From: bryson@nas.nasa.gov (Steve T. Bryson)
Subject: Re: VR theory?
Date: 16 Sep 91 17:49:23
Organization: Applied Research Office, NASA Ames Research Center



In article <1991Sep16.172930.3699@milton.u.washington.edu> esz001@cck.
coventry.ac.uk (Will Overington) writes:

   In article <1991Sep12.181705.17181@milton.u.washington.edu>,
   tbm19061@uxa.cso.uiuc.edu (Thomas B MacIukenas) writes:

   >How about other types of Virtual Reality than just copies of our
   >world?  It seems that all the work in Virtual Reality is really
   >focused on producing a Virtual Copy of Reality (hence the need
   >for 3-dimensions, tap-dancing on airplane wings, etc.).
   >
   >Here are some ideas I've had.  Probably none of them are actually
   >useful, but they would be interesting to explore:
   >
   >     4 or more dimensions

   I have just returned from holiday and so missed the start of this thread,
   but your suggestion of 4 dimensions is interesting and links to
   something that I was going to try to find out about.

   I was recently looking through a report from the (British) Science and
   Engineering Research Council, entitled Mathematics, strategy for the future.
   June 1991, ISBN 1 870669 32 0.

   On page 8 of the report is the following ....

	Seemingly abstruse recent pure mathematical results in geometry and
	topology concerning the existence of certain kinds of structure in
	four-dimensions (but no other!) have proved to be of enormous interest
	to theoretical physicists probing the ultimate mysteries of space and
	time. As a result there is now intense activity at the interface of
	physics and pure mathematics, in which UK researchers are playing 
	leading roles.

   Does anyone know what these structures are, and whether they could
   be vizualized and manipulated in some sort of virtual reality?


First, a reply to Thomas...our world really is four dimensional, so exploring
four dimensions would be just more copying of reality :-)

Seriously, though, it is no big deal to work in four or more dimensions.  
I'm doing it in my VR work here, and many people in the field of scientific
visualization are doing the same.  On the other hand, your point is well 
taken that we should be showing considerably more imagination in our design
of virtual worlds.

The structures in four dimensions quoted by Will are, on the other hand, a
very big deal.  They are also very difficult to understand, and I've wondered
for some time if clever graphics could be useful in fleshing them out.
Note that this is not really a VR issue, but a visualization issue.  These
structures are very hard to describe, and were discovered primarily by
Mike Freedman and others about 1981-1982.  Basically, they say that the
geometry of four dimensions may not be anywheres near as simple as we thought.
I was fortunate enough to take a class taught by Freedman on this topic at
Berkeley about this time, and it was very hard to follow what was going on.
There are two books out on the subject, neither of which are for non-
mathematicians.  I'm not sure of the titles but am sure of the authors:
"The Topology of 4-Manifolds" by Freedman and Quinn is probably the simpler
(but not simple!!), and "The Geometry of Four-Manifolds" by Donaldson and 
somebody is the harder book.  

I'm going to be at Viz '91 in San Diego, which is where Mike Freedman is.
Maybe I'll ask him if he has any ideas about visualizing this stuff...

Steve