Time Trouble

A letter from 14-year-old Jim Nicholson to Wonder Stories, February 1931:

Some time ago you asked us (the readers) what our opinions on time-traveling were. Although a bit late I am now going to voice four opinions …

(1) Now, in the first place if time traveling were a possibility there would be no need for some scientist getting a headache trying to invent an instrument or ‘Time-Machine’ to ‘go back and kill grandpa’ (in answer to the age-old argument of preventing your birth by killing your grandparents I would say: ‘now who the heck would want to kill his grandpa or gandma?’) I figure it out thusly:

A man takes a time-machine and travels into the future from where he sends it (under automatic control) to the past so that he may find it and travel into the future and send it back to himself again. Hence the time machine was never invented, but! — from whence did the machine come?

(2) Another impossibility that might result would be:

A man travels a few years into the future and sees himself killed in some unpleasant manner, — so — after returning to his correct time he commits suicide in order to avert death in the more terrible way which he was destined to. Therefore how could he have seen himself killed in an entirely different manner than really was the case?

(3) Another thing that might corrupt the laws of nature would be to:

Travel into the future; find out how some ingenious invention of the time worked; return to your right time; build a machine, or what ever it may be, similar to the one you had recently learned the workings of; and use it until the time you saw it arrive, then if your past self saw it, as you did, he would take it and claim it to be an invention of his (your) own, as you also did. Then — who really did invent the consarn thing?

(4) Here’s the last knock on time traveling:

What if a man were to travel back a few years and marry his mother, thereby resulting in his being his own ‘father’?

Now I ask you, do you think traveling in time, in the manner most of your authors put it, is possible? (Now please don’t get the idea that I think it can’t be done, to some extent, because it might be done through Suspended Animation).

Editor Hugo Gernsback responded, “Logically, we are compelled to admit that he is right — that if people could go back into the past or into the future and partake of the life in those periods, they could disturb the normal course of events, as Mr. Nicholson has pictured it.”

| Literature · Science & Math

Inventory

The following pair of sentences employ 2 ‘0’s, 2 ‘1’s, 9 ‘2’s, 5 ‘3’s, 5 ‘4’s, 4 ‘5’s, 5 ‘6’s, 2 ‘7’s, 3 ‘8’s and 3 ‘9’s.

The sentences above and below employ 2 ‘0’s, 2 ‘1’s, 8 ‘2’s, 6 ‘3’s, 5 ‘4’s, 6 ‘5’s, 3 ‘6’s, 2 ‘7’s, 2 ‘8’s and 4 ‘9’s.

The previous pair of sentences employ 2 ‘0’s, 2 ‘1’s, 9 ‘2’s, 5 ‘3’s, 4 ‘4’s, 6 ‘5’s, 4 ‘6’s, 2 ‘7’s, 3 ‘8’s and 3 ‘9’s.

(From Lee Sallows and Victor L. Eijkhout, “Co-Descriptive Strings,” Mathematical Gazette 70:451 [March 1986], 1-10.)

| Science & Math

The British Flag Theorem

https://commons.wikimedia.org/wiki/File:British_flag_theorem_squares.svg

Draw a rectangle and pick a point inside it. Now the sum of the squares of the distances from that point to two opposite corners of the rectangle equals the sum to the other two opposite corners.

Above, the red squares have the same total area as the blue ones.

| Science & Math

Extended Engagement

https://commons.wikimedia.org/wiki/File:Green_rim_of_the_setting_sun.jpg
Image: Wikimedia Commons

The upper edge of the setting sun is sometimes seen to take on a green tinge, an effect of atmospheric refraction. Normally this is apparent only briefly, but for Richard Byrd’s Antarctic expedition of 1928-1930 it lasted more than half an hour:

Here the sun descends so slowly that it seems to roll along the horizon and as it will be only two days until it is above the horizon all the time for the rest of the summer it clings interminably before, with seeming reluctance, dropping from sight. As its downward movement is so prolonged the last rays shimmer above the barrier edge as it moves eastward, appearing and reappearing from behind the irregularities of the barrier surface. It trembles and pulsates, producing a vibration light of great beauty.

The night the green flash was seen some one ran into the administration building and called, ‘Come out and see the green sun.’

There was a rush for the surface and as eyes turned southward, they saw a tiny but brilliant green spot where the last ray of the upper limb of the sun hung on the skyline. It lasted an appreciable length of time, several seconds at least, and no sooner disappeared than it flashed forth again. Altogether it remained on the horizon with short interruptions for thirty-five minutes.

When it disappeared momentarily it seemed to have been shut off by a tiny spurt, an inequality in the skyline caused by the barrier surface.

“Even by moving the head up a few inches it would disappear and reappear again and after it had finally disappeared from view it could be recaptured by climbing up the first few steps of the [antenna] post.”

(From an account by witness Russell Owen, San Francisco Chronicle, Oct. 23, 1929.)

| Science & Math

Evolution

I just ran across this anecdote by Jason Rosenhouse in Notices of the American Mathematical Society. In a middle-school algebra class Rosenhouse’s brother was given this problem:

There are some horses and chickens in a barn, fifty animals in all. Horses have four legs while chickens have two. If there are 130 legs in the barn, then how many horses and how many chickens are there?

The normal solution is straightforward, but Rosenhouse’s brother found an alternative that’s even easier: “You just tell the horses to stand on their hind legs. Now there are fifty animals each with two legs on the ground, accounting for one hundred legs. That means there are thirty legs in the air. Since every horse has two legs in the air, we find that there are fifteen horses, and therefore thirty-five chickens.”

(Jason Rosenhouse, “Book Review: Bicycle or Unicycle?: A Collection of Intriguing Mathematical Puzzles,” Notices of the American Mathematical Society, 67:9 [October 2020], 1382-1385.)

| Puzzles · Science & Math

Bottema’s Theorem

Grab point B above and drag it to a new location. Surprisingly, M, the midpoint of RS, doesn’t move.

This works for any triangle — draw squares on two of its sides, note their common vertex, and draw a line that connects the vertices of the respective squares that lie opposite that point. Now changing the location of the common vertex does not change the location of the midpoint of the line.

It was discovered by Dutch mathematician Oene Bottema.

(Demonstration by Jay Warendorff.)

| Science & Math

Podcast Episode 346: A Desperate Winter in Antarctica

https://commons.wikimedia.org/wiki/File:Yasmina_-_Belgica.JPG
Image: Yasmina

In 1898 a Belgian ship on a scientific expedition was frozen into the sea off the coast of Antarctica. During the long polar night, its 18 men would confront fear, death, illness, and despair. In this week’s episode of the Futility Closet podcast we’ll describe life aboard the Belgica during its long, dark southern winter.

We’ll also consider a devaluing signature and puzzle over some missing music.

See full show notes …

| History · Podcast · Science & Math

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