# Is infinity impossible?

If infinity were to be possible, it would seem that nothing in it's surrounding environments could be segmented or finite. How do we record segments of something that is infinite like for example time? It's almost as if infinity is really points of end, causing new beginnings. Thus causing an idea of never ending patterns, but a pattern has definitive points. It seems that we need a new and third aspect beyond infinity and infinite to really describe or grasp what is occuring all around us. Another example, the atom, it is distinct, but on a grand scale part of never ending amounts calculating existance. What is this and what does it mean?

ZapperZ
Staff Emeritus
If infinity were to be possible, it would seem that nothing in it's surrounding environments could be segmented or finite. How do we record segments of something that is infinite like for example time?

This is a very strange statement because you have ignored what we know in mathematics completely.

A function such as f(z) = 1/z is analytic everywhere except at z=0, even when we consider z to be in a complex plane. In complex calculus, we know exactly how to deal with any integration, for example, that has to go through that point (contour integral using the Residue theorem comes to mind). The FACT that we can do calculus around it implies that the region surrounding z=0 is analytic, continuous, and well-defined.

Thus, your starting premise that "it's surrounding environment" cannot be "segmented or finite" is clearly false here.

Zz.

If infinity were to be possible, it would seem that nothing in it's surrounding environments could be segmented or finite. How do we record segments of something that is infinite like for example time? It's almost as if infinity is really points of end, causing new beginnings. Thus causing an idea of never ending patterns, but a pattern has definitive points. It seems that we need a new and third aspect beyond infinity and infinite to really describe or grasp what is occuring all around us. Another example, the atom, it is distinct, but on a grand scale part of never ending amounts calculating existance. What is this and what does it mean?

The opposite approach this is to ask if anything is really discrete, or if our perception of discrete entities is merely an illusion. Conversely, no one has ever proven that any infinities actually exist in the real world.

Lao Tzu recognized the problem with infinity over two thousand years ago when he wrote:

Tho it has no limit, I call it limitless.

Linguistically speaking the infinite and finite are relative terms like up and down, hence the difficulty describing one without referring to the other. To say that something has no limit is to utter a paradox. If it has no limit than this imposes a limit, the limit that it has no limit. Such is not mere word play, words only have demonstrable meaning according to their function in a given context. If the context is too broad, such as life, the universe, and everything, then the words become meaningless.

The same is true for words like "existence", which philosophers and linguists alike have spend eons debating.

I can't picture infinity not existing. By my reasoning at least, a finite universe would lead to an inescapable paradox:

Say the universe is finite (by universe I mean everything that exists), then what is beyond that end?

If it is finite then the answer is nothing. nothing lies beyond that end; it just ends.

But "It" exists— therefore It, at some point, came to be... so how can something (not to mention everything :yuck:) arise into or out-of nothing?

Then the only answer left would be that the universe didn't need to be created into that nothing, because it has always existed... but that too would contradict infinity not existing: something that is but never not-was, by definition, has been being for an infinite amount of time.

I personally can't form any rational argument for a finite universe that doesn't ball up into a chaotic mess of such paradoxes, but my arguments are obviously purely philosophical.

What's the physicist's point of view on infinity (not just mathematical infinity)? Or on a finite universe?

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You asked your question with a presupposition. You can't ask about the possibility of infinity and then attempt to use the word 'is'.

DaveC426913
Gold Member
I can't picture infinity not existing. By my reasoning at least, a finite universe would lead to an inescapable paradox:
You are simply substituting one inconceivable concept for another. You simply find infinity an easier concept to stomach than the others you reject.

What's the physicist's point of view on infinity (not just mathematical infinity)? Or on a finite universe?
The physicist's point of view is that the universe is quite finite: about 13.7 billion years old and about 156 billion light years in diameter.

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The physicist's point of view is that the universe is quite finite: about 13.7 billion years old and about 156 billion light years in diameter.

you are describing the current calculated size of the observable hubble volume- but observation shows that the universe has either a nearly flat or totally flat topology- which suggests it IS spatially infinite-which is the genreal consensus among physicists and astronomers- see the Cosmolgy forum for many threads about this subject: https://www.physicsforums.com/forumdisplay.php?f=69 [there is one right at the top in fact]

You are simply substituting one inconceivable concept for another. You simply find infinity an easier concept to stomach than the others you reject.

how am I doing that? what concept am I rejecting? my whole post was a question.

The physicist's point of view is that the universe is quite finite: about 13.7 billion years old and about 156 billion light years in diameter.

I don't mean the observable universe, that's why I clarified:
(by universe I mean everything that exists)

what wouldn't make any sense to me would be that our universe started out of nothing. that there was literally nothing, then all of a sudden our universe came to be. where did it come to be? what caused it to come to be?

if there is nothing beyond the visible universe, and it has not always existed, that would imply something simply popped into existence out of nothing; that it was not a reaction to anything because there was nothing to react to... that seems to violate various natural and rational laws.

that's why I ask. I know there are physicists who have hypotheses about multiverses, and branes, and other weird things going on outside of our universe. I was wondering if there are physicists who believe in a finite universe (I don't know what word to use other than universe. but I don't mean simply the observable. I mean a finite everything, as in there being literally nothing before or after our universe), how do they explain this? how do they explain a universe coming into existence without it being a reaction to anything or existing in anything?

I'm not trying to be confrontational. I'm just curious. I'm just saying it makes no sense to me, but neither did special relativity when I first heard of it and now I understand it enough to understand that it does makes sense.

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DaveC426913
Gold Member
how am I doing that? what concept am I rejecting? my whole post was a question.
? But ... I quoted you... how can it be any more explicit?

"...can't picture infinity not existing..."
"...what wouldn't make any sense to me would be that our universe started out of nothing..."
"...if there is nothing beyond the visible universe, and it has not always existed, that would imply something simply popped into existence out of nothing; that it was not a reaction to anything because there was nothing to react to..."

These are all simply concepts that you find harder to accept than you find infinity to accept. You have made an arbitrary choice of how the universe needs to be in order for you to believe it.

First of all I'd like to distance myself from the previous bunch of posters; I have no clue what the hell they're talking about with the whole sheep thing, I don't share their views, so don't assume I'm agreeing with them.
? But ... I quoted you... how can it be any more explicit?

"...can't picture infinity not existing..."
"...what wouldn't make any sense to me would be that our universe started out of nothing..."

These are all simply concepts that you find harder to accept than you find infinity to accept.
You have made an arbitrary choice of how the universe needs to be in order for you to believe it.
what assumption have I made? I'm not clear on that. the assumption that I can't picture infinity not existing? can you prove that I can? was it the the assumption that the universe existing in a vacuum of space and time doesn't make sense to me? can you disprove that it doesn't make any sense to me?

I don't understand why you have such a problem with me not understanding something or having trouble picturing a concept, but ok.

I was simply asking a question. whether there is a theory that would explain a finite universe that exists all by itself. I made no "assumptions," I just presented why I would have trouble understanding a finite universe with nothing beyond it. If I was wrong in my reasoning, I was hoping you could explain to me how I'm wrong, instead of carping about my question or my choice of words.

"...if there is nothing beyond the visible universe, and it has not always existed, that would imply something simply popped into existence out of nothing; that it was not a reaction to anything because there was nothing to react to..."

is there an error in my reasoning there? wouldn't a finite universe beyond which there is nothing have to have had come into existence out of nothing? wouldn't something created out of nothing violate natural laws?

if I'm wrong, tell me how I'm wrong; that's why I ask questions on this forum; don't just tell me that I have problems accepting ideas I'm uncomfortable with or other such stuff. I can handle being wrong; I can't handle being told I'm wrong without being given a proper explanation.

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I don't know about infinity but eternity was explained this way.

A mountain a mile high and a mile square was visited once every thousand years by a little bird that would sharpen his beak. When the mountain is gone from this, that is one day of eternity.

DaveC426913
Gold Member
First of all I'd like to distance myself from the previous bunch of posters; I have no clue what the hell they're talking about with the whole sheep thing, I don't share their views, so don't assume I'm agreeing with them.
Agreed. And yes, I am separating the wheat from the chaff.

But I did answer the one you asked that ended in a '?'. You asked what physicists thought. I answered that the standard view of a finite universe in space and time is what is almost universally accepted.

what assumption have I made? I'm not clear on that. the assumption that I can't picture infinity not existing? can you prove that I can?
I'm not actually disagreeing with what you said, or dismissing it, I'm simply stating that I don't see how any of the other concepts of the universe that you mention are any more objectively palatable than one in which the universe is finite. They all lead back to some concept that we can't fully grasp. I just don't know why you picked one (that the universe is infinite) over any of the others. I think it needs fleshing out.

Does any here wonder why the major problem of philosophy has been condensed to one of language? Words such as infinity, God, spirit, etc. that do not have referents perceived by our physical senses result in misunderstandings. How ridiculous for a Frenchman and Englishman to fight over "livre" and "book" when the thing referred to is in front of both. It is proper to agree in discussion first on the definitions of words used. Mathematics, even though using imaginary numbers, strictly defines there proper agreed upon usage that may not agree with the layman's.

DaveC426913
Gold Member
Does any here wonder why the major problem of philosophy has been condensed to one of language?
Yep. Outside of science, many discussions will come down to semantics - meaning of terms.

A classic being 'What is art?'

Everything has a limit. We just can't reach that limit as proven in calculus. Anyone who, and I bet almost everyone in this forum, has taken Calculus know that I f they were 8 feet away from the wall and that each time he would take a half step closer he would never reach the wall(Conceptually) It's on going. We can get really close but not touch it. Infinity is just is a concept used to explain what we cannot accomplish. I really don't believe that infinity is really points of end, causing new beginnings. It's like a long line that you'll never see the end, that goes only forward.

Hurkyl
Staff Emeritus
Gold Member
Everything has a limit. We just can't reach that limit as proven in calculus.
"Reach" is such a vague term. But if I guess what you probably meant, then I should point out that it's the limiting process that might never 'reach' the limit state. Calculus says nothing about being unable to 'reach' the limit state through other means. And depending on what you mean by 'reach', it can even be possible for the limiting process to reach the limit. For example, what can you say about the limit of f(x) = 2, as x approaches some number?

Hurkyl
Staff Emeritus
Gold Member
Infinity is just is a concept used to explain what we cannot accomplish. I really don't believe that infinity is really points of end, causing new beginnings. It's like a long line that you'll never see the end, that goes only forward.
Infinity is not something to be discussed vaguely or by analogy. The various uses of the word "infinite" and "infinity" have very precise meanings.

arildno
Homework Helper
Gold Member
Dearly Missed
As an addition to what Hurkyl said, I'd like to say that in some number systems, infinity happens to be a number, which has individual properties just like any other of those numbers have their own individual properties.
Infinity is not a real number, though..