I doubt this has a truly factual answer, so I’ll put it here.
Beyond the conceptual and mathematical constructs, is there anything we’ve discovered, measured, or observed that can truly be said to be infinite? If not, is there any current theories that might lead to discovering an infinity? The most obvious place to look for now is at singularities and the expanse of space-time, but from what I understand these are infinite dead-ends, so to speak. Then again, I don’t truly understand much.
In theory, space could be of infinite size, and if the universe is open the future of infinite duration.
Singularities actually may well NOT be infinitely small & dense, or even real *; they are where the equations of the better understood theories break down.
Wouldn’t a space of infinite size, take an infinite amount of time to create? And since current cosmological theories say there was a creation event at some point in our past, wouldn’t that mean our universe is finite.
IOW, at any point in time, if you could take a snap shot of all that is, it would be finite. Even time itself. You can say it’ll just keep going on forever, a priori, but that’s not the same as it actually being the case, is it?
It depends a bit on what you call ‘really existing’; you seem to exclude mathematical concepts and such, which is fine, but I’d say there’s some argument there – for instance, there are infinitely many numbers between 0 and 1, do they really exist? Does the infinitely long curve delimiting the Koch Snowflake really exist? If space isn’t quantized, to the infinitely many parts you can slice any interval into really exist?
If tangibility is your criterion for existence, we run into problems with infinite amounts of stuff – infinitely many apples need infinitely much space to put them, and it seems tough to prove their infinitude – i.e. I can’t offhand think of a way to discern ‘infinitely many’ from 'really really lots of ‘em’ (indeed, that seems to me a nontrivial problem with infinite amounts).
EDIT: 666th post! Somehow a bit anticlimactic.
No; in that case, the infinite universe would have be created all at once. The Big Bang wasn’t an expanding fireball in a void; it occurred everywhere at once.
If you could “take a snap shot of all that is”, at least according to some physicists ( who as I understand it essentially regard the passage of time as an illusion ) that would include all of the future and the past.
Let’s define infinity then we can decide if we have one.
For instance The fractions between 1 and 2 are infinite but are contained between those two numbers, is that a pretty small infinity? and contained in a very finite set. Are the fractions between 2 larger numbers a larger infinity? Or are all infinite sets the same size?
So can an infinite universe be contained within a larger Universe? Can the larger universe be finite?
Half Man Half Wit: That’s the problem with the mathematical concepts of infinity. There are an infinite amount of numbers on the number line, but to count them out would take an infinite amount of time, which in reality, is ridiculous. There might even be an infinite amount of primary numbers, within an infinite amount of real numbers. Anyone can cherry-pick a number as high as they want, but that doesn’t mean it’s a tangible reality.
So yes, I’m concluding there can’t be any tangible infinity. You can divide the space between 0 and 1 mathematically forever. But if you do that with space-time, you bump into the Planck Length.
It looks like Infinity can only exist as a concept of something that goes on forever. Not a tangible reality.
Well, mathematically, you can have an infinite amount of space within a finite circumference.
You can even have an infinite circumference within a finite space (fractals)
But none of these actually exist in nature, do they?
There are indeed infinities of ‘different sizes’; mathematically, infinite sets are compared via establishing so-called ‘one-to-one and onto’-correspondences between the elements of the two sets, i.e. you try to find a function that takes an element of one set, and gives you an element of the other set in such a way that each element of the other set is only visited once, and every element is visited (you could draw a line between an element of the first and an element of the second set for every element in both sets).
If you try to do that, but find it’s impossible to visit all the elements of the second set, you have established that there are more elements in the second, even if the first already has infinitely many elements. There was a recent thread that discussed these things by way of Cantor’s diagonalisation argument, you can find it here.
I’m interested in this… anyway you can expand on it?
If space is of infinite size, how can you measure it?
In the broadest terms, I would answer thus:
“X exists” means “X has a place in our language.” Infinity exists. It is a grammatical remark: a place is prepared for this word, it has a use.
“X exists” means “X generates phenomenal content” or some other kind of non-solipsistic phrasing to appease philosopher gods. Infinity doesn’t exist.
On (2), I’d be interested in hearing in what way experience of infinity differs from experience of the very large from those who disagree. I feel that the concept of infinity is rooted in the phenomenal content of space, but that there is no such content or aggregation of content that we can say is infinity. (To my mind, electrons exist in this latter sense as an aggregation of content, if that helps clarify. Electrons don’t exist like apples exist. I don’t experience electrons; I use electrons to account for experiences like the readings on a meter or display of a piece of equipment.)
Just as a slight hijack:
cmyk, I think you’d also be interested to know that the “size” of infinity can vary. Two infinite sets are not necessarily the same size. The set of all integers, albeit infinite, is smaller than the set of all real numbers. Check out some reading on Georg Cantor’s aleph numbers sometime.
ETA: I guess my post is related: It’s hard to answer whether or not infinity exists in the infinite world without mentioning which infinite set you’re talking about. For example, if we were to surmise that there are infinite stars in the universe, what set would that belong to? Can you have half a star? Can you have 0.7928392342238349… of one? Your answer changes which order of infinity we’re discussing.
-space is finite and being created at a rate that is faster than light so you’ll never be able to “reach the edge” thus effectively making it… infinite.
-the number of fractions between 1 and 2 doesn’t make it part of a finite set because you’re measuring two different things. the fraction itself is measuring one metric - things between 1 and 2, and the infinite sum is measuring another - the number of fractions.
-infinity exists but i don’t know how anyone would expect to “discover” “identify” or “measure” it. something that’s infinitely large would not be tangible since it would encompass everything - which means it exists here at my desk simultaneously as it would at yours. The only thing fitting would be… space. thus if nothing can be infinitely large, let’s go infinitely small. that means it would be so small that it takes up no space. Again, something that would be infinitely hard to measure when it doesn’t exist in our measurable dimensions.
i guess the easiest way to prove that infinity exists is to take a marker. start at a point. draw concentric spirals until you run out of paper. then start drawing it on your desk. then when you run out of desk, use your walls, keeping the concentric relation. Then when you run out of wall space, go outside and switch to a bucket of paint. the next step up, your state. then the US. go out into space, leaving a trail of paint. keep going. forever. then you would effectively be the first man to ever prove the existence of infinity.
Yes, I am familiar with Cantor’s Set Theory and even the various sizes of resulting infinities. But this seems to arise only in the mathematical and conceptual sense (such as “Hotel Infinity”).
All measurements so far are indicating the universe has a “grain” to it. The infinities in mathematics do not. You can just keep drilling down into a fractal algorithm, and go forever. But, in the natural world, all ostensible fractals are really just approximations. Eventually, the recursive shapes and patterns come to an end. There’s a resolution to space-time, that can’t support infinities, no matter the size we’re talking about.
Don’t get me wrong, math is great. And I find its explorations into the idea of infinity fascinating and illuminating. However, it appears our universe has no analog to the concepts described within.
That’s precisely my point. Infinity is self-defeating. The only way to create or measure something infinite is with an infinite amount of time. But no one can really come up with a great definition of time, anyway.
Let’s step back here, for a moment. Before we try to figure out if infinity actually exists, let me ask you: Does 1 exist? I have, at various points in my life, seen 1 apple, or 1 chair, or 1 yo-yo, but I’ve never seen just a 1.
The problem with that argument is that infinity is a limit, not a number.
“in finite” pretty much means “without limits”. To measure something is to limit it. Therefore, it is not possible to measure ‘infinite’.
Well, you could try, but since it is without end, your measuring process would likewise be without end.
Kinda like saying “I’m going to count until I run out of numbers”.
I think it’s just an analogy. You could use lim n-> infinity (n / n+1) if you prefer.
That was my point. In another thread, Der Trihs is maintaining that the ability to measure a thing is a prerequisite to the thing being real. Since he makes the claim here that the universe is basically immeasurable, he seems to be claiming that it isn’t real.