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 fro=
m my name that=20
I am a girl: you would not be the first person to make this mistake. This i=
s 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.
Welcome to the Group Ilia!
On Monday, August 14, "ilia.smilga"
>(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)
In view of the fact that we are talking about
terminology for a relatively new area of endeavor, I
think use of words like "incorrect" or "proper" to
apply to such terminology is not justified. It is a
matter of convention how old words may be adapted to
apply in the new context.
IMO, when talking about the 4D analogue of the puzzle,
it is entirely appropriate to take the attitude that
the 4D analogue of a face of a 4-cube is a 3-cube and
that it is OK to call such a 4D face a "face" in this
context. I do believe that there is plenty of
opportunity for confusion, and I would urge folks to
use additional notations or comments to emphasize the
dimensionality context of what they are talking about.
For example, occasionally writing "4-face" in the
context of the 4D puzzle could be used to help
disassociate the 2D semantic reaction which seems to
cause Ilia concern with an unqualified "face".
I would say that the 4-face of the (order-3) 4-puzzle
facing in a given direction consists of the set of 27
4-stickers (3-cubes) all of which face in the given
direction.
Regards,
David V.
> >(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)
>=20
> In view of the fact that we are talking about
> terminology for a relatively new area of endeavor, I
> think use of words like "incorrect" or "proper" to
> apply to such terminology is not justified. It is a
> matter of convention how old words may be adapted to
> apply in the new context.
Yes, you're right: I shouldn't have said it in this way. I only wanted to s=
ay that to my mind,=20
this terminology seemed more logical; I did not mean to offense anyone. Of =
course, everyone=20
is free to use the words that they prefer, as long as people understand eac=
h other, and I am=20
not denying that. I apologize for my words.
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Hi Ilia,
I enjoyed your post :) I wanted to answer the question you posed about the
5D cube.
> 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?
We are not planning to do a Mac or Unix version. However, much of the
program was written in portable C++, and we tried to restrict the Microsoft
stuff to the UI. So if someone ends up being interested in creating UI for
these other platforms, porting it should hopefully not be too much trouble.
Also, I wanted to say I believe there is no need to apologize for statements
like the one you made about faces. I think a good way to hone in on
understanding things, finding nice descriptions, etc. is to make clear,
sometimes bold statements and then see how they sit with you and the group
:) Anyway, I personally like the term "cell" when dealing with 4d
polytopes. David's terminology is nice because it can apply to other
dimensions as well.
Take Care,
Roice
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Hello Ilia!
Glad to hear from a quiet member. I enjoyed hearing your story.
ilia.smilga wrote:
> [...] 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!
>
That's very funny! You may be impressed by a half hour solution but I
have not yet solved the 4D cube with or without Roice's solution, so I'm
very impressed by your 3 hour solution!
> [...]
> 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!
>
Your suggestion of the little squares on each cubie face sounds
reasonable. This could be especially useful for showing some of the
state of the invisible face
There is another option which should interest you though in the end it
is probably not practical for solving. Specifically, it is possible to
choose projection parameters such that the stickers of each cubie (or
"tessie" as you call them) exactly touch each other. This is what the
Edit->Edit Prefs->Contiguous Cubies check box is for which works by
locking the face-shrink and sticker-shrink values together so that
adjusting one will change the other to keep the stickers just touching.
There are several problems with this feature but you may enjoy playing
with it. The first problem is that the view does not refresh when you
select the check box. After selecting it, just make a tiny adjustment to
either Face Shrink or Sticker Shrink to see the results. You will then
probably also need to adjust the Eye W Scale and View Scale parameters
to get a reasonable view. The next problem you will notice is that at
some angles, some of the sticker faces will seem to disappear. This is a
problem with our painting algorithm. These views are arguably more
"faithful" to the puzzle than the default one but it does not look
possible to find a parameterization with which you could solve the cube
with reasonable ease.
> 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?
>
Macros are new to the Java version and are not yet complete or
documented. The use of reference stickers allows you to define a set of
moves that can later be applied to any part of the puzzle similar to the
part where the macro was defined. To do that, you first click three
stickers in whatever pattern is most appropriate for your macro. For
example, if your macro will affect three faces, you might want to click
on one particular sticker on each face. Perhaps the 3 such stickers that
are closest to each other. It doesn't really matter which 3 you choose.
You just need to be able to remember how to repeat the same pattern when
you go to apply the macro.
Regarding extra or missing moves, it is also possible that you found a
bug in my implementation. Try defining your macro on a pristine puzzle.
Then take a screen shot of the result. Next, reset the puzzle and apply
your new macro in exactly the same place as you had defined it. The
picture that results should be the same. If not, please save your macro
and send me the macro file and the screen shot.
Let me know how it goes, and good luck with the larger puzzles, Ilia!!
-Melinda
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.
>
>
>
>
>
>
>
>
> Yahoo! Groups Links
>
>
>
>
>
>
--
Don Hatch
hatch@plunk.org
http://www.plunk.org/~hatch/