Wednesday, March 23, 2016

The idea of a simplex

Simplicial: from or of simplex, a simple shape like a triangle; a triangle, a connected three-sides, is an example of 2-simplex, that is how we learned to draw a triangle on a piece of paper. From three vertices, we can create at most a triangle, a 2-simplex. In three dimensions, we can trace with four vertices, a tetrahedron, also called a 3-simplex. In four dimensions, we will have a 4-simplex, think of a 3-simplex with one vertex located in a dimension of time. Our idea of spacetime, a mathematical structure of four dimensions, three dimensions of space, and a fourth one for time can also be similar to a 4-simplex. Of course this is an approximation. There a lot of technicalities involved for example when you make a statement like: spacetime is a 4-simplex! If you could really prove that consistent across physics and mathematics, then you have done a lot. Here, I am interested in the relational aspects of simplexes (or simplices) extended to higher dimensions. By higher dimension, I am not necessarily talking about hyper space or a super space, your typical Excel table of M rows by N columns is already a multi-dimensional space. Ron Atkin was a British mathematician who explored this kind of thinking and wrote about them. I will talk about his work and my ideas on this blog. I think he was way ahead of his time! Strangely, he is not well known outside of his immediate community.

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