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:

“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.”

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.)

Consider a finite list of n statements:

S₁: At least one of statements S₁-S_n is false.
S₂: At least two of statements S₁-S_n is false.
…
S_n-1: At least n-1 of statements S₁-S_n is false.
S_n: At least n of statements S₁-S_n 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.”

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)