Thursday, September 07, 2006

Buddhism and Category Theory

In my previous post today I mused about using standard ontologies in programs as a way of grounding the web of connections between your objects in a framework of common terminology.

There is a concept in Buddhist metaphysics called , which states that nothing exists on its own, but only manifests itself through its connections with everything else in its environment. One illustration of the concept is Indra's Net, an infinite spider web with little silver balls at all the junctions, each reflecting all the others in a way that would gum up any ray tracer.

A program that doesn't refer to much of anything external to itself is like that -- you can define data structures and pointers and files that all point to each other, but it's all meaningless without the interpretation that a programmer or user gives to it in the data they feed to it and their interpretation of its output.

I'd say that is a mathematical restatement of Dependent Origination.

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gaspaheangea said...

Yes, yes, yes!

Marc said...

Of course, dependent origination is crucial in category theory.

Consider the following example: topological spaces (other than the empty set) can be thought as pointed -- with a distinguished basepoint. Requiring this point only excludes the empty set, but the category of topological spaces is much different than the category of pointed spaces: for instance, the coproduct in Top is disjoint union, but it is wedge sum in pointedTop!

The moral: the environment of an object affects its possible behaviors.