On Fri, Jul 29, 2011 at 9:03 AM, Wesley Smith <[email protected]> wrote:
> > I like to think about simplicity as coming up with the right core > abstractions and the optimal way to distribute complexity among them to > support a large set of use cases. > > > This phrase comes up so much when talking about computational systems > that I wonder if it can be made more tangible. It would be really > interesting to see different sets of abstractions and some > representation of the computational space that they cover. > > So far, the only material I've seen that might possibly be applied to > such an approach are things like Synthetic Topology, which from what I > understand is a generalization of topology from a category theory > perspective. Has anyone here worked with the concepts of synthetic > topology? Anyone actually understand it? > > http://www.cs.bham.ac.uk/~mhe/papers/barbados.pdf > We had a discussion on the FONC mailing list, around March 2010?, that touched upon different ways of viewing complexity in a system. One person gave an example using two pictures from a famous system's theory book, another argued for Gelman's effective complexity metric, and so on. (I think you may have replied to this discussion.) There are many examples in computer science where two different logics, algebras or calculi are required to have a complete definition of a system's properties. Axel Jantsch has some interesting examples in a book of his I own.
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