apeiron
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wofsy said:Appealing to authority convinces no one.
That was a cite.wofsy said:There is no doubt that analysis is a pillar of modern mathematics.
Analysis is the thirdness that arises out of the mixing of the dichotomy of discrete~continuous - creating continuous geometry via discrete steps. You call it a pillar supporting something. I see it as the middle ground that forms from the mixing of two opposed metaphysical conceptual extremes.
wofsy said:As far as category theory goes I guarantee you that mathematicians do not even spend 1 second on it except maybe these system analysts who I don't know anything about. We call it "abstract nonsense". There is a deep unity to mathematics. But category theory has nothing to do with it.
Interesting. Perhaps you can appeal to...err, I mean cite some authority for such a definite view. Such statements really convince me you have no idea what you are talking about.
Meanwhile go argue with these guys...
http://plato.stanford.edu/entries/category-theory/
Category theory has come to occupy a central position in contemporary mathematics and theoretical computer science, and is also applied to mathematical physics. Roughly, it is a general mathematical theory of structures and of systems of structures...Category theory is an alternative to set theory as a foundation for mathematics. As such, it raises many issues about mathematical ontology and epistemology. Category theory thus affords philosophers and logicians much to use and reflect upon.
wofsy said:One last point - much of early algebra can be derived directly as theorems in Euclidean geometry. When I taught algebra and trigonometry I taught it using Euclidean geometry proofs. It is something of an illusion to think that all of algebra is separate or even different from geometry. In a certain sense there is only geometry and analysis.
That is the point. Two languages for describing the same thing. The descrete can be used to describe the continuous (via additive construction). And the continuous can be used to describe the discrete (via a process of downward constraint).