Message #3838

From: Joel Karlsson <joelkarlsson97@gmail.com>
Subject: Re: [MC4D] Yes, there is handedness in 4D, 5D, etc
Date: Fri, 24 Nov 2017 20:04:39 +0100

Hi Marc,

I agree with most of what you said. Regarding the L, you are absolutely
correct, giving the two sides different colours makes the L chiral in 3D
(mathematically this makes the object an oriented surface which basically
is a surface with a specified normal). With the standard set of legal moves
for magic cubes, there are no moves that change the orientation of a
sticker (ie, if you put an arrow on a sticker that points away from the
center of the cube it will always point away from the center no matter how
you twist the cube). This property is equivalent to the cube being "stiff",
you can’t turn it inside out, and I agree that this is not a flaw but
rather a property of these puzzles.

This isn’t really important for the discussion regarding chirality but
still an interesting topic. Regarding "a […] 2D object […] does not
exist [in 3D]" I do not agree. Although the statement might be true for our
physical universe (however, an object don’t have to be made of atoms so if
our universe is continuous we can construct 2D object, although that is not
my point right now) I would, personally, say that the Rubik’s Cube is an
abstract object rather than a physical one and that the stickers are indeed
n-1 dimensional.

Best regards,
Joel

2017-11-24 15:20 GMT+01:00 Bob Hearn bob.hearn@gmail.com [4D_Cubing] <
4D_Cubing@yahoogroups.com>:

>
>
>
>
> > On Nov 24, 2017, at 8:41 AM, ‘Eduard Baumann’ ed.baumann@bluewin.ch
> [4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:
> >
> > Handedness of 2^4 appears only after the 4D/3D projection and you have
> two possible projections.
> > MCD4 has chosen one specific projection. The physical 2^4 should chose
> the same projection for practical reasons.
> >
> > Hmph.
> >
> > Best regards
> > Ed
>
> But that’s just a matter of color assignment. The physical 2x2x2x2 colors
> are not even the same set as the default MC4D colors, let alone the same
> assignment. So I don’t see what the issue is here?
>
> Bob
>
>
>