Message #287

From: John Bailey <jbaile2@rochester.rr.com>
Subject: Re: 4D topologies and optics
Date: Wed, 21 Jun 2006 20:04:38 -0400

Thanks for your reply. Your revised article was a
refreshing re-read, showing me how much I do not
know about the formalism of the subject.
(http://www.bayarea.net/~kins/thomas_briggs/)

Oddly, I suppose, I have a very clear intuitive
feel about many aspects of 4D space. My webpage
with a 4D Rubik’s cube is my attempt to
demonstrate
this.(http://home.rochester.rr.com/jbxroads/4cube.html)

I am hardly alone, it turns out. Over the last
month, my mailbox has been filled as a discussion
group called 4D_Cubing@yahoogroups.com reacted to
an evolving 5 dimensional Rubik’s cube design at:
http://www.gravitation3d.com/magiccube5d/ Five
participants have filed logs demonstrating they
have solved the 5D cube problem expressed at this
website.

Not wanting to rain on their parade, I have
refrained from observing that certain
transformations get easier as the dimensionality
of the space goes up. Inverting a glove is a
simple example. I maintain that there are more
solution paths in a 4d cube relative to the number
of positions and similarly for 5d. Thus, such
problems are easier to solve–subject to the
condition that the player has an adequate
representation of the state of the configuration
and controls with which to manipulate. Alas, I
have been to busy to download the actual 5d
virtual cube.

John Bailey
http://home.rochester.rr.com/jbxroads
—– Original Message —–
From: "Tom Briggs" <tbriggs845@yahoo.com>
To: "John Bailey" <jbaile2@rochester.rr.com>
Sent: Wednesday, June 21, 2006 4:05 PM
Subject: Re: 4D topologies and optics

> John,
>
> Sorry about the long delay in answering your
> email- thank you for looking at my posted
> article. I read your interesting lensing
> article and have been going over some of the
>references.
>(http://home.rochester.rr.com/jbxroads/interests/sci.astro/3d_4s_skymap.html
> ) I printed
> the Gausmann, et. al. paper and found it
> difficult. Their next paper "Cornish N. Spergel
> D. and Starkman G. 1998 in Class. Quantum
> Gravity 15, 2657" is a little easier to follow.
> Also, their reference "10", which I am now
> studying, goes over this material in more
> detail (M. Lachieze-Rey, J. P. Luminet/Physics
> Reports 254 (1995) 133-214). Spherical
> geometry with time thrown in still escapes me.
>
> I "tuned up" my posted article a bit since your
> email and hope it is adequate.
>
> —- Tom Briggs