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

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’.”

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

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.”

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.)

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.