Chapter 2

Finding something in Hilbert space

When you see how a Hilbert space can create vast number of possibilities from even a small number of parameters, a little bell goes off in your head to tell you there must be something wrong here because we deal with objects every day and never get the feeling that every object is a unique selection from a space full of billions of possibilities. If we want a red rubber ball about the size of a tennis ball we can focus solely on this specific object without the mind being confused by billions of other things.

How do we manage to do this? How can we so quickly ignore everything else to quickly focus our attention on a single object?

The answer is that Hilbert space is highly flexible. Our human brain's can define it with as few or as many parameters as we like. The smaller the number of parameter, the easier it is to deal with. When we want to buy a red rubber ball, our minds simply conjure up a Hilbert space with the parameters red. round and rubber, then a parameter with a list of stores where we can go to buy the ball. Our mind then sees just a few stores in Hilbert space, each of which we can visit to try to buy the ball.

This offers a clue as to one of the strategies we can use to find things in Hilbert space. We can cut down the number of parameters to where the number of possibilities is within our capability of being able to handle them.

Take the problem of trying to find a perfect partner in a Hilbert space. We know instinctively that we cannot sample everyone in the world, so we construct a simplified version of a Hilbert space that contains only a a number of possibilities that we can cope with. This we can do by creating a Hilbert space that has parameters that eliminate most of the unlikely possibilities by limiting the search area to certain defined areas. Perhaps the local social scene, plus the business environment. This can be extended by including visits to selected social functions, holiday environments etc. The possibilities can be further limited by including a few other parameters such as an age range, a dress code, a type of culture etc.

Clearly, this strategy of finding an object in Hilbert space is based upon a compromise. It isn't about finding the absolute best but limiting the search area to be able to find the best available.

In this example of finding a perfect partner, it immediately becomes obvious that even by reducing the search area, the actual selection will involve all kinds of considerations, considerations that if expressed in terms of parameters would present us with a Hilbert space of gigantic proportions.

Unfortunately, we cannot use a strategy of elimination here because we wouldn't even begin to be able to construct a parameter list to be able to describe our perfect partner. We can't just say cut out all blondes, cut out all people with big noses, cut out people with freckles, etc. We know that it would be impossible to create such a list because nobody would be perfect and the strategy would most likely eliminate everyone.

Somehow, the strategy has to be able to combine all the characteristics of a person together and then come up with a composite value. This is beyond our human powers of computation, reasoning and logic. So, we have to rely on emotions to handle this kind of Hilbert space for us.

It is in understanding how emotions can do this that can explain the nature of life and this is what we are now on the brink of being able to do.

Emotional decision making

It is easy to just shrug the shoulders and say that the way emotions are able to help us find options in a Hilbert space is beyond our understanding. But, this is no longer true. We are now beginning to understand how emotions work.

For starters, we know that emotions are not metaphysical experiences. They are generated in specific areas of the brain and triggered by identifiable networks of nuerons that are activated by chemical and electrical signals. These sequence of events can be positively associated with the way our sensory organs are perceiving and interpreting the external world.

We know this because we can now trace what happens in the brain when people are exposed to external stimuli. We can ask people what emotions they are feeling when the observed neural activity takes place. We can place probes inside the brain to activate single neurons that give rise to specific emotions. We can see where emotional sensations are lost when certain parts of the brain are damaged through disease, surgery or accidents.

Of course, we still can't get anywhere near mapping the complete circuitry of the brain or know how it works in its entirety, but, we now have detailed knowledge of many specialized areas that give us a pretty good idea of what is going on in the brain when we experience emotions.

Emotional strategy

Having a clear knowledge of the way in which emotions manifest, takes us out of the area of magical mystery. It allows us to concentrate upon the fact that they are tangible outputs from the brain: outputs that are giving us the results of the brain's ability to make selections in the kind of Hilbert space that we cannot deal with consciously.