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http://antwrp.gsfc.nasa.gov/apod/ap050925.html

After reading this and reading information in some of the connected links, I have a question. I don't expect anyone to be able to answer it, but i'll go ahead and ask anyway.

If the universe was created by the big bang, and is expanding, doesn't that imply that it has a size and shape? So then, does that not also imply that it has an edge? A border? What could lie beyond the edge of the universe? I'm guesing there are lots of things i'm not taking into account, so forgive me if this doesn't make any sense...

Well, it's probably like the computer game, Asteroids, where you go off one edge of the screen and appear on the opposite one.

In fact Asteroids was an early computer model of the universe, but most people missed the point and thought it was a game.

Blacknad

I like your analogy using the computer game but I see my monitor frame surrounding the screen. Seems like there's always something outside.
It's like we're in a self contained sphere of immeasurable expanse and we can't penetrate the confines of this habitat. If we launch a projectile out into the depths of our sphere the projectile will never reach the edge. It would seem in order to reach the outer boundary we would need more force than all the energy available to us so that would make it impossible to even know if there is an outside. We can speculate though.
What I mean by projectile is: a light beam, radio wave or any kind of particle. I also mean by this statement that any wave/beam/particle leaving the outer boundary of our sphere would not have enough energy to reach us therefore making information transfer from us to there and from there to us impossible. By not enough energy I mean, not enough energy to go faster than light.

Ric asks:
"If the universe was created by the big bang, and is expanding, doesn't that imply that it has a size and shape?"

The error in your question is in the assumption that any serious physicist believes the universe was created by the Big Bang: It wasn't.

Big Bang theory has nothing to say about anything that existed prior to the instant of the Big Bang. The Big Bang (with Inflation to be more accurate) theory only describes what has happened since.

No. All 4(pi) steradians of direction at every location in the universe point exactly at the Big Bang. Every point in the universe is at its exact center. The universe is finite but unbounded. You can only see that part of it within your light cone.

The Big Bang was not an explosion in space, the Big Bang was an explosion of space. It made for an interesting geometry. Be glad that the resulting volume is orientable. OTOH, we could use more surface area/volume. My desk is a mess. Go hyperbolic!

Da Morgan and Uncle Al:

What was there before the Big Bag and what was the source of the Mass for the Big Bang? Thanks.
jw

Jim,

I have never heard of the Big Bag theory and I certainly don't know what was there before it - maybe a Big Bong.

Regards,

Blacknad

JJW004,
I couldn't agree more.

Ric,
"What could lie beyond the edge of the universe?"
Possibly - more universes.

Blacknad,
Are you serious? You've never heard of the Big Bang theory?!

jjw004 wrote:
"What was there before the Big Bag and what was the source of the Mass for the Big Bang?"

I love how those that have nothing worthwhile to contribute make fun of an obvious typo. What a 'Christian' thing to do.

To answer your "what was there before" is an invalid question. First it assumes that there was SOME THING before: We don't know that that was true. Second it assumes that time existed prior to the event: We don't know that to be true either. We are completely ignorant of anything prior to a very small faction of a second after the event.

Keep in mind that the Big Bang with Inflation is described as an expansion of SPACE-TIME. Both time and space were created. Thus our anthropomorphic need for a before may just be a weakness of human imagination: Not physics.

Now to your question about mass. As we humans have mass and live in an environment in which things seem massive we care about mass a lot. But from a Quantum Mechanical point of view mass may just be, to use a very bad analogy, something like molasses. It causes things to resist acceleration.
It seems to be a consensus that it relates to interactions with Higg's Bosons (look it up with google). But I have increasing doubts given the inability to find any evidence of them yet.

Naively there are reasons, from fundamental physics, to believe that the Universe should have produced about as much matter as antimatter. At the time of the "Big Bang" should there not have been equal amounts of matter and anti-matter?

Does every atomic particle have a polar opposite "anti" equivalent (eg. electron and antielectron); or does anti-matter only birth from energy being transformed into matter?

If so.. where is all of this anti-matter? There does not seem to be large collections of antimatter that we can detect. In PET scans, the positrons come from the decay of radioactive nuclei incorporated in a special fluid injected into the patient. The positrons then annihilate with electrons in nearby atoms. As the electron and positron are almost at rest when they annihilate, there is not enough annihilation energy to make even the lightest particle and antiparticle (the electron and the positron), so the energy emerges as two gamma-rays which shoot off in opposite directions to conserve momentum. Fine, so we can produce anti-matter in labs with PET scans and the Large Electron Positron (LEP) collider at CERN. But where is the rest of it from the "big bang"? Is the cosmic background radiation all that is leftover from the matter-antimatter annihilations...which, somehow, left only a billion to one ratio of matter to antimatter? Apologies if this sounds jumbled.
Sincerely,

Rob,

'Blacknad,
Are you serious? You've never heard of the Big Bang theory?! '

I was referring to the Big Bag theory - referring to a typo in gest.

DA Morgan,

I am sure I didn't hurt Jim's feelings - I am sure by what I have read from him that he would understand it was just gentle ribbing.

Regards,

Blacknad.

oh, now I see.

Mung asks about antimatter:

You are correct. Based on our understanding of symmetry there is every reason to believe there should have been as much matter as antimatter.

But based on B Factory work we also know that there are some asymmetries between matter and antimatter. They are not "just" mirror opposites.

Clearly we do not know why we don't see an equal amount of antimatter but keep in mind that baryonic matter is the smallest, percentage wise, constituent of the universe. Basically it, we, are about as meaningful as a carbon inclusion is to a diamond. It may well be that at one point in time there were essentially equal amounts. That they annihilated each other. And what is left is just the very small asymmetry from the original. We just do not know ... YET!

is there such a thing as neutral matter?

Neutral in what sense? Electrical charge ... definitely. Color charge? Definitely not. Matter that won't annihilate? I can'think of a single example as even photons will annihilate other photons.

I have no idea what is on the edge of the universe however surfaces of free floating fluids take the shape of a sphere when no forces act on it, I would say it?s a sphere but I really have no idea, as to what happened before it, I look to the universe expanding. . Will it stop? Will it teeter for a moment and reverse back to the centre. . In a sort of "Big Crunch" will it then explode as all the matter and energy collide like a giant particle accelerator this is pushing physics to its most mind boggling limits.
Back to the question what?s on the other side. . Is there even a theory or school of thought to challenge? It would be interesting to be on the great verge in a space ship only to pass through . . .

DA Morgan, what I meant was, if there's matter, and there's antimatter, shouldn't there be neutral matter?

Its hard to think of yet more grey in between the binaries of matter and anitmatter, what properties whould it have? can somthing exist of equal halves of a substance that destroys one another?

D.A. Morgan response to jjw, about 10//11

To answer your "what was there before" is an invalid question. First it assumes that there was SOME THING before: We don't know that that was true. Second it assumes that time existed prior to the event: We don't know that to be true either. We are completely ignorant of anything prior to a very small faction of a second after the event.

Keep in mind that the Big Bang with Inflation is described as an expansion of SPACE-TIME. Both time and space were created. Thus our anthropomorphic need for a before may just be a weakness of human imagination: Not physics.

Now to your question about mass. As we humans have mass and live in an environment in which things seem massive we care about mass a lot. But from a Quantum Mechanical point of view mass may just be, to use a very bad analogy, something like molasses. It causes things to resist acceleration.

Thank you DA. As to Rob, Please assume my feelings defy even intentional hurts.

When I read the above I see the shadow of a concept frequently offered by the religious. We know of nothing before, neither matter nor time and this Big Bag- err this Big Bang, came out of nowhere. Something of which we know not created space and time on the spot and then banged into an inflationary state of its own accord.

DA, this has all the earmarks of accepting some thing on faith because we admit we know nothing of what went before, if any thing and we know not what could have caused the ?event? to occur. When I look at the stars and consider the apparently endless quantity of stuff (forget Mass) that is out there I am personally compelled to wonder where it all came from. Inflation assumes compression existed prior to the inflation or you are compelled to use substitute creation as part of the inflation. If we can assume something in a state of compression then we have a pre-existence of stuff of which the Big Bang is constructed.

I do not intend a play on words. You offer that ?what was there before? is an invalid question? If invalid it is only because the theory is not capable of providing an answer.
From my standpoint a theory that does not provide a beginning should not presume to provide an ending. Why don?t we just believe there was a big bag of stuff there first?

I think I brought up Mass in another discussion so I will let that rest to conserve space.

With your skills you can understand why some of us may find the Big Bang theory hard to swallow. When the issue discusses the ?after? we think in terms of what was before.
When some one talks of inflation we think of compression unto inflation. When one of us thinks of expansion we automatically think that yesterday it was smaller. The Theory provides these descriptors, not the reader.
I always appreciate you insights and explanations and I continue to learn stuff.
jw

I missed a point.

I thought that it was basic physics that you can not make something of nothing? For your concept to fit we can think that while we do not know what was there before the Big Bang we just don't know what it was. Happy days.
jw

To repeat what others have said, requires education;
LINEAR(Known,Space)
to challenge it, requires brains.
NON-LINEAR(Unkonwn)
-Mary Pettibone Poole

Thats what lies outside Universe.

dkv, if you have a point, make it. In your own words, not someone else's. A parrot can repeat what it has heard someone say. We deserve better than just a parroting of someone else's signature lines. Get on topic or face deletion.

Yeah Rose!

Rose ... the last post should be sufficient. Sharpen the blade and let it fall.

Sorry I havent replied... i've been unable to get on my computer...

The confusing thing about the whole "big bang" for me is that something must have happened to make it happen... which makes it seem that there would have been something around before the "big bang." Things don't just happen without some kind of stimuli... and without material to create with...

So logically one would assume that there would have been SOMETHING around to "Start" it... things don't just appear from nothingness...

In the quantum mechanical sense, yes things can come into existance out of nothing. They soon however go out of existance. You can see the chaotic undeterministic events when you go into space-time on an incredibly magnified level, e.g. plancks length magnitude. You see that there are rips and chaos even in the apparantly smooth surface of space.

Edge of the universe: the universe can be seen in diffrent ways. You can see it as flat, and no curve. This is infinite and you will never return to a place you just left. There can also be a spherical structure, in which space-time is round and so it is finite, and you will eventually get back to where you started. Etc etc. In basic physics, and as far as humans comprehend, the universe is flat. In the beginning of time, there was no space, so there can be no boundry as space itself was created in the big'un IMO.

Ric wrote:
"So logically one would assume that there would have been SOMETHING around to "Start" it... things don't just appear from nothingness..."

Not necessarily. Let me give you an example. There is every reason to believe that our universe is fractal. In other words created by recursion just as miles of beach can be created from individual grains of sand.

Now take a good look at those grains of sand. What's there? Well if you strip the space out between the nucleus and the electrons essentially nothing. Then remove the space between the quarks and you really do have essentially nothing. At least when compared with the volume you thought you understood. And what is left? Mass? That is now believed to just be an interaction between the point-like strings that compose the electrons and quarks and a field known as a Higgs Field. So remove that interaction and you are even closer to nothing.

This is not all that different from looking at what appears to be a chessboard and then discovering it is really just the thin film of a holographic projection. Another version of the appearance of something when in fact there is next to nothing.

So while it is true that there may have been something, in some manner of thinking, that something may have been remarkably close to nothing. Or even, if one considers quantum mechanics, nothing but the inevitability of change.

no, no, no, 'Nothing' doesn't exist, in how many ways will I have to explain this?
Imagine a photon, it is obviously made of matter (particles) which can be divided further into smaller particles for ever. Just because these extremely small (from our perspective) particles can't be seen (or sensed in general) by us, that shouldn't suggest that they do not exist and 'nothingness' is in their place.

PS DA, here?s an interesting idea, this big bang is a grenade exploding in a higher level of fractals.

Rob wrote:
"Imagine a photon, it is obviously made of matter (particles) which can be divided further into smaller particles for ever."

There is no basis in science for this statement. A photon is not only NOT obviously made of matter but there is nothing anywhere supporting your infinite divisibility idea. Nothing!

I would suggest you stop trying to use overly conventional analogies to describe what is, without a doubt, not conventional.

Just found this site and stumbled onto this topic. I think you have all moved on from the shape of the universe but my understanding is you are talking of a 3D shape i.e. sphere. The nature of the universe is at least 4D with time as the 4th dimension, and possibly more yet discovered dimensions. Therefore the shape may not have sides edges or boundaries and I could not describe how it looks.

With regards to what was there before, something which is so small it is considered nothing, as something very large can be described as infinite. By definition the size can never be measured, so in the case of infinitely small, it is described as nothing.

As science progresses the smallest items become finite, that used to be nothing, until the smallest object that started the universe is found it will always be nothing.

As for the religion concept, faith is the belief in the unproven. In the past it encompassed science we have now answered, that which is still undiscovered but requires an answer leads to faith. Be it hypothesis, a greater being, etc.

The question of a greater being, leads to the question where are they? what are they and what existed before them?

shambles: you are talking of a 3D shape i.e. sphere. The nature of the universe is at least 4D with time as the 4th dimension, and possibly more yet discovered dimensions.

Yes there are 4 dimensions as we understand now, although in superstring theory, there are 11 dimensions, existing on a micro scale. Simply I was not refering to the physical shape as we often perceive, but as space-time itself. Space itself doesn't have a boundry.

The fact that people can accept that there is a LIMIT to how small or large particles can get shocks and bewilders me. Also, the fact that people believe in nothingness and a finite number of particles gives me severe doubts about the human race. Humans seem to have a need to put a limit on everything, possibly because they fear the concepts of both infinity and nothingness because they can't understand them. If you take a second to actually think about particles you will realise, without the need for proof, that no particle can ever be or even come close to being nothingness and thus non-existent.

Hi Amara,

That was really my point, that the big bang theory is often visualied as an explosion in 3 dimensions i.e. the expanding sphere. But as it is a 'shape' complex beyond 3 dimensions (4 at least) then it is possible that an 'edge' to the universe does not exist

Rob: The fact that people can accept that there is a LIMIT to how small or large particles can get shocks and bewilders me. Also, the fact that people believe in nothingness and a finite number of particles gives me severe doubts about the human race. Humans seem to have a need to put a limit on everything, possibly because they fear the concepts of both infinity and nothingness because they can't understand them. If you take a second to actually think about particles you will realise, without the need for proof, that no particle can ever be or even come close to being nothingness and thus non-existent.

In superstring theory, the basic concept is that all mass is fundamentally composed of strings, which open or closed oscillate and there unique oscillations and 'spins' determine their properties. So according to this very promising theory, which curiously enough depends on gravity to work at all, there is a fundamental limit on the size of particles. Your view of infinite divisibility has opposition. However, strings themselves are thought to be extremely small, in the leagues of Planck's length.

Thanks for answering my questions everyone

Amara,
A lecturer at Cambridge said that to me, I explained to him that the strings need to be made of SOMETHING. Look at a rubber band as an example - it is made of atoms. He agreed with me.

Rob wrote:
"A lecturer at Cambridge said that to me, I explained to him that the strings need to be made of SOMETHING. Look at a rubber band as an example - it is made of atoms. He agreed with me."

I would disagree.

I think we would say that strings ARE something as a matter of convention. That is not exactly the same thing.

Sorry Rob, but you do not understand the concepts of superstring theory. In string theory, the strings themselves (not like rubber bands) are the most fundamental of "particles". Try researching and reading a few books here and there before you make comments about subjects in which you do not understand.

"A lecturer at Cambridge said that to me"
Please...

Actually, when I spoke to the lecturer, I didn't use the rubber band example, What I really I said to him was; "But then you could divide the strings into smaller strings." Secondly, I must point out that he didn't actually 'agree' with me, he just said "I suppose so."

And it was really Cambridge Ontario Canada ... not Cambridge England.

Rob: Actually, when I spoke to the lecturer, I didn't use the rubber band example, What I really I said to him was; "But then you could divide the strings into smaller strings." Secondly, I must point out that he didn't actually 'agree' with me, he just said "I suppose so."

Obviously he's not a string physicist then.

Perhaps a rubber- band physicist. ;-)

can you find a number that can't be sub divided?
and zero is not a number, it's an abscence of numbers. point proved (hopefully).

Probably absolutely nothing-a void

a void is what zero is.

how can anything that exists have an abscence of mass?

It can't. It just can't.

Except, of course, for photons.

Case closed.

You need to distinguish between mass and rest mass. Anything can exist without rest mass. Perhaps everything fundamental actually does. The problem here is that you are assuming that you know what mass is ... an that is something I doubt so lets examine what it is.

Mass is the resistance of an object to accelleration: Nothing more. Put your hand into the air and wave it about. Now do the same thing in a bucket of water. Feel the resistance to accelleration? Did your arm experience a corresponding increase in mass? I hope not.

ok then, just pretend that all the times I said mass, I was actually saying matter. Therefore, nothing that has no matter can exist.

Depending on how one defines "matter" you may or may not be correct.

Are photons matter?
Are phonons matter?

One of them definitely is not. The other arguably not.

Grrr, all these technicalities are annoying. Ok, look, MY own personal definition for matter which is the one I am going to be using from now on is this; Matter: something with weight.
Now you could say a photon has no weight, but look at it this way. A feather would appear weightless on a scale designed to weigh elephants.
YET AGAIN, I go back to my original point; nothing can be said to exist unless it has WEIGHT.

Your personal defintion of anything is irrelevant.

If you wish to communicate with this planet's other inhabitants you need to use a common language. And guess what ... in physics ... it isn't whatever you decide it is.

I did not say a photon has no weight though that is true as weight does not exist. The question is mass and the question specifically is with respect to rest mass.

Weight is not a concept with any meaning thus you don't have a point to return to. You really should either stop posting on a science site or learn the value of staying awake in school.

I don't go to school.
Let's go back to numbers YET AGAIN. Divide infinity by two infinity times but you'll never get to zero. That's the point I've been trying to make since I GOT HERE.

Rob wrote:
"I don't go to school."

Obviously!

Rob wrote:
"YET AGAIN, I go back to my original point; nothing can be said to exist unless it has WEIGHT."

then Rob wrote:
"YET AGAIN. Divide infinity by two infinity times but you'll never get to zero. That's the point I've been trying to make since I GOT HERE."

Compare the two paragraphs above? Go back to school and this time concentrate on getting an education. Alternatively learn to ask "Do you want fries with that?"

hehehe

Rob, let me ask you something. Consider the polynomial fraction (x-1)/[(x-2)(x-3)]. What is the value of this fraction as x becomes infinitely large (in the dedicated lingo as x tends/goes to infinity)?

Pasti, hold on one second

DA Morgan,
?Obviously!?
Yawn, how predictable.

"Compare the two paragraphs above? Go back to school and this time concentrate on getting an education."
Compare the two paragraphs above? I don't see your point.

Forget infinity; divide the number 1 by 2 forever and you still wont reach zero, EVER! Do you need an education to realise that?

Wow Rob ... you've proven you have a junior high school level education if one assumes a C average.

No doubt Pasti, working on his degree is physics, is marveling at your grasp of the elementary. But you didn't respond to the question he asked: Why?

"Forget infinity; divide the number 1 by 2 forever and you still wont reach zero, EVER! Do you need an education to realise that?"

Slight miscommunication.

It doesn't have to reach. It "tends to" zero, in the jargon. That's why in math, we use the limit:

lim (x-c)/[(x-a)(x-b)]
n->inf

What is it "in the limit," regardless of whether that limit is ever reached. As n "increases without bound," the value of the function approaches zero. (This should be intuitive, but you can also use L'Hopital.)

OTOH, there is a semantic gap in that mathematics doesn't necessarily have to correspond to our physical reality - and vice versa.

I disagree with your assertion that nothing exists unless it has weight. I think that's far too specific a definition. A slightly better one might be that nothing exists unless it is capable of producing "some (putatively) observable effect on something else."

Yours is a dangerous assertion in that there's no justification for it. We might as well declare that nothing can be said to exist unless it's made of peanut butter.

The argument about not having an instrument fine enough to measure (either weight or mass) of a photon is also flawed (not just on lack of evidence, but of even being scientifically legitimate) unless you can propose an experiment that might prove you're wrong, if you are wrong.

Rob, let's review. You say:

Rob:" Let's go back to numbers YET AGAIN. Divide infinity by two infinity times but you'll never get to zero. That's the point I've been trying to make since I GOT HERE."

And I gave you a traditional example. The fraction
(x-c)/[(x-a)(x-b)] IS zero in the limit x->infinity. Alvernatively, as The FF said, you can use l'Hospital theorem, and you get the same thing, zero, although in this case l'Hospital is unnecessary.

Then you are not happy with this example, because it involves the concept of infinity, and you say:

Rob: "Forget infinity; divide the number 1 by 2 forever and you still wont reach zero, EVER! Do you need an education to realise that?"

Well Rob, even in this example you cannot forget the infinity, since mathematically, your latest example can be rewritten as:

lim[n->infinity]{1/(2^n)}=0

You only think that you avoided the concept of infinity, but in fact you haven't. You still need to define what infinity is, and without any further consideration, mathematically it can be defined as 1/(2^infinity)=0. And this definition is also consistent with the previous fraction,if you can see that.

In both math and physics, you need to understand the concept of infinity. Infinity is not like any other number (integer, rational or real). It has special properties, but nevertheless, it can be consistently defines, say as above.

So, unless you still have some problems with these limits, we can put these issues to rest.

"Rob, let me ask you something. Consider the polynomial fraction (x-1)/[(x-2)(x-3)]. What is the value of this fraction as x becomes infinitely large (in the dedicated lingo as x tends/goes to infinity)?"

The answer is 1, if x = infinity.
I don't know what it is when x is infinitely large.
I'll get back to you on that, I have to go.

""Rob, let me ask you something. Consider the polynomial fraction (x-1)/[(x-2)(x-3)]. What is the value of this fraction as x becomes infinitely large (in the dedicated lingo as x tends/goes to infinity)?"

"The answer is 1,"
"The answer is 0, because the question is implicitly asking for a limit."

"if x = infinity."

X can never equal infinity. That's why we use the clumsy limit notation instead of just writing infinity in for those variables.


"I don't know what it is when x is infinitely large."

I don't understand the distinction between x being equal to infinity and x being infinitely large. This stuff is not actually calculus at this point. So far this is stuff that's covered pretty thoroughly near the end of algebra II.

To Rob: Rob, the limit of the fraction as x->infinity (which is exactly the same as saying that x is infinitely large) is zero, not 1 as you say.

To The FF: You can actually include "infinity" in the real axis, and define R^=[-infinity, infinity] instead of R=(-infinity, infinity). Formally, you just include into the real line the accumulation point of all divergent sequences, or series. It doesn't matter that much whether you define the real line as compact or non-compact, at least not at this level. So formally, you can make such that the number infinity is included in the real line.

"So formally, you can make such that the number infinity is included in the real line."

I can't say that you're wrong, but I can say truthfully that I don't follow the argument. (In particular, I'm not able to decipher "include into the real line ..."

I've read many scientific, mathematical, and (mostly) technical papers over the past 25 or so years that made use of infinity in one way or another. Not one has ever used infinity is as anything other than a transfinite number. In particular, none has ever used infinity as a real number.

I'm aware that some kinds of software (mathematica, for example) treat it as if it were a number. I always considered this to be a notational convenience. (It pretty much says exactly that on one of Wolfram's mathworld pages.)

The most dependable sites I can find on the web say that infinity is not a number. In fact, the only ones that I've found so far that maintain it IS a number are a newage site and an astrology site.

Do you have a reference that clearly expresses this idea? Doesn't necessarily have to be on the web.

TFF, the real line is another expression for the set of real numbers (there is a natural isomorphism between the set of real numbers and the points along an infinite straight line).

Now, if you think in terms of a line, an infinite line is a non-compact set as defined traditionally (does not include the end points at infinity). You can simply compactify it by including these points, and make the real line a closed interval.

Hm, references. Try something on modules, rings, fields,algebraic topology something like that. I will have to look for a more explicit reference.
But the ideea is simple to follow, algebraically speaking. Sure, it is a transfinite number. But you have to define how it behaves withe respect to the real numbers and the operations defined on the real numbers (infty +infty=infty, 1+infty=infty, infty*infty=infty, and so on and so forth). And the only problems you have are infty-infty, infty/infty, 0*infty and the similar. So you might as well treat it as a number, with these potential problems in mind.

"But you have to define how it behaves withe respect to the real numbers and the operations defined on the real numbers (infty +infty=infty, 1+infty=infty, infty*infty=infty, and so on and so forth). And the only problems you have are infty-infty, infty/infty, 0*infty and the similar. So you might as well treat it as a number, with these potential problems in mind."

That's part of my problem. If you include Inf with the reals (or integers), they violate the criteria of a ring. 0*Inf must equal 0 for it to be a ring. Nor is it a field, since there is no additive inverse for Inf. It is, however, a semiring. Alas, my background is in engineering math and not pure math, so I'm out of my depth beyond this point. It could be that forming a semiring is sufficient.

Nevertheless, we see at http://mathworld.wolfram.com/SurrealNumber.html the term "surreal number," which includes the real numbers and the transfinites, and also the term "Omnific Integer." The implication, I think, is that the transfinites are distinct from the reals (or the integers).

I know this part of my comment amounts to argument from authority. Wolfram could be wrong. Or he could be outdated. But if one is going to argue from authority, I reckon we ought to argue from the good one - and this is the best one I could find on the web.

"I don't understand the distinction between x being equal to infinity and x being infinitely large."

3.3333333333... is infinitely large, but it is not infinity. Actually, maybe it is...

Rob:"3.3333333333... is infinitely large, but it is not infinity. Actually, maybe it is... "

No Rob, this is not an infinitely large number. A practical definition for an infinitely large number, let's call it, say N , is something like this N-a~=N for whatever a a finite number (~= meaning "approximately the same", "almost the same").

"Largeness" of a number is not related to the number of its decimals, but to the ordering relation on the set of the real numbers (the ordering relation saying that any number is larger than another number and smaller than yet another number like 3.2<3.333333<3.4 ) So your example is incorrect.

TFF:"That's part of my problem. If you include Inf with the reals (or integers), they violate the criteria of a ring. 0*Inf must equal 0 for it to be a ring. Nor is it a field, since there is no additive inverse for Inf. It is, however, a semiring. Alas, my background is in engineering math and not pure math, so I'm out of my depth beyond this point. It could be that forming a semiring is sufficient.

You are right, including Infty in the real line will spoil your ring and field structure. So what? It is sufficient to have all structures valid (additive group and multiplicative semigroup ? this is mainly the ring structure) lest 1 point, the Infty. You have gotten to the same thing I was saying. You include Infty and you keep in mind that certain operations are not uniquely defined. This is in fact what you do in calculus, you just call it differently, and the differences are purely academic (for this purpose, that is). In fact, in calculus, you use Infty as a real number, when appropriate (when the operations are unambiguous like 1*Infty). When the operations are ambiguous, you deal with them differently, and you don?t particularly care too much for the fact that such operations are multivalued (in the sense that sometimes Infty/Infty in an expression can give you 1 and some other times, in a different expression it yields say 5).

TFF:?Nevertheless, we see at http://mathworld.wolfram.com/SurrealNumber.html the term "surreal number," which includes the real numbers and the transfinites, and also the term "Omnific Integer." The implication, I think, is that the transfinites are distinct from the reals (or the integers).?

As I said, I agree with you that it spoils the algebraic structures. At one point, and not all operations. Algebraically speaking. Not that it matters much, unless indeed you pursue a different goal, where such structures are fundamental.

But then, think of topology. You include Infty on the real line as a topological space without any problem, as the accumulation point of certain sequences. Just a different viewpoint, with no algebraic structure.

TFF:"I know this part of my comment amounts to argument from authority. Wolfram could be wrong. Or he could be outdated. But if one is going to argue from authority, I reckon we ought to argue from the good one - and this is the best one I could find on the web."

I am fine with refs, as long as they can be checked. But in the end, think about it. It is a matter of viewpoint and application. For algebraic structures, it doesn't make sense to include Infty in the real line because it spoils the structures, in calculus, you can do it as a matter of practicallity, if you remember that there are certain finer issues regarding multiplication and additive inverse, and in topology, you don't exactly care for any of these issues.

I agree that it's largely a matter of efficacy. The only reason I'm tied up on the ring/field thing is that I know that there are certain mathematical benefits to such things.

I suppose I had thought that the issue was decided long ago. I was warned back in algebra II that using Inf as a number was an expediency that was "not technically correct." I've seen people do this in lectures and presentations before, but never in a journal article. OTOH, we often *think* this way.

Topology is something I've studied cursorily on my own. It's not something that's covered in engineering curricula. I don't recall using algebra with it, but I was reading mostly on a baby level. Regardless, I can see the advantage in regular calculus of treating Inf as a number, if no other reason than to simplify notation of more complicated problems.

I'll take your word for it till I have a chance to look into this in more detail. I'm a pretty slow guy - and I gotta work through it at my own pace.

"3.3333333333... is infinitely large, but it is not infinity. Actually, maybe it is..."

You're having the same problem my youngest daughter had when I first taught her about pi. Neither pi nor 3.33... is "infinitely large." You "could" say that - and I understand your reasoning. But that's a sure fire way to confuse yourself.

Maybe a clearer way to think of it is:
"It has an infinite number of digits, BUT it's value is not infinitely large." Don't get discouraged. It took us (humanity) till the 1800s (Georg Cantor) to figure this stuff out - and the concepts were so strange and counter-intuitive that many brilliant mathematicians of the day rejected them outright.

To: TFF

Thank you for misunderstanding Pasti and stating the obvious.

Coming from you; your comments are condescending. And that is the nicest thing I can say about them.

DA said: "Thank you for misunderstanding Pasti and stating the obvious."

No idea what you're talking about, which is to say that I don't know what you're talking about and I suspect that you, as usual, don't either.

If you check back, I was responding to Rob, not Pasti on that last post ... apparently it wasn't all that obvious to him. But unlike you who looks for every opportunity to say something nasty and condescending, I prefer to clarify the issue for him.

Regardless of which post you've just responded to, next time, before you post, DA, try taking a crow bar and prying your head from its current location.

TFF:"Topology is something I've studied cursorily on my own. It's not something that's covered in engineering curricula. I don't recall using algebra with it, but I was reading mostly on a baby level."

Think about it, it's really simple. You don't need too much topology.Topologically,the numbers are simply points on a line (the real line), and as such you don't need to define addition and multiplication of points (you don't need algebraic structures like groups, semigroups or fields/korps). You only need some ordering relation between points. So nothing stpos you to include -Infty and Infty into the real line as the inf and supp of the set of points. In this way you have just compactified the real line.

TFF:"Regardless, I can see the advantage in regular calculus of treating Inf as a number, if no other reason than to simplify notation of more complicated problems."

That was (part) of my point. The other part of the point was that as you said (better that I did), you can define a consistent algebraic structure over the real numbers that includes Infty - the semiring - in spite of the traditional wisdom that claims that in fact Infty is not a number. It is for a semiring, it isn't for a unitary ring or a field, depends on the aplication, context, etc.

TFF:"I'll take your word for it till I have a chance to look into this in more detail. I'm a pretty slow guy - and I gotta work through it at my own pace."

Fine by me, but hopefully the above cleared a bit what I wanted to say from the topological viewpoint.

The word "topologically" kinda threw me off. I thought you meant something more complicated than that. I see where this is heading.

The implication, then, is that Inf and -Inf are now taken as actual points on the number line.

I'm not familiar with 'compactification.' Is this a way of circumventing the common notion of orderliness, usu we think something along the lines of given a point x and a positive c, there exist x-c and x+c, such that x - c < x < x + c, obviously not true when x=Inf. The "compactification" is a way of getting around this common idea?

TFF:"The implication, then, is that Inf and -Inf are now taken as actual points on the number line."

Yep.

TFF:"I'm not familiar with 'compactification.' Is this a way of circumventing the common notion of orderliness, usu we think something along the lines of given a point x and a positive c, there exist x-c and x+c, such that x - c < x < x + c, obviously not true when x=Inf.The "compactification" is a way of getting around this common idea?"

No, this is not the ideea. BTW, you have already introduced an additive group structure on the real line when you wrote the ordering relation the way you did above. Think points - not coordinates - and sets of points. And even in your case it works if you define Infty=supp{<R>}, -Infty=inf{<R>} with respect to this ordering relation, where <R> is a s previously the real line with the infties included.

The ideea of compactification is something along these lines: (0,1) is a non-compact interval while [0,1] is a compact interval (you have included the ends of the interval in the latter set. Same thing with the real line, you include the infties and you end up with the compactified real line.

Ric: Edge of the universe:

Site: antwrp.gsfc.nasa.gov/apod/apo50925.html

Explanation: Analyses of a new high-resolution map of microwave light emitted only 380,000 years after the Big Bang appear to define our universe more precisely than ever before. The eagerly awaited results announced last year from the orbiting Wilkinson Microwave Anisotropy Probe resolve several long-standing disagreements in cosmology rooted in less precise data. Specifically, present analyses of above WMAP all-sky image indicate that the universe is 13.7 billion years old (accurate to 1 percent), composed of 73 percent dark energy, 23 percent cold dark matter, and only 4 percent atoms, is currently expanding at the rate of 71 km/sec/Mpc (accurate to 5 percent), underwent episodes of rapid expansion called inflation, and will expand forever. Astronomers will likely research the foundations and implications of these results for years to come.
There is an egg shaped picture offered in the above, which would, I think, cause many to imply that the universe has a positive shape and that our chicken got there first. We have narrowed down the origins to within 1% (no small thing) and the rate of expansion, about 71 km/sec., is concluded accurate to 5% of what may be happening in real time. With out the accepted credentials normally offered I must offer one layman?s view. Any average person reading and looking at the depiction should think that there is some edge to the universe. If the universe is constantly expanding we might wonder into what are we expanding? Possibly our universe is compressing some other universe that is compressing some other universe, etc.?

I suppose we can chalk it up to my ignorance of the relativity of space-time and I will concede that up front. Possibly we could best convey the idea by saying that the CONTENT of the universe is constantly expanding and that would offer some of us the prospect that the universe itself is everywhere so there is no need for an outside or an edge. If space, our idea of the universe is everywhere, then we are only concerned with the contents and edges play no part in our understanding.
So, while there is no apparent proof that our universe has an edge, or limit, there is evidence that the contents of our universe become larger as we improve vision.
jjw

If the universe is infinite, then it has no edge.
If the universe isn't infinite, and there are others, then the edge of this universe is about as interesting as the edge of a bubble in liquid, or an explosion in air.

Rob wrote:
"If the universe is infinite, then it has no edge.
If the universe isn't infinite, and there are others, then the edge of this universe is about as interesting as the edge of a bubble in liquid, or an explosion in air."

Your assumption seems to be that a finite universe has an edge, a barrier, a point beyond which one can not travel. Your assumption is not necessarily valid.

Consider a black hole and assume you were in the center. As you travel in any direction you will find that there is no edge, there is no barrier, there is, however, a very finite volume.

OK, black holes are tricky, say you were at the centre of the earth and were travelling outwards, you would one day get to outer space and no longer be in or on earth.

Your example has nothing to do with your original premise. You might as well have said that if you lock yourself into the bathroom you need to open the door to get out.

You might want to reread your original post.

in that context, what were you saying? I don't understand your black - hole example.

You indicated in your original post that a finite universe has an edge, a barrier.

My point was that the volume inside of a black hold is also finite ... but there is no edge or barrier.

That which is outside is outside ... but you can go in one direction forever and never do other than loop back upon yourself.

There is no reason to believe the universe, as a whole, should be any different.

I'm sorry if this was covered(6 pages is a bit beyond my attention span atm) but when people are asking about "what was there before there was everything?" I ask you this. Is it possible that all things always were, and the idea of non-existence came about by our quest of curiosity to explore the unknown? In the the universe all things happen as they should happen, unlike human behavior or a crappy program. So the notion of something being wrong, or incorrect also would not occur in the universe. It wouldn't be too large of a leap to transition over to the idea that non-existence only exists in our minds, because when we eat food it is no longer there to be eaten. Although to a universal logic, the food still exists within your body, not caring for what purpose it had once served, continually existing as it had before. The idea of change is something the universe does not understand.

yeah, you've literally died before. your infant you is blowing in the wind. i've said this before but you may not come across it. so, sorry to those that have.

DA, could you do a diagram or something. By your statement on looping I assume you are talking about walking (impossible, I know) on the surface in an apparent straight line till you reach your original point like Christopher Columbus. Or did you mean that you could send a rocket off into space but the immense gravity would draw you back in, in some kind of loop?

Pick up a copy of one of Briane Greene's books such as "The Elegant Universe" and read it: No math required.

If you are anywhere in a black hole, or perhaps our universe, and you travel at any speed you wish in a straight line, you will never encounter a barrier or edge.

One can travel an infinite distance in a finite space.

well duh. But you will (if you are travelling faster than light) escape the black hole and drift away for ever into nothingness. (assuming the black hole is the only thing in the universe)
That's what I was thinking of when I was talking about an edge.

Rob wrote:
"you will (if you are travelling faster than light) escape the black hole"

And if you are an invisible purple rhinoceros you can redefine pi as 3.0 and it will work.

"and you travel at any speed you wish in a straight line"

"(x-1)/[(x-2)(x-3)]."
= -4x + 4 with remainder 2
How is this equal to 0??

I think you reduced the problem incorrectly. Try to solve for x again. also, the expression reduces to zero when x = 1. It is undefined when x = +2 or +3.

Just focusing on the main question :
What is an Edge ?
Is it the boundary condition ?
Or is it something which gives a sense of End or start?

Take for a Moment our Own Earth.. now do we know where is the Edge?

Good morning. Have you folks had a chance to read Maldacena's article in the November issue of Scientific American on "the illusion of gravity"? It has me thinking over the past few weeks and seemed relevant to a few points you were discussing.
In particular I found the point about the thickness of a string at the holographic boundry (without gravity) being the equivalent of the location of the particle in the '3D middle' (with gravity) mentally consuming.

I have also picked up a book called 'The Mind's I, Fantasies and reflections on self and soul' by DR Hofstadter and DC Dennett. It is an interesting compendium of writings on what consciouness might be and I found the excerpts from Richard Dawkins' 'The Selfish Gene' very interesting. Helped me pick up some new thoughts.

Glad to have found the site.