Wednesday, March 25, 2009

Mathematical Representation of Understanding

What is understanding? What do we mean when we say that a facet of life is understood? One definition of understanding is a mathematical one.

It can be said of everything that we understand that we create a mathematical representation of it. We are unable to create such models of things we do not understand. By creating models we are able to see if our understanding is correct by comparison with the real and where there are discrepancies we know we must improve our understanding.

Our understanding of solar orbits is such that our models can be used to make accurate predictions of the positions of celestial bodies, we can model a neurone and its electrical and chemical composition and explain how action potentials arise and how they are propagated. Yet we are not able to model emotions but who can claim complete understanding in that field?

It is a very common to hear "its impossible to model emotion". Why? At first we must assume there was no understanding and no maths. As the first levels of understanding emerged so too came the dawn of maths. At which point the notion of calculating distance in n-dimensional space would have been far beyond the level of understanding. Thankfully Pythagoras sorted triangular relationships out and so today this problem is a simple extension of Pythagorean theorem. However I think all of our great math geniuses of old would be baffled by the mathematics of a modern cpu chip or a metabolic pathway. My point is this; understanding continues to swell and what was impossible today is 1st grade school tomorrow. We can't mathematically model emotions now but 100 years ago we barley knew of the existence of neurones let alone their function. It is a matter of time, whether we have the time is another matter entirely.

Whether or not it is believed that something can or can not be mathematically modelled does not detract from the fact that once something is understood we are able to model it. In short understanding is the mathematical dissemination of something such that accurate predictions can be made.

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