Today Miles Cranmer (Princeton) chatted with Weichi Yao (NYU), Soledad Villar (JHU), and me about things related to symbolic regression, dimensional analysis, and so on. He brought up a very interesting problem in the history of physics: The black-body radiation law, which is attributed to Planck. Planck knew about temperature, wavelength, the speed of light, and Boltzmann's constant k. Dimensionally, these can be combined into only one thing that has units of intensity, and that one thing is the long-wavelength black-body law. At short wavelengths, the behavior can't be explained without the introduction of a new constant, and that constant has to have non-trivial dimensions (units). He figured it out, and that constant ended up governing the hydrogen atom spectrum, quantum mechanics, and everything else. Indeed that constant, h, bears his hame. Could we have learned this ourselves just from the data directly with a machine? After all, that's what Planck did, right?
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