Tuesday, September 08, 2009

Cantor and Spatial Dimensions

God made space; the rest is the work of man..

Georg Ferdinand Ludwig Philipp Cantor revolutionised our concept of space. One line has the same number of points as a square, or any dimensional object. This comes about when numbers are put into one to one correspondence with elements of infinite sets.

Besides the logical paradoxes uncovered by thinkers after Cantor, we have here a precise construction of multidimensional space. I am more certain about what I understand, than about a space that my senses do not allow me to navigate, be it because there are tiny turns and holes, or because they are made of dark matter that has a very weak interaction with the baryons and leptons I am made of. Those same elements generated in the high temperature ovens we call stars.

Math has and can direct us in our quest of what space is.

fMRI and other medical scanning tools can help us now to understand the neural phenomena that I believe, to the last analysis, will teach us how is it that we construct this three dimensional space that we learn at school.

I feel that we haven't heard the last word on the dimension of space, the nature of the continuum, and several other open ideas that so far we have been smart enough to ask, but not smart, or wise enough to answer.

The Universe is as interesting as it can be.

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