Community Spirit

Considerable amusement was excited, a few years ago, by the announcement that a society for mutual autopsy had been formed among the savants of Paris, with a view to advancing knowledge of the structure and physiology of the brain by a correlation of intellectual characteristics with post mortem appearances. The whole thing was generally regarded as a scientific joke of more than ordinary magnitude. But the society appears to have been a genuine fact, and one of its members, M. Asseline, having recently deceased, his brain was carefully examined by his surviving associates, who made a full report of the result to the Anthropological Society of Paris. The following account of the matter is found in Nature, Aug. 14, 1879, p. 377:

‘M. Asseline died in 1878, at the age of 49. He was a republican and a materialist; was possessed of enormous capacity for work, great faculty of mental assimilation, and an extraordinarily retentive memory; and had a gentle, benevolent disposition, keen susceptibilities, refined taste and subtle wit. As a writer he had always displayed great learning, unusual force of style and elegance of diction, and in his intercourse with others he had been unassuming, sensitive and even timid. Yet the autopsy showed such coarseness and thickness of the convolutions that M. Broca pronounced them to be characteristic of an inferior brain. The fossa or depressions, regarded by Gratiolet as a simian character, and as a sign of cerebral inferiority which are often found in women, and in some men of undoubted intellectual inferiority, were very much marked, especially on the left parietooccipital. But the cranial bones were at some points so thin as to be translucent; the cerebral depressions were deeply marked, the frontal suture was not wholly ossified, a decided degree of asymmetry was manifested in the greater prominence of the right frontal, while, moreover, the brain weighed 1,468 grams, i.e., about 60 grains above the average given by M. Broca for M. Asseline’s age. The apparent contradictions between the weight of the brain and the marked character of the parieto-occipital depressions, attracted much attention, and the members of the Société d’Anthropologie have been earnestly invited by M. Hovelacque, in furtherance of science, to join the Société d’Autopsie, to which anthropology is already indebted for many highly important observations. This society is forming a collection of photographs of its members, which are taken in accordance with certain fixed rules.’

Chicago Medical Journal and Examiner, quoted in New Orleans Medical and Surgical Journal, January 1880

A Knotty Problem

In a 2002 article in Nature, Australian mathematician Burkard Polster concluded that most of us are doing a pretty good job lacing our shoes: “No matter whether you prefer to lace them straight or criss-crossed, you come close to maximizing the total horizontal tension when you pull on the two ends of one of your shoelaces.”

When it comes to tying them, though, we don’t do so well. “A very large number of people, possibly even the majority, do tie their shoe laces much worse than the rest,” Polster wrote in his 2006 book-length followup, The Shoelace Book. Most of us tie a shoe by placing one half-granny knot on top of another, but this can produce either a very unstable granny knot (left) or a very stable reef knot (right), depending on whether the two half-knots have the same or opposite orientation. (It’s not essential that the second half-granny is typically tied with loops; these are omitted in the diagrams.)

“Hundreds of years of trial and error have led to the strongest way of lacing our shoes,” Polster wrote in Nature, “but unfortunately the same cannot be said about the way in which most of us tie our shoelaces — with a granny knot.”

(Burkard Polster, “What Is the Best Way to Lace Your Shoes?” Nature 420:6915 [Dec. 5, 2002], 476.)


When I was a child, it was believed that animals became extinct because they were too specialized. My father used to tell us about the saber-tooth tiger’s teeth — how they got too big and the tiger couldn’t eat because he couldn’t take game anymore. And I remember my father saying, with my brother sitting there, ‘I wonder what it will be with the human beings that will be so overspecialized that they’ll kill themselves off?’

My father never found out that my brother was working on the bomb.

— Richard Feynman’s sister Joan, quoted in Christopher Sykes, No Ordinary Genius, 1994

Sweet Home,_early_morning_-_Google_Art_Project.jpg

I am determined & feel sure, that the scenery of England is ten times more beautiful than any we have seen.– What reasonable person can wish for great ill proportioned mountains, two & three miles high? No, no; give me the Brythen or some such compact little hill.– And then as for your boundless plains & impenetrable forests, who would compare them with the green fields & oak woods of England?– People are pleased to talk of the ever smiling sky of the Tropics: must not this be precious nonsense? Who admires a lady’s face who is always smiling? England is not one of your insipid beauties; she can cry, & frown, & smile, all by turns.– In short I am convinced it is a most ridiculous thing to go round the world, when by staying quietly, the world will go round with you.

— Charles Darwin, letter to his sister, July 18, 1836. He was on board the Beagle, bound for Ascencion. He had written the previous December, “How glad I shall be, when I can say, like that good old Quarter Master, who entering the Channel, on a gloomy November morning, exclaimed, ‘Ah here there are none of those d—-d blue skys’.”

Budget Trouble

An energetic boy got a piggy bank for his birthday. He decided that from then on he will number every bill he gets from his grandparents (1, 2, …) and put it all in his bank. During the first half year he got 2 bills, but at the end of this period he pulled out 1 bill (chosen at random). In the next 1/4 year he got 2 more bills, but at the end of this period he pulled 1 bill chosen at random from the 3 bills in his bank. In the next 1/8 year he repeated the same routine etc. (each period is half the length of the previous period). What is the probability that any of the bills he got during this year will remain in his bank after a full year of the above activity? Paradoxically the probability is 0, even though it is clear that he only spent half of his money. Can we offer the boy good financial advice without making him cut his expenses?

— Talma Leviatan, “On the Use of Paradoxes in the Teaching of Probability,” Proceedings of ICOTS 6, 2002

The Meaning of Life

Along with art and love, life is one of those bedeviling concepts that we really ought to have a definition for but don’t. Philosophers tend to regard the question as too scientific, and scientists as too philosophical. Linus Pauling observed that it’s easier to study the subject than to define it, and, J.B.S. Haldane noted, “no definition will cover its infinite and self-contradictory variety.”

Classical definitions of life typically refer to structural features, growth, reproduction, metabolism, motion against force, response to stimuli, evolvability, and information content and transfer. But definitions built on these elements are prone to exceptions. Fire grows, moves, metabolizes, reproduces, and responds to stimuli, but is “nonliving.” So are free-market economies and the Internet, which evolve, store representations of themselves, and behave “purposefully.” I am nonreproducing but, I hope, still alive.

If we we look around us, it’s hard to find a property that’s unique to life, and even if we could, our observations are limited to Earth’s biosphere, a tiny, tenuous environment like a film of water on a basketball. But if we expand our list to include abstract properties such as resistance to entropy, then we risk including alien phenomena that we might not regard intuitively as living.

Perhaps the answer is more poetic. “As I see it, the great and distinguishing feature of living things … is that they have needs — continual, and, incidentally, complex needs,” wrote botanist Donald C. Peattie in 1935. “I cannot conceive how even so organized a dead system as a crystal can be said to need anything. But a living creature, even when it sinks into that half-death of hibernation, even the seed in the bottom of the driest Mongolian marsh, awaiting rain through two thousand years, still has needs while there is life in it.”

Extra Credit

cooper malaria watercolors

In studying the parasitic protozoan Plasmodium ovale in 1954, English parasitologist William Cooper volunteered to receive the bites of about a thousand mosquitos, and nine days later underwent a laparotomy in which a piece of his liver was removed. On recovering, he stained the sections himself, located the malaria parasite stages in his own tissue, and painted these in watercolors to accompany the resulting article.

His coauthor, University of London protozoologist Cyril Garnham, wrote that Cooper “attained everlasting fame by this episode.”

(P.C.C. Garnham et al., “The Pre-Erythrocytic Stage of Plasmodium Ovale,” Transactions of the Royal Society of Tropical Medicine and Hygiene 49:2 [March 1955], 158-167) (Thanks, Andrew.)


A gram is the mass of one cubic centimeter of water; the earth’s gravitational attraction is approximately 10 in metric units (9.8 meters/second2); and atmospheric pressure works out to about 1 kilogram per square centimeter.

This shows that the pressure under 10 meters of water is about one atmosphere. Ten meters of water is 1000 centimeters, so a column one centimeter square would weigh one kilogram and exert a pressure of 1 kilogram per square centimeter.

(Thanks, Steve.)


The autobiography of the 12th-century Muslim poet Usama ibn Munqidh tells of an incident in which the invading Crusaders appealed for a doctor to treat some of their number who had fallen ill. The Muslims sent a doctor named Thabit, who returned after 10 days with this story:

They took me to see a knight who had an abscess on his leg, and a woman with consumption. I applied a poultice to the leg, and the abscess opened and began to heal. I prescribed a cleansing and refreshing diet for the woman. Then there appeared a Frankish doctor, who said: ‘This man has no idea how to cure these people!’ He turned to the knight and said: ‘Which would you prefer, to live with one leg or die with two?’ When the knight replied that he would prefer living with one leg, he sent for the strong man and a sharp axe. They arrived, and I stood by to watch. The doctor supported the leg on a block of wood, and said to the man: ‘Strike a mighty blow, and cut cleanly!’ … The marrow spurted out of the leg (after the second blow) and the patient died instantaneously. Then the doctor examined the woman and said: ‘She has a devil in her head who is in love with her. Cut her hair off!’ This was done, and she went back to eating her usual Frankish food … which made her illness worse. ‘The devil has got into her brain,’ pronounced the doctor. He took a razor and cut a cross on her head, and removed the brain so that the inside of the skull was laid bare … the woman died instantly. At this juncture I asked whether they had any further need of me, as they had none I came away, having learnt things about medical methods that I never knew before.

Afghan Bands

afghan bands

Most people know that if you cut a Möbius band in two lengthwise you’ll produce one band rather than two. But splitting the ends and joining them also creates some surprising effects.

Starting with the figure above, join ends A and D directly, then pass B under A and join it to E. Now pass C over B and under A; pass F over D and under E; and join C and F. Extend the slits along the length of the band and you’ll have three linked rings.

Now compare this variant, suggested by Ellis Stanyon in 1930: Starting again from the diagram, give E a half-twist to the right and join it to C; give F a half-twist to the right and join it to B; then pass A under B and join it to D (without turning it over). Cut along the two slits and you’ll produce a small ring linked to a large one. What became of the third ring?

There’s a surprisingly simple way to produce a similar effect: Draw a line along the length of a Möbius band, one-third of the way across the strip. Cutting along this line will produce a large band linked to a small one — and this time the small band is itself a Möbius band, on which you can repeat the feat.