An addendum on the highly intriguing diagram with the arrows
connecting three mathematical concepts: Formal Systems, Mathematical
Structures and Computations. I think you're definitely on to something
big with that intriguing diagram but you need to get it exactly right.
I don't believe that this is a complete classification of mathematical
concepts. What is missing are the concepts from probability theory:
things like Probability Distributions. Also (as I pointed out in my
last post), the term 'Mathematical Structures' should really be spit
in two: you could distinguish between specific Algebraic structures
and the most general structures from Category Theory. My own diagram
has SIX of those circles.
You've made some intriguing preliminary attempts to show the
relationships between the various mathematical concepts but I don't
think you've got them right yet. For instance (as I mentioned) I
think computations are special cases of formal systems. (*not*, as
you have in your diagram, special cases of mathematical structures).
I would be particualrly interested to hear what Bruno has to say about
that diagram and the nature of the relationship between the various
mathematical concepts.
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Received on Sun Apr 22 2007 - 02:36:03 PDT