[Inquiry] Re: Higher Order Categorical Logic -- Discussion
jawbrey at att.net
Wed Jan 7 11:20:44 CST 2004
HOC. Discussion Note 3
JP = Jack Park
JP: My sentiments, precisely.
JP: I must say, however, that the book 'Conceptual Mathematics:
A first introductiton to categories' by F. William Lawvere
and Stephen H. Schanuel really do start out simple diagrams,
spreadsheet tables, and real-world examples worked out to
introduce the concepts. I'm getting a lot from it.
yes, that's a good book. the reason for tackling the lambek and scott,
though, was because of the connection they make to logic and computation.
JP: What I have asked for is something akin to some real-world problem.
One that's, at once, simple, and potentially hairy, one that can start
simple and grow like mad. Rosen introduced a "metabolism-repair" object
as the canonical living organism that his teacher Raschevsky was looking
for. When he drew it as a commutative diagram, he noticed that reproduction
fell out for free. I'd like to understand how that can come to pass. Then,
I'd really like to imagine or learn how to take the nodes in that commutative
diagram and expand on them, turning them into some higher-order organism with
real, functional, relational components. In the end, I see that as a prototype
for a lot of real-world things, like social systems, diseases, and everything
that's not driven by pure newtonian mechanics.
can you draw me a copy of this here, or supply a link?
i only looked into rosen once many years ago, and have
hysterical amnesia for my time on the complexity list.
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