In the Dark

In 1963, French geologist Michel Siffre descended into a glaciated cavern under the French-Italian Maritime Alps and spent more than two months without sun to “investigate time, that most inapprehensible and irreversible thing.” He could telephone scientists on the surface, who recorded the time of each call, but they never told him the time or date. From his diary:

Forty-second awakening. … I really seem to have no least idea of the passage of time. This morning, as an example, after telephoning to the surface and talking for a while, I wondered afterward how long the telephone conversation had lasted, and could not even hazard a guess. … Fifty-second awakening. … I am losing all notion of time. … When, for instance, I telephone the surface and indicate what time I think it is, thinking that only an hour has elapsed between my waking up and eating breakfast, it may well be that four or five hours have elapsed. And here is something hard to explain: the main thing, I believe, is the idea of time that I have at the very moment of telephoning. If I called an hour earlier, I would still have stated the same figure. … I am having great difficulty to recall what I have done today. It costs me a real intellectual effort to recall such things.

The outsiders could see that his waking and sleeping remained near a cycle of 24.5 hours, but Siffre’s conscious understanding of time was greatly affected. Misunderstanding the length of his day, he began to husband his rations, thinking he had weeks more to endure. At his 57th awakening, the final day of the experiment, he thought it was August 20; in fact it was September 14. “I underestimated by almost half the length of my working or waking hours; a ‘day’ that I estimated at seven hours actually lasted on the average fourteen hours and forty minutes.” NASA has pursued these inquiries to consider the implications for space travelers.

(From Jane Brox, Brilliant: The Evolution of Artificial Light, 2010.)

| Oddities · Science & Math

Streets and Order

https://appliednetsci.springeropen.com/articles/10.1007/s41109-019-0189-1

This is interesting: USC urban planning professor Geoff Boeing examined the street networks of 100 world cities as a measure of their spatial logic and order.

The cities with the most ordered streets are Chicago, Miami, and Minneapolis; most disordered are Charlotte, São Paulo, and Rome.

“On average, US/Canadian study sites are far more grid-like than those elsewhere, exhibiting less entropy and circuity.”

(Geoff Boeing, “Urban Spatial Order: Street Network Orientation, Configuration, and Entropy,” Applied Network Science 4:1 [2019], 1-19.) (Via Ethan Mollick.)

| Science & Math · Society · Technology

Podcast Episode 344: Martin Couney’s Incubator Babies

https://commons.wikimedia.org/wiki/File:Baby_incubator_exhibit,_A-Y-P,_1909.jpg

For more than 40 years in the early 20th century, Martin Couney ran a sideshow in which premature babies were displayed in incubators. With this odd practice he offered a valuable service in an era when many hospitals couldn’t. In this week’s episode of the Futility Closet podcast we’ll describe Couney’s unusual enterprise, which earned both criticism and praise.

We’ll also marvel over an Amazonian survival and puzzle over a pleasing refusal.

See full show notes …

| History · Podcast · Science & Math · Society · Technology

Rendezvous

How does an outfielder know where to run in order to catch a fly ball? Previously it had been thought that the fielder estimates the ball’s arc, acceleration, and distance; predicts where it will land; and runs straight to that spot.

“That was a really elegant solution,” Kent State psychologist Michael McBeath told the New York Times in 1995. “The only problem is that keeping track of acceleration like that is something that people are very bad at.”

McBeath and his colleagues analyzed fly balls and catches visually, mathematically, and subjectively from the players’ perspective, using a video camera. They found that fielders learn to run so that the ball follows a straight line in their visual field. “If you are faster than the critter you are trying to catch, if you can keep the prey on a simple path in your vision — hold it as if it’s moving in a straight line in your eye — then you’ll catch it.”

Among other things, this explains why fielders sometimes collide with walls when chasing uncatchable home runs. They haven’t calculated in advance where the ball will come down; instead they’re following an algorithm that’s directing them, accurately, to a landing point that’s not on the field.

(Michael K. McBeath, Dennis M. Shaffer, and Mary K. Kaiser, “How Baseball Outfielders Determine Where to Run to Catch Fly Balls,” Science 268:5210 [1995], 569-573.) (See Shortcuts.)

| Entertainment · Science & Math

Getting Around

Jakob von Uexküll used to say: ‘When a dog runs, the dog moves its legs; when a sea urchin runs, the legs move the sea urchin.’ This assertion was based on the following experiment reported by von Uexküll. A sea urchin was broken in half and the inner sides of both halves of the shell were scraped using sandpaper. The whole of the ambulacral system as well as the nervous system was thus completely removed. Then the two halves were joined together again by means of a spring clasp. The spines of the sea urchin still worked in coordination with one another. In this special case, the riderless horse of von Holst’s parable does indeed exist; the sea urchin’s reaction of fleeing from a star fish still functioned. And in this sense, von Uexkull’s description of a sea urchin being a ‘reflex republic’ is justified, provided one keeps in mind that the ‘reflex’ no longer plays the all-important role ascribed to it during von Uexküll’s time.

— Konrad Lorenz, The Foundations of Ethology, 1982

(Lorenz described this direct mutual influence among the peripheral organs as “a panic spreading among the spines.”)

| Science & Math

Letters and Numbers

ONE + TWO – THREE – FOUR + FIVE = 1

That’s true if we replace each word either with the number it denotes or with the quantity of its letters: Either way we’re left with 1. Another:

ONE + TWO – THREE – FOUR + FIVE – SIX + SEVEN + EIGHT + NINE – TEN + ELEVEN + TWELVE – THIRTEEN – FOURTEEN = 5

These are the only two such sequences using 20 or fewer consecutive number names, found Leonard Gordon, although other sequences of plus and minus signs are possible.

In a separate but related project, Gordon assigned the number names ONE through FIFTEEN, ONE through NINETEEN, and ONE through TWENTY to either side of an equals sign so that the denoted equation is mathematically correct and each equation “balances,” with the same number of letters on each side:

ONE + FOUR + SEVEN + TEN + ELEVEN + THIRTEEN + FOURTEEN = TWO + THREE + FIVE + SIX + EIGHT + NINE + TWELVE + FIFTEEN

ONE + THREE + FIVE + SEVEN + NINE + SIXTEEN + SEVENTEEN + EIGHTEEN + NINETEEN = TWO + FOUR + SIX + EIGHT + TEN + ELEVEN + TWELVE + THIRTEEN + FOURTEEN + FIFTEEN

ONE + THREE + SIX + NINE + TEN + TWELVE + THIRTEEN + FIFTEEN + SEVENTEEN + NINETEEN = TWO + FOUR + FIVE + SEVEN + EIGHT + ELEVEN + FOURTEEN + SIXTEEN + EIGHTEEN + TWENTY

(“Self-Referential Sums Revisited,” in “Kickshaws,” Word Ways 28:3 [August 1995], 170-180.)

| Language · Science & Math

Relative

https://commons.wikimedia.org/wiki/File:Albert_Einstein_photo_1920.jpg

During an eclipse in 1919, Sir Arthur Eddington confirmed Albert Einstein’s prediction of the gravitational bending of light rays, upholding the general theory of relativity. That Christmas, Einstein wrote to his friend Heinrich Zangger in Zurich:

“With fame I become more and more stupid, which, of course, is a very common phenomenon. There is far too great a disproportion between what one is and what others think one is, or at least what they say they think one is. But one has to take it all with good humor.”

(From Helen Dukas and Banesh Hoffmann, eds., Albert Einstein, the Human Side: New Glimpses From His Archives, 1979.)

| Quotations · Science & Math · Society

The Seconds Pendulum

An interesting historical fact from these MIT notes: Christiaan Huygens proposed defining the meter conveniently as the length of a pendulum that produces a period of 2 seconds. A pendulum’s period is

\displaystyle T = 2\pi \sqrt{\frac{l}{g}},

so, using Huygens’ standard of T = 2s for 1 meter,

\displaystyle g = \frac{4\pi ^{2}\times 1\ \textup{meter}}{4s^{2}} = \pi ^{2}ms^{-2}.

“So, if Huygens’s standard were used today, then g would be π2 by definition.”

| History · Science & Math

An Elevated Perspective

tetrahedron example

Consider a triangle ABC and three other triangles (ABD1, BCD2, and ACD3) that share common sides with it, and assume that the sides adjacent to any vertex of ABC are equal, as shown. The altitudes of the three outer triangles, passing through D1, D2, and D3 and orthogonal to the sides of ABC, meet in a point.

This can be made intuitive by imagining the figure in three dimensions. Fold each of the outer triangles “up,” out of the page. Their outer vertices will meet at the apex of a tetrahedron. Now if we imagine looking straight down at that apex and folding the sides down again, each of those vertices will follow the line of an altitude (from our perspective) on the way back to its original position, because each follows an arc that’s orthogonal to the horizontal plane and to one of the sides of ABC. The result is the original figure.

(Alexander Shen, “Three-Dimensional Solutions for Two-Dimensional Problems,” Mathematical Intelligencer 19:3 [June 1997], 44-47.)

| Science & Math

“Appendicitis”

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.

| Poems · Science & Math