Edge of a bounded universe

I was wondering what the two dimensional inhabitants of a flatland would see
if they came to the edge of their world - say these 2D people lived on disk
or a Moebius strip.

My immediate thought was that they would see a black line - a wall in 2D
circling their Universe. But that wouldn't allow the laws of thermodynamics
to work - the system would lose heat for example.

Thinking about it, the edge must appear to be a perfect mirror, as it must
reflect all energy back into the 2D world to conserve energy in the 2D
universe.

Which then makes me think that in the very unlikely event that our 3D/4D
Universe has an "edge", this is what it must be - a perfect mirror
encircling the Universe. And not a black wall, as one might imagine.

"Peter Webb" wrote in message
u...
|I was wondering what the two dimensional inhabitants of a flatland would
see
| if they came to the edge of their world - say these 2D people lived on
disk
| or a Moebius strip.
|
| My immediate thought was that they would see a black line - a wall in 2D
| circling their Universe. But that wouldn't allow the laws of
thermodynamics
| to work - the system would lose heat for example.
|
| Thinking about it, the edge must appear to be a perfect mirror, as it must
| reflect all energy back into the 2D world to conserve energy in the 2D
| universe.
|
| Which then makes me think that in the very unlikely event that our 3D/4D
| Universe has an "edge", this is what it must be - a perfect mirror
| encircling the Universe. And not a black wall, as one might imagine.
|
yawn
The inhabitants fall apart, they have a hole from mouth to anus.

"Sorcerer" ha scritto nel messaggio
o.uk...

yawn
The inhabitants fall apart, they have a hole from mouth to anus.

Isnt't this our situation?
So we can eat without exploding...

Luigi Caselli

Peter Webb wrote:

I was wondering what the two dimensional inhabitants of a flatland would see
if they came to the edge of their world - say these 2D people lived on disk
or a Moebius strip.

My immediate thought was that they would see a black line - a wall in 2D
circling their Universe.

The dimensions of the wall would be what, the
circumference of the disk by the height? A 2D
disk doesn't have thickness so the wall has no
height, you are still thinking 3D.

But that wouldn't allow the laws of thermodynamics
to work - the system would lose heat for example.

Thinking about it, the edge must appear to be a perfect mirror, as it must
reflect all energy back into the 2D world to conserve energy in the 2D
universe.

Which then makes me think that in the very unlikely event that our 3D/4D
Universe has an "edge", this is what it must be - a perfect mirror
encircling the Universe. And not a black wall, as one might imagine.

Same problem, you are still thinking in 3D. As
the boundary of flatland, the mirror and the wall
are 1D lines, they have zero area.

George

In article , ics_e says...

"Peter Webb" wrote in message
u...
|I was wondering what the two dimensional inhabitants of a flatland would
see
| if they came to the edge of their world - say these 2D people lived on
disk
| or a Moebius strip.
|
| My immediate thought was that they would see a black line - a wall in 2D
| circling their Universe. But that wouldn't allow the laws of
thermodynamics
| to work - the system would lose heat for example.

There is really no need to require that the total energy of the universe is conserved so the boundary could be a
mirror, or a black body at some temperature, or just about anything you desire. Imagine, for example, a steady state
expanding universe. To be truely steady state the energy density per unit volume has to remain constant. This could be
achieved either via FGred Hoyle's idea of continuous creation throughout the universe, or by energy being injected into
the universe (as either matter or energy) at the boundary.
|
| Thinking about it, the edge must appear to be a perfect mirror, as it must
| reflect all energy back into the 2D world to conserve energy in the 2D
| universe.
|
| Which then makes me think that in the very unlikely event that our 3D/4D
| Universe has an "edge", this is what it must be - a perfect mirror
| encircling the Universe. And not a black wall, as one might imagine.
|
yawn
The inhabitants fall apart, they have a hole from mouth to anus.

Not if they have an internal "zipper"-like device at either end. Alternately, maybe they just absorb food across a
surface membrane a la amoeba.

Mike

"Peter Webb" wrote:

I was wondering what the two dimensional inhabitants of a flatland would see
if they came to the edge of their world - say these 2D people lived on disk
or a Moebius strip.

My immediate thought was that they would see a black line - a wall in 2D
circling their Universe. But that wouldn't allow the laws of thermodynamics
to work - the system would lose heat for example.

Thinking about it, the edge must appear to be a perfect mirror, as it must
reflect all energy back into the 2D world to conserve energy in the 2D
universe.

Which then makes me think that in the very unlikely event that our 3D/4D
Universe has an "edge", this is what it must be - a perfect mirror
encircling the Universe. And not a black wall, as one might imagine.

Why put them on a disc or Moebius strip? Just put them on the surface of a
sphere, then they have no centre, no edge, and the sphere can expand or shrink
as required. And anyone farsighted enough could see the back of his own head.
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In article ,
Patrick Hamlyn wrote:

"Peter Webb" wrote:

I was wondering what the two dimensional inhabitants of a flatland would see
if they came to the edge of their world - say these 2D people lived on disk
or a Moebius strip.

My immediate thought was that they would see a black line - a wall in 2D
circling their Universe. But that wouldn't allow the laws of thermodynamics
to work - the system would lose heat for example.

Thinking about it, the edge must appear to be a perfect mirror, as it must
reflect all energy back into the 2D world to conserve energy in the 2D
universe.

Which then makes me think that in the very unlikely event that our 3D/4D
Universe has an "edge", this is what it must be - a perfect mirror
encircling the Universe. And not a black wall, as one might imagine.

Why put them on a disc or Moebius strip? Just put them on the surface of a
sphere, then they have no centre, no edge, and the sphere can expand or shrink
as required. And anyone farsighted enough could see the back of his own head.

Or even on a Klein bottle surface or a projective plane.

"Mike" wrote in message
...
In article ,
ics_e says...

"Peter Webb" wrote in message
u...
|I was wondering what the two dimensional inhabitants of a flatland would
see
| if they came to the edge of their world - say these 2D people lived on
disk
| or a Moebius strip.
|
| My immediate thought was that they would see a black line - a wall in
2D
| circling their Universe. But that wouldn't allow the laws of
thermodynamics
| to work - the system would lose heat for example.

There is really no need to require that the total energy of the universe
is conserved so the boundary could be a
mirror, or a black body at some temperature, or just about anything you
desire.

Agreed. perhaps I should say "a Universe which obeys the laws of
thermodynamics" - which includes conservation of energy. In the real world,
if something doesn't obey the law of thermodynamics, then its not a closed
system, and hence not the entire "Universe".


Imagine, for example, a steady state
expanding universe. To be truely steady state the energy density per unit
volume has to remain constant. This could be
achieved either via FGred Hoyle's idea of continuous creation throughout
the universe, or by energy being injected into
the universe (as either matter or energy) at the boundary.
|
| Thinking about it, the edge must appear to be a perfect mirror, as it
must
| reflect all energy back into the 2D world to conserve energy in the 2D
| universe.
|
| Which then makes me think that in the very unlikely event that our
3D/4D
| Universe has an "edge", this is what it must be - a perfect mirror
| encircling the Universe. And not a black wall, as one might imagine.
|
yawn
The inhabitants fall apart, they have a hole from mouth to anus.

Not if they have an internal "zipper"-like device at either end.
Alternately, maybe they just absorb food across a
surface membrane a la amoeba.


Agreed. There are lots of models of how biological organisms and computers
could in theory be built in 2D, assuming materials that are analogues of
existing 3D materials. All highly speculative, of course, but very
hypothetically possible (and yes I know about instability of orbits etc, but
the people live on a Moebius band, so we should cut them some slack).

Mike

"Virgil" wrote in message
...
In article ,
Patrick Hamlyn wrote:

"Peter Webb" wrote:

I was wondering what the two dimensional inhabitants of a flatland would
see
if they came to the edge of their world - say these 2D people lived on
disk
or a Moebius strip.

My immediate thought was that they would see a black line - a wall in 2D
circling their Universe. But that wouldn't allow the laws of
thermodynamics
to work - the system would lose heat for example.

Thinking about it, the edge must appear to be a perfect mirror, as it
must
reflect all energy back into the 2D world to conserve energy in the 2D
universe.

Which then makes me think that in the very unlikely event that our 3D/4D
Universe has an "edge", this is what it must be - a perfect mirror
encircling the Universe. And not a black wall, as one might imagine.

Why put them on a disc or Moebius strip? Just put them on the surface of
a
sphere, then they have no centre, no edge, and the sphere can expand or
shrink
as required. And anyone farsighted enough could see the back of his own
head.

Or even on a Klein bottle surface or a projective plane.

Because none of these have an "edge" (a boundary), which is what the post is
about.

In article ,
"Peter Webb" wrote:

"Virgil" wrote in message
...
In article ,
Patrick Hamlyn wrote:

"Peter Webb" wrote:

I was wondering what the two dimensional inhabitants of a flatland would
see
if they came to the edge of their world - say these 2D people lived on
disk
or a Moebius strip.

My immediate thought was that they would see a black line - a wall in 2D
circling their Universe. But that wouldn't allow the laws of
thermodynamics
to work - the system would lose heat for example.

Thinking about it, the edge must appear to be a perfect mirror, as it
must
reflect all energy back into the 2D world to conserve energy in the 2D
universe.

Which then makes me think that in the very unlikely event that our 3D/4D
Universe has an "edge", this is what it must be - a perfect mirror
encircling the Universe. And not a black wall, as one might imagine.

Why put them on a disc or Moebius strip? Just put them on the surface of
a
sphere, then they have no centre, no edge, and the sphere can expand or
shrink
as required. And anyone farsighted enough could see the back of his own
head.

Or even on a Klein bottle surface or a projective plane.

Because none of these have an "edge" (a boundary), which is what the post is
about.

Bounded does not necessarily imply an "edge".
A spheres and a torus are dimensional objects of bounded area.