Message #320

From: Don Hatch <hatch@plunk.org>
Subject: Re: [MC4D] Hi everyone!
Date: Wed, 16 Aug 2006 11:45:16 -0700

Hi Ilia,

Regarding the use of the word "face"…
It’s true that "face" is’t great terminology because
it could reasonably be understood to mean a 2d slab of hypercubies,
so it’s confusing.
I think when we are being careful
we use the words "hyperface", "hypercubie", and "hypersticker",
especially when first describing the puzzle to someone.
But it has degenerated informally to "face", "cubie" and "sticker"
since we rarely use those words to mean anything else when
talking about the 4d or 5d puzzle.

Don

On Mon, Aug 14, 2006 at 01:57:18PM -0000, ilia.smilga wrote:
> Hello everyone!
> My name is Ilia Smilga, I’m 17 and I live in Nantes, France (but I’m
> soon moving to Paris), though I’m actually Russian. Please do not infer from my name that
> I am a girl: you would not be the first person to make this mistake. This is my first
> message on the list; I have been planning to post something for quite a
> long time, but I didn’t have the time to write it.
> In spring 2005, two things happened in my life: I bought a Rubik’s cube
> and I started to take interest in multi-dimensionnal geometry. So at
> some moment, the idea of a 4D analog to a Rubik’s cube came to my mind.
> I was not at all sure whether there was an obvious and beautiful way to
> do this. Then a year ago, I did a Google search and I found MC4D; it
> made me very enthusiastic because I discovered that other people had
> already done what I had thought about! I took up the challenge of trying
> to solve the Rubik’s Hypercube without looking at the answer or taking
> any hint. I was not at all sure that I would succeed: I told myself that
> if I would, I’d have something to be proud of!
> Unfortunately, I have a Mac and MC4D didn’t first work on my computer,
> but I followed a link on the MC4D webpage and downloaded a Macintosh
> Rubik’s Hypercube program. It is basically about the same object, but
> the representation is quite different. The hypercube is shown as three
> cubes side-to-side, each cube representing one hyperlayer. Each tessie
> is represented by a single cubie. Those of its hyperstickers that are
> facing in one of the three spatial dimensions are represented by 2D
> stickers on the cubie, and the hypersticker facing the fourth dimension
> is represented by the color of the cubie itself. You can rotate the
> cubes in 3D to turn them around, but you cannot do actual 4D rotations;
> instead, there is an operation called "reslicing", which is quite weird
> because it seems to change the orientation of the whole thing. It is
> maybe hard to explain, but easy to understand once you see it. This
> representation has a big advantage and a big drawback when compared to
> MC4D. The big advantage is that it is much easier to grasp and to
> manipulate: the twists that do not involve the 4th dimension are
> straightforward to understand; the others are a bit trickier, but still
> easy to handle; the whole hypercube is spread out before you, and you
> need very few view rotations. The big drawback is that it is much less
> symmetrical: there is one dimension which is handled very differently
> from the other three; hence, it is much less beautiful. This
> representation influences your way to solve the puzzle, by making some
> twists easier to see than others.
> I started solving and in fact, it turned out to be much easier than I
> thought it would be. The point is that although the structure of a
> Rubik’s hypercube is more complex, in 4-space there are more degrees of
> freedom, so it is easier to continue building the solution without
> breaking what has already been done. For example, when you have done the
> 2 upper layers of a 3D Rubik’s Cube, if you don’t know any formulas you
> are quite stuck: it’s very difficult to go any further. With the
> tesseract, you can always turn a "side" cell (BTW : people often call
> "faces" the elements of a 4D Rubik’s hypercube that you can twist: this
> is incorrect, because a face is 2D. The proper name for a "3D face" is a
> "cell"; a face, on a 4D Rubik’s hypercube, is a two-colored tessie),
> then do some manipulations with the "bottom" and the "side" cells and
> end up with the side cell in the same state as before, but some useful
> work done on the bottom cell. So in a few weeks, I solved the Mac
> version.
> Then I realized that at school, there were PC’s so I was able to run
> MC4D from my school. I immediately downloaded MC4D and this time, it
> took me only a week to finish. I already knew approximately what to do
> and I knew I could do it. On the other hand, I had to adapt myself to
> the different representation, so the second time the algorithm was not
> quite exactly the same as the first time. My log file is currently in
> the `Solutions’ folder.
> Later, the Java version was developed, and we bought a new computer, so
> now I am able to play MC4D from home. I hadn’t touched it for almost a
> year, but when the summer holidays came, I returned to it and solved it
> another couple of times. I don’t understand how you guys manage to solve
> it in less than half an hour: it usually takes me a week or more to
> solve! Once I have tried to solve it as fast as possible in one sitting.
> I’ll never try it again: I spent almost three hours, staring into my
> monitor and trying to imagine how it all worked in 4D; I do not know
> whether my eyes or my brain were more screwed up at the end!
> I haven’t yet tried the 4^4 or 5^4 puzzles, because I do not know yet
> how to solve 4^3 and 5^3; however, when I move to Paris, I will be able
> to borrow those cubes from some friends and hopefully solve them; then
> I’ll be ready to move one dimension up. I have seen that 5D Rubik’s
> hypercube have been built; it must be great, I really look forward to
> trying it! Unfortunately, it is only for Windows… will there ever be a
> Mac version?
> I have got a proposal concerning MC4D. There is a problem: it is
> difficult to grasp any single tessie in a single look, especially those
> that have a lot of stickers (edges and corners), because the tessies
> have their stickers spread far apart in the puzzle. The option to
> highlight all the stickers belonging to any tessie is quite handy, but
> not quite sufficient. What if on each hypersticker, each 2D face facing
> another hypersticker had on it a mark (for example, a little square)
> showing the color of the hypersticker it is facing? In this way, each
> hypersticker would bear enough information to identify the whole tessie;
> of course, it would be redundant, but still very useful. In this way,
> you could solve the whole puzzle without making a single 4D rotation!
> Yes, and I have another technical question: I don’t understand at all
> how the macros work. I have tried to use them, but the reference
> stickers system is rather obscure for me, and it seems to me that
> something really weird is going on: I sometimes get the impression that
> macros are executed with one move more or less than they sould have, or
> that some more different cells get twisted that should. Can someone help
> me?
>
> See you!
> Ilia.
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> Yahoo! Groups Links
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–
Don Hatch
hatch@plunk.org
http://www.plunk.org/~hatch/