Message #2211

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] MagicTile solving
Date: Tue, 29 May 2012 21:38:33 -0700

Did I misspeak? You are right that you don’t need 4D senses to look
inside the classic Rubik’s cube but you definitely need a good 3D sense,
and in many ways that is a much bigger requirement than sensing the
pattern of stickers on it’s surface. MagicTile shows us you only need 2D
ability for that. By analogy you need 3D ability to deal with the 3D
surface of a hypercube and you will need 4D ability to understand its 4D
interior. I have no such ability and therefore have no idea what sort of
mechanisms might work for 4D beings. I also have very little interest in
that problem because I am much more interested in what the physical
models can show us compared to how they might physically do that.

-Melinda

On 5/29/2012 9:21 PM, Andrey wrote:
> 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.
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> Andrey
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> — 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.
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>> 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.
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>> -Melinda
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>> 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 ;_;
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