The Unreasonableness of Math is Context Independence

Mathematics has produced some of the most beautiful and elegant abstractions in human history, what can system thinkers learn from their accuracy?

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There’s a concept known as the “unreasonable effectiveness of mathematics.” Coined by physicist Eugene Wigner, it refers to the idea that math is unreasonably good at expressing the natural world, that mathematics often developed to describe one set of observations can be reused to describe other scenarios far beyond what could have been predicted.

I’ve always really liked Mario Livio’s description of this concept:

As a software engineer and a systems geek, I’m fascinated by the language of abstractions. I strive to form abstractions that are resilient in the face of changing circumstances and the discovery of new edge cases. So examples of abstractions that have survived hundreds, in some cases thousands of years is super interesting. The form some mathematical concepts appear in today is very much the same as when they were first recorded. They endure even as measurements get more precise and instrumentation more complex. Is that because there really is no iteration? Or much like Euclid, are the great historic mathematicians simply the ones smart enough to write tutorials on preexisting work? (As a person who has been known to write the occasional technical tutorial I can confirm it is a very efficient way of getting people to associate you with other people’s innovation 😉)

I’m not the only computer person who likes to think about these things. In 2013, Professor Derek Abbott of The University of Adelaide published a column in the Proceedings of the IEEE attempting to debunk the notion that there’s anything magical about the effectiveness of mathematics. Abbott’s argument in a nutshell is that the appearance of unreasonableness is a product of survival bias. Mathematical abstractions that fail to survive as technology advances are simply discarded and forgotten:

The Platonist will point out that the inverse square law for…