Message #2021

From: Brandon Enright <bmenrigh@ucsd.edu>
Subject: Re: [MC4D] Re: New here (on understanding higher dimensions)
Date: Wed, 08 Feb 2012 19:41:44 +0000

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[… On the topic of 3D -> 4D -> nD …]

On Wed, 8 Feb 2012 11:24:09 -0600
Roice Nelson <roice3@gmail.com> wrote:

> For myself, even having solved MC5D once many years ago, I’ve never
> felt I could really make the jump to visualizing 4D. To think about
> things, I’m always a slave to dimensional
> analogy<http://en.wikipedia.org/wiki/Four-dimensional_space#Dimensional_analogy>,
> and when interacting with the puzzles, I have to do so in the most 3D
> way I can (a nice part of this group’s puzzle representations is that
> they still allow you to interact with things in a 3D-like way). It
> would be great to be able to "see" the hypercube and hypersphere in a
> truly 4D way though, and I’ve read about people who claim they have.

I totally agree that nobody (or very close to nobody) can understand all
aspects of a 4D object simultaneously like it seems we can with 2D (and
possibly 3D) objects.

I definitely "understand" many of the 4D objects offered up by MC4D but
my understanding is a very mechanical one. It’s basically a mental
table of how turns affect pieces, how pieces interact with each other,
what happens when you do a 4D rotate, etc. It’s more just a list of
properties than it is and understanding of the fundamental underlying
geometry that creates the properties.

I’m actually not completely convinced that we even understand the
entirety of a 3D object at one time. I’m pretty sure we just take in
the view of the object projected into 2D (with a bit of stereo for
depth) and reconstruct what the 3D object is by rotating it and feeling
it and looking at it over some period of time. We’re just so used to
doing this that it seems like we fully understand 3D objects – even
though our understanding is built out of a solid understanding of 2D.

I wonder if the folks that claim they can visualize / understand 4D are
actually being tricked by the same reconstruction of 4D out of an
understanding of 3D. I think it would take a 4D being to completely
understand a 3D object in one look just as I think it would take a 5D
being to understand a 4D object at a glance.

But whether you "understand" 4D or 5D at the fundamental level is
somewhat unrelated to the ability solve puzzles in 4 and 5 dimensions.

Brandon

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