean speed of all the other cars on the highway.” Details at the link below.
Temple University anthropologist Wayne Zachary was studying a local karate club in the early 1970s when a disagreement arose between the club’s instructor and an administrator, dividing the club’s 34 members into two factions. Thanks to his study of communication flow among the members, Zachary was able to predict correctly, with one exception, which side each member would take in the dispute.
The episode has become a popular example in discussions of community structure in networks, so much so that scientists now award a trophy to the first person to use it at a conference. The original example is known as Zachary’s Karate Club; the trophy winners are the Zachary’s Karate Club Club.
09/01/2024 Reader Peter Dawyndt points out that the reason for the single exception in Zachary’s prediction is notable. The person whom Zachary assigned to the wrong faction corresponds to node 9 in this graph of the network:
“This person joined the newly founded karate club with supporters of the teacher (node 1) after the split, despite being a weak supporter of the president (node 34). This choice stemmed mainly from opportunism: he was only three weeks away from a test for black belt (master status) when the split in the club occurred. Had he joined the president’s club, he would have had to give up his rank and begin again in a new style of karate with a white (beginner’s) belt, since the president had decided to change the style of karate practiced in his club. Having four years of study invested in the style of the original club’s instructor, the individual could not bring himself to repudiate his rank and start again.”
This cottage, at 112 Mercer Street in Princeton, New Jersey, has been home to three Nobel winners: Albert Einstein lived there from 1935 to 1955; physicist Frank Wilczek between 1989 and 2001; and economist Eric Maskin until 2012.
It resides on the National Register of Historic Places and has been designated a U.S. National Historic Landmark, but it bears no outward marker of its significance.
“Quantities of liquid expressed in gallons, pottles, quarts, pints, etc. were essentially written in binary notation,” Knuth writes. “Perhaps the true inventors of binary arithmetic were British wine merchants!”
