The Fourth DimensionDate: 8/24/95 at 17:38:37 Date: Thu, 24 Aug 1995 17:38:35 -0400 From: Anonymous Subject: Fourth dimension Question: What is the fourth dimension mathematically? Date: 8/25/95 at 13:49:57 From: Doctor Ken Subject: Re: Fourth dimension Hello! Well, there are several ways one might interpret things in four dimensions. Sometimes it's convenient to think of four dimensional space as three of ordinary space and one of time. That's the way that most non-mathematicians know about. What a lot of mathematicians like to think of them about though, is to make them all spatial dimensions. You can build them up from the bottom: If you have one dimensional space, you can only move in one direction, i.e. along a straight line: <---------------------------------------------> When we add another dimension, we usually think about it as perpendicular to the ones we already have. So if we add one here to make 2-d space, we have a plane: ^ | | | | | | | | | <-----------------------|----------------------> | | | | | | | | v To make three dimensional space, you add one perpendicular to both of these, that would stick straight out of the page (here's a perspective version). ^ | / | / | / | / | / | / | / | / |/ <-----------------------|----------------------> /| / | / | / | / | / | / | / | / v So where do you go from there? Well, you'd add another dimension perpendicular to these three. We can't visualize it, because all we know is three dimensions, but that's what you would do. You then represent points in this space with four coordinates: three vectors in four-space that are all perpendicular to each other would be (1,0,0,0) (0,1,0,0) (0,0,1,0) (0,0,0,1) Don't blow your brain up trying to think too hard about this! -Doctor Ken, The Geometry Forum |
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