Friday, February 10, 2012
"Phase Space" is definitely a phrase I wish I had known about back when I created this project, because its definition conveys so perfectly what we're talking about with not just the sixth dimension, but all of the dimensions as we're visualizing them here. Each dimension has its own unique set of possibilities, each is apparently infinite, and yet each is also a subset of the ones that follow.
If the "point" we start from represents a position within a system, then the "system" defines the nature of each of those points. Many times people visualize a point as only being of infinitesimally small size, which is valid but it's only one possible interpretation: so even a single geometric point, by virtue of being of indeterminate size, has an infinite quality to it, since a point of indeterminate size can be of any size you care to assign to it. So no matter what dimension you're visualizing, there's a way to think of a point within that system as encompassing the entire dimension, while still being only a subset of the possibilities contained in a system where further dimensions are added. Is that hard to visualize? Let's try it from the beginning.
A one-dimensional line is a simple system, which can have a phase space of possible states, or points, that lie upon the line. A two-dimensional plane would have a phase space with even more possible states, or points, that lie within the plane, and the phase space of the first-dimensional line we looked at could be a tiny subset of the second-dimensional phase space. This continues with each additional dimension, and the mind-boggling leap in possibilities from one dimension to the next quickly overwhelms us if we try to hold more than a few adjacent dimensions in our minds at once. Nonetheless, taking this logic one step at time, building one gigantic concept and then letting it become a tiny subset of the following one, is something our brains are more easily adapted to.
The video for Imagining the Sixth Dimension may help you to visualize further what we're talking about here, so for those of you who haven't seen it yet, let's take a look:
A direct link to the above video is at http://www.youtube.com/watch?v=OdnhKE95AqM
Enjoy the journey!
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Posted by Rob Bryanton at 3:50 AM
Labels: phase space