| Topic: |
Science > Physics |
| User: |
"Xevious" |
| Date: |
10 Feb 2004 08:26:02 PM |
| Object: |
The Nature of Space-Time |
Horizons: Exploring the Universe by Seeds gives lower-dimensional
projections as examples of different types of constructions of the
unverse (closed, flat and open.)
A plane is given as a flat universe, the surface of a sphere as a
closed universe, and the surface of a saddle as an open universe.
Seeds says that a two dimensional creature could measure the curvature
of its two dimensional universe by drawing circles.
"On a flat universe, the area of a circle would always be pi * r^2, no
matter how big the circle was. But on a spherical surface, large
circles would contain less than pi * r^2. On a saddle-shaped surface,
large circles would contain more than pi * r^2. In the same way, we
can detect the curvature of our three-dimensional niverse, but we must
make measurements over very large distances."
The exposition is confusing. If the ant draws a large circle around
the plane of a sphere, then is Seeds referring to the area of the
*cross-section* created by the circle? Because the area encompassed on
the sphere would be *greater* than pi * r^2.
But a cross-section wouldn't make sense, because all of the area of
the cross-section would lie *outside* that universe.
What is the significance of this? And how can we do the same in our
three dimensional universe? With superlarge spheres?
Xevious
.
|
|
| User: "Raymond N Moore" |
|
| Title: Re: The Nature of Space-Time |
11 Feb 2004 12:50:59 AM |
|
|
He is using the arc on the surface of the sphere to define it's diameter.
This is diameter accessable in the two dimensional world.
Ray Moore
Xevious wrote:
Horizons: Exploring the Universe by Seeds gives lower-dimensional
projections as examples of different types of constructions of the
unverse (closed, flat and open.)
A plane is given as a flat universe, the surface of a sphere as a
closed universe, and the surface of a saddle as an open universe.
Seeds says that a two dimensional creature could measure the curvature
of its two dimensional universe by drawing circles.
"On a flat universe, the area of a circle would always be pi * r^2, no
matter how big the circle was. But on a spherical surface, large
circles would contain less than pi * r^2. On a saddle-shaped surface,
large circles would contain more than pi * r^2. In the same way, we
can detect the curvature of our three-dimensional niverse, but we must
make measurements over very large distances."
The exposition is confusing. If the ant draws a large circle around
the plane of a sphere, then is Seeds referring to the area of the
*cross-section* created by the circle? Because the area encompassed on
the sphere would be *greater* than pi * r^2.
But a cross-section wouldn't make sense, because all of the area of
the cross-section would lie *outside* that universe.
What is the significance of this? And how can we do the same in our
three dimensional universe? With superlarge spheres?
Xevious
-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----
.
|
|
|
|
| User: "Uncle Al" |
|
| Title: Re: The Nature of Space-Time |
11 Feb 2004 10:14:22 AM |
|
|
Xevious wrote:
Horizons: Exploring the Universe by Seeds gives lower-dimensional
projections as examples of different types of constructions of the
unverse (closed, flat and open.)
OK, git, how do you reconcile WMAPS data plus Sloan Digital Sky Survey
data plus Jeffryy Weeks connected dodecahderal universe fit (and its
impled intrinsic chirality) with a 2-D projection?
Google
"Jeffrey Weeks" dodecahedron 153 hits
"Jeffrey Weeks" dodecahedral 82 hits
Why don't you tell us how to flatten a Seifert-Weber dodecahedral
space?
A plane is given as a flat universe, the surface of a sphere as a
closed universe, and the surface of a saddle as an open universe.
You don't know ***** about the subject. There are lots of compact
minimal surfaces with that are Euclidean without being flat planes.
There are fully *eight* simply-connected geometric 3-manifolds with
compact quotients,
Bull. Amer. Math. Soc. 6 357-381 (1982)
Bull. Lond. Math. Soc. 15(5) 401-487 (1983)
WP Thurston, "Three-dimensional geometry and topology," Vol. 1.
Princeton Mathematical Press, Princeton, NJ, 1997.
Seeds says that a two dimensional creature could measure the curvature
of its two dimensional universe by drawing circles.
Or triangles with light rays, summing their interior angles and
comparing with 180 degrees. Perhaps he knows what he is talking about
and you do not.
"On a flat universe, the area of a circle would always be pi * r^2, no
matter how big the circle was. But on a spherical surface, large
circles would contain less than pi * r^2. On a saddle-shaped surface,
large circles would contain more than pi * r^2. In the same way, we
can detect the curvature of our three-dimensional niverse, but we must
make measurements over very large distances."
The exposition is confusing.
Learn some geometry. When you know something you can use that
knowledge to think thoughts.
[snip]
--
Uncle Al
http://www.mazepath.com/uncleal/qz.pdf
http://www.mazepath.com/uncleal/eotvos.htm
(Do something naughty to physics)
.
|
|
|
| User: "Xevious" |
|
| Title: Re: The Nature of Space-Time |
12 Feb 2004 10:09:57 AM |
|
|
On Wed, 11 Feb 2004 08:14:22 -0800, Uncle Al <UncleAl0@hate.spam.net>
wrote:
You don't know ***** about the subject. There are lots of compact
minimal surfaces with that are Euclidean without being flat planes.
There are fully *eight* simply-connected geometric 3-manifolds with
compact quotients,
You're right, I don't, you tactless crybaby! This is a ***** course
to fulfill my science requirement, and Seeds' analogies are almost as
poor as your exposition. You have the worst case of professor's
syndrome I have ever seen.
The author was obviously comparing the area of circles on his planar
examples to some other area, but HE DIDN'T SPECIFY in what type of
dimension. The surface area enclosed by a circle will obviously be
some pi * r^2, since it can be calculated by taking an equation of its
cross-section to the perimeter of the circle and then rotating it
about an axis. Basic calculus. To what area is Seeds comparing this? I
don't understand why this is such a hard question.
.
|
|
|
| User: "Spaceman" |
|
| Title: Re: The Nature of Space-Time |
12 Feb 2004 04:44:21 PM |
|
|
The nature of space-time?
<ROFLOL>
The nature of cubic feet-seconds?
The nature of cubic meter-days?
<LOL>
space-time
Still funny, still stupid,
Still worshipped like the false god it is.
Space is not part of time,
time is not part of space.
They are 2 different measurement factors.
They should remain seperated,
not joined as if they are one.
Got a cubic inch-hour?
How many cubic mm-seconds are in it?
<LOL>
.
|
|
|
|
|
|
|
Related Articles |
|
|
