me said:If it's true that infinitesimals are logically unsound ...
That was something from my textbook. It's in the quote in post 619, and not attributed to you.someguy1 said:I never said that. Nor did the quotes you posted.
me said:If it's true that infinitesimals are logically unsound ...
That was something from my textbook. It's in the quote in post 619, and not attributed to you.someguy1 said:I never said that. Nor did the quotes you posted.
That was something from my textbook. It's in the quote in post 619, and not attributed to you.
Can "Infinity" ever be more than a mathematical abstraction? Without any real world evidence, for me the answer would be "no".
Yet, our Universe is thought to be flat and without a special topology that would seem to imply infinity. Many concede that the Universe likely is infinite. How can science so readily concede that infinity is a real possibility when there is no evidence of infinity outside of math?
Here I'm speaking of infinity of space and time and not some situation where the infinity is just do to the framework imposed such as walking around the North Pole and calling space there a Singularity just because the time zones all converge or some such example.
What's your evidence that the universe isn't infinite in (spatial) size?Infinity is of course nothing but an abstraction but in physics it means something pertinent, it refers to an non-physical situation; this would explain why there are no infinities observed in nature. Even the universe as large as it is, still has a finite amount of mass in it. Infinities simply do not exist in nature but they are good mathematical abstractions for calculus.
It could've been created infinite in size, and then start expanding; as far as I know, there's nothing in the big bang model excluding that possibility.Well for one simple reason, the universe HAS a finite past and the only way a universe in that sense, would have to expand and expand and expand...
What does the size of the observable universe have to do with the size of the full universe? I can't follow your jump in logic there.and it will never reach that infinity because, as infinity is an abstraction, it's not a number that increases like $$(1 + 2 +3 \rightarrow \infty)$$ - under Cantor, he thinks an infnity can be countable but twist is, there is no such thing. Also, we do have an observable horizon and we can trace that horizon back to a hot dense state.... I mean, based on that alone, it doesn't look promising that a universe is infinitely large. Or ever will.
Totally irrelevant: I'm talking about infinite size in space, not infinite size in time.Here's a thought experiment, how many times do you need to count to reach infinity? The answer is you would have to count for all eternity and the end of time itself. So instead we create a computer that will be constructed to count from 1, to 2, to 3 and so on, until it reaches infinity.
Now in that last passage, some things need to be clear, like parts of it were wrong. First of all, you cannot count to infinity (because infinity is not a number) once again, its an abstraction. Second of all, the part in which I state, can you count to infinity and my answer being no I hold to, I also hold the universe is finite in principle because even that expansion has only been going on for about 15 billion years - I'd hardly call that infnite... would you?
Again you claim the universe isn't infinite in size; please provide actual evidence for that.And even though the number of particles in the observer horizon is very large of order $$2 \times 10^{80}$$ .... this too is no were near infinity, because infinity isn't a thing. It's not a number, at best its a concept and one that has no support in nature.
Again you claim the universe isn't infinite in size; please provide actual evidence for that.
And I never claim otherwise.Big Bang was emergence of time and space, you cannot have one and not the other
What Pythagorean triangle are you talking about? And why is it impossible to have an infinite space but only a finite time? And why would time be finite; it can still be infinite, even if it has a starting point.- you can't talk about an infinite space alone because time is actually part of the Pythagorean triangle.
No, the problem is that you aren't answering the question: I asked you for evidence that the universe is finite, and you aren't giving any.My point is everything I said is relevant, you just don't understand what I have said.
Why?Plus try and remember if you talk about an infinity of space, you have to deal with an infinite time,
Your strawman indeed does crumble because of that.sorry, but your whole arguments crumble because of us.
Sure, but that doesn't mean that at the moment the big bang happened, only a finite-size space could have emerged. Why, according to you, couldn't the big bang have produced an infinitely sized space?I already told you, the fact it has a finite past ensures that we had a moment in both space and time which exploded and became the big bang we know today.
I don't disagree with that, but once again, I don't see how an infinite time must lead to an infinite space. I don't follow that jump in logic in your argument. Can you please elaborate?Considering this means the universe has to be roughly 15 billion years, I'd call that a penny towards the journey to infinity.
I'm sorry, what? "In a night"? Me manic? I have no idea what you are getting at?Oh common, I have a 1o minutes at best you're hitting out with what I believe are genuine questions, but you're way too manic for me if you think I can explain any of that in a night.
Oh c'mon.Sorry I don't remember what the context was and didn't go back to check. But nothing can "agree perfectly with experiment" unless it's a discrete measurement like counting the eggs in a dozen. The world's best experiment gets 12 decimal places of accuracy.
Irrelevant. I'm observing that computable numbers already model the known physical world, sufficient, that no smaller set of the reals does, necessary, and so we have evidence that the infinities thereby included match real infinities - that they model "something else", that these infinities are "more than" abstraction.Some guy wrote a book on computable physics but he's the only guy. It is a VERY obscure pastime to be trying to redo physics on computable math.
All of them.What model is that?
There are no holes in the computable real line, and it appears to model the continuum of the physical world just fine.* The noncomputables plug all the holes in the computable real line, so that you can have a continuum!
I appear to have misled you, accidentally. On this thread, I am talking about the uses of math for modeling some presumed physical world, implying the existence of a correspondence between features of the math and features of the physical world - from which we can discover where to look for infinities that are "more than abstractions".Oh but there are uses for noncomputables. Let me tell you two of them.
I guess it tried to but failed during the "inflationary epoch".......Sure, but that doesn't mean that at the moment the big bang happened, only a finite-size space could have emerged. Why, according to you, couldn't the big bang have produced an infinitely sized space?
Oh c'mon..
What's your evidence that the universe isn't infinite in (spatial) size?
And I never claim otherwise.
What Pythagorean triangle are you talking about? And why is it impossible to have an infinite space but only a finite time? And why would time be finite; it can still be infinite, even if it has a starting point.
Irrelevant. I'm observing that computable numbers already model the known physical world, sufficient, that no smaller set of the reals does, necessary, and so we have evidence that the infinities thereby included match real infinities - that they model "something else", that these infinities are "more than" abstraction.
Well, I'm reasonably sure there are lots of people who think the hyperreals, Robinson's "extensions" to the reals with infinitesimals, and whateverelse, do give Zeno some help.someguy1 said:I don't think you're right that the hyperreals give Zeno much help one way or the other. That's one substantive thing we might kick around.
But calculus says they exist.
Information theory and physical measurement says they don't.