Natural optimization

Often we try to find the best solution to a problem. It can be, lowest price for a specific item, the loan with lowest interest or the stock with the highest expectations. Sometimes we even bring out our calculator and try to use maths to get to the answer, for example, how should I construct a can that can hold a certain volume using the least amount of material. Optimization like this can be thought of like finding the highest hill in a vast landscape. If you are lucky there is only one hill and you will get to the top just by walking upwards. If you are unlucky there are many hills and mountains. The problem turns into finding the highest peak in the Alps just by walking about. Just going upwards won't help you as you will just end up on the top of the hill closest to where you started.

How does nature do it? Think of Newton and his apple. The apple will fall to the ground because of gravity. This phenomenon can be thought of as an optimization problem. Nature wants to find the lowest potential energy. In this case nature doesn't do any better than hill climbing, it just finds the closest valley.

But sometimes nature can do better. Think of a cup of water you have put in the fridge. It will freeze. When liquids freeze the molecules line up very neatly in a configuration holding the least energy. How does nature find this configuration? It is done in a process called annealing.Using the mountain range analogy this process can be imagined by replacing Newtons apple with an extremely restless child. It will skip across the mountains randomly and slowly loose energy. The more tired the child becomes less likely it is to go uphill. Finally the child will be totally out of energy and tumble down into the closest valley. This process often comes close to a minimal energy but often the final crystal will have some flaws indicating that a local minimum has been reached.

And then we have the process of evolution. In the mountain range analogy we will have millions of creatures scattered all over the mountain range. The creatures on the hilltops will be called inferior and the creatures in the valleys are superior(or vice versa). Evolutionary selection will remove the creatures on the hilltops to a greater extent and the creatures in the valleys will mix, share traits and create a new creature that will get a position(genes determine position in the landscape) somewhere between the two parents. This process will lead to communities being formed in some of the best valleys, breeding between those will sometimes create a new creature located perhaps in an even better valley and a new community will be formed there. Finally the majority of the creatures will live in the same, possibly deepest valley.