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Beautiful Equations

I just watched Matthew Collings exploration of the beauty in the maths of science, Beautiful Equations. He said a lot that needed unpicking, not least that equations are a metaphor for reality. The connection is deeper and more direct - you can't choose to use the Dirac Equation to accurately describe the angle of slip in a snow drift, much as you might like to.

I guess the programme might have worked better if he'd gone into the science a bit more or looked at what it is in each equation that causes scientists to marvel.

For example in the e=mc2 he asked could it have been a 3 instead of a 2. The answer should have been about how that would have messed up the units on either side, instead of a reference to experiment. What's more incredible to me about this equation is how the constant is exactly the speed of light squared. This says something very deep about the way the universe works. It was however useful to find out that the total energy contained in an aspirin at rest was about the same as released in a 15Kt explosion.