Great Minds

boullee newton cenotaph

In 1784, French architect Étienne-Louis Boullée proposed building an enormous cenotaph for Isaac Newton, a cypress-fringed globe 500 feet high. A sarcophagus would rest on a raised catafalque at the bottom of the sphere; by day light would enter through holes pierced in the globe, simulating starlight, and at night a lamp hung in the center would represent the sun.

“I want to situate Newton in the sky,” Boullée wrote. “Sublime mind! Vast and profound genius! Divine being! Newton! Accept the homage of my weak talents. … O Newton! … I conceive the idea of surrounding thee with thy discovery, and thus, somehow, surrounding thee with thyself.”

As far as I can tell, this is unrelated to Thomas Steele’s proposal to enshrine Newton’s house under a stone globe, which came 41 years later. Apparently Newton just inspired globes.

Succinct

In 2011 M.V. Berry et al. published “Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?” in Journal of Physics A: Mathematical and Theoretical.

The abstract read “Probably not.”

In 1978 John C. Doyle published “Guaranteed margins for LQG regulators” in IEEE Transactions on Automatic Control.

The abstract read “There are none.”

(Thanks, Dre.)

The Parity Paradox

Consider a finite list of n statements:

S1: At least one of statements S1-Sn is false.
S2: At least two of statements S1-Sn is false.

Sn-1: At least n-1 of statements S1-Sn is false.
Sn: At least n of statements S1-Sn is false.

Is this a paradox? It depends: The statements form a self-consistent system if n is even, but not if it’s odd.

From Roy T. Cook’s new book Paradoxes — which is dedicated in part to “anyone whom I don’t discuss in this book.”

The Hypergame Paradox

http://commons.wikimedia.org/wiki/File:Boilly-Checkers-1803.jpg

Call a game finite if it terminates in finitely many moves. Now consider Hypergame, which has two rules:

  1. The first player names a finite game.
  2. The two players play that game.

Is Hypergame a finite game? It seems so: It consists of a single game-naming move, followed by a subgame with a necessarily finite number of moves. But what if the first player names Hypergame itself as the subgame, and the second player names Hypergame as the sub-sub-game, and so on?

In presenting this question to students and colleagues at Union College, mathematician William Zwicker found that many saw the catch and quickly pointed out that it leads to infinite play, thinking that this settles the matter. But the proof that Hypergame is finite seems sound. “I … have to convince them that mathematicians cannot simply abandon a proof once a counter-example has been found, for if the internal flaw in such a proof cannot be identified then the counterexample threatens the entire edifice of mathematical proof.” What is the answer?

(William S. Zwicker, “Playing Games with Games: The Hypergame Paradox,” American Mathematical Monthly 94:6, 507-514)

Field Trip

http://commons.wikimedia.org/wiki/File:Van_Gingelen_Vollmondnacht.jpg

In the early 1600s, Johannes Kepler wrote a fantasy in which he imagined a journey to the moon:

We congregate in force and seize a man of this sort; all together lifting him from beneath, we carry him aloft. The first getting into motion is very hard on him, for he is twisted and turned just as if, shot from a cannon, we were sailing across mountains and seas. Therefore, he must be put to sleep beforehand, with narcotics and opiates, and he must be arranged, limb by limb, so that the shock will be distributed over the individual members, lest the upper part of his body be carried away from the fundament, or his head be torn from his shoulders. Then comes a new difficulty: terrific cold and difficulty in breathing. The former we counter with our innate power, the latter by means of moistened sponges applied to the nostrils.

Somnium is largely a treatise on lunar astronomy, describing the motions of the planets as observed from the moon. But Kepler also considers the appearance of the moon’s inhabitants, who “wander in hordes over the whole globe in the space of one of their days, some on foot, whereby they far outstrip our camels, some by means of wings, some in boats pursue the fleeing waters, or if a pause of a good many days is necessary, then they creep into caves.” Carl Sagan and Isaac Asimov called it the first work of science fiction.

“The Skeptic’s Horoscope”

For Capricorn, Aquarius, Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, and Sagittarius:

The coming year is likely to present challenges; these trials are when your true character will show. Trusted friends can provide assistance in particularly pressing situations. Make use of the skills you have to compensate for ones you lack. Your reputation in the future depends on your honesty and integrity this year. Monetary investments will prove risky; inform yourself as much as possible. On the positive side, your chances of winning the lottery have never been greater!

(By Tim Harrod.)

Business as Usual

http://commons.wikimedia.org/wiki/File:Zoologist_Thomas_Bell.jpg

On July 1, 1858, the Linnean Society of London heard a joint presentation by Charles Darwin and Alfred Russel Wallace on the theory of evolution by natural selection.

In his annual report the following May, society president Thomas Bell wrote, “The year which has passed has not, indeed, been marked by any of those striking discoveries which at once revolutionize, so to speak, the department of science on which they bear.”