Well it's very nice to meet you! Congrats on the solve. Hope you can
try one of the higher ones now.

--- In 4D_Cubing@yahoogroups.com, "jwgibson3" <jwgibson3@...> wrote:
>
> My name is John Gibson, and I recently solved the 3^4 (yay!).  I'm a
> graduate from Houston Baptist University (winter '06) with a Bachelor of
> Music in piano performance.  I am 23, happily married, and have 2
> daughters, ages 6 months and 20 months.  Presently, I am applying to
> law school.  My time (today - ask me again in a month and it'll
> probably be different) is spent bending nails (60d so far), studying
> set  theory/logic, playing the piano (Scriabin 7th and 9th sonatas
> right now), and mowing lawns (got to pay the bills, right?)  If
> anybody has any questions, feel free to email me or look me up on
> facebook.
>

Okay, this may seem confusing, but I'm notiboyicr@... (who
joined the group today as well :p).

Long story. notiboyicr is my old yahoo account that's been deserted
for years. But I used it to join this group since I've got no other
yahoo account. Two seconds after registration, I felt like having a
new account (for fun I guess?) so I terminated notiboyicr and created
zzzonked90, but yahoo won't allow me to terminate the old one right
away for some funny reason (it says I'll have to wait 90 days for the
old account to be 'officially' terminated), so now both accounts
coexist but I'll only be using zzzonked90. Understooded?

Oh about that intro thingy new members have to make: I'm Chester and
I'm 16 and I'm Malaysian (some country in Southeast Asia that's shaped
like a potato) and I'm doing my A Levels (first year) now. Nice to
meet all of you (:

Try Dan Harris' CubeStation at www.cubestation.co.uk.
The link to the solution is somewhere in the left column.
Happy solving (:

Oh here's a suggestion from me: once you can solve the Revenge, try
the Professor's on your own without referring to Internet or book
solutions, you'd be surprised that you can solve it only with 3^3 and
4^3 methods, that's what I did anyway. Took me 40 minutes to solve it
right after I bought it. There's a GREAT sense of achievement after
solving it all by your own (:

--- In 4D_Cubing@yahoogroups.com, "Jesse Thompson" <jesset@...> wrote:
>
> Yep, back here in terestrial land I just bought me up a Rubik's
Revenge. ;)
>
> Does anyone know if there is a solution guide for this somewhere
online, for
> the plus yellow coloring? All the solution guides I can find are for
> white/blue coloring. While I know the concepts would still work I
need me
> some illustrations to understand what they are on about and without the
> solid signposts of accurate color I'm pretty lost.
>
> Before I bust out photoshop and start color replacing someone's
> illustrations, I'm just wondering if such a thing already exists. ;)
>
> It is embarrasing to be able to solve a greater percentage of a 3^4 cube
> (~80%) than a 4^3 (45%)  :P
>
> Thanks ;]
>
> - - Jesse
>

I've never solved a rubik's cube.  the idea for my presentation is to
take the techniques that I'm learning in my abstract algebra class,
and use them to derive a solution to the cube.  I want to extend that
to also deriving a solution to the 4D Magic Cube.

I'm at the beginning now... I know what properties of the cube make it
a mathematical group, but that's as far as I've gotten.  I have a
strong feeling that jumping from the cube as a group to a full blown
solution involves the study of subgroups, but I'm not really sure
where to start.

do we have any math people in there that could kind of point me in the
right direction?

thanks!
dave

On Tuesday, November 13, "iatkotep" <iatkotep@...> wrote:
>I've never solved a rubik's cube.  the idea for my
>presentation is to take the techniques that I'm
>learning in my abstract algebra class, and use them
>to derive a solution to the cube.

Good luck!  I would be surprised if you succeed in
this venture; but it will be an impressive achievement
if you do succeed.

Yes, Rubik's Cube is a good example of a non-trivial
group.

You might want to start with a simpler permutation
puzzle - like the 2x2x2 analogue of Rubik's Cube.

>I want to extend that to also deriving a solution to
>the 4D Magic Cube.

If you do succeed for the 3D puzzle, then extending
for the 4D puzzle should not be so hard.  Aside from
the fact that there are a lot more pieces to fool
with, there is a sense in which manipulating the 4D
puzzle is actually easier than the 3D puzzle.

>I'm at the beginning now... I know what properties of
>the cube make it a mathematical group, but that's as
>far as I've gotten.  I have a strong feeling that
>jumping from the cube as a group to a full blown
>solution involves the study of subgroups, but I'm not
>really sure where to start.

There is plenty of information out there which
addresses the puzzle from the Group Theory point of
view.  The source of this sort to which I have paid
the most attention is W. D. Joyner's Web page here:
http://web.usna.navy.mil/~wdj/rubik_nts.htm

>do we have any math people in there that could kind
>of point me in the right direction?

The truth of the matter is that every method I have
ever seen for working Rubik's Cube approaches it from
a rather empirical point of view.  There are some
important facts about what you can and cannot achieve
that are implied by the theory, but you don't really
need to know the theory to take advantage of the facts
themselves.  (Indeed, the facts can eventually become
apparent even without having known about the theory
which implies them.)

I first laid my hands on a Rubik's Cube in 1979.  I
was actually pretty well trained in Group Theory at
the time, and I did realize that the puzzle could be
regarded as a representation of a group.  However, my
knowledge of Group Theory played little role in my
figuring out how to work the puzzle.  I suppose it did
lead me to try things like commutators and
conjugation; but I probably would have done so even if
I had not known what such operations were called in
Group Theory.

Regards,
   David V.

If all you want to do is make a program solve a rublix cube you could
always solve it using the brute force method where you try all
possible combinations of moves until the you find the solution. This
works on the 2^3 and maybe on the 3^3 and only because the cube is
always within about 15 moves of being solved.

On 14 Nov 2007 10:27:02 +0000, David Vanderschel <DvdS@...> wrote:
>
>
>
>
>
>
> On Tuesday, November 13, "iatkotep" <iatkotep@...> wrote:
>  >I've never solved a rubik's cube. the idea for my
>  >presentation is to take the techniques that I'm
>  >learning in my abstract algebra class, and use them
>  >to derive a solution to the cube.
>
>  Good luck! I would be surprised if you succeed in
>  this venture; but it will be an impressive achievement
>  if you do succeed.
>
>  Yes, Rubik's Cube is a good example of a non-trivial
>  group.
>
>  You might want to start with a simpler permutation
>  puzzle - like the 2x2x2 analogue of Rubik's Cube.
>
>
>  >I want to extend that to also deriving a solution to
>  >the 4D Magic Cube.
>
>  If you do succeed for the 3D puzzle, then extending
>  for the 4D puzzle should not be so hard. Aside from
>  the fact that there are a lot more pieces to fool
>  with, there is a sense in which manipulating the 4D
>  puzzle is actually easier than the 3D puzzle.
>
>
>  >I'm at the beginning now... I know what properties of
>  >the cube make it a mathematical group, but that's as
>  >far as I've gotten. I have a strong feeling that
>  >jumping from the cube as a group to a full blown
>  >solution involves the study of subgroups, but I'm not
>  >really sure where to start.
>
>  There is plenty of information out there which
>  addresses the puzzle from the Group Theory point of
>  view. The source of this sort to which I have paid
>  the most attention is W. D. Joyner's Web page here:
>  http://web.usna.navy.mil/~wdj/rubik_nts.htm
>
>
>  >do we have any math people in there that could kind
>  >of point me in the right direction?
>
>  The truth of the matter is that every method I have
>  ever seen for working Rubik's Cube approaches it from
>  a rather empirical point of view. There are some
>  important facts about what you can and cannot achieve
>  that are implied by the theory, but you don't really
>  need to know the theory to take advantage of the facts
>  themselves. (Indeed, the facts can eventually become
>  apparent even without having known about the theory
>  which implies them.)
>
>  I first laid my hands on a Rubik's Cube in 1979. I
>  was actually pretty well trained in Group Theory at
>  the time, and I did realize that the puzzle could be
>  regarded as a representation of a group. However, my
>  knowledge of Group Theory played little role in my
>  figuring out how to work the puzzle. I suppose it did
>  lead me to try things like commutators and
>  conjugation; but I probably would have done so even if
>  I had not known what such operations were called in
>  Group Theory.
>
>  Regards,
>  David V.
>
>

On Wednesday, November 14, "Jenelle Levenstein" <jenelle.levenstein@...>
wrote:
>If all you want to do is make a program solve a
>rublix cube you could always solve it using the brute
>force method where you try all possible combinations
>of moves until the you find the solution.

Note that dave explicitly stated that he wanted to use
techniques he was learning in his abstract algebra
class to _derive_ a solution.

>This works on the 2^3 and maybe on the 3^3 and only
>because the cube is always within about 15 moves of
>being solved.

Sorry, not for 3^3.  The search tree expands way too
rapidly.  Not only is a solution within 15 moves of an
arbitrary start, but so is every other possible
configuration of the cube.  The number (on the order
of 10^20) is way too large to admit a brute force
approach.  Fortunately, there exist more intelligent
approaches which do work.  Indeed, Don Hatch has
posted a general one (for nD) here:
http://www.plunk.org/~hatch/MagicCubeNdSolve/

Brute force, when it works, can find the shortest
solution.  Don's method does not claim to be optimal.

Regards,
   David V.


On 14 Nov 2007 10:27:02 +0000, David Vanderschel <DvdS@...> wrote:
> On Tuesday, November 13, "iatkotep" <iatkotep@...> wrote:
>  >I've never solved a rubik's cube. the idea for my
>  >presentation is to take the techniques that I'm
>  >learning in my abstract algebra class, and use them
>  >to derive a solution to the cube.

>  Good luck! I would be surprised if you succeed in
>  this venture; but it will be an impressive achievement
>  if you do succeed.

>  Yes, Rubik's Cube is a good example of a non-trivial
>  group.

>  You might want to start with a simpler permutation
>  puzzle - like the 2x2x2 analogue of Rubik's Cube.


>  >I want to extend that to also deriving a solution to
>  >the 4D Magic Cube.

>  If you do succeed for the 3D puzzle, then extending
>  for the 4D puzzle should not be so hard. Aside from
>  the fact that there are a lot more pieces to fool
>  with, there is a sense in which manipulating the 4D
>  puzzle is actually easier than the 3D puzzle.


>  >I'm at the beginning now... I know what properties of
>  >the cube make it a mathematical group, but that's as
>  >far as I've gotten. I have a strong feeling that
>  >jumping from the cube as a group to a full blown
>  >solution involves the study of subgroups, but I'm not
>  >really sure where to start.

>  There is plenty of information out there which
>  addresses the puzzle from the Group Theory point of
>  view. The source of this sort to which I have paid
>  the most attention is W. D. Joyner's Web page here:
>  http://web.usna.navy.mil/~wdj/rubik_nts.htm


>  >do we have any math people in there that could kind
>  >of point me in the right direction?

>  The truth of the matter is that every method I have
>  ever seen for working Rubik's Cube approaches it from
>  a rather empirical point of view. There are some
>  important facts about what you can and cannot achieve
>  that are implied by the theory, but you don't really
>  need to know the theory to take advantage of the facts
>  themselves. (Indeed, the facts can eventually become
>  apparent even without having known about the theory
>  which implies them.)

>  I first laid my hands on a Rubik's Cube in 1979. I
>  was actually pretty well trained in Group Theory at
>  the time, and I did realize that the puzzle could be
>  regarded as a representation of a group. However, my
>  knowledge of Group Theory played little role in my
>  figuring out how to work the puzzle. I suppose it did
>  lead me to try things like commutators and
>  conjugation; but I probably would have done so even if
>  I had not known what such operations were called in
>  Group Theory.

>  Regards,
>  David V.

Just wanted to say congratulations on the solves for the 3^4, 4^4, and
5^4. Keeping the cubing world of higher dimensions alive, I give you a
big hearty "Well done!"

Hello Remi,

I guess I should have announced when your 3^4 checkerboard record was
taken from you last year! Well you have your record back now and the
universe is once more in balance.

Congratulations also to Chris Ahna, our first new solver of the year,
and to all the other recent solvers. I'm looking forward to seeing what
amazing accomplishments you guys will come up with this year.

-Melinda

Remigiusz Durka wrote:
> Hi Melinda.
>
> I've noticed that someone took my record in 3^4-checkerboard! From 40
> twists suddenly there was only 28 twists. Impressive. Why nobody told me?
>
> One hour later I noticed this fact I came up with 24 twist solution...
> (attached files for your page).
>
> All the best,
>
> Remi

Hi, I recently joined the MC4D group after solving the 3x3x3x3 and
thought I'd send an introduction message along the lines of those
submitted by other solvers.

My name is Chris Ahna.  I live in the United States, specifically in a
town called Puyallup outside of Seattle in Washington state.  I'm 25
years old and work as a computer programmer, first for Intel and now for
Microsoft.  I've been working as a programmer since graduating from
Pacific Lutheran University where I studied math, computer science, and
physics.  Outside of work I play competitive Scrabble, fool around with
Rubik's cubes, solve crossword puzzles, and go bowling.

I first saw MC4D about a year ago during a brief period where I spent a
lot of time solving Rubik's cubes.  I was interested then but didn't
attempt a solve until getting back into Rubik's cubes late in 2007.

I know how to solve 3D Rubik's cubes of all different sizes, although
I'm pretty dang slow at all sizes compared to speedcubers.  For example,
it usually takes me at least 90 seconds to do the 3x3x3 and at least 10
minutes to do the 5x5x5.  I've made some progress toward learning the
CFOP method used by speedcubers, focusing on the version nicely
described at http://www.cubestation.co.uk.  That said, I only know the
CFOP F2L algorithms and still solve the last layer using the basic
solution found at http://cubeland.free.fr.

To solve MC4D I designated one hyperface (blue) as the "top," the
opposite hyperface (green) as the "bottom," and the remaining hyperfaces
as the "middle."

I started by solving the first layer, i.e., all of the top hyperface and
all adjacent components of the middle hyperfaces.  Next I solved the
second layer, i.e., the components of the middle hyperfaces adjacent to
neither the top nor the bottom hyperface.  Solving the first two layers
in this manner took about 1000 twists and was done without macros and
with very minimal application of algorithms from the 3D cube solutions
mentioned above.

Finally I solved the last layer, i.e., all of the bottom hyperface and
all adjacent components of the middle hyperfaces.  This was almost
entirely done using macros that applied different combinations of
straightforward generalizations of many of the PLL and OLL algorithms
from the two 3D cube solutions mentioned above.  Viewing the bottom
hyperface like a 3x3x3, I solved the centers (two color pieces), then
the edges (three color pieces), and finally the corners (four color
pieces).  Each group of pieces was solved by first permuting all of them
into the correct locations and then orienting them in place.  Solving
the last layer in this manner took about 2000 twists and probably isn't
something I would have had the patience to complete without macros.

All in all, this took 3070 twists and lots of time, at least 20 hours
spread over many different days.  This seems similar to my 3D cube
solutions in that it's slow and reliant on algorithms formulated by
others, however it was also eventually effective and a lot of fun to
figure out!  :-)

Chris

Hello, my name is Marvin Castellon. I am 14 years old. I live in
Alexandria, Virginia and I joined soon after I soved the 3x3x3x3. The
first time I solved the 3x3x3x3 it took me 7732 twists. The second time
it was 2650 twists. I have also solved the 2x2x2x2, so far my best on
it is 324 twists.

I live in an apartment with my parents and my little brother, Jeremy. I
liv by a very woody area where I have seen all sorts of animals. I go
to Francis C. Hammond Middle School. Right now I am in the eighth grade
and I am about to graduate middle school. In school so far I hold every
rubik's record from the pocket cube (2x2x2), to all big cubes, to the
3x3x3x3.

Solving the 3x3x3x3 was the hardest puzzle I solved so far. It took me
pretty long considering I was using Roice's solution. Well I glad to
have have solved the 3x3x3x3 and to be in this group.

                                          Marvin

Congratulations indeed!!
This is definitely a tour de force, Noel. Congratulations on setting a
record that can never be taken from you. There is no question that you
are the first human being to perform this feat and for all we know this
may be the first time in the universe!

One thing that I'm confused about is why you say that you won't face
parity problems in the 5^5. Doesn't the 5^5 contain the 4^5? I know that
it's been said that after 5^d there are no more new combinatorial
elements for all dimensions. Can someone please spell out exactly what
the issues are and why this is true?

I can certainly understand why Noel says that he'll never do the 4^5
again. I can imagine that other people might accomplish that if they
feel that they can turn in a shorter solution, and I'll also make a
guess that this is the year that someone will solve the 5^5 for the
first time. I'm also on record for predicting that it will be a very
long time before a second person slays that monster if ever! The lure of
the shortest 5^5 may simply not be attractive enough for anyone to
attempt it.

So please tell us, Noel. What was it like to battle this beast and did
it really only take you a week? Any advice for others thinking about
attempting to repeat your achievement? And are you *really* going to
take a break before attempting the 5^5 or are you just trying to make
other would-be solvers *think* that they don't need to hurry to be the
first? No need to answer that last question, BTW.   :-)

-Melinda

jwgibson3 wrote:
> CONGRATS!!!!  Fantastic!  Although, I must admit, I'm a little
> jealous.  I was hoping I could be first ;)  And Noel, your solution is
> a great length; it's shorter than the median solution for the 3^5.
> I'm still pairing up edges and have reached 4000 moves.  Roice - the
> finder will be fantastic.  It's pretty mind-rotting looking through
> 1000 pieces with the shift key held down hoping the next one is it.
> Congrats Noel!  And thanks for the new features, Roice!
>
> Best wishes,
>
> John
>
> --- In 4D_Cubing@yahoogroups.com, "Roice Nelson" <roice@...> wrote:
>
>> Hey guys,
>>
>> I wanted to let you all know the Revenge version of the 5D cube has been
>> solved for the first time!  I just uploaded Noel Chalmer's solution to the
Hall of Insanity if you'd like to take a look.
>>
>> *www.gravitation3d.com/magiccube5d/hallofinsanity.html*
>> **
>> This puzzle has 2560 stickers and 1024 cubies and as best I can tell from our
emails, I think it only took him about a week!  But I'll let him expound if he's
interested.
>>
>> Since they have so many pieces, Noel requested a new feature (a cubie
>> finder) to help him out with the Revenge and Professor 5D puzzles, and this
is part of the install now.  It is on the options menu or you can CTRL+F. Also,
thought I'd mention redo was added last year as well (that had been requested a
lot so I finally did it, but I never mailed out about it).
>>
>> I hope this finds everybody well,
>>
>> Roice
>>
>>
>>
>> ---------- Forwarded message ----------
>> From: Noel Chalmers <ltd.dv8r@...>
>> Date: Wed, Mar 19, 2008 at 1:43 AM
>> Subject: Re: small thing
>> To: roice3@...
>>
>>
>> Hey Roice,
>>
>> Well, I said I'd do it and it's done. This thing was HARD. I had a parity
error at every step of solving it like a 3x3 and I had to kind of make up a
sequence on the fly that would correct it. I'm looking forward to the 5^5 where
I won't have to worry about parity! But I think I'll take a bit of a break
before that.
>> This is by no means a shortest move solution, I gave up on trying to have a
low move count when I hit the parities. I suspect that if someone else
>> solves it they'll have less moves but that's fine by me, I don't plan on
>> doing this ever again. Thanks again for the update to the program, I
>> couldn't have done it without your help!
>>
>> Cheers,
>> Noel

Given that all of the solutions are posted in clusters around Winter
holidays and Summer (except Noel - Spring Break maybe?), I'm going to
stretch and say most of the hypercubers do this to... relax?

--- In 4D_Cubing@yahoogroups.com, "Jenelle Levenstein"
<jenelle.levenstein@...> wrote:
>
> too many!!!!!!!!!!!! y'all are crazy I don't even know when you
find the
> time to attempt these crazzy puzzles much less solve them.
>
> On Mon, Mar 24, 2008 at 7:17 AM, Remigiusz Durka <thesamer@...>
> wrote:
>
> >    I also would like to congratulate Noel of his achivement.
4x4x4x4x4 is
> > real monster. I definetly will not even try to solve it. Although
if there
> > be 6D cube I'll give a try :P. (As I remembered, we agreed that
we start
> > discussion after all 5D cubes being solved :)))) It turned out
that it can
> > be sooner that we thought :)
> >
> > BTW. Any guess how many possible states 4^5 has got? Even rough
estimate?
> >
> > All the best,
> >
> > Remigiusz D.
> >
> >
> >
> >  -----------------------------------------------------------------
-----
> > Asy i Cieniasy pilkarskiej ekstraklasy
> > kliknij >> http://link.interia.pl/f1d27
> >
> >
>

Hi! My name is Marcin Kostrzewa and I live in Krakow, Poland. I'm 14
and I'm going to school. I interested in cubing since October 2007. A
few weeks ago I interested in more-than-3 dimensional cubies. So
yesterday I finished solving 3x3x3x3 and now I'm here :)
                                                             Marcin

Proof that god's algorithm for the 3^3 is no more than 25 twists:
http://arxivblog.com/?p=332
-Melinda

Many congratulations on your amazing achievement Noel! This is
excellent news and I trust you are enjoying all the buzz and
stisfaction you deserve with this effort. Being in the most
exclusive club possible (i.e. with one member) must be a great
feeling, although you may not get to enjoy the complete exculsivity
for too long (and no, I am not hinting that I have plans to climb
the 4x4x4x4x4 mounatain any time soon).

Two other (light-hearted) and general points also came to mind from
Melinda's comments. Although I often believe we are not alone in
this universe I am happy to accept that we could be (just to make
you the ultimate 5-D Revenge solver!) but I wonder if there are (a)
viable 4-D, 5-D etc univserses that exist somewhere, and that (b)
beings from those places might be solving analogous cubes themselves.

Secondly, it is no mean feat for us 3-D beings to represent (and
then solve!) a 5-D cube in a format that our brains can deal with,
but I wonder if a 4-D being would find a 6-D cube, for example,
easier to solve (relatively speaking) than a 5-D cube is for us;
since maybe their (hyper)brains are 'more geared' to dealing with
extra dimensions. What do people think?


--- In 4D_Cubing@yahoogroups.com, Melinda Green <melinda@...> wrote:
>
> Congratulations indeed!!
> This is definitely a tour de force, Noel. Congratulations on
setting a
> record that can never be taken from you. There is no question that
you
> are the first human being to perform this feat and for all we know
this
> may be the first time in the universe!
>
> One thing that I'm confused about is why you say that you won't
face
> parity problems in the 5^5. Doesn't the 5^5 contain the 4^5? I
know that
> it's been said that after 5^d there are no more new combinatorial
> elements for all dimensions. Can someone please spell out exactly
what
> the issues are and why this is true?
>
> I can certainly understand why Noel says that he'll never do the
4^5
> again. I can imagine that other people might accomplish that if
they
> feel that they can turn in a shorter solution, and I'll also make
a
> guess that this is the year that someone will solve the 5^5 for
the
> first time. I'm also on record for predicting that it will be a
very
> long time before a second person slays that monster if ever! The
lure of
> the shortest 5^5 may simply not be attractive enough for anyone to
> attempt it.
>
> So please tell us, Noel. What was it like to battle this beast and
did
> it really only take you a week? Any advice for others thinking
about
> attempting to repeat your achievement? And are you *really* going
to
> take a break before attempting the 5^5 or are you just trying to
make
> other would-be solvers *think* that they don't need to hurry to be
the
> first? No need to answer that last question, BTW.   :-)
>
> -Melinda
>
> jwgibson3 wrote:
> > CONGRATS!!!!  Fantastic!  Although, I must admit, I'm a little
> > jealous.  I was hoping I could be first ;)  And Noel, your
solution is
> > a great length; it's shorter than the median solution for the
3^5.
> > I'm still pairing up edges and have reached 4000 moves.  Roice -
the
> > finder will be fantastic.  It's pretty mind-rotting looking
through
> > 1000 pieces with the shift key held down hoping the next one is
it.
> > Congrats Noel!  And thanks for the new features, Roice!
> >
> > Best wishes,
> >
> > John
> >
> > --- In 4D_Cubing@yahoogroups.com, "Roice Nelson" <roice@> wrote:
> >
> >> Hey guys,
> >>
> >> I wanted to let you all know the Revenge version of the 5D cube
has been
> >> solved for the first time!  I just uploaded Noel Chalmer's
solution to the Hall of Insanity if you'd like to take a look.
> >>
> >> *www.gravitation3d.com/magiccube5d/hallofinsanity.html*
> >> **
> >> This puzzle has 2560 stickers and 1024 cubies and as best I can
tell from our emails, I think it only took him about a week!  But
I'll let him expound if he's interested.
> >>
> >> Since they have so many pieces, Noel requested a new feature (a
cubie
> >> finder) to help him out with the Revenge and Professor 5D
puzzles, and this is part of the install now.  It is on the options
menu or you can CTRL+F. Also, thought I'd mention redo was added
last year as well (that had been requested a lot so I finally did
it, but I never mailed out about it).
> >>
> >> I hope this finds everybody well,
> >>
> >> Roice
> >>
> >>
> >>
> >> ---------- Forwarded message ----------
> >> From: Noel Chalmers <ltd.dv8r@>
> >> Date: Wed, Mar 19, 2008 at 1:43 AM
> >> Subject: Re: small thing
> >> To: roice3@
> >>
> >>
> >> Hey Roice,
> >>
> >> Well, I said I'd do it and it's done. This thing was HARD. I
had a parity error at every step of solving it like a 3x3 and I had
to kind of make up a sequence on the fly that would correct it. I'm
looking forward to the 5^5 where I won't have to worry about parity!
But I think I'll take a bit of a break before that.
> >> This is by no means a shortest move solution, I gave up on
trying to have a low move count when I hit the parities. I suspect
that if someone else
> >> solves it they'll have less moves but that's fine by me, I
don't plan on
> >> doing this ever again. Thanks again for the update to the
program, I
> >> couldn't have done it without your help!
> >>
> >> Cheers,
> >> Noel
>

On Monday, March 31, "Jenelle Levenstein" <jenelle.levenstein@...> wrote:
>Your forgetting that the complexity of the moves
>required to solve the cube increases as you add
>dimensions,

Most folks seem to believe this, but I think there is
a sense in which it is not so.  The sense in which it
is clearly true is that there are more things to keep
track of as the dimension goes up.

Consider the following for the 3x3x3x3 puzzle: Because
the possiblities for reorienting a hyperslice of the
4D puzzle are so much richer, the orientation of any
hypercubie can be changed to any of its possible
states - with the hypercubie remaining in the same
position - simply by twisting any one of the
hyperslices which contain it.  (An (external)
hyperslice is a 1x4x4x4 set of hypercubies
corresponding to a hyperface, and it reorients like a
3D cube.)  In the 3D case, we lack the flexiblity
required to achieve an analogous capability.  Given a
set of fairly simple moves that will isolate any given
hypercubie from one of the hyperslices in which it
lies into another hyperslice parallel to the first and
otherwise leaving the first unchanged, you wind with a
rather general and easily understood approach to doing
anything.

>... By the way would a 3x3x3 cube be possible to make
>in a 4D would or would it just fall apart. It could
>be analogous to the slide puzzles we make.

It would be analogous to an interlocking type of 2D
puzzle.  (I.e., stays together when constrained to lie
in a hyperplane one dimension down from that of the
universe in which it exists.)  Clearly any piece can
be translated without hindrance in the direction
perpendicular to the 3D hyperplane containing the 3D
puzzle.

Regarding the perception of the problem by beings in
other dimensional spaces, I have posed the reverse
analogous question - wondering what solving the 3D
puzzle would be like for a 2D being.  Indeed, my own
simulation of the 3D puzzle will produce a display
that corresponds to what a 2D being could perceive
when the 3D puzzle is implemented in a manner
analogous to MC4D, so you can try your hand at 3x3x3
solving from the perspective of a Flatlander.  Though
this unusual capability is not the main value of my
program, I'd be interested in feedback from anybody
who tries it: http://david-v.home.texas.net/MC3D/

Regards,
   David V.

Thanks guys for the comments/feedback: I found them all very interesting.

 

Certainly there are more things to keep track of as the dimensions go up, but I wonder if that necessarily implies that the moves HAVE to be more "complex", or just that there are longer sequences needed? Obviously one can solve, say, the 5-D cube by small steps; moving each class of cubie into place one by one with small sequences of moves. It just takes longer and needs more patience. Also, it may not be the quickest (or most elegant) means. If nothing else, I assume a 4-D (or 5-D etc) being could always resort to such an approach. Crucially, however, this does not exclude the possibility that a 4-D being could have a fundamentally superior insight, and might be able to see the most efficient sets of moves more intuitively than us every time.

 

I hadn't considerd the practicalities of how the 3-D or 4-D cubes would be assembled physically in 4-D space, and again it may be that the engineering hurdles are equivalent regardless of the actual dimension of the space in question. It reminds me of the initial confusion form many people (myself included) when they had seen the 3-D cube for the first time, wondering how it could even be made without everything falling apart once it was turned! Still, clearly the 3-D cube is physically possible,a nd I have no doubt that equivalent ones are possible - at least in principle.

 

Of course, it is easy to imagine that 4-D and 5-D hypercomputer screens could represent any of these cubes with ease, but again the issue of how to usefully represent extra dimensions on a screen with a fixed maximum number of dimensions would occur there as well. (I have always felt that a large part of the genius of Charlie, Melinda, Remigiusz and Roice was finding a way to do this for the 5-D cube on a 2-D screen, so thanks again guys!)

 

One final point: are the 4-D/5-D hypercomputers still just Turing machines at heart, or is it possible that there can be some fundamentally more powerful means of computing in the higher dimensions? (Or am I now wandering too far from the main group topic???)