Thread: "MagicTile solving"

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Maybe try some of the simple edge turning puzzles that Ed and I have
been having fun with? I enjoy those that do not require any algorithms
beyond a [1,1] commutator. That means that I can do it purely
intuitively and is actually a relaxing activity, probably similar to the
tedious parts of the 120-Cell and other large puzzles. It's also great
to get a feel for the 3D and 4D spaces in which these manifolds live.
You probably already have about as much of a sense of the 4D cube as one
can have. These puzzles offer similar understandings.

As for your quest for a 4D mechanism, I'm guessing that the difficulties
have something in common with 5D puzzles. That's because in the 4D cube
puzzle, our activity is analogous to an ant crawling on the surface of a
3D cube but being completely unaware about the volume of stuff under
that skin. What we see in MC4D shows exactly that 3D skin. When I 4D
rotate an object, I can sometimes get a sense that there is a kind of
volume that is being contained by the 3D geometry but I can't "see"
anything about the 4D volume. You could really use a 5D sensing ability
in order to look into the interior of a 4D object which is what you are
trying to do.

-Melinda

On 5/28/2012 6:31 PM, Ray Zhao wrote:
>
>
> You all make me seriously want to solve some puzzles ^_^, but right
> now I'm more interested in finding better solutions for the 3^4 and
> visualizing a mechanism for it as well. =P
> I also have summatives ;_;

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Maybe try some of the simple edge turning puzzles that Ed and I have
been having fun with? I enjoy those that do not require any
algorithms beyond a [1,1] commutator. That means that I can do it
purely intuitively and is actually a relaxing activity, probably
similar to the tedious parts of the 120-Cell and other large
puzzles. It's also great to get a feel for the 3D and 4D spaces in
which these manifolds live. You probably already have about as much
of a sense of the 4D cube as one can have. These puzzles offer
similar understandings.



As for your quest for a 4D mechanism, I'm guessing that the
difficulties have something in common with 5D puzzles. That's
because in the 4D cube puzzle, our activity is analogous to an ant
crawling on the surface of a 3D cube but being completely unaware
about the volume of stuff under that skin. What we see in MC4D shows
exactly that 3D skin. When I 4D rotate an object, I can sometimes
get a sense that there is a kind of volume that is being contained
by the 3D geometry but I can't "see" anything about the 4D volume.
You could really use a 5D sensing ability in order to look into the
interior of a 4D object which is what you are trying to do.



-Melinda



On 5/28/2012 6:31 PM, Ray Zhao wrote:
cite="mid:CAOFi9udO-XZdftuo=NYEaKomMBLBjKCxVxi8gjq+v6TAK+-9bw@mail.gmail.com"
type="cite">


You all make me seriously want to solve some puzzles ^_^, but
right now I'm more interested in finding better solutions for the
3^4 and visualizing a mechanism for it as well. =P

I also have summatives ;_;



--------------090704090200050703050507--

But you don't need 4D senses to look inside the classic Rubik's cube - scre=
wdriver works better for it. So for 3^4 mechanism it's enough to have power=
ful 4D viewer (to visualize and investigate non-convex bodies) or good 4D i=
magination (it a question of couple of months to develop it for a short tim=
e).
But I see a problem with physical implementation of 3^4. Consider two cel=
ls A and B with common ridge Q. You can rotate any of these cells around th=
e axis going throwgh the center of Q (90 deg twists). And these twists have=
exactly the same plane of 4D rotation: it's plane containing centers of cu=
be, of A and of B. So if we take block 3x3x1x1 at the ridge Q, its points w=
ill have the same physical movements in both twists. I afraid that it will =
allow you to twist just Q without moving of the rest of A and B cells - tha=
t is not a model that we use to play with.=20=20

Andrey








--- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
>
> Maybe try some of the simple edge turning puzzles that Ed and I have=20
> been having fun with? I enjoy those that do not require any algorithms=20
> beyond a [1,1] commutator. That means that I can do it purely=20
> intuitively and is actually a relaxing activity, probably similar to the=
=20
> tedious parts of the 120-Cell and other large puzzles. It's also great=20
> to get a feel for the 3D and 4D spaces in which these manifolds live.=20
> You probably already have about as much of a sense of the 4D cube as one=
=20
> can have. These puzzles offer similar understandings.
>=20
> As for your quest for a 4D mechanism, I'm guessing that the difficulties=
=20
> have something in common with 5D puzzles. That's because in the 4D cube=20
> puzzle, our activity is analogous to an ant crawling on the surface of a=
=20
> 3D cube but being completely unaware about the volume of stuff under=20
> that skin. What we see in MC4D shows exactly that 3D skin. When I 4D=20
> rotate an object, I can sometimes get a sense that there is a kind of=20
> volume that is being contained by the 3D geometry but I can't "see"=20
> anything about the 4D volume. You could really use a 5D sensing ability=20
> in order to look into the interior of a 4D object which is what you are=20
> trying to do.
>=20
> -Melinda
>=20
> On 5/28/2012 6:31 PM, Ray Zhao wrote:
> >
> >
> > You all make me seriously want to solve some puzzles ^_^, but right=20
> > now I'm more interested in finding better solutions for the 3^4 and=20
> > visualizing a mechanism for it as well. =3DP
> > I also have summatives ;_;
>

Did I misspeak? You are right that you don't need 4D senses to look
inside the classic Rubik's cube but you definitely need a good 3D sense,
and in many ways that is a much bigger requirement than sensing the
pattern of stickers on it's surface. MagicTile shows us you only need 2D
ability for that. By analogy you need 3D ability to deal with the 3D
surface of a hypercube and you will need 4D ability to understand its 4D
interior. I have no such ability and therefore have no idea what sort of
mechanisms might work for 4D beings. I also have very little interest in
that problem because I am much more interested in what the physical
models can show us compared to how they might physically do that.

-Melinda

On 5/29/2012 9:21 PM, Andrey wrote:
> But you don't need 4D senses to look inside the classic Rubik's cube - screwdriver works better for it. So for 3^4 mechanism it's enough to have powerful 4D viewer (to visualize and investigate non-convex bodies) or good 4D imagination (it a question of couple of months to develop it for a short time).
> But I see a problem with physical implementation of 3^4. Consider two cells A and B with common ridge Q. You can rotate any of these cells around the axis going throwgh the center of Q (90 deg twists). And these twists have exactly the same plane of 4D rotation: it's plane containing centers of cube, of A and of B. So if we take block 3x3x1x1 at the ridge Q, its points will have the same physical movements in both twists. I afraid that it will allow you to twist just Q without moving of the rest of A and B cells - that is not a model that we use to play with.
>
> Andrey
>
>
>
>
>
>
>
>
> --- In 4D_Cubing@yahoogroups.com, Melinda Green wrote:
>> Maybe try some of the simple edge turning puzzles that Ed and I have
>> been having fun with? I enjoy those that do not require any algorithms
>> beyond a [1,1] commutator. That means that I can do it purely
>> intuitively and is actually a relaxing activity, probably similar to the
>> tedious parts of the 120-Cell and other large puzzles. It's also great
>> to get a feel for the 3D and 4D spaces in which these manifolds live.
>> You probably already have about as much of a sense of the 4D cube as one
>> can have. These puzzles offer similar understandings.
>>
>> As for your quest for a 4D mechanism, I'm guessing that the difficulties
>> have something in common with 5D puzzles. That's because in the 4D cube
>> puzzle, our activity is analogous to an ant crawling on the surface of a
>> 3D cube but being completely unaware about the volume of stuff under
>> that skin. What we see in MC4D shows exactly that 3D skin. When I 4D
>> rotate an object, I can sometimes get a sense that there is a kind of
>> volume that is being contained by the 3D geometry but I can't "see"
>> anything about the 4D volume. You could really use a 5D sensing ability
>> in order to look into the interior of a 4D object which is what you are
>> trying to do.
>>
>> -Melinda
>>
>> On 5/28/2012 6:31 PM, Ray Zhao wrote:
>>>
>>> You all make me seriously want to solve some puzzles ^_^, but right
>>> now I'm more interested in finding better solutions for the 3^4 and
>>> visualizing a mechanism for it as well. =P
>>> I also have summatives ;_;
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

I have reached 90.

83 Solving of MT hyp {8,3} 12B E 1:0:0 ----- 05/29/2012 (497 twists)
84 Solving of MT hyp {8,3} 12B F 0:1:0 V 1:0:0 ----- 05/29/2012 (620 twis=
ts)
85 Solving of MT ell sph octa E 0:1:0 ----- 05/29/2012 (52 twists)
86 Solving of MT ell sph cube E 1:0:0 ----- 05/29/2012 (65 twists)
87 Solving of MT ell sph icosa E 0:1:0 ----- 05/29/2012 (277 twists)
88 Solving of MT ell sph dodeca E 1:0:0 ----- 05/29/2012 (232 twists)
89 Solving of MT ell sph octa F 0:1:0 V 1:0:0 ----- 05/30/2012 (77 twists=
)
90 Solving of MT ell sph icosa F 0:1:0 V 1:0:0 ----- 05/30/2012 (325 twis=
ts)

ad no 83:
Change from flip of singe color in the orbit to flip of doubled color in th=
e orbit!

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Same here; I just thought that it would be interesting to visualize a basic
mechanism.
Also, I have almost solved the 3^4 again, but this time using the layer by
layer approach, which works alright.
For the last layer I tried to use Dan Brown's method, but I learned that
his method for 4d cubes is as inefficient as his method for 3d cubes (in
move count, not algorithm count).

--
while(true)
Console.Writeline("HI!")

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Same here; I just thought that it would be interesting to visualize a basic=
mechanism.
Also, I have almost solved the 3^4 again, but this time usin=
g the layer by layer approach, which works alright.
For the last layer I=
tried to use Dan Brown's method, but I learned that his method for 4d =
cubes is as inefficient as his method for 3d cubes (in move count, not algo=
rithm count).


--