X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f996b,aed89f7a2fcf37e8 X-Google-Attributes: gidf996b,public From: mariposa@ricochet.net (The Right Rev. Felix Roy Mariposa, Prophet) Subject: Re: HyperCube (Diamond Explained) Date: 1997/06/11 Message-ID: X-Deja-AN: 247788478 References: <339D4F82.1296@garnet.fsu.edu> <339E953B.51A8@garnet.fsu.edu> Organization: ULC Newsgroups: alt.ascii-art In article <339E953B.51A8@garnet.fsu.edu>, Michael Naylor wrote: > You may call time the fourth dimension if you wish, but it is no more > the "official" fourth dimension than, say, width is the offical second > dimension. In fact, if you've ever drawn a distance vs. time graph like > we all probably have in physics class, then you've designated time as > either the first or second dimension. It's all what you want to call > it. Ok, point taken. I should have said that the accepted convention is to call time the fourth dimension. >As for time being 90 degrees from length, width, and depth, well... > that's like saying that red is 90 degrees away from blue. If you drew > it that way on a color wheel, then fine, but make sure we have some kind > of frame of reference or the statement is meaningless. Again, I should have been a little more clear: as I remember learning it, each dimension is 90 degrees off from the previous one (with the first being an arbitrary frame of reference for the ones after it). So, if we call time the fourth dimension, then it is 90 degrees from the third dimension, which by convention would be one of the three spatial dimensions. > > The problem with this discussion, despite Michael's valiant attempt, is > that hypercubes are almost impossible to draw on paper/computer screens. ^^^^^^ > Michael's was a good start, but it takes a 3-D model to best show what > we're talking about. > Hypercubes are not impossible to draw on paper or computer or a > blackboard... we've just seen several examples. Unless you mean that > cubes and other 3-D objects are impossible to draw in two dimensions as > well, which you could argue. My point was that to really start to see this, you should see a 3-D model of what a hypercube might look like -- I've seen some pretty good ones, but not only is it beyond me how to draw them on paper, I couldn't even hope to ASCII 'em. > > > >That's why the hypercube is only a theory -- it SHOULD be possible, but in > >realistic, practical terms it doesn't exist. Outside of advanced math > classes, the best use of the hypercube is as an example of where logic > ends and common sense begins. > The hypercube is not where "logic ends", it is a very logical extension > of the concept of dimension. It exists as surely as any mathematical > object. I was trying to wrap my post up quickly, but since there is NOTHING brief about this thread, I'll go verbose... I use "realistic" as short-hand for the way we percieve the world, which is primarily in 3-D. We percieve time, too, as the fourth dimension, but in a far less tangible way, and DEFINITELY seperate from our three tangible, spatial dimensions. But according to physics, time and space are the same thing -- and the hypercube is an example of that. A solid object, with equal sides and vertices, that has four dimensions. In short, time made as tangible as the "spatial" dimensions. So, our sensory input, which is views space in three dimensions, doesn't reconcile with an object that can only exist in four-dimensional space. This is what I meant by "common sense" -- the way we're used to seeing the universe. But since the universe existsi in four dimensions (at least), hypercubes DO exist, but can't be percieved by our senses, which only see the universe in three. This is how I learned Hypercubes, at least... not in math class (oh, those many years ago), but in AP Physics (even more years ago) as an illustration of the 4-D universe. (I can anticipate a reply arguing that we can sense the passage of time -- well, yes and no. Yes, we sense the PASSAGE of time, but only as an infinite progression, not the same as the perception a spatial dimension, which time is no different from. So we sense time the same we sense distance by falling off a cliff.) Now if anybody mentions the fifth dimension, I will sharpen all 30 edges of a hypercube until they are razor-sharp, come to your house with it, and insert it in you. FRM "The Fifth Dimension? Didn't they get to Number 3 with 'Baby, I Want your Love Thing'?" -- Dave Lister, "Red Dwarf" -- Do you hate Spam in your e-mail? Don't just delete it, do something about it! Report incidents of Spam, and get the offender kicked off the net. Do this: 1. Check the header for the REAL domain name that the Spam was sent from -- often Spammers disguise their email address. 2. Send a forward of the Spam to their Postmaster. The Postmaster's address will be "postmaster@[domain name here]". Put the domain name from the header in place of [domain name here]. 3. Any reputable ISP will cancel the Spammer's account immediately. Fight Spam! Join CAUCE (Coalition Against Unsolicited Commercial Email) at http://www.cauce.org/ and tell your Congresspeople how Spam mailings hurt you. Help protect genuine Internet commerce: Outlaw UCE Spamming. (This anti-Spam signature is available rent-free. Use it as your own.) The Right Rev. Felix Roy Mariposa, Prophet mariposa@ricochet.net O- ULC <*>