Watch this:

Infinity + 1 = infinity.

That second infinity isn't any less or more than that first infinity, but it just got bigger. By one. You see how that works? It's a bit weird, I know, but it seems to be how the universe actually is.

By the way, if you think THAT'S weird, don't ever look into quantum mechanics. It will bend your bones.

This is how mathematics actually is...I'm curious about an example from physical reality that would illustrate this, or justify the claim that this quality is 'how the universe actually is'. We can't even find infinity (ever smaller divisions) between two points in space, as we can between any two numbers - space itself appears to be quantized.

Where is there any kind of infinity in the physical universe?

Even the number of possible ways we could arrange all the atoms in the universe is finite.

Infinity, as a number, is not an accepted concept in mathematics. Something that is infinitely large cannot be made larger by adding to it, it's a contradiction in terms. In math, you have two sides to every equation. Infinity * 2 = Infinity. Now remove Infinity from the equation by dividing each side by Infinity and you get "2 = 1", which isn't true. Infinity is a concept, not a number.

You're not "removing infinity from the equation", you're dividing by infinity, which... what's your grounding in basic math? I need to know how to pitch this.

First of all, I feel duty-bound to point out that there is a difference (and sometimes a massive one) between the way the universe is, and what makes sense.

All the other galaxies seem to be moving away from us at close to the speed of light, as though we were the center of some massive space-wheel. However, relativity indicates that it would look like this *no matter where we were* in the universe. And also, relativity dictates that none of these views are incorrect. They are both right.

This might be hard to take.

Think about some guy on a train moving out of a station. He sees all the people on the platform moving backwards, essentially the entire planet, moving backwards relative to his own position, at whatever speed the train is going. Meanwhile, the people on the platform just see the train moving out. The kick is that Einstein worked out that it's not just a word trick - to that guy on the train, the rest of the planet ACTUALLY is moving backwards at that speed... and the people on the platform are seeing something else entirely. And they're both 100% correct.

It doesn't make sense, but it's the way things are in reality.

It's the same with this infinity thing. It might not make much sense, but it seems to be the way things are.

Spider's statement, as worded (words 2-4 especially), is accurate.


Not really. Wasn't hard to accept when I was eight, either. Ah, I still remember the "cosmology for children" book illustrating this concept by talking about the expansion of a loaf of raisin bread.




Thats a nice little educational aside, I'm sure it served the audience well.

Back to the question: do you have any evidence of anything infinite in the material universe? (Since I last posted, I thought of a possible example, but some would argue that it is outside of the material universe.)

Do you hold that anything in the material universe is infinite, in any meaningful way?




Thats just a collection of words with no specific meaning. What infinity 'thing'? What is the way things are?

This might be hard to take ... but the galaxies are not moving away from us at close to the speed of light. The ones on the far opposite side are, however, moving pretty fast relative to us. The universe makes perfectly good sense right now although there is plenty to learn. There are some primers on relativity on you-tube that might help your obvious confusion with red-shifting and relativity.

Relativity is the relationship between time and space. Einstein did some studies of a moving train (thought experiments) to show how time is relative to speed. He rode on a beam of light to show it better.

The expansion of space is what makes the universe look the same from many points, not relativity.

Division by zero.

equals... undefined.

Infinity is not a number... Therefore it can be anything the minds eye assigns to it.

I like this explanation the best, but the balloon could deflate as well or pop at any moment.

I can't be sure over the internet. Was that sarcasm?

That's just a collection of words with no specific meaning. You could argue that the concept of infinity, whether or not it's demonstrable in the real world, has no meaning.

Oh come on! You could say that about anyone's post on anything! Just "a collection of words with no specific meaning". I'm not getting into a whole semiotics thing with you. If I try to post something intelligent, you respond with sarcasm. If I try to post something basic, you'll call me patronizing. There's no winning with you, is there?

Meet me half way.

How exactly do you explain what that means without using relativity?

No it can't.

No, it wasn't sarcasm, exactly. I do hope that someone reading this forum, previously unaware of the idea of reference frames or their importance in physics may have had their first taste of them.

((Technically, its not completely correct to say that the train and the station are equal, since the earth itself is a rotating frame, and the departing train is constrained to the surface of the earth. But for everyday purposes the example works well, and is easy to translate (haha) to true translated frames of reference.))




Yes, its absolutely correct that this could be said about anyones post. I could also say "Architects mate springtime flagellum" in response to just about any post, as well. I jest. You are also correct that the true relationship between language and meaning could be legitimately called into question at any time, in any conversation.

The fact that all members of a set have the same quality to some degree, does not make all members of the set equal, not even with respect to that quality.

I found your particular post especially ambiguous:



"It's", "the same with", "this infinity thing", "It", "it", your statement is composed of about 40% ambiguous terms/phrases; you seemed to have presumed context, without giving it earlier.

I have no idea which of several possible ideas you might have regarding "this infinity thing" you might be referring to.



Oh, there is definitely winning with me - strive for clarity, honesty, accuracy, evidence-based positions, and if you are going to respond to a question, have your response be related to the question.



I don't know what you mean by 'intelligent' and 'basic' here; I have no issue with educated or examined claims, nor (appropriately) simple and straightforward statements.

I'm giving you a hard time because you responded to my straightforward question (about examples of infinity) with what appeared to be off-topic non-answers.

I'm honestly curious about the possibility that infinity might be relevant to the physical universe, as I see only two (similar) cases where that might be true, and no cases where its definitely true.



Are you saying that you find that position agreeable? I can be literal - are you not just saying that 'it can be argued', but that 'it can be intelligently, meaningfully argued'?

OK, massagetrade, first of all I have to say that I thought you were being sarcastic. I really did. I was expecting you to come back with some gibberish troll argument full of antagonism and ad hominem. So: sorry for underestimating you.


Yes, it's the example Einstein used. So I guess it's close enough.

I was referring to the existence of infinity in the natural world, which is what you were doubting, or looking for examples of. It doesn't make much sense, in the sense that the human mind isn't good at comprehending it. But it seems to be the way things are, in the sense that, no matter how badly the human mind can comprehend it, it seems to exist in reality.

Example from maths: pi. 3.14259...infinity. Circles and all sorts of shapes occur in nature, and their relationships to themselves and each other is often expressed in terms of infinities.

"But," you will justifiably point out, "this is rubbish. Numbers aren't real! I can't hold them in my hand, and in any case, they're only like that because of our arbitrarily selected base 10 numbers system. Some other pi-based numbers system would just call it 1."

Right. Make a Moebius strip: http://en.wikipedia.org/wiki/M%C3%B6bius_strip The side is infinite. And you're holding it in your hand. It's a real thing.

"But," you will point out, "this isn't what I was talking about. This is a man-made object. I want you to show me infinity!"

I can't. I can't take you by the hand and lead you to the middle of a black hole where you will see the infinite density of a zero-volume singularity. I don't think that will ever be a possibility. Until then, we're stuck with slightly artificial examples, like the Moebius strip or relationships between objects. But it does exist.


Fair enough. You'll have to forgive me. I've been on the internet way too long. I thought you were a troll.

I'm saying that once you try to identify what you mean by "meaningful" without using any words derived from the word "meaning", you could run into trouble. And it is entirely a semantic sort of trouble. It's not a practical trouble. I think sometimes these debates can get hung up by WHAT I MEAN BY THIS and WHAT YOU MEAN BY THAT when, for all intents and purposes, it's obvious.

That's an infinite number of places, not an infinitely large number. There is a huge difference. An infinitely long number of digits can be rounded off, an infinitely large number cannot be used in math.



Numbers are real and are one of the only "necessary" ideas that mankind knows. Even if humanity disappeared, 2+2 would still be 4.



That's not infinitely long! That's a closed shape, but it is finite in length. Yes, an ant could walk forever on it and never reach the end, but it's measurable. Infinity is by definition unmeasurable. I'm starting to get the impression that you aren't clear on the definition of infinity.

How exciting it is to see this thread, because the information being exchanged here is of great interest to me, but alas I am far less knowledgeable than most of the posters here.

I would really like to understand more so I’m going to make some observations and apply a little philosophy, NOT because I think I'm correct but specifically for those who are patient enough to make corrections to my observation & inquiries. I would greatly appreciate the guidance

FIRST: About how we ‘understand’ (abstract) (concepts): (PLEASE read because this will be important information to understand the end of the post.

Humans continually add bits of information to that storage unit we call brain. In order to utilize that information either heuristically or abstractly we must arrange the bits of information into highly correlated units called constructs.

A construct can be anything, for example; understanding what a chair is and recognizing a chair when we see it with little regard for its physical appearance. Likewise, we find relationships between bits of information in order to formulate a new construct we might call an idea.

Utilizing particular bits of information for one construct does not limit the use of those bits in any other construct. When we conceptualize a thought we are using the bits of information that already have a basis in reality (“concrete” bits of information). When that line of thought creates new relationships between bits of information, we are thinking abstractly.

We are only able to communicate abstract ideas in concrete ways, in other words we must be able to build a construct that can be concretely demonstrated. When we do this we are trying to make others bring together the same bits of concrete information to form the same relationships as we have made.

The problem is that no two individuals have formed exactly the same bits of information relationally, in their minds, nor can we explicitly identify every bit of information or its relevance in the thought process. In essence we depend of the audience to visualize what has not been presented OR to conceptualize beyond the concrete.

Which now brings me to what’s being discussed.

Massagetrade used a concrete example of a balloon to demonstrate how a closed environment can be everything right now and still be everything even though it expands.

Then Spider, responding to other posts said:



I had a ‘thought’ in connection to those two ideas. First I thought, if the closed system of our universe is expanding into infinite space does infinite space decrease?

Followed by: how can infinity be increased or decreased? Oddly, Spider’s statement >> “Now remove Infinity from the equation by dividing each side by Infinity and you get ‘2 = 1’.” << made me think a different way.

Now remove the mental construct of the balloon which is used only to indicate that at least some portion of infinity includes closed systems.

Now let me digress back to the beginning of my post to information bits and the constructs we formulate from them.

How many bits of information do you suppose it would take in order to have enough to form an infinite number of constructs? Remember that our senses function continuously and new information is perceived bit by bit whether we are conscious of it or not. Every bit of information includes many properties and any of those properties can correlate to any other bit or group of bits in varying degrees. Do we need an infinite number of bits in order to formulate infinate constructs?

Does a closed environmental system that exists in infinite space preclude infinity in any way? Reduce it in any way? Does the expansion of a closed environmental system dilute infinity in some way? What does infinity consist of?

If our brains can formulate infinite constructs (whether they can be translated concretely, realistically or not, can infinity be composed of a limited number of bits that can form an infinite number of constructs – couldn't our closed environment be only one of those constructs?

>> “Now remove Infinity from the equation by dividing each side by Infinity and you get ‘2 = 1’.” <<

Perhaps infinity cannot be confined and perhaps the infinate constructs are beyond our scope of knowledge or understanding, but can infinity exist with a limited number of variables whose properties are many and whose combinations become the unique constructs of closed systems?

Does infinity preclude closed systems or define them?

I saw this last night and it just blew my mind. So, would it be like having a box with no space limit and just putting more stuff in the box?

I am sometimes rudely indifferent to how I come across, but I almost never deliberately incite anyone. If that happens, its an unintentional side effect.







Okay, fair enough. As it stands, I see absolutely no evidence of any kind of infinity existing this side of an event horizon. (The two examples I had in mind were black holes and the big bang.)



Funny how closely your self-counter-argument matches my first thought upon reading your suggestion that irrationals are a kind of 'infinity' that 'exists' in the material universe. I hold that numbers themselves don't exist in the material universe. The relationships which we use numbers to express might exist, and the symbols we use to represent numbers exist, but the numbers themselves don't. It doesn't matter that I can't hold them in my hand - there is much that does exist which I can't hold.

Using a number system for which 1 is the ratio of circumference to diameter isn't some trick, it makes clear the fact that this 'infinity' is nothing more than a side effect of our numbering system. It shows that an integer based number system can't 'capture' the irrationals in a finite expression - thats it. It says something about the relationship between integers and irrationals, but there is no actual infinity there.



The fact that the strip is an artifact is irrelevant to me. There is simply no infinity on a mobius strip. Its a nice shape to lead a human to contemplation of infinity, but in terms of 'suggesting infinity' its actually not much different than the surface of an orange, or if you prefer boundaries the round surface of a cylinder. In all cases, there is a closed path.

This may lead us to think of infinitely travelling that path, but there is no infinity there.




I'm really not trying to play a semantic game in order to hold the ground of 'no infinity exists in the material universe', its just that black holes have this odd feature of the event horizon. I find it amazing that an infinity of any kind might exist within a black hole, which can be contained within an imaginary 3D sphere whose surface is entirely 'within' our material universe. Many would hold that this automatically means the black hole and all of its possibly infinite innards are 'within' our universe, but I don't. Acknowledging that some black holes spin off energy and have shrinking event horizons - at any point in time the 'other side' of the event horizon is simply inaccessible to the material universe. I'm not convinced that all of the black hole is part of our universe anymore.

An infinitely large number can't be used, but we take limits to infinity all the time. Usefully. Infinity (not as a number, exactly) is a tremendously useful concept in mathematics.



And, of course, in our universe, an ant can't actually walk on it forever, as the ant would die. Entropy trumps infinite time.



I don't think he's actually arguing that 'infinity really exists' position anymore, but simply trying to present food for thought.

'Basis' is an interesting word, here. Reality is the means by which cognition occurs, and some would argue that all of our thoughts are due to biochemical events, all of which were effected by the material reality.

Using the phrase 'have a basis in reality', I'm concerned that some people may think that this legitimizes our fictional thoughts as being more 'real' than they are.




I don't understand your question. If we use the '2d surface on an expanding 3d object' metaphor - are you asking whether the 'amount of space outside the closed 2d surface' decreases? We don't presume that this 'space' exists, or is real. The fabric of spacetime appears to have a particular topology; our natural way of conceiving of this is 'within' a higher dimensional space, but this doesn't mean that all of those higher order dimensional spaces exist. (I'm fairly certain that when people speak of our universe possibly having a larger number of collapsed higher dimensions, they are speaking of a completely different topic/issue than the higher dimensions we use to conceptualize our 3space being curved.)

In short, our 3space is finite, and expands. Contrary to our intuition, there is no need for kind of any infinity 'existing' outside of our 3space - you know, one that we would be expanding into. Our space simply exists, is all that we know exists, doesn't prevent nor require the existence of other spaces (setting aside 'first cause' issues), and can expand without there needing to be something to 'expand into'.



In math, you can take unions and intersections of infinite sets, and say that one infinite set is larger than another infinite set. As spider keeps pointing out, infinity is not a number, so we don't expect the same rules to apply.



If you are asking 'how many bits do you need to hypothetically create an infinite number of arrangements, given infinite time' the answer is 'very few'. Counting towards infinity in binary shows this.

If you are asking 'how many bits does it take to actually form an infinite number of constructs, in our universe, the answer appears to be 'you can't'. It would take an infinite number of bits, more than there are particles in the universe.



In finite time, yes.



I think you are thinking of the balloon metaphor, with the balloon suspended in some infinite void. This is how we naturally are, as creatures living within our 3space - for everything that we experience, something contains it. Its hard to imagine our universe existing with nothing outside of it, not even a measured nothingness, not even a void into which it expands.

Yes. Now imagine all that without the box.

It might not be. We'll never know. We can barely detect the things as it is. We certainly can't see them. We have to watch for "wobbles" and Hawking radiation and so on. There isn't even a theoretical way to work out what's going on in there.

However, the same physics which led to the correct prediction that they exist at all leads to the prediction that the singularity has zero volume and hence infinite mass.

Some will argue that quantum mechanics (the movement of sub-atomic particles, which is at great variance with the movement of everything else) allows for alternative interpretations, but there's no reason to believe any of them at the moment, and there is a strong reason to believe Einstein (namely, that he predicted their existence before anyone saw them).

There is an argument which states that anything that has parts is divisible, and hence cannot be infinite, the logic being that something infinite must either have no parts at all (like the concept of freedom) or just the one part that goes on forever (like a singularity - good luck breaking that up into bits).

Singularity is a gateway between two universes. (one hopes that in delving into sub-atomic shotguns mankind does not inaverdantly create one - they just might be shooting god in the foot).

Gate boundry is at the point of the acceleration of indiviual atoms to light speed (98th percentile). AT that boundry gravitational forces combined with speed of light relativistic compression cause the atom to shrink (thats why your miss ratio is so high in a man made maching). This causes the structure of the universe at that point to 'flex' into the gravitation well also. Individual atoms do have gravity and atomic structure near the 'event' will be drawn into the event by its increased gravity. 'Flex' is quite small because only individual atoms close to the 'stress point' will actually enter it. And the universal field will 'flex' back to normal at the speed of light (good luck detecting that... with your gaze focused steadfastly on the hole you are missing the truth of the reality).

Einstein gave us the key but no one seems to know which end fits in the lock.

There are two sides to every equation.

There are two sides to every boundry horizon.

And the universe ain't 'expanding'... We have entered the event horizon of the Galactic center... (If you understand Einstein you will understand the truth of this)...

We entered it perhaps 10000 years from now but the shrinkage 'event horizion' is stretched over time and its effects are 'slow' realitive to the speed of man.

Put that theroy in you computer and have fun with it.

If one looks down with the same tools one uses to look up...

The universe may contain small discrete packets... but underneath those packets lies a greater reality and beyond the universe lies that same greater reality.

You know, I understand each individual word of that, but put them all together...