Message #2210

From: Andrey <andreyastrelin@yahoo.com>
Subject: Re: [MC4D] MagicTile solving
Date: Wed, 30 May 2012 04:21:03 -0000

But you don’t need 4D senses to look inside the classic Rubik’s cube - screwdriver works better for it. So for 3^4 mechanism it’s enough to have powerful 4D viewer (to visualize and investigate non-convex bodies) or good 4D imagination (it a question of couple of months to develop it for a short time).
But I see a problem with physical implementation of 3^4. Consider two cells A and B with common ridge Q. You can rotate any of these cells around the axis going throwgh the center of Q (90 deg twists). And these twists have exactly the same plane of 4D rotation: it’s plane containing centers of cube, of A and of B. So if we take block 3x3x1x1 at the ridge Q, its points will have the same physical movements in both twists. I afraid that it will allow you to twist just Q without moving of the rest of A and B cells - that is not a model that we use to play with.

Andrey

— In 4D_Cubing@yahoogroups.com, Melinda Green <melinda@…> wrote:
>
> Maybe try some of the simple edge turning puzzles that Ed and I have
> been having fun with? I enjoy those that do not require any algorithms
> beyond a [1,1] commutator. That means that I can do it purely
> intuitively and is actually a relaxing activity, probably similar to the
> tedious parts of the 120-Cell and other large puzzles. It’s also great
> to get a feel for the 3D and 4D spaces in which these manifolds live.
> You probably already have about as much of a sense of the 4D cube as one
> can have. These puzzles offer similar understandings.
>
> As for your quest for a 4D mechanism, I’m guessing that the difficulties
> have something in common with 5D puzzles. That’s because in the 4D cube
> puzzle, our activity is analogous to an ant crawling on the surface of a
> 3D cube but being completely unaware about the volume of stuff under
> that skin. What we see in MC4D shows exactly that 3D skin. When I 4D
> rotate an object, I can sometimes get a sense that there is a kind of
> volume that is being contained by the 3D geometry but I can’t "see"
> anything about the 4D volume. You could really use a 5D sensing ability
> in order to look into the interior of a 4D object which is what you are
> trying to do.
>
> -Melinda
>
> On 5/28/2012 6:31 PM, Ray Zhao wrote:
> >
> >
> > You all make me seriously want to solve some puzzles ^_^, but right
> > now I’m more interested in finding better solutions for the 3^4 and
> > visualizing a mechanism for it as well. =P
> > I also have summatives ;_;
>