Tuesday, September 27, 2005

Dirac's Hidden Geometries

I find this interesting because I like to visualizze as much as possible, and I sometimes think the basis of the leading ideas in science would had to follow a progression. Klein's Ordering of Geometries was one such road that seem to make sense. The basis of relativity lead through in geometrical principals?

Such an issue with string theory had to have such a basis with it as well, although how do you assign any views to the very begininngs of the universe below planck length? Well there are images to contend with what are these and how are they derived? Rotations held in context of te progression of this universe and all thoughts held to the very nature of particle creation and degrees fo freedom?


When one is doing mathematical work, there are essentially two different ways of
thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

While I am very far from being the mathematician, I understand that this basis is very important. Such summations in mathmatical design, leave a flavour, for conceptiual ideas to form in images, so I understand this as well. It is a progression of sorts I think, as I read, and learn. Geometry lies at the very basis of all such progressions in science?

So Feynmans toy models arose from the ideas of Dirac?

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