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Why math is sooo great!

June 5, 2012

One thing that’s great about mathematics is that it can illustrate deep connections between very different sciences. For example, Cauchy-Schwarz is the mathematical generalisation of the triangle inequality from geometry, the uncertainty principle from quantum mechanics, and the reason why correlation coefficients from statistics work. The chain rule is similarly awesome. It forms the basis for the continuous Price equation from evolutionary biology, Hamilton’s equations from classical mechanics, and like tons of other stuff, including the use of Hamilton’s equations in Monte Carlo simulation. Can’t forget about the normal distribution / central limit theorem.

I guess I just wished that more ecologists appreciated how wonderful mathematics are. And I’m not just talking about the thing that (I think it was) Robert May said something like mathematical thinking is just valid reasoning, nothing more, and that is why ecologists should use it. At least this is better than fear of math, but I don’t think it will entice everyone. Similarly, I don’t completely agree with Ellison and Dennis‘ approach of scaring ecologists into math by telling them that they will not understand statistics without it…although I wholeheartedly agree with the general motivation of E&D. Maybe I’m going to sound too Dirac-ish, but its the beauty — not just of mathematics themselves — but of their use in science, that makes them so wonderful. I mean honestly, who isn’t blown away that triangles, sub-atomic particles, and statistical correlations can all be understood in terms of the same mathematical theory!

Don’t get me wrong, I’m completely against over-metaphoring and over-analogyising…as is Robert Root-Bernstein. Much of my thesis is about problems in multivariate statistical ecology that arise when we think about communities as points in multivariate ‘species space’; communities are not geometrical points…they are communities. The problem here is very ‘when you’ve got a hammer everything looks like a nail’-esque. Or, just because communities can be thought of as points in multivariate space doesn’t mean that they should. But if viewing communities as points in multivariate space facilitates the discovery of a quantitative insight about communities, then I am all for it.

This is why math and science have been such great partners. They keep building off each other. What’s been quantitatively learned in physics could be useful in biology and vice versa (although the vice versa certainly seems less frequent). Its the idea that the same abstract mathematical results can be used to provide insight into a wide wide variety of phenomena. So…maybe we shouldn’t be looking for the unified theory of everything (I don’t have much hope for that) but rather a few unified theorems for lots of stuff.


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