Message #2275

From: schuma <mananself@gmail.com>
Subject: [MC4D] Re: Regular abstract polytopes based on {5,3,4} and {4,3,5}
Date: Thu, 14 Jun 2012 02:12:28 -0000

Nice explanation!
The space is so weird. The light rays first diverge, pass the equator
and then converge. This is what a lens does to the light rays. So, in
optical terminology, it’s fair to say that the space acts like a lens,
which creates an image of someone near the antipode as if he/she’s in
front of you. Some curved physical space do behave like a lens, for
example the space around a massive star, or black hole, can create
images (gravitational lens)
<http://en.wikipedia.org/wiki/Gravitational_lens> .
"Myself turned inside out". This reminds me of an episode of Futurama,
in which Bender turns himself inside out so that the universe outside of
the "cave" is "inside" him. This video clip can be watched here:
<http://www.comedycentral.com/video-clips/p2ztps/futurama-trial-of-the-f arnsworths>
Nan
— In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:>> Hi
Nan,> > I like the {3,5,3}. That’s a lot of edges going into each
vertex!> > There is a fantastic two page explanation about what the
world would look> like from inside S3 in Thurston’s book "Three
Dimensional Geometry and>
Topology<http://www.amazon.com/gp/product/0691083045/ref=as_li_ss_tl?ie= UTF8&tag=gravit-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0 691083045>".> The section is "Example 1.4.2 (the three-sphere from
inside)", and can be> read in isolation. He uses dimensional analogy to
provide intuition on> your question about seeing yourself in each
direction. He leads you up to> this:> > In the background of everything
else, you see an image of yourself, turned> > inside out on a great
hollow sphere, wih the back of your head in front of> > you.> > > You
can read the section on google>
books<http://books.google.com/books?id=9kkuP3lsEFQC&lpg=PP1&dq=three%20d imensional%20geometry%20and%20topology&pg=PA32#v=snippet&q=three-sphere% 20&f=false>> (starts> on page 32). Do check it out! After rereading it
just now, I suspect the> youtube video you sent has some inaccuracies
when it comes to how edge> thicknesses are displayed.> > Also, I should
have thought to mention this earlier as well, but check out>
geometrygames.org, specifically the "CurvedSpaces" program. It will
let> you navigate through spherical and hyperbolic spaces, from inside
the space.> > Even though there are existing youtube videos and
programs, S3 would still> be a nice addition to your applet. It’s great
to be able to run this stuff> right on a web page, without anything to
install.> > Cheers,> Roice>