From: Eric Armstrong <eric.armstrong@eng.sun.com>
Jack Park wrote:
>
> Robert Rosen followed his teacher N. Raschevsky at Chicago in the 50's
> with the idea of a Relational Biology. Raschevsky (one of the fathers
> of mathematical biology) started with graph theory, graduated to
> organismic set theory, then passed away. Rosen took that work to
> category theory -- a mathematics of the relations amongst components.
> He brings back the 4 Aristotelian causalities and ties everything
> together with category theory. The book, Life Itself (and a new one
> published just after his death, Essays on Life Itself) discusses and
> develops this mathematics -- at least, to the level of a theoretical
> understanding. Nobody, to my knowledge, has managed yet to map his
> thinking to, say, the mathematics of a single-celled animal.
> There's a helluva lot of thinking going on in that direction, however.
>
> The more I read, the more I discover that things really are related,
> and it is the mathematics of those relations that jumps beyond my level
> of mathematical maturity. Simple relational algebra seems a place to
> start, but discovering the topology of those relations is something else
> again.
>
Wow. That is exciting, exciting, stuff.
Early on, I posited the potential need for a "knowledge mathematics"
that lets us abstract our knowledge and manipulate it. At the time,
I had no idea how much work had been done in Ontologies. Now this
comes along. A "mathematics of relationships" might well be the key
to abstract "understanding".
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