People don't like detours: Selecting the optimal solution by Sabine Hossenfelder

Lawns in public places all suffer from the same problem: people don't like detours. In cities throughout the world, people search for the fastest route to the workplace, the shortest way to the restroom, the least pricey airline, the most convenient parking spot. Depending on resources and personal preferences, we optimize our day with regard to criteria we regard important. Cooks experiment with recipes to create the most delicious meals, politicians argue about taxation to score in polls, you aim to find the most comfortable position on your couch. In most cases, these are optimizations through incremental modifications and evaluation of the change - little steps of trial and learning and eventual selection of the optimal solution.

Not only do our daily lives reflect our aim to optimize under variation, but Nature does as well A soap bubble minimizes surface area [1]. Electric currents prefer the way of least resistence, water runs downhill around obstacles in its way.

In all cases we have a system with a quantity which is optimized for one of many possible configurations, and the configuration optimal in this regard is the one realized in Nature. Optimization can mean either lowering a quantity to a minimal value, or obtaining a maximal value, whether that is you slouching on the couch with your feet on the table because it's the most comfortable way to spend your evening or dozens of students trampling their traces in the campus' lawn because it's the fastest way to coffee.

The same idea underlies theoretical physics. For every system we want to describe, we have a quantity whose value has to be optimized. The way we find the optimal configuration is to make small changes and take the configuration that would get less optimal under any change. These small changes are called 'variations'and are denoted with a small delta δ, and the process is called the 'variational principle'. For the optimal configuration, the variation has to vanish. In physics, in most cases the quantity optimized is called the 'action', and is usually denoted with a capital S. The requirement then reads