Nothing is "certain" when discussing "infinity"
Posted by Zero 9 years, 10 months ago to Philosophy
(This post is an obvious response to SOLVER's post a couple of days ago. But as that thread was getting a kinda fat, I decided to post anew rather than reply. Apologies.)
Discussions on "infinity" illustrate what we DON'T understand, not what we do.
Remember ".999... = 1" from Jr. High? The classic example of infinity coalescing into the finite - perhaps the closest we have to an "understandable" discussion of infinity. And yet, though mathematically valid, conceptually it is a nightmare.
I am an OBJ, but if there was ever an example of "A not equaling A", when a thing is both one thing AND another....
Even AR's genius (and Aristotle's) cannot encompass that which cannot be understood.
We exist within our framework. We cannot perceive - nor conceive - beyond it.
Science readily accepts this limitation. (The center of black holes and "time before the Big Bang" are just two examples.)
As for the "certainty" of parallel existence in an "infinite" universe, consider this:
Take a simple helium balloon. You could fill any finite universe with just the permutations of this one balloon - repeated over and over again - each exactly the same - except one atom (of zillions) is moving in a almost imperceptibly different direction.
And that's just one balloon.
Change the balloon to the Observable Universe.
Now your Infinite Universe MUST contain countless OU's each exactly the same as the others except one atom is moving at the slightest variance. Now take that infinitude and copy it over again except now TWO atoms are slightly different. And again with 3 atoms - and so on, and so on, and so on....
And that's just our OBSERVABLE universe - that spherical volume of the Universe bounded by a 13.8 billion light-year radius with Earth at the center. But since the discovery of Inflation there is reason to believe the actual Universe is larger than the OU. You'd have to "infinitely" duplicate this Meta-Universe ad-infinitum each with only one atom in the slightest variance. Then two atoms, then three...;
And, of course, if the Meta-Universe is truly infinite how can you duplicate it at all? How can you have an infinite number of infinite universes, each exactly the same as the other except some atom(s).
Come on now. Seriously. This is just mental masturbation. We may as well be stoners around a campfire.
Don't speak to me of "certainty" as regards Infinity.
This is truly unknown and unknowable.
But don't despair, perhaps it will not always be so.
Three million years ago, "Lucy" possessed the greatest mind on earth but she could never have been taught Chaos Theory.
What will our descendants understand, three million years from now, that we cannot fathom now?
Discussions on "infinity" illustrate what we DON'T understand, not what we do.
Remember ".999... = 1" from Jr. High? The classic example of infinity coalescing into the finite - perhaps the closest we have to an "understandable" discussion of infinity. And yet, though mathematically valid, conceptually it is a nightmare.
I am an OBJ, but if there was ever an example of "A not equaling A", when a thing is both one thing AND another....
Even AR's genius (and Aristotle's) cannot encompass that which cannot be understood.
We exist within our framework. We cannot perceive - nor conceive - beyond it.
Science readily accepts this limitation. (The center of black holes and "time before the Big Bang" are just two examples.)
As for the "certainty" of parallel existence in an "infinite" universe, consider this:
Take a simple helium balloon. You could fill any finite universe with just the permutations of this one balloon - repeated over and over again - each exactly the same - except one atom (of zillions) is moving in a almost imperceptibly different direction.
And that's just one balloon.
Change the balloon to the Observable Universe.
Now your Infinite Universe MUST contain countless OU's each exactly the same as the others except one atom is moving at the slightest variance. Now take that infinitude and copy it over again except now TWO atoms are slightly different. And again with 3 atoms - and so on, and so on, and so on....
And that's just our OBSERVABLE universe - that spherical volume of the Universe bounded by a 13.8 billion light-year radius with Earth at the center. But since the discovery of Inflation there is reason to believe the actual Universe is larger than the OU. You'd have to "infinitely" duplicate this Meta-Universe ad-infinitum each with only one atom in the slightest variance. Then two atoms, then three...;
And, of course, if the Meta-Universe is truly infinite how can you duplicate it at all? How can you have an infinite number of infinite universes, each exactly the same as the other except some atom(s).
Come on now. Seriously. This is just mental masturbation. We may as well be stoners around a campfire.
Don't speak to me of "certainty" as regards Infinity.
This is truly unknown and unknowable.
But don't despair, perhaps it will not always be so.
Three million years ago, "Lucy" possessed the greatest mind on earth but she could never have been taught Chaos Theory.
What will our descendants understand, three million years from now, that we cannot fathom now?
It's best represented by the old comparison between a mathematician and an engineer. Place both against one wall of a space and a beautiful, nude, female model on an opposite wall. The condition is that both can move 1/2 the distance separating them from the model each step. How long will it take to reach the model? The mathematician can never get there, the engineer will get close enough.
Is it more likely that something infinite exists or that God exists?
The difficulty for a beginning and an end is to imagine what was, before the beginning and what will be, after the ending. As to a god that creates and ends it all, who or what created god? It's all pure speculation and superstition to me. Nonsense!!
("Close enough!" That's funny)
Now, if you want to accept that the universe is finite, then we can have a discussion.
I understand the CONCEPT of infinity, just like I understand the concept of a decimal fraction forever approaching one. But if "point-nine-repeating" equals one - and it does - what does that imply for the real-world application of YOUR concept.
Anyway, my only point was that we should cast a wary eye on discussions of infinity. "Blue-sky"-ing is fun but not really worth much.
Besides, I thought the current, prevailing view among astrophysicists is that the universe is not infinite.
http://en.wikipedia.org/wiki/0.999
You really should take a look. It is not controversial at all. It is a well established mathematical fact.
But - and this is very important - there are many mathematical concepts that have no place in the physical universe.
That was most of my point. A mathematical concept of "infinity" may not apply to the physical universe.
Don't freak, Rob. It throws me too.
But I gotta point out that even your example shows a break with reality.
An infinite number of elements, each infinitely thin?
I'm pretty sure the current consensus is that time is not made up of an infinite number of infinitely small elements. That in fact time has a minimum length. Planck Time, the smallest possible unit of time - part of the "graininess" of reality - is roughly 10^-43 seconds.
Of course, it changes nothing - the calculus still works - but it illustrates my point. That math is often an "idealization" of the physical world.
And to my original point - it's easy to "talk" about infinite time & infinite space (and the required infinite mass) it may be quite another for it to be real. Who knows, maybe "infinite mass" is hard to come by.
Maybe the idea that "Everything-that-can-be-imagined-MUST-be-happening-right-now-somewhere!" is just a silly as it sounds.
And y'know, just to have it said,
They're not only saying "everything that can be imagined" but, in fact, "everything possible - in even the remotest possibility - even that which is utterly UN-imaginable - so long as POSSIBLE - MUST be happening somewhere RIGHT NOW. And it will happen again - no matter how improbable - a split-second second later somewhere else.
I said stoners around the campfire and I meant it.
[Big smile - proffered hand.]
Well met, indeed.
.111111111111111111111... (to infinity) * 9 = .99999999999999... (to infinity)
1/9 * 9 = 1
That was easy.
An infinite series doesn't end, thus you cannot multiply it by a whole number and get a rational number, that is a mathematically illogical.
You can, however, multiply a fraction with a whole number and get a rational number. That does not mean that you can equate the two. Illogical. Proof refuted.
Remember how IMAGINARY numbers are based on "i", the square root of -1. Called Imaginary for good reason, such numbers cannot exist in the real world.
Yet this branch of mathematics is hardly frivolous or trivial. And certainly valid. (Not that I know anything about it, but apparently it is of great importance in electrical engineeering among other things.)
Again, a concept based firmly in the UNREAL, shows us that mathematics can go places reality cannot.
Just like that forever-approaching-never-arriving curve of numbers - that somehow defies all logic and - arrives.
The math is well-founded and is, in-fact, incontrovertable.
And my original point is equally valid.
One needs to be careful applying math to reality.
Is it that you contest some part of the logic? What part?
Is it just one of those - "I'm not sure what I'm missing but I don't believe THAT!"
That's cool. That happens.
But when the "scientists" (mathematicians) are united in their opinion, it's more likely my/your comprehension is faulty. Doesn't HAVE to be, but probably is.
Does 9.99999999999... = 10*.999999999999...?
"..." represents an infinite series of numbers
But y'know, as an OBJ myself, and similarly wedded to the concept of A = A, I just used this truth as a springboard to understanding the difference between thought and reality.
Our minds can go places protons can't follow.
I don't assume that this universe is all of existence. What Rand said or not does not limit me in thinking about how could existence exists or what it is.
How do you know, if existence has always been, that “the entire universe would already be in thermal equilibrium.”?
Maybe this universe has expanded, then contracted. BANG, expanded again... Who knows what the BANG could be.or do?
I also think that some things are impossible thus can't be true. Others say I limit myself thinking this.
One thing I know for certain is that there are at least a universe of things to know. :)
Here's a question,
Is existence and the universe the same container?
The next step is to have the "line" represent time."
I don't understand it at all, but time seems to be inseparable from space itself. Much like the other three known dimensions, length, width and depth have no meaning without the fabric of space.
And a great deal of current evidence seems to show that space/time had a beginning.
What came "before". Unknown and unknowable. Hell, probably not even a valid question.
You stand on a spot. In front of you see a line that goes on forever. Is the line infinite?
You turn around and discover the same line ends right at the spot you are standing on. Is the line infinite?
If the line did go on forever both ways, is the line infinite? If it is, would that also make the universe the line is in infinite?
"I see a line that goes on forever, Is the line infinite?" If we're talking real world, not thought experiment, then no, there is no reason to believe if is infinite. In the real world it is far more likely to end at some point beyond my horizon.
A line that comes around behind me is definitely not infinite. The Equator is 25k miles, not zillions.
"If the line did go on forever both ways, is it infinite?"
I swear I'm not trying to be difficult, but it seems you just defined it as such. What is "infinite" but something that goes on "forever"
Am I expected to challenge your definition?
"If it is, would that also make the universe it is in infinite?"
Yes, I believe it would. It seems impossible to have an infinite line in a finite universe. I'm probably missing something important, but that seems a valid conclusion.
Remember though, at this point we are squarely in "thought experiment" land, be careful how/what you try to translate into reality.
The reason for this thought experiment is to test the question, could existence have no beginning (the forever line that ends right where you are standing), but still exist?
Questions 1 and 2 are the exact same (straight) line but with different perceptions. If each questions would create an infinite universe it fails the test.
"A line that comes around behind me is definitely not infinite. The Equator is 25k miles, not zillions."
Actually that is not what I was trying to point out.
When I said, “You turn around and discover the same line ends right at the spot you are standing on.”,
I was trying to show that when you turn around you discover that the “(straight) forever line” starts (or ends) right at the point you are standing, and goes straight on forever from there.
'Kay, got it. Then yes, I think a line can have a beginning and still be infinite - in one direction only. The Natural number line comes to mind.
Just to be clear though, I wasn't positing a competing theory.
I think concepts like "forever" and "infinity" are just too nebulous to be effectively manipulated.
I don't think we CAN know the answers to these questions - YET.
extending indefinitely
Thus, if it extends indefinitely, the line must extend in both directions.
Definition of a Ray. A ray is a part of a line that begins at a particular point (called the endpoint) and extends endlessly in one direction.
That at least helps simplifies the theory. Thanks.