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Since I'm not connected with mathemathics in any way, and my solving method=
s are based on my visual sense of space, I think I can share my point of vi=
ew (which is very close to Brandon's and Roice's):
I think understanding the 4 or 5d space is not possible. The problem is tha=
t the brain can't understand what the sense-organs can't sense. The brain o=
nly process the information coming from the sense-organs. You have no organ=
s for recepting any information coming from the 4 dimension - no informatio=
n, no processing. What really happens here: the solvers can understand the =
3d projection of higher dimensional objects visualised by the computer prog=
rams, and with this fundamental, one can build a raw image of the whole obj=
ect, which is fairly enough to solve a rubik-type puzzle based on that part=
icular shape. If you understand how the line follows from the point, the sq=
uare follows from the line, the cube follows from the square, the tesseract=
follows from the cube (penteract follows from the thesseract etc.), you'll=
realize that no matter how many dimensions you face, the problem will be a=
lways the same: you must solve a puzzle. Everything you must know to
that, can be applied in one dimension higher and higher and higher. Unders=
tanding 4 or 5d space and objects is not required (and not possible as I me=
ntioned). Understanding what you see on the screen is sufficient. With this=
approach, I was able to solve the MC4d and MC5D.
If you ask Roice why he never=20
finished the MC6D (there are some pictures of it somewhere on the=20
yahoogroup page), I bet he will tell you, that the 3d projection just looke=
d too complicated to take in.The story ends here for me: no convenient 3d p=
rojection, no solution.
Andrey solved the problem=20
of the projection of the 6+ dimension "cube" with a very smart and elegant =
fractal-like structure, but this projection has nothing to do with=20
the real look of the 6 or 7d 'cube'. For this reason, I don't think I could=
solve them (never tried tho). To do this, I should think more like a mathe=
matician, which I'm not :)
(again: sry for the poor english, I'm hoping it's understandable)
A
________________________________
From: Brandon Enright
To: 4D_Cubing@yahoogroups.com=20
Cc: bmenrigh@ucsd.edu=20
Sent: Wednesday, February 8, 2012 8:41 PM
Subject: Re: [MC4D] Re: New here (on understanding higher dimensions)
=20
=C2=A0=20
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1
[... On the topic of 3D -> 4D -> nD ...]
On Wed, 8 Feb 2012 11:24:09 -0600
Roice Nelson
> For myself, even having solved MC5D once many years ago, I've never
> felt I could really make the jump to visualizing 4D. To think about
> things, I'm always a slave to dimensional
> analogy
> and when interacting with the puzzles, I have to do so in the most 3D
> way I can (a nice part of this group's puzzle representations is that
> they still allow you to interact with things in a 3D-like way). It
> would be great to be able to "see" the hypercube and hypersphere in a
> truly 4D way though, and I've read about people who claim they have.
I totally agree that nobody (or very close to nobody) can understand all
aspects of a 4D object simultaneously like it seems we can with 2D (and
possibly 3D) objects.
I definitely "understand" many of the 4D objects offered up by MC4D but
my understanding is a very mechanical one. It's basically a mental
table of how turns affect pieces, how pieces interact with each other,
what happens when you do a 4D rotate, etc. It's more just a list of
properties than it is and understanding of the fundamental underlying
geometry that creates the properties.
I'm actually not completely convinced that we even understand the
entirety of a 3D object at one time. I'm pretty sure we just take in
the view of the object projected into 2D (with a bit of stereo for
depth) and reconstruct what the 3D object is by rotating it and feeling
it and looking at it over some period of time. We're just so used to
doing this that it seems like we fully understand 3D objects -- even
though our understanding is built out of a solid understanding of 2D.
I wonder if the folks that claim they can visualize / understand 4D are
actually being tricked by the same reconstruction of 4D out of an
understanding of 3D. I think it would take a 4D being to completely
understand a 3D object in one look just as I think it would take a 5D
being to understand a 4D object at a glance.
But whether you "understand" 4D or 5D at the fundamental level is
somewhat unrelated to the ability solve puzzles in 4 and 5 dimensions.
Brandon
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ed with mathemathics in any way, and my solving methods are based on my vis=
ual sense of space, I think I can share my point of view (which is very clo=
se to Brandon's and Roice's):
the 4 or 5d space is not possible. The problem is that the brain can't unde=
rstand what the sense-organs can't sense. The brain only process the inform=
ation coming from the sense-organs. You have no organs for recepting any in=
formation coming from the 4 dimension - no information, no processing. What=
really happens here: the solvers can understand the 3d projection of highe=
r dimensional objects visualised by the computer programs, and with this fu=
ndamental, one can build a raw image of the whole object, which is fairly e=
nough to solve a rubik-type puzzle based on that particular shape.
If you understand how the line follows from the point, the sq=
uare follows from the line, the cube follows from the square, the tesseract=
follows from the cube (penteract follows from the thesseract etc.), you'll=
realize that no matter how many dimensions you face, the problem will be a=
lways the same: you must solve a puzzle. Everything you must know to that, =
can be applied in one dimension higher and higher and higher. Understanding=
4 or 5d space and objects is not required (and not possible as I mentioned=
). Understanding what you see on the screen is sufficient. With this approa=
ch, I was able to solve the MC4d and MC5D.
finished the MC6D (there are some pictures of it somewhere on the=20
yahoogroup page), I bet he will tell you, that the 3d projection just looke=
d too complicated to take in. The story ends here for me: no c=
onvenient 3d projection, no solution.
ndrey solved the problem=20
of the projection of the 6+ dimension "cube" with a very smart and elegant =
fractal-like structure, but this projection has nothing to do with=20
the real look of the 6 or 7d 'cube'. For this reason, I don't think I could=
solve them (never tried tho). To do this, I should think more like a mathe=
matician, which I'm not :)
for the poor english, I'm hoping it's understandable)
div>A
From: Br=
andon Enright <bmenrigh@ucsd.edu>
bold;">To: 4D_Cubing@yahoogroups.com
weight: bold;">Cc: bmenrigh@ucsd.edu
-weight: bold;">Sent: Wednesday, February 8, 2012 8:41 PM
on understanding higher dimensions)
=20=20=20=20=20=20
=20=20=20=20=20=20
Hash: SHA1
[... On the topic of 3D -> 4D -> nD ...]
On Wed, 8 Feb 2012 11:24:09 -0600
Roice Nelson <target=3D"_blank" href=3D"mailto:roice3%40gmail.com">roice3@gmail.com&g=
t; wrote:
> For myself, even having solved MC5D once many years ago, I've never
> felt I could really make the jump to visualizing 4D. To think about
> things, I'm always a slave to dimensional
> analogy<ipedia.org/wiki/Four-dimensional_space#Dimensional_analogy">http://en.wikip=
edia.org/wiki/Four-dimensional_space#Dimensional_analogy>,
> and when interacting with the puzzles, I have to do so in the most 3D<=
br>
> way I can (a nice part of this group's puzzle representations is that<=
br>
> they still allow you to interact with things in a 3D-like way). It
> would be great to be able to "see" the hypercube and hypersphere in a<=
br>
> truly 4D way though, and I've read about people who claim they have.
I totally agree that nobody (or very close to nobody) can understand all
aspects of a 4D object simultaneously like it seems we can with 2D (and
possibly 3D) objects.
I definitely "understand" many of the 4D objects offered up by MC4D but
my understanding is a very mechanical one. It's basically a mental
table of how turns affect pieces, how pieces interact with each other,
what happens when you do a 4D rotate, etc. It's more just a list of
properties than it is and understanding of the fundamental underlying
geometry that creates the properties.
I'm actually not completely convinced that we even understand the
entirety of a 3D object at one time. I'm pretty sure we just take in
the view of the object projected into 2D (with a bit of stereo for
depth) and reconstruct what the 3D object is by rotating it and feeling
it and looking at it over some period of time. We're just so used to
doing this that it seems like we fully understand 3D objects -- even
though our understanding is built out of a solid understanding of 2D.
I wonder if the folks that claim they can visualize / understand 4D are
actually being tricked by the same reconstruction of 4D out of an
understanding of 3D. I think it would take a 4D being to completely
understand a 3D object in one look just as I think it would take a 5D
being to understand a 4D object at a glance.
But whether you "understand" 4D or 5D at the fundamental level is
somewhat unrelated to the ability solve puzzles in 4 and 5 dimensions.
Brandon
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