Thursday, December 6, 2007

Numbers and Structures and Functions

In my previous post I had mentioned that there are structures which repeat but with differences depending on the dimension or sense (sight, sound, smell, touch, taste, and the yet to be established sixth sense). We are all familiar with points, lines, shapes from geometry, groups, rings, homomorphisms from Algebra and even things like knots, chaos and synchronicity. All of these structures are organized by what mathematics knows as functions which in turn are defined by numbers. For example time and space parameters are necessary to observe the phenomenon of synchronicity. Events, actions occur in the world. These actions occur in groups/simultaneously or independently. For example on a highway on would think there are cars more or less evenly distributed along its length. But in fact what is noticed is that as one is driving along, cars travel together in clumps, groups, and in between these groups there will be a few lone cars travelling on the highway. Depending on what the action is it can be seen (or not), felt (or not), etc. I wonder which sorts of numbers and which of these numbers are relevant and which structures organize this phenomenon.