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?
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?
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.
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.
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 not at all an attempt to banish infinity in any general sense.
Of course it is. Nothing infinite has been spotted so far.
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.
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.
I don’t give a damn about infinity. If it is doable, why not? But is it? That’s the only question.
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”.
Empty words. So every theory which encompasses them is flawed. More than likely.
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.
Physics is built on top of mathematics, and almost all of mathematics can be built on top of ZFC (there are other choices). But there is as much time in ZFC as there are words in a single pixel on your screen.
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?
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.
I don’t think this conversation is being very productive so this is likely my final reply.
Just answer me a simple question.
? How do the first 1000 naturals look like, after mixing supertask described above has finished its job,
You may say that this supertask is impossible.
You may say that there is no set of all naturals.
The resulting pointwise limit exists, and it gives each positive integer a probability of zero. This is fine because the pointwise limit of a distribution on a countable set is not necessarily itself a distribution. Please take a basic real analysis course.
I doubt that any proof in FAI will use infinitary methods.
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?
Physics is only good, when you expel all the infinities out of it.
Even more so for a subset of physics, such as FAI or molecular dynamics or something.
Well, some of us think that this should be applied to the mathematics itself.
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?
https://physics.aps.org/articles/v2/70
http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/#.Vh0LnHqqpBc
Now, when there in no God, the Infinity is its substitute, most people would love to exist. But it’s just another blunder.
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.
This is rhetoric without content.
Of course it is. Nothing infinite has been spotted so far.
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.
I’m not sure how your sentence is a response to my sentence.
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.
I don’t give a damn about infinity. If it is doable, why not? But is it? That’s the only question.
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”.
Empty words. So every theory which encompasses them is flawed. More than likely.
And yes, supertask can be established in ZFC.
The topic is also exercised here:
http://mathforum.org/kb/thread.jspa?forumID=13&threadID=2278300&messageID=7498035
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.
So you say, ZFC has nothing to do with time? Time in physics is uncovered in ZFC?
Physics is built on top of mathematics, and almost all of mathematics can be built on top of ZFC (there are other choices). But there is as much time in ZFC as there are words in a single pixel on your screen.
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.”
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?
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.
Just answer me a simple question.
How do the first 1000 naturals look like, after mixing supertask described above has finished its job,
You may say that this supertask is impossible.
You may say that there is no set of all naturals.
Whatever you think about it. Everything else is pretty redundant.
I don’t think this conversation is being very productive so this is likely my final reply.
The resulting pointwise limit exists, and it gives each positive integer a probability of zero. This is fine because the pointwise limit of a distribution on a countable set is not necessarily itself a distribution. Please take a basic real analysis course.