> 4. Perhaps even more strangely, but more practically, there may be some
> very interesting uses for Cypherpunks visions. Weirder than Baez,
> weirder than Egan...in some ways. The basic insight is that just as
> category theory is about "objects/things" (called categories) and the
> "transformations/functions" (called arrows) between them, this is what a
> lot of crypto protocols are. (Note that I'm not explicitly talking about
> object-oriented programming, a la Java or Smalltalk, but more about
> viewing crypto protocols are transformations.)
Category theory is nice, but would be nicer if could draw in
information theoretic and cognitive metaphors. Maths is a programming
language selected over time for execution on (perhaps slightly
modified) human brains. The failure to recognize this deeply held
anthropomorphism is excusable in other areas of mathematics, but
not in foundational studies. Human beings look at the world through
their own mental "axioms" which have evolved to understand the
physical world and each other. These axioms must be chased down
and stated instead of allowing them to subtly invade the mathematical
process. For category theory, this failing likely evolved from
its birth as a theory of mathematical classification as opposed to
a theory of _origin_, although to be fair no foundational theory
seems to be free of it.
...
About 15 years ago category theory leaked into programming language
design. See http://www.haskell.org/ and http://www.ocaml.org/ (yes,
thats me) for the two major real-world-useful category theory
inspired languages.
OO programming is classification from above. Classification
comes first and is then acts as (an often inconsistent and poorly
realized) behavioral constraint. For category theory inspired
languages, classification (types) are inferred from _behavior_. For
these languages, behavioral inconsistency is discovered by the
inability to come to consistent classification which describes it.
--
Julian Assange |If you want to build a ship, don't drum up people
|together to collect wood or assign them tasks and
[EMAIL PROTECTED] |work, but rather teach them to long for the endless
[EMAIL PROTECTED] |immensity of the sea. -- Antoine de Saint Exupery
