Message #453

From: Jenelle Levenstein <jenelle.levenstein@gmail.com>
Subject: Re: [MC4D] Noel conquers the 4^5!
Date: Mon, 31 Mar 2008 22:08:59 -0500

I have found by teaching other people to solve the 3x3x3 rubix cube that the
hardest part of solving it is to figure out how the puzzle moves in 3
dimensions. I think this may be because they have trouble seeing the puzzle
in 3 dimensions. They see 54 individual stickers instead of seeing the 26
peices. You can tell this because someone new to the cube will pick one
color and try to get as many of that color on one side as possible, without
regard to what pieces get knocked out. Now it may sound odd that we have
trouble thinking 3 dimensionally even though we live in a 3D world, but
there are a lot of 2 dimensional things in our world. This Computer screen
is 2D The layout of our streets is 2D. Even the buildings we live although
they are 3D simply consist of a bunch of 2D floors stacked on top of each
other. It would be interesting to see whether a society run by monkeys would
be better at solving these insane puzzles than we are since they have more
spacial minds.

Wait I had a point. Whether a four dimensional creature would be able to
intuitively understand a 3x3x3x3 would depend on how they thought and what
there world looked like which is something we have no way of even imagining.
My guess is that they would have to figure it out just like we did, but it
would be easier because they could hold the thing in their hands and see it
form all angles.

On 01 Apr 2008 02:01:35 +0000, David Vanderschel <DvdS@austin.rr.com> wrote:

> On Monday, March 31, "Jenelle Levenstein" <jenelle.levenstein@gmail.com<jenelle.levenstein%40gmail.com>>
> wrote:
> >Your forgetting that the complexity of the moves
> >required to solve the cube increases as you add
> >dimensions,
>
> Most folks seem to believe this, but I think there is
> a sense in which it is not so. The sense in which it
> is clearly true is that there are more things to keep
> track of as the dimension goes up.
>
> Consider the following for the 3x3x3x3 puzzle: Because
> the possiblities for reorienting a hyperslice of the
> 4D puzzle are so much richer, the orientation of any
> hypercubie can be changed to any of its possible
> states - with the hypercubie remaining in the same
> position - simply by twisting any one of the
> hyperslices which contain it. (An (external)
> hyperslice is a 1x4x4x4 set of hypercubies
> corresponding to a hyperface, and it reorients like a
> 3D cube.) In the 3D case, we lack the flexiblity
> required to achieve an analogous capability. Given a
> set of fairly simple moves that will isolate any given
> hypercubie from one of the hyperslices in which it
> lies into another hyperslice parallel to the first and
> otherwise leaving the first unchanged, you wind with a
> rather general and easily understood approach to doing
> anything.
>
> >… By the way would a 3x3x3 cube be possible to make
> >in a 4D would or would it just fall apart. It could
> >be analogous to the slide puzzles we make.
>
> It would be analogous to an interlocking type of 2D
> puzzle. (I.e., stays together when constrained to lie
> in a hyperplane one dimension down from that of the
> universe in which it exists.) Clearly any piece can
> be translated without hindrance in the direction
> perpendicular to the 3D hyperplane containing the 3D
> puzzle.
>
> Regarding the perception of the problem by beings in
> other dimensional spaces, I have posed the reverse
> analogous question - wondering what solving the 3D
> puzzle would be like for a 2D being. Indeed, my own
> simulation of the 3D puzzle will produce a display
> that corresponds to what a 2D being could perceive
> when the 3D puzzle is implemented in a manner
> analogous to MC4D, so you can try your hand at 3x3x3
> solving from the perspective of a Flatlander. Though
> this unusual capability is not the main value of my
> program, I’d be interested in feedback from anybody
> who tries it: http://david-v.home.texas.net/MC3D/
>
> Regards,
> David V.
>
>
>