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MrMind comments on Open thread, Oct. 12 - Oct. 18, 2015 - Less Wrong Discussion

5 Post author: MrMind 12 October 2015 06:57AM

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Comment author: Thomas 12 October 2015 03:20:04PM 0 points [-]

Yes. It's not the Choice axiom which is problematic, but the infinity itself. So it doesn't mater if ZF or ZFC.

Why do I believe this? It's known for some time now, that you can't have an uniform probability distribution over the set of all naturals. That would be an express road to paradoxes.

The problem is, that even if you have a probability distribution where P(0)=0.5, P(1)=0.25, P(2)=0.125 and so on ... you can then invite a super-task of swapping two random naturals (using this distribution) at the time 0. Then the next swapping at 0.5. Then the next swapping at 0.75 ... and so on.

The question is, what is the probability that 0 will remain in its place? It can't be more than 0, after the completion of the super-task after just a second. On the other hand, for every other number, that probability of being on the leftmost position is also zero.

We apparently can construct an uniform distribution over the naturals. Which is bad.

Comment author: MrMind 13 October 2015 08:20:08AM 0 points [-]

Yes. It's not the Choice axiom which is problematic, but the infinity itself. So it doesn't mater if ZF or ZFC.

I doubt that any proof in FAI will use infinitary methods.

Comment author: JoshuaZ 13 October 2015 12:55:23PM 1 point [-]

I'm not sure why you think that. This may depend strongly on what you mean by an in infinitary method. Is induction infinitary? Is transfinite induction infinitary?

Comment author: Thomas comment score below threshold [+] (12 children)

Comment author: JoshuaZ 13 October 2015 12:56:55PM 0 points [-]

Physics is only good, when you expel all the infinities out of it.

I'm not sure what you mean by this, and in so far as I can understand it doesn't seem to be true. Physicists use the real numbers all the time which are an infinite set. They use integration and differentiation which involves limits. So what do you mean?

Comment author: Thomas comment score below threshold [+] (10 children)

Comment author: JoshuaZ 13 October 2015 02:15:46PM 3 points [-]

I'm not sure what you mean by this, and in so far as I can understand it doesn't seem to be true. Physicists use the real numbers all the time which are an infinite set.

https://physics.aps.org/articles/v2/70

The problem there is that certain specific models of physics end up giving infinite values for measurable quantities - this is a known problem and has been an area of active research since early work with renormalization in the 1930s. This is not at all an attempt to banish infinity in any general sense.

Now, when there in no God, the Infinity is its substitute, most people would love to exist. But it's just another blunder.

This is rhetoric without content.

Comment author: Thomas comment score below threshold [+] (8 children)

Comment author: JoshuaZ 13 October 2015 03:58:13PM 1 point [-]

This is not at all an attempt to banish infinity in any general sense.

Of course it is. Nothing infinite has been spotted so far.

I'm not sure how your sentence is a response to my sentence.

This is rhetoric without content.

Is it? Is this same "rhetoric" against aliens also without a content? If I say that people want aliens, because they have lost angels, is this really without a content?

Not only that there is no infinite God, even infinite sets are probably just a miracle.

Generally, yes, the content level is pretty low. It essentially amounts to Bulverism, where one is focusing on claimed intents and motives rather than focusing on the substantive issue of whether there's an inconsistency in PA or ZFC that can arise due to issues with supertasks or other ideas related to infinity.

It may well be that specific people or groups are adopted aliens in a way that is essentially replacing deities. The Raelians and other New Age groups certainly fall into that categoyr. But it is a mistake to therefore claim that in general, people believe in aliens as a replacement for belief in a deity. And it is an even more serious mistake to make such claims about infinite sets. If you see physicists praying to infinite sets, or claiming that infinite sets are responsible for the creation of the universe or humanity, or claim that infinite sets will somehow save us, or claim that infinite sets have an agency to them, or claim that infinite sets have a special mystery and majesty to them that merits worship, or if they start wars with or excommunicate people who don't believe in infinite sets or believe in a different type of infinite set, then there would be an argument.

Comment author: Thomas comment score below threshold [+] (6 children)

Comment author: entirelyuseless 13 October 2015 05:33:16PM 1 point [-]

There is an argument there, but it certainly is not one based on ZFC, since no axiom of set theory says anything about time or what can be accomplished in time.

continue this thread »

Comment author: JoshuaZ 13 October 2015 07:51:40PM 0 points [-]

I don't give a damn about infinity. If it is doable, why not? But is it? That's the only question.

I'm not sure what you mean by this, especially given your earlier focus on whether infinity exists and whether using it in physics is akin to religion. I'm also not sure what "it" is in your sentence, but it seems to be the supertask in question. I'm not sure in that context what you mean by "doable."

Then, a supertask mixes the infinite set of naturals and we are witnessing "the irresistible force acting on an unmovable object". What the Hell will happen? Will we have finite numbers on the first 1000 places? We should, but bigger, no matter which will be.

The "irresistible force" is just an empty word. And so is "unmovable object". And so is "infinity" and so is "supertask".

I'm not at all sure what this means. Can you please stop using analogies can make a specific example of how to formalize this contradiction in ZFC?

The topic is also exercised here:

http://mathforum.org/kb/thread.jspa?forumID=13&threadID=2278300&messageID=7498035

This seems to be essentially the same argument and it seems like the exact same problem: an assumption that an intuitive limit must exist. Limits don't always exist when you want them to, and we have a lot of theorems about when a point-wise limit makes sense. None of them apply here.

continue this thread »

MrMind comments on Open thread, Oct. 12 - Oct. 18, 2015 - Less Wrong Discussion

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