American Scientist

To the Editors: 

I very much enjoyed Daniel S. Silver’s article, “Stop Me If You’ve Heard This Theorem Before.” Like the author, I have a great interest in the history of science. One question that I have had for quite some time is, How can we explain that natural phenomena many times follow very neat and elegant mathematical formulas? 

For example, how does it just happen to be true that E=mc2 ? And that length contraction factor turns out to be 1−v2 /c2 ? I find it unlikely that nature would just so happen to follow the language of mathematics. 

Gary S. Flom
Stockbridge, GA 

Dr. Silver responds: 

Your question is a deep one. The penultimate paragraph of my article mentions a famous paper by the late physicist Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” You might find it enlightening. Alas, I don’t. 

My answer to your question is summarized in that paragraph. Nature, I believe, does not follow mathematical principles. We merely find those phenomena that conform to mathematics. Our brains are filters. If what I write is true, then imagine how much we are missing—and how hopeless is the task of “understanding” the universe. 

I don’t mean to sound like a mystic. I just have tremendous respect for our tremendous ignorance about the world. 

To the Editors: 

I read Daniel Silver’s article, “Stop Me If You’ve Heard This Theorem Before,” and enjoyed it and learned from it. 

Silver’s piece reminded me of a 1984 article I coauthored with Shirley Willis Maase and Stan A. Kaplowitz titled “Incongruity in Humor: The Cognitive Dynamics,” published in the Annals of the International Communication Association. In it, we used ideas from metric multidimensional scaling models to measure the cognitive roots of humor. I wonder what Dr. Silver might think of our approach. 

Edward L. Fink
Philadelphia, PA 

Dr. Silver responds:

Thank you for pointing me to the article about modeling humor. I enjoyed reading it. 

I confess that the problem of mathematically modeling humor frightens me. The only definition of funny I can understand is an operational one: See whether people laugh. 

If that is the only definition possible, then how do we know that ancient Greeks laughed for the same reasons we do when, for instance, someone slipped on a banana peel? Do we even know that they had bananas? (Can one slip on fresh dates and olives?) 

Putting aside my fruitful doubts for now, I wonder whether more exotic spaces such as surfaces or generally manifolds might be useful for modeling humor. Often in such spaces we can get from one point to another along paths that are very different, paths that cannot be deformed into one another. When Koestler drew his bisociation diagram as planes intersecting in a moment of “Aha!,” he could equally well have drawn two geodesic paths going around a torus that started out in opposite directions. 

To the Editors: 

I enjoyed Daniel Silver’s entertaining and insightful article, “Stop Me If You’ve Heard This Theorem Before.” Silver recalled hearing a professor’s dismissive comment that some bad mathematics was “not even wrong!” This particular expression originated with Austrian theoretical physicist Wolfgang Pauli (1900–1958). It was his response when, near the time of his death, he was asked by a friend to assess the paper of a young colleague. 

Along the same lines, when Soviet physicist Lev Davidovich Landau pleaded with Pauli for an admission that not everything Landau had said was complete nonsense, Pauli replied, “Oh, no. Far from it. What you said was so confused that one could not tell whether it was nonsense or not.” Pauli was notorious for such snarky remarks. 

Similarly, in a 1986 essay by American science fiction writer Isaac Asimov, he discussed—with typical panache—what he labeled the “relativity of wrong.” He went on to describe a hierarchy of wrongness: “When people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together.” 

Most recently, in a 2009 episode of The Big Bang Theory, Stuart argues with Sheldon over gradations of wrongness. “Oh, Sheldon, I’m afraid you couldn’t be more wrong,” said Stuart. “More wrong?” demanded Sheldon haughtily, before asserting that “Wrong is an absolute state and not subject to gradation.” Stuart retorted, “Of course it is. It’s a little wrong to say a tomato is a vegetable; it’s very wrong to say it’s a suspension bridge.” 

Douglas J. Lanska
Tomah, WI