T.H. Huxley defined “four stages of public opinion” of a new scientific theory:

  1. Just after publication — The novelty is absurd and subversive of religion and morality. The propounder both fool and knave.
  2. 20 years later — The novelty is absolute truth and will yield a full and satisfactory explanation of things in general. The propounder man of sublime genius and perfect virtue.
  3. 40 years later — The novelty won’t explain things in general after all and therefore is a wretched failure. The propounder a very ordinary person advertised by a clique.
  4. A century later — The novelty is a mixture of truth and error. Explains as much as could reasonably be expected. The propounder worthy of all honour in spite of his share of human frailities, as one who has added to the permanent possessions of science.

J.B.S. Haldane had a more concise list:

  1. This is worthless nonsense.
  2. This is an interesting, but perverse, point of view.
  3. This is true, but quite unimportant.
  4. I always said so.

Law and Order

Niels Bohr liked westerns but found them exasperating. After one feature he told his friends, “I did not like that picture, it was too improbable. That the scoundrel runs off with the beautiful girl is logical, it always happens. That the bridge collapses under their carriage is unlikely but I am willing to accept it. That the heroine remains suspended in midair over a precipice is even more unlikely, but again I accept it. I am even willing to accept that at that very moment Tom Mix is coming by on his horse. But that at that very moment there should be a fellow with a motion picture camera to film the whole business — that is more than I am willing to believe.”

He did approve of movie gunfights, where the villain always draws first and yet the hero always wins. Bohr reasoned that the man who draws first in a gunfight is using conscious volition, where his opponent is relying on reflex, a much faster response. Hence the second man should win.

“We disagreed with this theory,” wrote George Gamow, “and the next day I went to a toy store and bought two guns in Western holders. We shot it out with Bohr, he playing the hero, and he ‘killed’ all his students.”

New Units

Since Helen’s face launched a thousand ships, Isaac Asimov proposed that one millihelen was the amount of beauty needed to launch a single ship. And one negative helen is the amount of ugliness that will send a thousand ships in the other direction.

When the taciturn Paul Dirac was a fellow at Cambridge, the dons defined the dirac as the smallest measurable amount of conversation — one word per hour.

Robert Millikan was said to be somewhat conceited; a rival suggested that perhaps the kan was a unit of modesty.

And a bruno is 1158 cubic centimeters, the size of the dent in asphalt resulting from the six-story free fall of an upright piano. It’s named after MIT student Charlie Bruno, who proposed the experiment in 1972. The drop has become an MIT tradition; last year students dropped a piano onto another piano:

Lecture Notes

“While I am describing to you how Nature works, you won’t understand why Nature works that way. But you see, nobody understands that.” — Richard Feynman

“I am no poet, but if you think for yourselves, as I proceed, the facts will form a poem in your minds.” — Michael Faraday

“Now, this case is not very interesting,” said Bell Labs mathematician Peter Winkler during a lecture at Rutgers. “But the reason why it’s not interesting is really interesting, so let me tell you about it.”

Ernest Rutherford addressed the Royal Institution in 1904:

I came into the room, which was half dark, and presently spotted Lord Kelvin in the audience and realised that I was in for trouble at the last part of the speech dealing with the age of the Earth, where my views conflicted with his. To my relief Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye, and cock a baleful glance at me. Then a sudden inspiration came and I said Lord Kelvin had limited the age of the Earth, provided no new source was discovered. That prophetic utterance referred to what we are now considering tonight, radium! Behold! the old boy beamed upon me.

When Antonie van Leeuwenhoek declined to teach his new methods in microbiology, Leibniz worried that they might be lost. Leeuwenhoek replied, “The professors and students of the University of Leyden were long ago dazzled by my discoveries. They hired three lens grinders to come to teach the students, but what came of it? Nothing, so far as I can judge, for almost all of the courses they teach there are for the purpose of getting money through knowledge or for gaining the respect of the world by showing people how learned you are, and these things have nothing to do with discovering the things that are buried from our eyes.”

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.


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

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)