Archive for June 9th, 2011

June 9, 2011

A mathematician’s take on phenomena

by Neil Rickert

This is, in part, a response to the recent John Wilkins blog post “More on phenomena.”  It is based on my ideas on human cognition and human perception.  Unavoidably, this will be a tad mathematical.  However, I will avoid getting into technical terminology to the extent that I can, though I’ll give enough as hints to the mathematical literature for those who want to pursue the underlying mathematics.

Think of the world as a topological space, call it W.  (For the mathematicians, I am taking W to be a normal Hausdorff space).  Because W is a topological space, we can think about continuous functions over that space.  So for a point x in W, and a continuous function f, there is a value f(x) for that function at that point.  For technical reasons, mathematicians usually take their continuous functions to have values that are complex numbers.  However, I suggest thinking about them as functions with values that are real numbers.

If we look at this in terms of science, then we can think of the function f as a method of measuring, and we can think of the value f(x) as an actual measurement (or as a datum).

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