“I think I’m hyper enough as it is. I think I’m hyper enough!”
--Superchunk
Hello Will! Sorry to leave you hangin’ like that, but I’ve been a little diZzy lately. 
I think that maybe it’d be better if we put aside some of that diZzy nonsense for now and instead perhaps we should start with the basics of geometry, and we’ll weave in some “brain stuff” as we go along:
0: the dimension of the singular point.
1: the dimension of the line (x).
2: the dimensions of the plane (x, y).
3: the dimensions of space (x, y, z).
Now it’s interesting to note that the singular point doesn’t have any existence, because it has no dimension in space. Points are, in some sense, ideal, and most people would agree that we don’t interact with points at all. However, if we collect enough of these points together, we get our good old friend the line (an infinite number of points for any length of line!). Now lines are ideal too, but yet, our senses make some of the things we interact with close enough to lines, that we call them lines, like the line that is the edge of this desk, ya?
Moving to the surface of this desk—the dimension of the plane—we have, in our ideal mathematical sense, an infinite number of lines stacked one over the other. And perhaps some of us might be surprised to know that the same number of points that make up a single line (an infinite number) make up the whole (x, y) plane. It is in the plane that we trace out the basic shapes: triangle, square, circle, etc. Some psychologists tell us that the brain builds our visual experiences of the world starting with these shapes as the ‘wire frames’ for more detail to be added as more of the received sense data becomes interpreted. We do receive all our visual information through the retinas and these are two dimensional screens, so I guess that makes sense, ya? We might find these shapes uninteresting, but there is a marvelous tale about A Square, related to us by Edwin A. Abbott.
From here we stack planes one atop the other to make our three dimensional space. This gives us the traditional Platonic Solids. Again, the very same number of points that make up the whole of the largest (x, y, z) space you can imagine also made up the lonely (x) line of any length. Now by some sorta’ magick (read: < shrug? > ) our brain takes the sense data that we receive and builds the space that we perceive around us as three dimensional at any given moment. But if we start stacking moments one atop the next, then we enter into
4: the dimensions of spacetime (x, y, z, t)
Now it seems to me that duality plays a role in our orientation in these four dimensions: we cut up the world into left/right (x), forward/back (y), up/down (z), and past/future (t). All together, this forms the (x, y, z, t) spacetime that we experience over the course of our lives. And now for your viewing pleasure (break out those red/blue 3-D glasses), here is a rare glimpse of A Square’s 4D self. Granted, to the hypercube, the fourth dimension is only another spatial dimension, but to us, the fourth dimension seems to be temporal.
But, in general, we only experience the dimension of (t) a point at a time—the Now. We do not usually perceive a whole series of moments—a line of time, our whole day perhaps, all at once; rather, we seem to take it one bit at a time. This is odd in contrast to the way we experience the (x, y, z) as extended, whereby that I mean we appear to gather up, with our senses, a whole collection of the points that make up our environment at any one moment. Yet our life traces out a line of collected (t) points from beginning to end.
I hope this is a good place to start. Any comments, questions or what-not about any of the above?
With this as a starting point, anyone with any thoughts on what the fifth dimension might be to us?
23 + 10 = 0 (mod 3)
[ 14-02-2002: Message edited by: modthree ] |
