Tuesday, November 09, 2010

Mathematics and Physics

I can't say whether I completely agree with the content of this report, but it is certainly interesting to consider.

This news article reports on a lecture given Dartmouth on the interaction between Physics and Mathematics, its common history, and how they are now different but interconnected. The lecturer has an interesting point on when in history the field of physics and mathematics split.

The fields began to divide in the late 1800s, she said, with individuals coming to identify with one of the two fields.

“The big question is, what happened between the early 1800s and late 1800s?” she said. “Why was there a split into mathematics and physics? The answer: Fourier happened.”

Joseph Fourier is best known for his development of the Fourier series, a method of breaking sounds into components. The method explains, for example, why a violin sounds different from a flute, Singer said. But in addition to the Fourier series, Fourier came up with the theory of heat distribution, a model for how heat travels on a thin, metal plate.

“This [theory] lit up a crisis in the scientific world,” Singer said. “And the resolution of this crisis split natural philosophy.”

Natural philosophers had formerly agreed upon the definition of a function as a formula and a formula as a function, according to Singer. But to support his theories, Fourier used functions, but not formulas — contradicting the commonly held notion that the two were interchangeable, she said.

As a result of this unprecedented disagreement, mathematics and physics diverged from one another. Those who agreed with Fourier became physicists and those who didn’t became mathematicians, she said.

Wow. So we can blame it all on Fourier? Or maybe some would think that we can thank it all on Fourier! :)



Pi-Guy said...

I'm not sure the Fourier argument is all that convincing to me. I think that mathematicians simply got to a point where they understood that mathematical systems needn't be analogous to realistic systems; that they could be studied and worked on as pure hypotheses with no pretense that they were discovering something about the real world. Physicists (at least the good ones) can never do that, because their whole endeavor is anchored to empiricism.

It's like what happened with artists: at some point they felt free to pursue works of high abstraction, leaving orthodox photography to record the real world with fidelity.

Googolplex Ideas! said...

I don't think it was just Fourier. The split was imminent because both the fields have become so enormous that it is now humanely not possible to excel in both.