Do you think the human notion of 'infinite'/'infinity' is actually real infinity?

[Kyriakos]

Couldn't define it more in the title, don't worry though cause this thread has more elaboration.

Infinity is a concept juxtaposed to finite things. For the pythagoreans, for example, Infinite and Finite were two of the "main opposites" of the cosmos, or of human perception of it. (other such opposites included Good/Evil, Male/Female, and Even/Odd).

If one goes by the thinker the concept is attributed to in Philosophy, it was first formalised in late 7th century BC/early 6th century BC Miletos, in the region of Caria, in southern Asia Minor Aegian coast. Anaximander used it as a noun, whereas Homer and others had used it as an epithet (eg an epithet for the vastness of the Sea).

In Anaximandrian philosophy the Infinite stands alone 'outside' of the Worlds (Cosmoi, plural), and is vastly larger than the Worlds. It also is where anything destroyed in the Worlds returns, and where anything new is sent to the Worlds. Moreover there is no way to get from the realm of the Worlds (finite) to the Infinite, and only movement is automatic at creation/annihilation.
A problem is that by and large there is only one passage salvaged by Anaximander, and it is the one describing this distinction, which he attributes to "Time demanding its compensation" from all things that once exist or get destroyed.

*

Infinity was of course a hugely important (maybe the most important) notion in Greek Philosophy. But lets fast forward a bit and reach 300 BC and Eucleid, who provided his proof of the prime numbers being more than can be bounded in any set (ie, by extention, they are infinitely many). Around the same time Archimedes exapnded a late 4rth century BC philosophical claim (by the Platonic philosopher Antiphon of Athens) in which a circle's periphery could be approximated by turning an inscribed regular polygon into the circle, into a polygon of a massive number of sides (so it approximates the periphery it is inscribed upon). Archimedes added a transcribed polygon there too, and argued that the periphery of the circle is given by a set that approximates that periphery from both sides (increasing in the case of the inscribed polygon, decreasing in the case of the transcribed), in a manner that some other math progressions tend to do (eg the so-called Fibonacci series approximates in those two ways the irrational number Phi, for the difference in size between two directly next to each other numbers in that sequence).

**

But an infinite progression is not something tied to the progression itself that much, as to the notion. Usually people examine elements of infinite progressions of more distinct numbers, eg primes are examined in a progression of the natural integers. Then again there is also an infinite number of positions (integer plus some decimals) between two integers, eg between 1 and 2. Likewise for any decimal and another. And if one tries to account for numbers of Real numbers, the irrationals are also included, and this means that they can be hugely more than any rational or subgroup.

The question

Hi, nice to see you reached this part of the post, the question which will greet you here is:

"Do you think that the polar opposite notions of finite and infinite are themselves tied to something inherent in infinities and non-infinities? Ie are there any real, not dependent on human thought, infinities/non infinities? OR do you think that those notions are essentially allegories for other sorts of logical juxtapositions in the particular human mind and its balances? Ie they have nothing at all to do with progressions of anything (of numbers, or size, or volume, or time, or movement or anything else)"

Personally i don't think they tie to anything real. Ie there are no direct (or reasonably indirect, but still tied) connections between our notions of infinity and finite, to any reality of the cosmos/universe(s).

 

[Zelig]

Yes.

5char

 

[Kyriakos]

Yes.

5char

Unoriginal
Very limited

'subject reacted according to known pattern'

 

[warpus]

The mathematical concepts of infinity are certainly equivalent to actual infinity. Otherwise calculus wouldn't really work, for one.

 

[Borachio]

"Do you think that the polar opposite notions of finite and infinite are themselves tied to something inherent in infinities and non-infinities? Ie are there any real, not dependent on human thought, infinities/non infinities? OR do you think that those notions are essentially allegories for other sorts of logical juxtapositions in the particular human mind and its balances? Ie they have nothing at all to do with progressions of anything (of numbers, or size, or volume, or time, or movement or anything else)"

Personally i don't think they tie to anything real. Ie there are no direct (or reasonably indirect, but still tied) connections between our notions of infinity and finite, to any reality of the cosmos/universe(s).

I don't think that the finite and infinity are polar opposites at all.

If anything, the infinitely large and infinitessimal are polar opposites. Even then the notion seems a bit contrived.

But people, myself included, very often confuse the infinite with the arbitrarily large. They're really not the same thing. Infinity isn't a number at all, whereas N (an arbitrarily large natural number) is.

As to whether anything - never mind the infinite - exists outside human knowledge of it (if this is what you're getting at), I don't have a clue. And in fact I don't think there can be any way of determining whether it does or not.

 

[Kyriakos]

I don't think that the finite and infinity are polar opposites at all.

If anything the infinitely large and infinitessimal are polar opposites.

But people, myself included, very often confuse the infinite with the arbitrarily large. They're really not the same thing at all. Infinity isn't a number at all, whereas N (an arbitrarily large natural number) is.

Depends on how you set things/think of it. For example in a pendulum the opposite edges in movement are the only positions of equilibrium (for a short time, and in any given meter of time or differing position). In that sense you could call those opposites. But in another sense they are opposite phenomena to the movement in the central position between them, when the pendulum has most speed so as to reach the other end.

In language both those can be seen as polar opposites, or absolute opposites, or evidently opposites, etc. Movement usually is seen as the opposite of immobility, not of movement in the same speed to an anti-symmetric position (although obviously it can).

The mathematical concepts of infinity are certainly equivalent to actual infinity. Otherwise calculus wouldn't really work, for one.

Even if infinity is just human and not tied to 'real' infinity (which in that case might not exist or exist), surely our own human-sensed infinity would still be functional as a notion used in human-examined phenomena studied with it?

 

[warpus]

Even if infinity is just human and not tied to 'real' infinity (which in that case might not exist or exist), surely our own human-sensed infinity would still be functional as a notion used in human-examined phenomena studied with it?

The concept of mathematical infinity is the real infinity, much like the mathematical concept of addition is the real addition. As in, it is a mathematical formulation of the concept, not just any concept.

 

[Giftless]

Probably not, since what I know about mathematics imposes a binary framework upon reality. Just because this framework "works" for most applications that I know of, doesn't mean that the extrapolations hold true when taken to the extreme. For example a theoretist might take for granted that two parallel lines will continue to be parallel onto an infinite length, but when taken on a massive scale would they eventually be curved by space-time? Which leads to the thought; well, at what point will all our conceptualizations break down?

Here's something else to think about; while the "when" is not completely understood, it is known that molecules will often behave differently individually and as an aggregate. Perhaps what we can see is akin to water as an individual molecule, whereas infinity would act more like a liquid. Can we then understand the liquid properties from the standpoint of residing upon a single molecule?

It raises the question of how far the human mind can reason upon matters which are difficult for us to perceive.

 

[Giftless]

I don't think that the finite and infinity are polar opposites at all.

If anything, the infinitely large and infinitessimal are polar opposites. Even then the notion seems a bit contrived.

But people, myself included, very often confuse the infinite with the arbitrarily large. They're really not the same thing. Infinity isn't a number at all, whereas N (an arbitrarily large natural number) is.

As to whether anything - never mind the infinite - exists outside human knowledge of it (if this is what you're getting at), I don't have a clue. And in fact I don't think there can be any way of determining whether it does or not.

I wonder how thermodynamics would work in an infinite system, as in, how would matter get itself organized in the first place given the potential for infinite disorder? Given infinite distance, the force of gravity would become so small as to make it so that matter would take forever to initially come together.

 

[Gigaz]

The whole question really comes down to asking if anything in mathematics is a description of something "real" that is being discovered or if it is just playing around with logic.
I don't think there will ever be a definite answer to that.

 

[Kyriakos]

^Cool posts, Gifted (x-post with Gigaz, btw )

The concept of mathematical infinity is the real infinity, much like the mathematical concept of addition is the real addition. As in, it is a mathematical formulation of the concept, not just any concept.

Well, what if the 'real' (ie the stuff there regardless of any particular point of view or observer or abilities to observe) is not infinite, but we have a notion of infinity anyway? I don't think that any such 'absolute reality' has to tie in such a manner to any human-particular notion. Maybe 'infinite' is not tied to anything 'real', like (in some sort of analogous) free-fall is not an observed state in a world of molecules that Giftless/Gifted mentioned

 

[warpus]

I'm not sure what you mean, to be honest. Infinity is just a concept, whether the universe is infinite in size or not. The size of the universe has no bearing on the concept of infinity.

The mathematical concept isn't an attempt to model something that's out there & infinite in size or that is countably infinite. It is just the description of a concept

"Real" infinity is the concept itself, not an example of it. But I suppose that's what you might be trying to say - that there might not be any examples of infinity in nature. I'm not really sure if there are or aren't, I wouldn't be surprised if there were some indirect examples. I'm not sure if the infinite density of a black hole counts or not. It should, but I'm not a physicist, so..

 

[Kyriakos]

I'm not sure what you mean, to be honest. Infinity is just a concept, whether the universe is infinite in size or not. The size of the universe has no bearing on the concept of infinity.

The mathematical concept isn't an attempt to model something that's out there & infinite in size or that is countably infinite. It is just the description of a concept

"Real" infinity is the concept itself, not an example of it.

But why would 'real infinity' be the concept we have, more than 'real object trait' is the concept we have or not? Eg a cube of suggar is cube-like (and moreso we turned it to an approximation of that shape), but that doesn't mean any alien observer would see such a shape there. Maybe some won't even be able to pick up shapes. Maybe some pick up something as the shape, but in a manner turning it into different phenomena (eg sound or color or heat or utterly unknown to us senses).

In theory, such an alien may not sense movement, or space, or time etc.

(and surely if an observer does not pick up progressions of any kind, they would not have any obvious use for a concept of 'infinite' there either? ).

Basically a 'real infinity' might tie to a question of whether the universe(s) is/are indeed comprised of distinct parts or not. If from some crucial POV it is just One, then maybe infinity is not really tied to it but only a fault of imperfect (to that POV) observer/thinker?

 

[gay_Aleks]

Barman! This round's on the weird Greek guy to the left!

 

[Kyriakos]

Barman! This round's on the weird Greek guy to the left!

Thanks

But wait, in a sphere that has an infinite periphery isn't any point its center?

(or is time non-linear and i already had that drink? )

 

[gay_Aleks]

Jeez, you can't have a drink without making it complicated.

Philosophers.

 

[warpus]

But why would 'real infinity' be the concept we have, more than 'real object trait' is the concept we have or not? Eg a cube of suggar is cube-like (and moreso we turned it to an approximation of that shape), but that doesn't mean any alien observer would see such a shape there. Maybe some won't even be able to pick up shapes. Maybe some pick up something as the shape, but in a manner turning it into different phenomena (eg sound or color or heat or utterly unknown to us senses).

I think maybe you misunderstand the true nature of infinity - it is not a property or something (like height or width or age or shape), but rather a vague concept that basically just used to describe "things without any limits".

Being such a vague concept, the mathematical model of it is pretty much equivalent to the actual concept itself. It basically just means "whoa look this thing has no bounds and continues forever, what the hell"

 

[Zelig]

Unoriginal
Very limited

'subject reacted according to known pattern'

It's because all the input is the same.

 

[Kyriakos]

I think maybe you misunderstand the true nature of infinity - it is not a property or something (like height or width or age or shape), but rather a vague concept that basically just used to describe "things without any limits".

Being such a vague concept, the mathematical model of it is pretty much equivalent to the actual concept itself. It basically just means "whoa look this thing has no bounds and continues forever, what the hell"

Sure. It is not an evidently sense-tied concept, yes, in the way that you can sense yourself as One person, or a book as One, or any other such thing, and thus argue that One as a concept is directly manifested in sense-picked stuff at any rate.
However, as with any human notion, infinity also appears not in a vacuum but in inevitable (albeit not very defined; vague as you said) connection to other human notions, and the totality of our mental world. In that sense it is indeed another notion we have, and despite its differences from sensory-tied ones it still is not logical to extrapolate that it exists as such in a critically different (or all-by-itself) category in our thinking.

But that does not mean that there is no way that an infinite-by-itself might exist in the cosmos. It might not, but then it might. And if it does the point is that it is no closer to our own concept of infinity than any other concept we have can be argued to be next to any other thing-by-itself.

Ultimately i am of the view that we cannot prove either way. What seems certain, though, is that infinity is a hugely important notion in human thought, whether consciously or not. It is tied to vagueness, and limits not to be reached, which i have to suppose is always used in human conscience, no?

 

[warpus]

Oh, so you are just talking about something being infinite in one of the dimensions - whether it's time or space? Then yeah, we might never know. But the mathematical concept of infinity doesn't really rest on us ever finding out; it's just a quite natural concept that would have arisen one way or another.

It's easy to go from "bounded" to "unbounded", you've just got to think a bit and there you go.