Consider the construction of a Mobius strip. Take a strip of paper, give it a twist, and connect the ends. Now, starting at the seam, trace a line along the length of the strip. Curiously, the line will be on both sides of the paper before it eventually meets back with itself. What this amounts to is that a 1-dimensional line going in a single direction on a 2-dimensional strip will loop back to itself without ever having left the line, and without ever noticing that the strip has been twisting and turning in 3-dimensional space.
Now consider this analogue. I am a 3-dimensional figure moving through 4-dimensional time in a single direction, but there is this possibility that time is actually taking a tortuous route through 5-dimensional space without me ever noticing. The existence of five dimensions would allow for me to loop back to myself on occasion, without having to leave the seemingly unidirectional path of time. This is a much less scientific and much more romantic way to mull over the origin of memories, and for the religiously inclined, of reincarnation.
Reality is much, much more than can ever be conceived.
PS. Ruminations on the Klein bottle next time.
Friday, August 28, 2009
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4 comments:
Is it weird that I was confused before I got past the first paragraph?
I don't think you needed the Mobius strip to make the point. On a circle, you could have just talked about a 0-dimension point going in a single direction on a 1-dimensional line. And just like your example, the curvature in 2-space is not noticed.
Interesting concept about time though. I've never thought of it that way. I wonder how this can be analyzed mathematically, considering the "dimensions" we're using are not orthogonal. The closest thing I can think of (with my limited geometry background) is integrating over a line, so it appears as though it's just one dimension.
On a different note, what would it mean to be back at the original point?
I like the idea that arriving at the original point would be like the universe "restarting" itself. It expands from a point, grows, then eventually collapses back to a point to start the cycle over again. I feel like this violates certain principles of entropy and uncertainty, but it has always attracted me.
Justin, you're right about the simpler example of the circle. It's just that I happened to be recently reading about Mobius strips (and Klein bottles).
The only thing about being able to loop time back around is that developments that happen throughout time cannot be undone, since, again, time is unidirectional. I have no idea what this would imply, or even how to begin thinking about this.
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