ONT Re: Higher Order Categorical Logic -- Discussion
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HOC. Discussion Note 12
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JA = Jon Awbrey
JP = Jack Park
Re: HOC Discussion 3. http://suo.ieee.org/ontology/msg05264.html
In: HOC Discussion. http://suo.ieee.org/ontology/thrd37.html#05262
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.
JA: 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.
JA: 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.
JP: If you visit:
http://www.people.vcu.edu/~mikuleck/PPRISS3.html
and scroll down just past mid way,
you will see 10C6 drawn and discussed.
jack,
this is bizarre! i was just now thinking about all the
old chestnuts about (ill, well)-posedness in connection
with the topic of information that was recently revived
on the global brain list.
okay, this helps. on looking into mikulecky's rosen, i begin
to remember that picture of the "modeling relation" and some
of the discussions that we had about it. mostly i remember
a passel of misencounters of the usual 2-adic/3-adic kind.
will get back to this ...
jon awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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