Message #457

From: Roice Nelson <roice@gravitation3d.com>
Subject: Re: [MC4D] Noel conquers the 4^5!
Date: Tue, 01 Apr 2008 23:40:42 -0500

Yeah, interesting reading for me too. I was swayed by some of the ideas,
but I think I’m sticking with my first thought when I heard the question
posed, which is that 4D beings would have an easier time, at least
conceptually (if the difficulty metric were tedium instead of understanding,
the piece counts could likely reverse my stance).
If MC6D was limited to rotations on coordinate planes like MC5D is for
instance, all the puzzle states would still be available without any real
extra twisting complexity. Even taking into consideration more general
rotations, I think that although the number of them grows combinatorially,
orthogonal components of the more complex rotations are still only limited
to a plane and that doesn’t change - in a way understanding the 3D rotations
is kind of all there is to it for this reason.

But my main rationale for leaning towards 4D aliens having the advantage is
that they would have more concept of dimensional analogy just built into
their way of thinking. The extra level does a lot to make dimensional
patterns clear whereas being exposed to only a line, a square, and a cube in
our physical world isn’t quite enough to make it easy to extrapolate to the
next level (really I’m just restating Mark’s thought that their brains would
be more geared for it).

Having said all that, I still agree with Jenelle too. MC4D would still be
hard, and I bet solving it in that universe would still be a great party
trick that would impress all your friends and be fun to teach :)
Permutation puzzles are just naturally difficult, 3D or not, which is a also
big part of why Rubik’s cubes are inexplicably impossible when we are first
exposed to them, and I don’t think a 4D brain would have any advantage
there. That is, unless 4D does lead to fundamentally more powerful
computing ;)

Finally, on the viability of such universes, I have no idea but it seems
that the laws of physics would certainly have to be different! Melinda has
made the interesting point to me in the past that when it comes to physical
dimensions, there seems to be nothing precluding multiple time dimensions
entering the picture as well…

On Tue, Apr 1, 2008 at 9:47 AM, Mark Oram <markoram109@yahoo.co.uk> wrote:

Thanks guys for the comments/feedback: I found them all very interesting.

Certainly there are more things to keep track of as the dimensions go up,
but I wonder if that necessarily implies that the moves HAVE to be more
"complex", or just that there are longer sequences needed? Obviously one can
solve, say, the 5-D cube by small steps; moving each class of cubie into
place one by one with small sequences of moves. It just takes longer and
needs more patience. Also, it may not be the quickest (or most elegant)
means. If nothing else, I assume a 4-D (or 5-D etc) being could always
resort to such an approach. Crucially, however, this does not exclude the
possibility that a 4-D being could have a fundamentally superior insight,
and might be able to see the most efficient sets of moves more intuitively
than us every time.

I hadn’t considerd the practicalities of how the 3-D or 4-D cubes would be
assembled physically in 4-D space, and again it may be that the engineering
hurdles are equivalent regardless of the actual dimension of the space in
question. It reminds me of the initial confusion form many people (myself
included) when they had seen the 3-D cube for the first time, wondering how
it could even be made without everything falling apart once it was turned!
Still, clearly the 3-D cube is physically possible,a nd I have no doubt that
equivalent ones are possible - at least in principle.

Of course, it is easy to imagine that 4-D and 5-D hypercomputer screens
could represent any of these cubes with ease, but again the issue of how to
usefully represent extra dimensions on a screen with a fixed maximum number
of dimensions would occur there as well. (I have always felt that a large
part of the genius of Charlie, Melinda, Remigiusz and Roice was finding a
way to do this for the 5-D cube on a 2-D screen, so thanks again guys!)

One final point: are the 4-D/5-D hypercomputers still just Turing machines
at heart, or is it possible that there can be some fundamentally more
powerful means of computing in the higher dimensions? (Or am I now wandering
too far from the main group topic???)