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"
To: "John Bailey"
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