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Caveat: I prolly sound a bit dogmatic, but these are only my opinions, which i'm not trying to force down anyones throat though it may sound like it. It's just my way of writing.
Time is seen as a fourth imaginery dimension, in the sense of the imaginery part of a complex number.
Distance in euclidean 3D space between two points is measured like this:
dist = sqrt((p1.x - p2.x)^2 + (p1.y - p2.y)^2 + (p1.z - p2.z)^2)
Distances in the space-time continuum are measured thusly:
dist = sqrt((p1.x - p2.x)^2 + (p1.y - p2.y)^2 + (p1.z - p2.z)^2 - (t1 - t2)^2
Notice the minus sign before time. It implies that if you're at point p1 at time t1 and want to get to p2 at t2, then you don't have to go as fast if you have ample time. ie, the distance is less in the space-time continuum.
Time as the fourth dimension is basically just a mathematical gimmick
to make some relativity equations easier to work with.
A fourth dimension in the mathematical sense is nothing special either. Basically you can say that the heat at point p1 (x,y,z) is the fourth dimension, if you feel like. Then if you get a temper, you're moving through the fourth dimension (from 37° centigrade to, say, 40° centigrade).
It's only if you insist on having the fourth dimension an actual physical dimension that you start getting into trouble :-)
And even then, mathematics can take care of that easily enough. It's just how it would work in the actual physical world, and visualizing it, that's problematic.
here's a non-link to a rubik cube in 4 dimension, represented in 2d, using perspective to fool you into that it's represented in 3d. It's mathematically sound and actually gives you a rather good abstract sense of the way rotation works in 4d ("rotating in a direction we don't have a name for" -invisibles).
http://www.hadron.org/~hatch/MagicCube4dApplet/
To try to answer some of those questions:
1. Thoughts and emotions in my experience don't have spatial dimensions at all, though the fact that we live in a 3D spatial world very much affects the things we *can* visualize. (though not think about). I think thoughts are more or less n dimensional, much like music is 2-dimensional (time and amplitude). Though there are implied multidimensions both in music and thoughts (frequency is just amplitude going up and down, melody is modulated frequancy).
Thinking about this, I feel like thoughts and music are n and 2 dimensional, respectively, but can have infinitely big fractal dimensions. I really can't say what number n is but for me it's usually 3, i.e. I think in 2d images moving over time, though this varies sometimes. I have been able to get a sort of visualizable flash of insight in 4 dimensions, when I had been thinking about quaternions(*) for over a month for 8 hours a day.
Emotions are multidimensional in a way, though people have different opinions about which axises make up the dimensions. I don't think that thinking about or visualizing them in 4 dimensions makes any difference at all, since I believe they have a higher dimension than that. But I think they are multidimensional only in an abstract sense, like the (x,y,z,temperature) example, not in any spatial sense.
So my answer to 1. is prolly: they don't.
2. stories are much like music, you can represent them in two dimensions, ones and zeroes one after another. However stories can invoke as many dimension as the skill of the storyteller and the imagination of the listener allow. If you make a story it becomes. If you write down a story on a piece of paper you're changing it's representation from a stream of (un)concsiousness to some squiggly lines on a 2D surface. If you'd somehow imprint the same story onto a 4D shape, you'd be changing it's representation to 4D. The story would remain the same though a 4D being might be able to grasp it all at once instead of getting it linearly. It'd be like speedreading, only better :-)
But I think the story itself, the information, never becomes solid, except in a metaphorical sense.
3. To reverse this question, what would a 4D being look like to us? If we use the mathematically sound analogy that it would be similiar to a flatlander seeing a 3D being it, we would see a 3D cross section of the 4D being.
Let's first take the simplest case, the being is a 4D hypersphere. A 3D crosssection of a hypersphere is simply a sphere. But depending on where it was located in the fourth dimension, it would change in size to us, or just disappear. It's pretty easy to picture, a 2D crosssection thru a sphere is just circles of varying sizes, if the crosssection doesn't go through the sphere, it appears as if there's nothing there.
A slightly more complicated shape is a 3D sphere that's bent like a horseshoe in the 4th dimension. What does a 2D crossection through a horseshoe look like? one to two ellipses, depending where the crosssection is taken. So such a being, moving a bit in the fourth dimension would look like two floating spheres, constantly changing sizes and positions, sometimes morphing into one, sometime disappearing completely to reappear elsewhere.
If we imagine something like the human body, but in 4D and how that would look like to us, it's would prolly be an amorphous bloody mass, changing to a white bone, becoming a gallbladder all of a sudden and being in manymany places at once, shifting. Think Lovecraft.
How that being would see us. We'd be flat to it. It could look at us just so, and we'd disappear from it's sight, like looking at a piece of paper on the edge. It could look at us from *this* direction and see our liver, touch it without us noticing a thing, move it's head a little to the akhgakn and see our heart instead. We'd be like a layer of skin, muscles, nerves, bones, innards, all spread out over the fourth dimension, though it would have a coherent structure.
4. It would see a colored line. If it had two eyes it would see two slightly different colored lines superimposed over one another. If it would move in a cirvle around the other one, the lines would change, and it could infer the other's shape from the way the lines changed when it moved. |
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