Hi...:)
I'm really excited joining this interesting group.
My name is Liat (I love when people call me "liati" :)), I'm 24 years
old, and I live in Israel.
I have a B.Sc in math and computers from Tel-Aviv university and I'm
interested mostly in complexity, computational models, information
theory and graph theory (If someone can't wait any longer to share
some ideas regarding the "P!=NP?" question...)
at the age of about 17, I solved the 3d-cube, not knowing any
algorithm exist. I started to look for more complicated related
games...I played and solved the "octagon", "megaminx" and "4*4*4".
Then I started to be interested in other algorithms and to compare
some of them. I was also interested in the algorithm for solving
3d-cube without looking while playing. I also studied some group
theory and found some good books in that context.
I was really amazed by the 4d-cube application.
It is fantastic.
When I started playing I used only the central cube of each 2d-surface
and the 3d and 4d rotations. starting from trying many many serieses
of moves with symmetry and anti-symmetry, and gatherring all really
complicated moves that has elagants affects, in the spirit of 3d-cube.
I was really excited to see the 3-color-series that was published,
especially the second and third, because I reached the second one
without using the 7 button(much long series), so it realy made things
more easy. I found great tips on the website, and in that in my mind,
I then started to play. all the process took me about 4 days.
mmm....I don't talk as much as I'm writing :)
Liat Blatman.
Hello Liati and all!
It is great to get to know that new 4D-solver appears.
Congratulations!
Forty solvers -- we are the powerful community!
Liat Blatman wrote:
l> I also studied some group theory and found some good books in that context.
Very magnificent!
I'd like to look through that good books, if they connect to Rubiks cube.
Could you provide a link, preferably, as electronic document.
I assembled 3x3x3x3 almost year ago and it is the second time I find
the term "group theory" in our yahoogroup.
I have read that Erno Rubik created his greatest puzzle
trying to _visualize group theory_.
Yet, I didn't find any instructions for studying groups using Rubiks cube.
In Maple math package there is a worksheet for 2x2x2 cube
"Group theory via Rubiks Cube"
http://www.maplesoft.com/applications/app_center_view.aspx?AID=11
Unfortunately, no visualization is implied.
What I found out myself?
What I call "series" as usual presents "commutant" in mathematics.
What I call "substitution before series" presents
"conjugate (adjoint?) commutant".
In cube one can see many famous finite groups.
Obviously, one-side rotations form cyclic C4 group.
Two neighbor-side 180 degree rotations form C12.
Two 180 degree central slice rotations are commutative and form
C2xC2 (Klein group). And so on.
All group theory notation is explained at Wolfram public
encyclopedia: Eric W. Weisstein. "Finite Group." From MathWorld -- A
Wolfram Web Resource. http://mathworld.wolfram.com/FiniteGroup.html
Also this encyclopedia has Rubik contest at
http://mathworld.wolfram.com/RubiksCube.html
--
Best regards,
Ivan Timofeev mailto:temaotheos@mail.ru
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(welcome, Okko!)
Hey, Ed, regarding Melinda's physical 2^4 puzzle,
(1) Nope, I haven't written down a big table of move equivalents,
although my videos will give you enough to figure it out. The
one-sentence version is: any mc4d move that leaves the stickers on the
R+L faces still on the R+L faces, has a simple twist in the phys 2^4
puzzle. With the addition of a single rotation to this common subset
-- any rotation that moves the R+L faces onto a different pair of faces,
FOro and FUro being the two phys 2^4 sequences discovered so far to do
this -- the entire mc4d state space can be reached on the phys 2^4 and
vice versa.
(2) Nope, nobody else has written down the move table either. That's
not too surprising, since nobody else but Melinda and me have made
physical versions of the puzzle yet. C'mon, gang, get building! It's
fun, and it'll only take you a couple of days. :) I suspect people
are waiting for Melinda or me to provide some nice step-by-step
instructions that can be completed in 3-12 hours, or even better, just
wheedle one of us into building them one.
(3) The "virtual physical" 2^4. It feels slightly goofy to take
Melinda's puzzle, whose key feature is the ability for a physical
realization, and then make a simulation of it. Heh. However, it
would actually be really useful, given that a lot of people won't manage
to surmount the energy barrier associated with building the physical
puzzles.
(4) Thinking about it, it would be really useful to create a virtual
physical 2^4 puzzle, in Javascript, shown side-by-side with the MC4D
style simulation, with each move being executed simultaneously on
both. And as a side-effect of creating the MC4d style rendering in
Javascript, we would easily be able to also produce a
web-browser-compatible version of all of MC4D's n^4 hypercube puzzles
that would make them that much more accessible to people who reluctant
to use the Java app. Such a version could be far less general and
tricky than MC4D itself, because it would be so much more limited (just
4d, in a particular simplified/hacked projection). Sort of a "gateway
drug" to full MC4D. It would be FANTASTIC if somebody programmed this.
(5) A teaser: I've been trying to work out an extension of
Melinda's physical 2^4 puzzle into a physical 3^4, and making some good
progress. However, with 81 pieces and 972 magnets, it's fairly
impractical to create physically in a way that can actually be operated
by hand. Pretty much the only way it is likely to come to exist is in
a "virtual physical" version in Javascript.
Cheers
Marc
On 6/24/2017 1:21 AM, 'Eduard Baumann' ed.baumann@bluewin.ch [4D_Cubing]
wrote:
>
> [Is there a] table which gives the "phys 2^4" moves for each "one
> click on mc4d" ?
>
> How about a "virtual physical 2^4" ?
>
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[Is there a] table which
gives the "phys 2^4" moves for each "one click on mc4d"
?
How about a "virtual
physical 2^4" ?