jbn@SU-GLACIER.ARPA.UUCP (05/18/86)
There are some ideas worth pursuing here. There is a class of
problems for which solid geometric modeling, rather than predicate
calculus, seems an appropriate underlying model. The hook and ring
problem seems to be of this type. Alex Pentland at SRI has done some
work on concise mathematical representations of the physical universe,
and I suspect that a system that could manipulate objects in Pentland's
representation, calculating interferences and contacts, driven by various
search strategies, would be an appropriate way to attack the hook and
ring problem.
One can dimly imagine a solid geometric modelling system with
approximate representations a la Pentland ("fuzzy solid modelling?")
enhanced by some notions of force, strength of materials, and inertia,
as a base for working on such problems. Unlike the Blocks World and
its successors, where the geometric information was transformed to
expressions in predicate calculus as soon as possible, I'm suggesting
that we stay in the 3D geometric domain and work there. We might even
want to take problems that are not fundamentally geometric and construct
geometric analogues of them so that geometric problem solving techniques
can be applied. (Please, no flames from the right brain/left brain
crowd). Has anyone been down this road yet and actually implemented
something?
Interesting thought: could the new techniques for performing
optimization calculations being developed
by the neural-nets people be applied to the computationally-intensive
tasks in solid geometric modelling? I suspect so, especially if we are
willing to accept approximate answers ("Will the couch fit through the
door?" might return "Can't be sure; within .25 inch error tolerance")
some of the closed-loop feedback analog techniques proposed may be applicable.
The big bottleneck in solid geometric modelling is usually performing the
interference calculations to decide what is running into what. The
brain is good at this, and probably doesn't do it by number-crunching.
John Nagle
415-856-0767