The Extrema Fondness

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Estimated Reading Time: 1-2 minutes

Humans have a penchant for optimisation. We tend to think of everything as an optimisation problem. We think that nature always operates in extrema conditions. Every field of physics can be viewed in terms of various types of optimisation problems, the most prominent one being the action principle. Even at lower meta-levels of physics, we are optimising quantities like entropy, energy, potential energy, time taken, path length etc.
Part of the reason is that we love mathematics and in turn mathematicians love extrema. Each mathematical model is analysed first by its extrema points and critical points. We somehow think that extrema characterise a mathematical function. In fact, we developed a whole branch dedicated to it – calculus and analysis. Since extrema characterise the function in our opinion, they are special points/states. But why should nature choose special states? (Why indeed should nature ‘choose’?)
This familiarity with optimisation and optimised quantities are the basis of a lot of our intuition. Whenever a not-so-special state is involved significantly, our intuition fails us. Take, for example, the case of quantum mechanics or statistical mechanics. Our intuitions go for a toss when along with the special extremum there is a non-zero probability for other states too.
Most of our algorithms are for optimisation objectives or are based on optimising certain quantities. They reflect the problems we want to solve. Take for example – Djikstra’s algorithm or A* (shortest path to all nodes in a graph), Quicksort (highest element last in each sublist), Minimax Algorithm (Highest winning chance moveset for player), Euclid’s Algorithm (Highest Common Factor) etc.
All of this implies that we, humans, look upon the world as a series of optimisation problems. But may be that might not be the best way in all situations. After all, there may be a function not well described by extrema. Consider the Cantor set for example, or the Dirichlet function. Perhaps there is a different perspective where these come off more naturally than with extrema. Perhaps that is the next frontier of physics. Perhaps.

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