Fourth dimension
This post is not about math, it is about how I perceive the world.
I know, fourth dimension is easy, for example you can easily create vector v=(1, 2, 3, 4) … but somehow, this is just numbers and tricks, I can’t really feel the fourth dimension. I recently had some free time to think about random stuff, and, well, I thought about this:
Let’s start with: 1 = x² + y². As we all know, this equation draws a circle.
The next step consists of substituting the one for another variable: z = x² + y². Now we get one more dimension. Although it might not be completely clear on the first sight, this is paraboloid. If we assume z is a variable that we can set to anything we want, different values of z create different circles (z is the height at which we cut the paraboloid to get that particular circle).
We had a circle already, so let’s bring the circle to the third dimension and make a sphere: 1 = x² + y² + z²
Now, what do we get when we make the transformation we made in the first step – substituting the one for yet another variable?
w = x² + y² + z²
I don’t know about you, but I can finally feel the fourth dimension within my reach. 
While I don’t know what exactly this “w = x² + y² + z²” looks like (neither know what it is called, for that matter), I can see that there is precisly the same relation – the same way circle is one “slice” of paraboloid, sphere is one “slice” of w = x² + y² + z² (for some concrete set value of w).
Posted on 2007-08-07 at 12:42 am, filed under random thoughts. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.
Well, it sbould be some kind of … ehrr … something, right?