cam@edai.edinburgh.ac.uk (Chris Malcolm) (04/10/89)
I have heard a rumour that someone implemented a 4-dimensional modelling system, which permitted the construction of 4D solids, and viewing them (2D projections) on a video screen, on sufficienlty fast machinery that users could use joysticks or whatever to navigate around (shift the point of view as though moving) in a 4D world. The story goes that about half of the people subjected to this exploratory experience would exclaim, after less than an hour, "I see it! I can see 4 dimensions!" This would be very interesting if it were true - e.g., it would suggest that the brain is not built to "see" 3 dimensions, but simply (why do I keep using that word!) to make sense of n dimensional spaces, and 3 happens to fit nicely onto the navigable world. Can anyone supply references, pointers, corroboration or debunking? -- Chris Malcolm cam@uk.ac.ed.edai 031 667 1011 x2550 Department of Artificial Intelligence, Edinburgh University 5 Forrest Hill, Edinburgh, EH1 2QL, UK
eugene@eos.arc.nasa.gov (Eugene Miya) (04/11/89)
In article <5050@hubcap.clemson.edu> cam@edai.edinburgh.ac.uk (Chris Malcolm) writes: >I have heard a rumour that someone implemented a 4-dimensional >modelling system, which permitted the construction of 4D solids, and ^^^^^^ That is a 3-D term. If true this could be interesting, but I don't think it would involve much at this time. You have to be skeptical. >viewing them (2D projections) on a video screen, on sufficienlty fast >machinery that users could use joysticks or whatever to navigate around >(shift the point of view as though moving) in a 4D world. The story >goes that about half of the people subjected to this exploratory >experience would exclaim, after less than an hour, "I see it! I can see >4 dimensions!" Half is not necessarily statistically significant. We already live in a 4-D universe. >This would be very interesting if it were true - e.g., it would suggest >that the brain is not built to "see" 3 dimensions, but simply (why do I >keep using that word!) to make sense of n dimensional spaces, and 3 >happens to fit nicely onto the navigable world. > >Can anyone supply references, pointers, corroboration or debunking? It is argueable whether or not we can perceive 3 physical dimensions. CRTs and retinas are 2-D. What makes 3-D is the human brain working with two eyes, and the structure of the eye itself. Cartographers have worked centuries on the problem of projecting a 3-D globe onto a 2-D service. Mathematicians have worked decades to generalize on this. Simply "seeing" this is harder to believe than room-temperature fusion. ;) See, the people working in computer animation have produced some relatively slick animations flying thru terrain. The problem is these videos are useless as maps as people use maps. They can't tell you how far London is to New York, or Los Angeles to San Francisco. They don't incorporate multiple levels of information which appear on maps as they exist today. They are strictly geometric and temporally fixed in most cases as well. There are probably interesting mathematical techniques for thinking about it, but I don't have them right here (perhaps more appropriate for comp.graphics or sci.math). I am working on a 4-D system for relativistic efforts with a friend (on spare time). So I would be interested in references or other pointers, but I can't debunk without more information. So be skeptical. Another gross generalization from --eugene miya, NASA Ames Research Center, eugene@aurora.arc.nasa.gov resident cynic at the Rock of Ages Home for Retired Hackers: "Mailers?! HA!", "If my mail does not reach you, please accept my apology." Live free or die.
ECULHAM@gatech.UUCP (Earl Culham) (04/12/89)
>I have heard a rumour that someone implemented a 4-dimensional >modelling system, which permitted the construction of 4D solids, and >viewing them (2D projections) on a video screen, on sufficienlty fast > ... > >Can anyone supply references, pointers, corroboration or debunking? Sure. This was the plot of some hokey science fiction, published in OMNI a few years back. They even took it further, developing 4D music.
loren@ucbvax.Berkeley.EDU (Loren Carpenter) (04/12/89)
In article <5050@hubcap.clemson.edu> cam@edai.edinburgh.ac.uk (Chris Malcolm) writes: >I have heard a rumour that someone implemented a 4-dimensional >modelling system, which permitted the construction of 4D solids, and >viewing them (2D projections) on a video screen, on sufficienlty fast >machinery that users could use joysticks or whatever to navigate around >(shift the point of view as though moving) in a 4D world. The story >goes that about half of the people subjected to this exploratory >experience would exclaim, after less than an hour, "I see it! I can see >4 dimensions!" >-- >Chris Malcolm cam@uk.ac.ed.edai 031 667 1011 x2550 >Department of Artificial Intelligence, Edinburgh University >5 Forrest Hill, Edinburgh, EH1 2QL, UK Back in 1969-70 when I was working for Boeing in Seattle, we had 2 CDC 6600's (2-8 Mflop, 60-bit words). I had been wanting to visualize 4D shapes for some time. A friend in the systems group told me about a "graphics" program he had written that would plot dots on the operator's console (2 512x512 resolution stroke character displays) using the "period" (.) character. Well, there were 2 consoles on each machine; the one used for tape staging was free on weekends. So, the program I eventually wrote generated several 4D shapes: hypercube, hypersphere, 4-simplex (analog of tetrahedron), and the 3 flavors of 4D torus analogs. Shapes were modelled with about 2000 uniformly distributed dots. Controls included 4D windowing (slice of +- W), rotation in a plane defined by any pair of axes, 3D-2D perspective, translation along any axis, and a few others. All controls had a duration or velocity parameter (this was a keyboard, remember). Depending on the number of visible dots, the frame rate varied from about 12 to over 50 frames/second. Anyway, after playing with this for a couple of weekends, I reached the point where I could predict exactly what I would see before I typed any command. I'm not sure if this counts as 4D visualization, but it was certainly 4D "understanding". Someday I intend to do this again with a system that displays surfaces in real time. Loren Carpenter ...ucbvax!pixar!loren
tce@ann.MN.ORG (Thomas C. Evans) (04/15/89)
In article <5050@hubcap.clemson.edu> cam@edai.edinburgh.ac.uk (Chris Malcolm) writes: >I have heard a rumour that someone implemented a 4-dimensional >modelling system, which permitted the construction of 4D solids, and >viewing them (2D projections) on a video screen ... >goes that about half of the people subjected to this exploratory >... exclaim, after less than an hour, "I see it! I can see 4 dimensions!" > >Can anyone supply references, pointers, corroboration or debunking? Ten years ago or so Thomas Banchoff(sp?) of Brown University gave a presentation at the Mineapolis Science Museum on the presentation of 4D solids. They had a vector (wire form only) graphics system that would ask for source (4D) and presentation, (2D) and would work with standard solid shapes. He made films of rotating hyper-cubes about various axises and YES, I could "see" in 4d {{ how do know i couldn't? }} The frame of reference, line/square/cube/hyper-cube and the motion greatly helped in the comfort level of the seeing... Please post any current references. Thanks. -- Thomas C. Evans tce@ann.MN.ORG self is like insanity, 7138 Knox Ave S. tce@ann!uunet its hereditary and you MPLS MN 55423 {amdahl|hpda}!bungia!datapg!ann!tce get it from your children
news@PARIS.ICS.UCI.EDU (Network News) (04/18/89)
From: honig@bonnie.ics.uci.edu (David A. Honig)
Path: bonnie.ics.uci.edu!honig
Look up some of J.J.Koenderink's work (he is at the U of Utrecht in
the netherlands). He suggests we figure out the dimensionality of
spaces from topological (overlap) relations observerd.
--
David A Honig
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