Friday, January 20, 2012
This was an idea discussed in Imagining the Third Dimension, and I'll end today's blog with the video for that entry for those of you who haven't watched it yet. This speaks to how easy it is for us to forget that "time" is part of what we're looking at every moment, so seeing space by itself is really impossible - the space we're looking at has to have a duration or it's not possible for us to see it.
With the way this poll question is phrased, it seems to me that it should be an open-and-shut case, but nearly one out of every five persons answering this poll question don't agree. Is it possible to ask this question any more simply? If the third dimension is space without time, and the fourth dimension is space with time, how can we talk about the third dimension by itself? In other words, how can we view anything in the third dimension without taking a certain amount of "time" to do so?
A way out of this conundrum would be to suggest that we're assuming that an abstract object like a 3D cube has infinite duration: like the original description of a meme as defined by Dawkins, the cube would then be an information pattern which can be transmitted across time and space, from one mind to another, instantaneously. Does that mean that it would be safe to assume that a 2D object has infinite duration in the third dimension, and that's how we would be able to see and talk about such an object? If we're talking about abstract forms similar to a plane or a cube, that reasoning follows.
But what about 3D objects like a human being, or a planet? Clearly, they don't have infinite duration, they have a point where they start to exist, and another point where their existence ceases. This, then, is where we can get into difficulties of language. If I say "this is a cube", am I referring to an abstract concept, or am I referring to a physical object like a child's building block? "This is a cube" could apply to either, but the two have very different expressions within the dimensional constructs that we're exploring here.
This confusion continues as we add dimensions: a tesseract is a four-dimensional hypercube. If I say "this is a tesseract", what am I referring to? A concept? Or something that really exists as an object which has a specific duration within the fifth dimension? Therein can lie some of the pitfalls of language - we need to make it clear which interpretation we're using, or these discussions can sometimes seem contradictory.
A direct link to the above video is at http://www.youtube.com/watch?v=-D4swzK4sKk
So remember - the next time someone tells you the second dimension can't exist because something with no depth is impossible, tell them the third dimension has the same problem. If you're talking about something that has length, width and depth, but no duration in the fourth dimension, then that would be impossible for us to see. And clearly, what you and I are a looking at right now with our eyes and their "3D" atoms and molecules, is something larger than the third dimension.
Enjoy the journey!
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Posted by Rob Bryanton at 6:57 AM