Thinking about infinity

[SteveII]

(unless you are Hawkings and then you don't).

???

Sorry, I mispoke. I may have remembered something I read incorreclty.

[SteveII]

My understanding is that infinities are useful fictions in math equations. When used in physics, they are always converted back to finite quantities (unless you are Hawkings and then you don't). CORRECTION

[Excited Penguin]

Some sets of infinities certainly seem logically possible. 

For example, the infinite set of natural real numbers seems to exist, which is to say that there is an infinity of natural real numbers existing even now, and there is none of them which do not yet exist.

There are an infinity of points on a line segment.

It is logically possible that reality has an infinite history of cause and effect (i.e. extending "backward" through the big-bang), and that it will have an infinite future.

In what sense could an infinity of simultaneously existing things exist together as a finite thing?

The set of natural real numbers aren't really infinite, we only think of them as such. Same holds for the points on a line segment. In the real world, nothing has been proven to be infinite, nor could it be. Feel free to dream of it though.

In my uninformed, uneducated opinion infinity is illogical and doesn't have a place in the real world.

Do correct my ignorance.

[robvalue]

I forgot another possibility: time being circular.

In this way, technically "the past" is infinite, although it will be repetitious.

[TheRealJoeFish]

I forgot another possibility: time being circular.

In this way, technically "the past" is infinite, although it will be repetitious.

Fry: "So, why did you freeze yourself?"

Dude: "Well, I wanted to meet Shakespeare, and I figured time was cyclical."

Fry: "Nope - straight line!"

[Ignorant]

What does it actually mean for the set of natural numbers to exist? It's not like all these numbers are somehow represented explicitly by anything in the universe. What we have is the notion of taking another step to the next one, and a notion of that being always possible. Does the existence of these ideas already warrant the statement that "the natural numbers exist in the universe"?

I certainly agree that, for our conceptualization of any such infinite set of numbers, we MUST rely on a notional reality of infinity as any number's potential addition by 1. I said it "seems to exist", for that very reason. It seems logically possible that it exists (in whatever way a number might exist in the abstract). Does such an infinite set, in fact, exist? I don't know. I certainly couldn't "point to" it. But logically, it seems possible.

So better to say "the natural numbers exist in potential"?...

I mean you could get to any of them with enough time, just take another step. <=

I think this is the classical definition of "potential infinity" going back to at least Aristotle, but I've been wrong before.

... Something exists if it can be uniquely identified as a subsection of our (assumed) objective reality.

Thoughts?...

That seems ok to me for now for the sake of this discussion.

For things like numbers, I would say they only exist abstractly; minds are able to have images that represent the concept. They are a step removed from reality. They can represent arbitrary groups of things in reality, but they do not themselves uniquely identify something in reality. You can of course have abstract concepts that do identify something existent. We could also have abstract concepts that represent qualities of existent things, such as length.

Things can theoretically be dissected into infinitely parts. We can model them mathematically, and slice them up as we wish. Can they in practice? That depends on the nature of reality. Maybe, maybe not. If there is some "smallest measurement" actually possible in reality, then such a thing wouldn't work.

I see no logical problem with an infinite past...

Great. Infinite time: yes. Infinite-divisibility: maybe. Infinity of numbers: only in concept, not as real "things". Sound like I've got it?

Line are defined as a string of points, and any 2 points are defined as being separable by another point between, so the infinities associated with lines are there because humans decreed it.

So, do you think the infinity associated with a finite line-segment is something other than an infinity existing as a finite thing?

My understanding is that infinities are useful fictions in math equations. When used in physics, they are always converted back to finite quantities (unless you are Hawkings and then you don't).

So actual infinities do not exist in reality? Do you think it is even possible for an infinite set of things to exist as a single thing?

[Ignorant]

The set of natural real numbers aren't really infinite, we only think of them as such. Same holds for the points on a line segment. In the real world, nothing has been proven to be infinite, nor could it be. Feel free to dream of it though.

In my uninformed, uneducated opinion infinity is illogical and doesn't have a place in the real world.

Do correct my ignorance.

I wish I could correct your ignorance [edit] but I don't think I can. Do you think it is impossible for an actual infinity to exist, and if so, what reasons would you give?

[robvalue]

Great reply

Theists, take note! This is how you have a discussion! We have a new contender for theist of the year come December

Great. Infinite time: yes. Infinite-divisibility: maybe. Infinity of numbers: only in concept, not as real "things". Sound like I've got it?

Sounds good to me, although I'd say infinite time would also be a maybe. I can't find any way to rule it out. Science, as a rule, doesn't generally rule things out unless they present a contradiction. But maybe there's some reason why time must actually be finite.

[Ignorant]

Great reply

Theists, take note! This is how you have a discussion! We have a new contender for theist of the year come December

HA! Too kind!

Sounds good to me, although I'd say infinite time would also be a maybe. I can't find any way to rule it out. Science, as a rule, doesn't generally rule things out unless they present a contradiction. But maybe there's some reason why time must actually be finite.

Does that mean it is a logical possibility? <= This is the nature of my question. Whether or not it is the case that time is infinite, I understand to remain an open question both logically and scientifically. If it is an open question, then it must mean that both possibilities are logically possible. I certainly think infinite time is logically possible.

[robvalue]

Oh, I see what you mean. So yes, it would appear to be a logical possibility, as far as I can tell.

To review what I said about dividing something up infinitely... that too would appear to be a logical possibility. But this is something we would potentially have more information on, so those well versed in QM may have a reasonable prediction as to whether it is possible based on what we observe. (Something about "stable wave formations" comes to mind.) However, there's always the chance that this prediction is wrong, and that we're just using the wrong techniques or tools. Certainty is not the job of science.

As to how a finite object can be made up of infinitely many parts, that is covered all the time (at least abstractly) in mathematics by such processes as summing an infinite geometric series, or performing integration to calculate the area under a curve.

I'm not convinced science could ever rule either of these out categorically (infinite past / subdivision)... but it may well be that there is enough evidence (now, or on the future) to make a pretty sensible estimate.

Another important point: even if time was finite in this reality, that doesn't stop time being infinite in another reality; and perhaps it could be viewed as "the past" if our reality actually came from it in some sense. I don't know if that has any bearing on your question.