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Q: Universe - finite or infinite? ( Answered 2 out of 5 stars,   30 Comments )
Question  
Subject: Universe - finite or infinite?
Category: Science > Astronomy
Asked by: andytheindoeuropean-ga
List Price: $20.00
Posted: 19 Jan 2005 15:54 PST
Expires: 18 Feb 2005 15:54 PST
Question ID: 460093
Have astronomers, astrophysicists, cosmologists, and general
physicists decided definitely whether the universe is infinite or
finite?
Also, what I don't understand about the Big Bang theory is if the
universe was once a microscopic point, doesn't that imply that there
was an "outside" beyond the bounds of the microscopic universe?  Would
this "outside" be not of the universe, or would it just be the empty
part of the universe, or another universe, or does no "outside" even
exist?  How can the universe have a size if there is no such thing as
"outside" or "beyond" the (limits of) the universe? Does the universe
have size?  Is the "universe" as implied by the Big Bang theory merely
phenomena within the universe, such as stars and nebulae, i.e. matter
and energy -- and the limit to the universe is the limit of occurrence
of these phenomena?  But what about beyond these phenomena?  Wouldn't
there just be empty space extending to infinity?  I actually find an
infinite universe much easier to grasp intellectually than a finite
universe, since a finite universe to me always implies something
"outside" the universe which defines the boundary of the universe.
Answer  
Subject: Re: Universe - finite or infinite?
Answered By: hedgie-ga on 03 Feb 2005 23:14 PST
Rated:2 out of 5 stars
 
The succint answer,

 such as may be subject of  wager offered in the comment 
  From: silver777-ga on 19 Jan 2005 23:58 PST 
" I will even bet you your 20 bucks .."

succint answer is NO. At this time of an universal evolution, cosmologists are
deeply engaged in educated guesses, arguments, complex calculations,
construction of models and invention and revision of theories and
speculations.
The cosmologists are definitely undecided and there is no concensus.

It is even worse with general public, which has same atitude to this question,
as adolescents have to sex: they do not understand it - but it fascinates them.
Result are myths and jokes, which do not seem funny any more, once you
get actually involved in the study of the subject.
 An example:
People speak of the 'dark matter' - but fact is that no-one ever saw it. Only
reason it was invented was to save some theories which are otherwise
falsified by recent experiments.
 We all understand that baloon, goldtooththriller-ga and others' keep
talking about, is boundless but finite - but that baloon is also
curved. To imagine a surface which is everywhere flat, and closed upon
itself is very dificult, in any number of dimensions.  I dare to say
that a region of a flat space (E.n) is either bounded or infinite (Is
that not a theorem, Mathtalk?)

Time before the Big Bang is discussed e.g. by physicist Paul Davies, I
believe it is in his book "Arrow of time"
http://www.usyd.edu.au/time/price/preprints/arrow.html
in the following context: Imagine the 'elliptic' (rather then
parabolic or hyperpbolic) case of a universe (for definition see
SEARCH TERM: elliptic universe )
which is  the case in which universe will eventually start shrinking,
reaching a Big Crunch ... and then what? We can imagine matter will
get very dense, very hot, atoms broken to smitereens, particles
bouncing apart, and new expansion  starting ...
Ancient greeks had a concept of such cycle called 'A Great Year'. Davies is
asking: are such (possible) cycles a 'steady state' - same each time 
- or are the oscillations damped?  If so, is universe evolving to some
future equilibrium - sort of neo-thermal-death?

That much for fashionable myths.

 We just do not know. Even hundred years from now, it is unlikely that
this question will be closed. Universe is very big, and we only know
the tiny bit.
All current cosmological models assume the
 SEARCH TERM : fundamental cosmological hypothesis
 according to which the universe is homogeneous (same everywhere - on
the scale of galaxies) and that hypothesis is likely to be soon
falsified experimentally.

So, we do not know the answer. Right now, in the year of physics, 100 years
after Einstein's discovery of spacetime, we are beginning to realize
how little we know. We do know that we need to think about universe as
a 'spacetime' - in
the framework of General Relativity Theory ot GTR.
 In most cases relativistic geometry M4 can be reduced to ordinary
Euklidian geometry and time (M4 --> E3+ E1) . If we do that with
current  mainstream
SEARCH TERM : Big Bang
model, we get the model you mention: Mostly empty, infinite space E3,
in which matter is flying apart, more and more slowly. It may stop and
start falling back (elliptic case), keep slowing down to zero,
(parabolic case) or, if it has enough kinetic energy to overcome the
gravity (hyperbolic case) it may keep expanding. We do not even know
which case we have - as sky surveys come too close to parabolic - to
zero energy case - to decide. Then Davies's speculation opens the door
to hybrid cases, where ratio of kinetic and gravitational energy is
changing, and hyperbolic universe can become elliptic, with time.

However, when it comes to universe, all non-relativistic aproximations are
very poor, as we cannot ignore the fact that speed of light is finite:
Light of the distant stars take a long time to reach us. Father they
are, the longer it takes. It is clear that there ARE REGIONS OF
SPACETIME from which the
light cannot reach us. We are not even saying 'never reach us' because
that is the E3+E1 (classical) thinking. To think about these issues,
we would have to be able to imagine the universe as a curved M4
surface, possibly imbedded in higher dimensional E.n (with n>4) where
the light does not propagates. The light rays are all already on the
models (are geodetics of that surface) and we
just study which regions are connected (and so inter-act) and which are not.

There are regions of that M4 surface, which we do not see - meaning
there are no geodetics (light rays) leading from there-and-then to
here-and-now.
Regions which do not influence us in any way. 
There are events which are beyond OUR Event Horizont.
Are these part of our universe? We may construct models, using the
current cosmological hypothesis. Subject to Occam principle, as our
knowledge of our corner of universe is expanding, we may introduce
more complex models.

But we have no way of knowing directly how this complex curved surface
 would look if we could see it. It is possible that this question will
never be decided. As long as the mankind is exploring the universe,
our knowledge will grow and our model will grow more complex. It is
also possible, even likely, the way some superpowers are acting out
lately, that civilisations reach certain level of technology and then
destroy themselves. That would not end the universe, but it would
definitely close this question. That possible outcome would explain
why we did not get any ET visits as yet.

If you are really interested in  exploring the meaning of some of
these M4 terms, the curved surfaces imbedded in higher dimensional
spaces, you can look at the visulisations  of GTR and of STR which
have been posted on the internet.
Start with
SEARCH TERM: light cone

Hedgie
andytheindoeuropean-ga rated this answer:2 out of 5 stars
Although I appreciate your honesty in providing a general answer to my
question, I found that your grammar and punctuation and even
occasionally spelling were atrocious - pardon me if you are a
foreigner.  Plus I didn't like your frequent interjections of "SEARCH
TERM".  But more importantly, you did not seem to address the second
part of my question, as to whether a finite universe implies that
there is something outside the universe which defines its limits, or
whether there is nothing (and what exactly would "nothing" be - same
as empty space, or something else?).  But you did convey effectively
the reality of the disaccord among scientists about the answer to my
basic question.  So for that part I am satisfied.  Nevertheless I feel
your answer could have been better, at least grammatically correct!

Comments  
Subject: Re: Universe - finite or infinite?
From: goldtooththriller-ga on 19 Jan 2005 20:11 PST
 
It has been theoretically determined that, from the amount of dark
matter and dark energy in the universe, the universe is indeed flat in
shape and finite in area.  Although the size of the universe is
finite, it is boundless.  To demonstrate this, the balloon analogy is
most often used, where the universe would be the surface of the
balloon.  As the balloon inflates, the area increases, but stays
finite.  Also, the balloon has no edge, and there is no "center of
expansion" therefore the balloon is boundless.  The only thing
differing in this analogy is that the universe is a three-dimensional
boundless surface, rather than the two-dimensional surface of the
balloon.  The Universe's size as far as we can tell is at least 14.3
billion lightyears across, because that is the last scattering surface
of light from the big bang, and which is, with present-day
instruments, impossible to see past that distance.

To talk about a time or space before the Big Bang from the perspective
of our Universe is folly, because there was no space and time as we
know it, and yet it seems to be a paradox to us because naturally
something has to come from somewhere.  There are present theories
today that describe our Universe as one in an infinite array of
universes known as the multiverse or the manifold of universes.  These
theories also describe how a universe such as ours could have "budded
off" another universe by the way of a singularity.
Subject: Re: Universe - finite or infinite?
From: tlspiegel-ga on 19 Jan 2005 20:39 PST
 
Perhaps this will be helpful to you:

The Universe: Finite or Infinite? Copyright  2002 by Ronald Pisaturo.
All rights reserved.
http://pages.prodigy.net/rpisaturo/Universe.htm

=========

The Universe: Still Boggling the Minds of 'Finite Creatures'
By Robert Roy Britt
http://www.space.com/scienceastronomy/astronomy/universe_overview_010605-1.html

http://www.space.com/scienceastronomy/astronomy/universe_overview_010605-2.html
Subject: Re: Universe - finite or infinite?
From: cynthia-ga on 19 Jan 2005 20:45 PST
 
Hi andytheindoeuropean,

I think String Theory might interest you.  I urge you to watch this
NOVA special.  It's phenomenal.

WATCH THE 3 HOUR SPECIAL (FREE):

The Elegant Universe
MAIN PAGE:  http://www.pbs.org/wgbh/nova/elegant/
DOWNLOAD PAGE:  http://www.pbs.org/wgbh/nova/elegant/program.html
Each of the 3 hours are broken up into 8 minute sections.


The Official String Theory Web Site
MAIN PAGE:  http://superstringtheory.com/

Cosmology - How Old Is The Universe?
http://superstringtheory.com/cosmo/index.html


Wikipedia - String Theory
http://en.wikipedia.org/wiki/String_theory


~~Cynthia
Subject: Re: Universe - finite or infinite?
From: mathtalk-ga on 19 Jan 2005 21:17 PST
 
The finite vs. infinite question is very interesting.  It is thought
that the universe has only finitely many dimensions, although it is
quite conceivable that the number of dimensions is eleven rather than
four.

Speaking of the fourth dimension, there's a good bit of concensus that
the universe has "existed" for a finite length of time up to "now", as
goldtooththriller-ga notes.  But the abundance of dark energy
theoretically causes an accelerating expansion of the universe.  The
universe will thus "exist" for an infinitely long time, or else after
10^30 years the universe will grow so dull that at the least it will
seem to be taking infinitely long for time to pass.

regards, mathtalk-ga
Subject: Re: Universe - finite or infinite?
From: silver777-ga on 19 Jan 2005 23:58 PST
 
Andy,

Fantastic question.

Some things, we are not meant to know I'm sure. Have you considered
infinite finiteness? Is infinity a paradox? Like the Moebious (sp)
strip with an unending single surface, might our understanding of
infinity in fact be finite? Theories of singularity and complimentary
universes help us to attempt understanding. As does string theory.
Turning your thoughts 180 degrees, what of infinity toward the
interior? A cell, a proton, a string .. fractions within a line .. yet
a point is a dividable line .. infinitely .. where does it end? Maybe
it never ends, but as we exist as humans, we seek closure to all
events. But then what lays beyond that closure? Logic suggests that it
is never ending, and raises further questions. We are intelligent
enough to ask the questions. Are we intelligent enough to accept the
answers if and when they arrive? Or, do we blindly accept what is, to
be just that without question?

A minor example:

http://chuck.charleshart.net/Mathomagic.php

If you can find the ultimate answer for 20 bucks, it's a cheap
investment for you and all who read your words in question. I will
even bet you your 20 bucks that there will be no succinct answer to
your question beyond theories.

Phil
Subject: Re: Universe - finite or infinite?
From: frde-ga on 20 Jan 2005 04:06 PST
 
I have always found the concept of infinity difficult to grasp

Especially when applied to the Universe

With an infinite Universe the chances on a little green man having set
off on a 1000 light year journey - and landing on my keyboard ... now
... are 1.

Of course it could be a finite Universe in an infinite void
- but that 'begs the question' - in the true sense of the phrase
Subject: Re: Universe - finite or infinite?
From: guzzi-ga on 20 Jan 2005 15:50 PST
 
Infinity is easy -- programming a video is what?s difficult.

Best
Subject: Re: Universe - finite or infinite?
From: pinkfreud-ga on 20 Jan 2005 16:02 PST
 
I like the "turtles all the way down" theory.
Subject: Re: Universe - finite or infinite?
From: silver777-ga on 20 Jan 2005 17:23 PST
 
" .. turtles all the way down .. " was debunked after much
deliberation, Pink. It turned out to be an error in dictation by a
hard of hearing note taker. Reference was to planetary orbits.

" .. hurtles all the way around .. " were the intended words.   

Phil
Subject: Re: Universe - finite or infinite?
From: pinkfreud-ga on 20 Jan 2005 17:28 PST
 
Oh, dear. I have based my entire view of cosmology on a typo.

Next you'll be telling me that Planck's constant was really not a
constant at all, but a contest, and it's too late for my photons to
enter it.
Subject: Re: Universe - finite or infinite?
From: silver777-ga on 20 Jan 2005 22:47 PST
 
Andy and Pink,

Andy .. I hope you will forgive our side notes. I also trust that you
enjoy a touch of humour.

Pink .. If Poker was wordplay, you'd win every hand. 
(Were the turtles female Russian ones by chance?)

Phil
Subject: Re: Universe - finite or infinite?
From: hedgie-ga on 04 Feb 2005 21:38 PST
 
Re:
 Is there something outside the universe

Andy,

 By definition, there is nothing 'outside' the universe.
 When we say 'finite' we mean 
                  boundless but finite
like that balloon - or surface of the Earth.

You could have asked for clarification, if these terms were not clear.

I do apologize about my spelling. English is indeed not my first language,
but I should run the answer through the spelling checker. Usually I do,
but I focused on the content too much, this time. Sorry about that. 
Thanks for the rating.
Subject: Re: Universe - finite or infinite?
From: silver777-ga on 04 Feb 2005 21:55 PST
 
Ummm .. Is there anything I can do here? If I make a bet and a
promise, I keep both.

I'm happy to split my ante on future meaningful questions for you
Andy. That is, I am willing to spend $10 of my own money if you two
will come to some agreement that will benefit the both of you and
perhaps the greater community of us so fortunate to have access to a
computer.

I respect your command of the English language Andy, however Hedgie
was simply providing you with search terms for your own use and for
the purpose of clarification in arriving at the information provided
to you.

Researchers may become tired after toiling away for hours. Provided
that the information is forthcoming to answer your question, and IS
decipherable, you have achieved an answer to your inquiry. I had no
trouble in following Hedgie's informative answer to your generalised
question. In fact, I learnt from it.

It's your call guys.

Phil
Subject: Re: Universe - finite or infinite?
From: andytheindoeuropean-ga on 05 Feb 2005 13:56 PST
 
OK, I received criticism from Phil (silver777ga) that my own criticism
was too harsh.  Sorry, Hedgie, perhaps I had a bad day.  I realize
that you're not exactly writing for a scientific journal, and now I
know (as I suspected) that English is not your first language.  I will
take advantage of the links (search terms)you and others have
provided, as well as the suggested books, to further research my
question.  I still would like to know, though, that if a boundless
finite universe has nothing outside it, how can it be boundless? 
Doesn't that mean it ends -- and if something ends, doesn't another
thing begin?  And is that other thing, the "nothing" that is at the
limits of the universe, not empty space?  Or is empty space not
nothing, and "nothing" cannot be conceived mentally?  Or is the idea
of true "nothing" and boundlessness a concept one is not meant to be
able to visualize, they're just words we must accept in describing the
universe?
Well, you don't have to answer once again, you've already provided
your answer.  Thanks.  I think perhaps I should have at least given
you three stars, since you did provide a lengthy answer and plenty of
cross-references.

Thanks again,

Andy the Indo-European
Subject: Re: Universe - finite or infinite?
From: silver777-ga on 05 Feb 2005 18:55 PST
 
Andy,

You're a gentleman. Well said.

Phil
Subject: Re: Universe - finite or infinite?
From: hedgie-ga on 06 Feb 2005 20:28 PST
 
Greetings from your fellow-indo-european, Andy,

 I accept the apology, but based on the average rating of 4.6 rating
of my other physics answers, I would still feel you did not  'got',
what I wrote, about the finiteness of the universe, if you would give
me  three stars.

 Problems with physics questions on GA is usually not the correct
science; that's the easy part. The challenge is to gear the answer to
the interest and background of the asker, often on too meager
information we get on his or her
prior knowledge. The problem with this question is that too much was
written about it, philosophy, math, physics,.. and it is very easy to
get lost in it. What people can get from GA, what you would be able to
get, if you would not end the dialog in such a haste, and can still
get posting another, more specific question, is customized guide to
literature. Literature is enormous and covers all those aspects on
different levels  (here is a small sample:
   http://www.reciprocalsystem.com/nlst/references.html
 )
  There are different views, but some common base of knowledge and
concepts: what is space, what is empty, curved and higher dimensional
space and various geometries, have been established and are
understandable, if approached well.

  If you want to get how, 
 ".. finite universe that has nothing outside it, how can it be boundless?  "
 
 then you need to pay more attention to these E3, M4, En, symbols,
which people use to describe different geometries and spaces of
different dimensions. At one time people where wondering if they can
fall 'of the end of the Eart as bible is referring to ".. [one] end of
the earth even unto the [other] end of the earth ..".  Some people
still believe in the Flat Earth and some in a flat universe. On the
surface of Earth there is no boundary - it is a sphere.
 You keep going North, and come back from the South. There is no end
and it is finite. There is no wall, no end. It is similar with
universe. There is a serious project underway, which is matching what
we see looking in two opposite directions of the sky, but this is just
one of many possible ways it can be,  and how it can be understood and
verified. To conclude: I would recommend this one book:
  http://www.amazon.com/exec/obidos/search-handle-form/ref=s_sf_b_as/104-2847508-5235145
  As an intro to the filed. It provides readable  overview of
evolution of the current philosophical concepts of space. It is
non-mathematical, but well informed about modern physics.
  Have a happy journey into the mysteries of space and time
  Hedgie
Subject: Re: Universe - finite or infinite?
From: hedgie-ga on 06 Feb 2005 20:31 PST
 
Correcting a typo:
 As an intro to the filed.
should be

as an intro into this field.

(I dit run it through a checker this time, but then I do some last
minute editing - and mess it up again. So, sorry about a typo.)
Subject: Re: Universe - finite or infinite?
From: hedgie-ga on 06 Feb 2005 20:42 PST
 
Ouch - That book link is messed up too. I will try again:

Recommended book is:
Boston Studies in the Philosophy of Science: The Concepts of Space and
Time - Their Structure and Their Development (Synthese Library : No
74)
by M. Capek (Paperback - December 1, 1975) 

Publisher: Kluwer Academic Pub (December 1, 1975)
 
ISBN: 9027703752

and amazon reference is
http://www.amazon.com/exec/obidos/tg/detail/-/9027703752/104-2847508-5235145
it looks like it got some 'rare and expensive' status now, but should
be available in most college libraries. Also available in hard cover:
http://www.amazon.com/exec/obidos/tg/detail/-/9027703558/qid=110775116/104-2847508-5235145
Subject: Re: Universe - finite or infinite?
From: andytheindoeuropean-ga on 07 Feb 2005 11:01 PST
 
Thanks once more for your further comment, "Hedgie".  I did say "at
least" three stars, so if spelling and grammar are overlooked I might
have given you four stars.  But the reason why I hesitate to commit
myself to four stars is that you, like other physicists, have invoked
the idea of a sphere, like the Earth or like an inflated balloon, to
describe the idea of "finite but boundless".  I have always found this
to be an unsatisfactory analog because to me at least the sphere does
have a boundary:  it is the surface of the sphere.  For once you go up
or out from the surface of the sphere, you no longer encounter that
surface, but rather encounter air.  So it is with the Earth: the
boundary of the Earth is the surface of the Earth, the Earth's crust
-- it ends where air (or, if you prefer to include the atmosphere as
part of Earth, space) begins.  Thus the Earth is finite and it does
have a boundary - its surface. "Outside" the surface of the earth is
air (or space if you include the atmosphere).  So if the universe is
like the Earth or like a balloon, then it does have a boundary, and
something lies outside the "surface" of the universe (empty space?
"nothing"?).  But I understand that this analogy to a sphere is only
an attempt to describe the nature of the universe, and we may be
dealing with something other than the simple 3-dimensional topology of
a sphere.  If this is the case then neither you nor anyone else can
help me to understand the topology of the universe, because as of yet
I cannot think outside 3 dimensions (or 4, including time)!
But you did give a much more than satisfactory answer to the first
part of my question, and the more important one, so for that answer I
should have given you four stars or more.  My apologies.
Subject: Re: Universe - finite or infinite?
From: andytheindoeuropean-ga on 07 Feb 2005 12:32 PST
 
Just another comment to patch up our relations.  I recently re-read
your answer to my question, and I realize you used much effort and
considerable explanation to try to describe to me the current
understanding of the topology of the universe.  So you should have
gotten the four or five stars.  However, some of your terminology is
confusing to me, who does not have a physics degree.  What is meant by
M4,E3, E1, E.n, GTR, and STR? What do you mean when you say "I dare to
say that a region of a flat space (E.n) is either bounded or infinite
(Is
that not a theorem, Mathtalk?)"  I did not understand - do you mean we
do not know whether it is bounded or infinite?  What does "The light
rays are all already on the
models (are geodetics of that surface) and we
just study which regions are connected (and so inter-act) and which
are not." mean?  I was confused by the wording.  So you see, part of
my problem with your answer was that you use language and symbology
that is above my understanding, thereby causing me to believe that
your answer was more complex than would be desired (and therefore
worthy of fewer stars).  But I suppose that's my fault, being a layman
who is addressing you deities of intellect (and that's not meant
facetiously).
Thanks for all the info and references, I will delve into those sources that I can.
Subject: Re: Universe - finite or infinite?
From: mathtalk-ga on 08 Feb 2005 08:13 PST
 
Mathematicians adopt the terms "sphere" and "disk" (in various
dimensions) to distinguish between the thing that has no boundary
(sphere) and the other thing whose boundary is the former!

In two-dimensions (plane) we have the 2-disk, whose boundary is the
ordinary circle (or 1-circle if we which to be precise).

In three-dimensions there is the "solid sphere" or 3-disk, whose
boundary is the "hollow sphere" or 2-sphere in "math talk".

There is an intriguing pattern here which illustrates that the
boundary of the boundary is empty.  That is, starting with a disk in
any dimension, its boundary is a sphere, and the boundary of the
sphere is empty.

"Bounded" is a word that is defined many ways in mathematics,
depending on the context, and confusion about the meaning can lead to
"paradoxes".  For example, one is often introduced in a second
semester of calculus to a solid of revolution which has finite volume
but infinite surface area.

In the absence of another definition, a bounded region of E^n
(n-dimensional Euclidean space, or "flat" space as hedgie-ga would
say) means a subset for which some real number M > 0 exists such that
every point is within distance M of the origin.  Said differently, a
region of E^n is bounded if and only if is is contained in some n-disk
of finite radius M > 0 (centered at the origin).

regards, mathtalk-ga
Subject: Re: Universe - finite or infinite?
From: andytheindoeuropean-ga on 08 Feb 2005 09:49 PST
 
I read your last comment, Mathtalk, and I concluded that I must be
very unintelligent, because I didn't understand a word of it.  No
offense!
Subject: Re: Universe - finite or infinite?
From: mathtalk-ga on 08 Feb 2005 12:18 PST
 
Okay, the disk is a nickel, and the circle is the rim on the nickel.

The nickel (disk) has a boundary, which is the rim (circle).

The rim itself has no boundary, or rather the boundary of the rim
(circle) is empty.  You can travel around the rim without ever
reaching a "stopping point".

If you move around inside the disk, however, by going far enough in
any direction you must eventually hit the boundary of the disk.

Having a boundary is then not the same thing (logically) as being
finite-size.  There are some finite-size things which have boundaries
and some which do not have them, and likewise some infinite-size
things which have boundaries and some which do not have them.

However what hedgie-ga is pointing out (or hinting at) is that in some
common cases (disks in "flat" spaces), the only way to avoid having a
boundary is to be infinite-sized, ie. to contain _all_ of
n-dimensional space.  That's what our intuition that being finite =
having a boundary is presumably based on.  Cf. the "antinomies of pure
reason" by Kant or earlier scholastic philosophers on the
finiteness/infiniteness of time and space, and you'll see that the
arguments hinge on the confusion of "bounded" (meaning finite) and
"having a boundary" (meaning something one can cross, at least in a
thought experiment).

regards, mathtalk-ga
Subject: Re: Universe - finite or infinite?
From: andytheindoeuropean-ga on 08 Feb 2005 13:59 PST
 
OK, but if the boundary of the disk is the rim, then when you say "the
rim itself has no boundary", that's equivalent, in my opinion, to
saying "the boundary itself has no boundary" or "the surface of the
Earth has no surface".  Is that true? It would seem to me that the rim
does have a boundary, since it occupies certain points in space which
are limited in extent.  The boundary of the boundary is itself, i.e.
the rim extends no further out (from the centre of the disk) and no
further in (from the rim itself) than its own width, which is no wider
than a point in space, which is zero.  The boundary occupies a
limited, defined position in spacetime, and is therefore finite and
bounded.  If you mean that this boundary (the rim of the disk) has no
boundary because its width is zero and therefore has no dimensions and
no limit or boundary itself, well OK but it still seems to me that the
boundary (the rim of the disk) occupies a limited position in space
and is therefore confined within certain limits, and "limits" to me
are the same as a "boundary". It's as though one had an orange peel
which has a certain thickness (and therefore boundaries), but can be
sliced ever thinner until its thickness approaches zero, at which
point it is equivalent to the boundary of the orange.  If its
thickness is zero, does that mean that the orange peel no longer has a
boundary? Or does the orange peel cease to exist, which implies that
the rim, or the boundary of the disk, is a non-thing and has no
boundary because it doesn't exist.  This would be saying that things
that don't exist have no boundary, which is self-explanatory.  But
things that don't exist are not finite, so the rim of the disk would
not be an example of a finite thing that has no boundary.
Does any of this make sense?  I started out saying that the boundary
has a boundary but finished by saying that the boundary does not exist
so it cannot have a boundary. Obviously I am still confused, despite
your attempt to simplify your explanation of a boundless finite
universe. I could edit this comment so that it is not contradictory
but I prefer to let you see how my thinking went on this one, so that
if you choose to answer it, you can refer to all my thoughts and
correct them as necessary.
And also, is a finite universe the same as a boundary (the rim of the
disk), which is what seems to be implied to me, and which implies that
the finite universe is equal to zero, or doesn't exist?  Or is the
finite universe rather the disk itself?  Or, what is the disk of which
the finite universe is the rim?
You see, it's not straightforward to me.  You can also see why I don't
have a degree in physics or mathematics.

Andy
Subject: Re: Universe - finite or infinite?
From: mathtalk-ga on 08 Feb 2005 14:25 PST
 
Hi, Andy:

Well, I think you see that I'm at least trying to make a distinction
between the notion of being limited in size and having a boundary.

I acknowledge that the confusion of these two concepts is the root of
a lot of philosophical argument by very bright, well-intended folks
over the ages.  And I acknowledge that there are some common
situations in which these concepts coincide.

To make precise the equation:

  boundary of boundary = nothing

one needs to limit the discussion to specific mathematical objects and
a well-defined operation "take the boundary of X" which applies.

I like this "equation" because it crops up in a variety of
mathematical contexts, some quite dissimilar.  In some geometric
subjects (manifolds with boundaries) the notion of "nothing" is an
empty set.  In some algebraic subjects (long exact sequences) the
notion of "nothing" turns into zero.

No accounting for the tastes of mathematicians!

regards, mathtalk-ga
Subject: Re: Universe - finite or infinite?
From: redshift-ga on 10 Mar 2005 08:09 PST
 
The universe is infinite. All this expansion is nonsense. I show here
http://www.lyndonashmore.com
that redshift is light interacting with photons in Intergalactic space.
I also show "ashmore's paradox' that measured values of the Hubble
constant H is just the electron in disguise.
Subject: Re: Universe - finite or infinite?
From: andytheindoeuropean-ga on 10 Mar 2005 15:54 PST
 
If that's what you truly believe, Vijay, I can't argue with you.  I
don't think anyone has the ultimate answer for the reason and origin
of existence, so if your explanation satisfies you, then very well.
Subject: Re: Universe - finite or infinite?
From: mike123106-ga on 14 Apr 2005 06:29 PDT
 
God said "let there be light"

He didn't say STOP! :)
Subject: Re: Universe - finite or infinite?
From: sanzyu-ga on 14 Apr 2005 12:18 PDT
 
To follow up, its quite strange; the universe is finite temporarly;
meaning that time itself had a beginning.

Some people thing that because the universe can be thought of as
infinite spacially, that there must be other civilizations in that
infinite space. However, this is not correct according to current
research. The universe is most uninhabitable for life due to some
extreme conditions present in every other galaxy ever discovered. For
more on this check out the book Rare Earth by Ward and Brownlee.
Subject: Re: Universe - finite or infinite?
From: ashurasai-ga on 05 Sep 2005 03:35 PDT
 
I think the easiest way to explain the boundary problem with spheres
and disks is to use mathtalks nickel again, well a big circle anyhow. 
If you draw a straight line, in the sand on a beach, coz I?m feeling
in a holiday mood, you can walk from one end to the other, then you
have to stop or turn around and go back again, no matter what length,
so long as its not infinite.  If you draw a circle in the sand the
same length and walk around it you never have to stop walking around
it, but its not infinitely long, you can just walk around it an
infinite number of times.

As for your thing about beyond the boundary of the universe, i can see
your problem with the whole boundary being the surface of the balloon,
or in the case of my analogy above the fact that you can walk away
from the circle to get an ice cream, analogies are a pain for most
scientists, physics especially.   People devote their entire careers
(mostly philosophers) to trying to explain this stuff to the general
public (who really do have a right to know, they're the ones paying
for it, and they are the ones who potentially could benefit from it).
Anyway, your quite understandable problem, cartoon characters and
indeed any drawing are two dimensional representations of three
dimensional things, but they are still two dimensional and can only
really know two dimensions, they exist only in those dimensions the
third doesn?t exist for them, so it can't really be considered a
boundary if you can't move at all in it.  When they use the sphere
analogy you've got to stop thinking of yourself walking on top of it
and imagine your self drawn as a cartoon character on it, totally
unaware that a third dimension even exists, you just get fat in the
two dimensions you know when it gets blown up in the three dimensions.

The temporary infinity thing is a good point, Steven hawking went on
about that in brief history and the guy who wrote the arrow of time. I
think the point was would the universe look the same if you ran it
backwards?  If there was a big crunch then it might do, but with the
whole accelerating universe thing going the big crunch seems unlikely
as a potential fate of the universe.

As to all the theories mentioned none have been proven, I don?t think
anybody in physics will ever say anything is proven, that would imply
we know everything about something, which we don't and I believe we
never will (but then who knows?).

And as for Lyndon Ashmore, anyone who invents a theory and names it
after themselves really should be shot.  Interesting as it is, logic
is a tricky thing to understand fully and this guy really doesn?t.
 
Godrealized, that?s stunning stuff mate, really cool

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