Friday, October 8, 2010

Higher Dimensional Thinking

So,...  I waste approximately too much time with this stupid plug-in called Stumble-Upon.  You give it some categorical preferences for information, it supplies Stumble! button which takes you to some random webpage which has been categorized by users as belonging in said category.  I, for example, have indicated I like information about math/science, DIY projects, anthropological information, etc.  My Stumble! button takes me to websites like physorg, this old house, make, phdcomics, etc.

Recently, when I whacked the ol' Stumble! button, it took me to a page about the possible dimensions of reality.  I generally find some of these types of discussions interesting, and reading through I found that I was up to date on most of his background material.  Then he starts spouting crap, which to my feeble mind seems like the tried-and-true, but it occurs to me that his #1 bullet point, the 3D nature of our universe is fundamentally lacking.

Lets say, for arguments sake, that you're an engineer and have studied dynamic systems extensively.  How many co-ordinates are required to describe the location of an object in space?  Ah.  3.  Excellent.  Good work.  What about if you want to know everything about the physical space of the object?  Now you need 6.  Huh?  3 for locating the object, and another 3 for determining the orientation. 

Why does the orientation matter?  Let's say you are located in a long dark train tunnel, and a train, also located in the long dark train tunnel, is tooting along towards you.  You start to run, but your orientation has been left undefined.  Where are you running?  Are you running toward the train, the wall, flailing to run straight up in the air (and not making it, b/c we included gravity in our scenario)?   Let's fix two degrees of your orientation so you are looking at the tunnel exit.  Now, are you right-side-up, upside-down, or lying on your side?  So, now, without your orientation being fixed in three degrees, you won't be able to scoot out of the tunnel in order to live another day and think about high level geometry ideas.

"Ah!" you say, "this is just a short-coming of thinking about the object in terms of dynamic systems, no?"  Well, what's your argument?  "If you were to think of the object as a bunch of small objects, i.e. atoms, then locate all the atoms in space in 3 coordinates, the orientation takes care of itself, Q.E.D!" 

Almost, but what about the orientation of the atoms?  "Why, atoms are the fundamental unit of matter, the orientation of them must not matter."  But clearly there is orientation in all elementary particles: Spin! So we can't even talk about the most fundamentally small parts of the universe without talking orientation. 

Let's argue that the smallest elementary particle is the basis for a geometrical point.  In order to locate this point in our universe, we now need to know where it is (3 dimensional space) and how it is (3 dimensional orientation).  Build up the universe from that assumption.  HOLY CRAP!  Now we live in 6D!

Let's not even talk about time...

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