Thread: "John Bailey explains N-teract 4"

------=_NextPart_000_000D_01C7D6A7.81CC97A0
Content-Type: multipart/alternative;
boundary="----=_NextPart_001_000E_01C7D6A7.81CC97A0"

------=_NextPart_001_000E_01C7D6A7.81CC97A0
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

I was asked by J.Bailey to post explanation of the puzzle which we discusse=
d few weeks ago.

----- Original Message -----=20
From: John Bailey=20
To: Remigiusz Durka=20
Sent: Saturday, August 04, 2007 2:43 PM
Subject: Re: N-teract 4


Remigiusz Durka wrote:
Monday, July 09, 2007, 9:21:54 AM | Remigiusz Durka
Hi! Could someone tell me what is that? http://home.rochester.rr.com/jbxroa=
ds/4cube.html I've tried and tried to see/understand how "that" is related =
to 2^4

John Bailey, author of http://home.rochester.rr.com/jbxroads/4cube.html ans=
wers:
Saturday, August 4, 2007, 6:58 AM John Bailey

N-teract-4 maps topologically to a 2x2x2x2 cube--in other words, it is a 4 =
dimensional version of the 2x2x2 pocket cube. The mapping is incomplete.
First let me list the complete parts: 1) number of corners, 2) number of si=
des 3) number of cubes (3D) These are 16, 24, and 8 respectively, just as w=
ith a mathematical tesseract or a 2x2x2x2 pocket cube. On the web page, th=
e 24 buttons correspond to the sides (or faces) of the hypercube. Clicking=
a button causes the corners of its associated face to move just as they wo=
uld on a 2x2x2x2 cube. The buttons are positioned graphically in the arran=
gement so that there is somewhat of a mnemonic sense to their location rela=
tive to the corners they move. The BLRF naming convention (for Bottom, Left=
, Right, or Front) refer to which face of the cubelet is twisted.

The mapping is incomplete with respect to orientation of the corners. As t=
he corners of N-teract-4 are moved, they do not change orientation. There =
is an illusion of rotation on the web page version--only because of the gra=
phic design of each face. Look carefully when you press a button. The cor=
ners change location but keep their original orientation.

Lastly, only one direction of twist is provided. A backward twist requires=
the button to be clicked three times.

Two other buttons are provided to make the resulting puzzle somewhat more t=
ractable. With its cumbersome buttons, a multi-twist macro would be somewh=
at tedious. By adding a single button (West L'U ...) a single macro is pro=
vided which breaks the symmetry of the west face. This is enough to recove=
r the home position of the game when it is used in combination with an appr=
opriate sequence of face buttons.

The design of the web page, ie its layout, is the result of attempting (suc=
cessfully, I think) to accomplish these operations within the limited confi=
nes of the scripting language, Javascript. Check out the page's source code=
. It is included directly within the web page's html and available using r=
ight click, select view source on your browser. Three functions use only 8,=
7, and 5 lines respectively. An additional 16 lines are used to initialize=
the corner images. That is the whole of the script! The remainder of the =
intelligence supporting the script is in the specific arguments of the func=
tion "twist()" which are associated with each button. These specify the re=
arrangement of corners to respond when that button is clicked. The script =
is embedded in a public key signed message as window dressing.

The puzzle is relatively simple to solve. I am no cuber but I can find my =
way out of the scrambled position by observation and simple trial and erro=
r. For a while, I explained this by the speculation that as the dimensions=
of a cube increase, the number of paths to solution increase faster than t=
he complexity. Thus there are more solution paths for a 4D cube than for a=
3D. Thus far, no one has commented on this conjecture.

One last observation. As inspection of the source code of the script shows=
, the programming of higher dimension cubes would be simple. The function: =
onClick=3D "twist(2,7,8,3)" needs only to be provided one additional argume=
nt to make a 5D version. On the other hand, arranging the graphics for a 2=
x2x2x2x2 showing the 32 corners in a recognizable pattern seems rather chal=
lenging.

Please feel free to relay this response to your discussion group. I would =
be happy to explain any points further. It may well be that N-teract-4 fai=
ls reasonable criteria for rubikness, however within its limitations it sta=
nds on its own. It was named thus because someone (possible Mark Newbold) =
suggested that if I called it a Rubik anything I would be liable for a visi=
t from the intellectual property police.

Depending on how this discussion goes, I might revive my interest in the 4D=
cube and install a randomization function for the scramble button. At the=
same time, I should update the dead links. Sorry about that. It was writ=
ten a long time ago (1998, check the Public Key Signature)

John Bailey
http://home.rochester.rr.com/jbxroads

----- Original Message -----=20
From: Remigiusz Durka=20
To: John Bailey=20
Sent: Saturday, August 04, 2007 5:23 AM
Subject: Re: N-teract 4


Hello!

Thank you for response. I'm really looking forward to the discussion so y=
ou can send me any information and I will send it to the yahoo group.
------=_NextPart_001_000E_01C7D6A7.81CC97A0
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable



>