The Collatz Conjecture has been proved. What next??

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4 hours ago, wtf said:

I was hoping you could educate me. You claimed that there might be a Collatz solution in a nonstandard model of the integers. I"m asking why you believe that. Trying to understand your earlier posts.

It was StringJunky who said that he thought that was the case, and then you said that this has not been proved, and I said that it would be interesting if it was true. Sure I believe that it might be the case, just as well as I can believe that it is not the case, so long as it has not been proved either way yet.

Is there anything wrong, in your opinion. with the suggestion that it would be interesting if the conjecture is undecidable? You seem to resist this possibility.

I said that it would be interesting. In comparison, there were people who found the fact interesting that it is possible to write up a multivariate polynomial equation with integer coefficients for which it is undecidable whether the equation has any integer solutions. Now for such an equation, if it did have a solution, then this would be straightforward to verify, by plugging in the suggested values of the variables and check that the solution is correct. Which gives an explanation as to why we can say that such an undecidable equation cannot possibly have a solution, since by the virtue of having a solution, it would be decidable. On the other hand, when the equation does not have a solution, you can go on forever trying to plug more and more values into the variables, without ever getting anywhere.

Collatz would be interesting because it is different. If the conjecture is true, it is not obvious how to prove it true. If it is false, it is not obvious how to show this either. I cannot think of any other statement like that which is known to be undecidable. Which is the reason that if it could be proved undecidable, it would be quite interesting and new.

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51 minutes ago, taeto said:

Is there anything wrong, in your opinion. with the suggestion that it would be interesting if the conjecture is undecidable? You seem to resist this possibility.

That's a totally different conversation than the one I thought we were having. You said (unless I'm mistaken and someone else said this, in which case I apologize) that Collatz might be provable in some nonstandard model of the integers but not in the standard model. If that's what you said, I have to ask you why you believe that might be the case, and what second-order property might be involved.

Collatz might well be undecidable. I hardly see how I'm "resisting" this possibility. We weren't even talking about it as far as I understood. I didn't go back to review the thread so perhaps I lost track of who was saying what at some point.

Could we be using nonstandard in different ways? I'm thinking of the hyperreals, which is the "standard" nonstandard model of the reals if you think about it that way. But perhaps you just mean undecidable in the sense that the axioms don't decide the issue. That would make sense.

Edited by wtf

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Hey guys I've started a new string.

Why?

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So that we could discuss my proof

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4 hours ago, Antony Howard Stark said:

So that we could discuss my proof

I read through this entire thread. You haven't presented any proof. Not even a sketch of an idea. What is there to discuss? Did I accidentally miss your proof?

Edited by wtf

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18 hours ago, wtf said:

That's a totally different conversation than the one I thought we were having. You said (unless I'm mistaken and someone else said this, in which case I apologize) that Collatz might be provable in some nonstandard model of the integers but not in the standard model. If that's what you said, I have to ask you why you believe that might be the case, and what second-order property might be involved.

The possibilities, as far as I am presently aware, are that Collatz might be provably true in first order Peano arithmetic, or provably false, or undecidable. It was commented by someone that they thought the latter is the case. You replied, and we agree on this, that all options are still open. I did remark that the latter one would be interesting. There are some aspects of the conjecture that sets it apart from statements that have so far already been proved undecidable. So yes, if it is undecidable, since it is a first order statement it would be either false in the standard model and true in some nonstandard model, or vice versa, by Gödel's completeness theorem. I do not understand the reason for considering any second order properties; Collatz can be stated in first order logic, so the nonstandard model would have first order properties that differ from the standard model, if the truth value of Collatz differs between them.

19 hours ago, wtf said:

Could we be using nonstandard in different ways? I'm thinking of the hyperreals, which is the "standard" nonstandard model of the reals if you think about it that way. But perhaps you just mean undecidable in the sense that the axioms don't decide the issue. That would make sense.

I think about the standard model being something like en.wikipedia.org/wiki/True_arithmetic

And to me undecidable means that the truth value of a well-formed statement cannot be decided from axioms, so something like "G is abelian" in group theory. I haven't been aware of other uses until now.

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How good are the people on this forum. I mean in terms of knowledge and experience obviously

13 hours ago, wtf said:

I read through this entire thread. You haven't presented any proof. Not even a sketch of an idea. What is there to discuss? Did I accidentally miss your proof?

Yup seems so.technically speaking I actually shared a pdf. Might ve missed that

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1 hour ago, Antony Howard Stark said:

Yup seems so.technically speaking I actually shared a pdf. Might ve missed that

I don't see it in this thread. Stop playing games. Post a proof or don't.

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1 hour ago, Antony Howard Stark said:

I actually shared a pdf.

Nope.

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Ok then here you go once again.

A-New-Dimension-to-Time-Dilation-3 (1).pdf

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4 hours ago, Antony Howard Stark said:

Ok then here you go once again.

How is that paper connected to the Collatz Conjecture? Anyway, I responded in another topic where you posted. Here are some of my concerns: The first part of the chapter INTRODUCTION/BACKGROUND states:

Quote

In 1905 the great physicist albert eintstein[10] published his theory of general relativity[11,13,14,18] followed by his theory of time dilation

(bold by me to highlight)

Maybe just a minor thing but not a promising start. And it is then contradicted by the paper's first reference:

Quote

Miller, arthur i. (1981), albert einstein's special theory of relativity. emergence (1905)

Unfortunately it does not look like this revision of the paper has quality issues. How was the paper reviewed?

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Well actually I had sent it to IJISRT. It's a peer reviewed journal and after a week they confirmed that the paper has been reviewed and is ready to be published. They did some kind of copyright agreement and then published it online.

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25 minutes ago, Antony Howard Stark said:

actually I had sent it to IJISRT

I am confused. What paper are you talking about? A Collatz paper? The A-New-Dimension-to-Time-Dilation paper you attached above? Something else?

Time dilation

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Thanks for the clarification, we are discussing the Time dilation paper.

1 hour ago, Antony Howard Stark said:

Well actually I had sent it to IJISRT. It's a peer reviewed journal and after a week they confirmed that the paper has been reviewed and is ready to be published.

Is the version of the Time Dilation paper you attached to this topic the same version you sent to IJISRT? If so, how come the paper is ready to be published? The paper has quality issues.

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6 hours ago, Antony Howard Stark said:

Ok then here you go once again.

You already have a thread to discuss this paper.

After repeatedly asking people to comment, you ignored it. Why? And why bring it up again here. (I’ll report it to the mods for you).

Also you said that your friend’s brother wrote it. Now you are claiming you wrote it. Why?

1 hour ago, Antony Howard Stark said:

Well actually I had sent it to IJISRT. It's a peer reviewed journal and after a week they confirmed that the paper has been reviewed and is ready to be published. They did some kind of copyright agreement and then published it online.

How much did you pay them to publish this without reviewing it?

On 23/09/2018 at 1:47 AM, Antony Howard Stark said:

So that we could discuss my prooF

Now that we have established that you haven’t presented your proof, will you do so now please.

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37 minutes ago, Strange said:

How much did you pay them to publish this without reviewing it?

It seems to be the sort of paid for journal which 'reviews' papers and always passes them.

I couldn't find anything specifically dodgy, but at less than one citation per paper it's not exactly a prestigious journal.

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46 minutes ago, Strange said:

You already have a thread to discuss this paper.

After repeatedly asking people to comment, you ignored it. Why? And why bring it up again here. (I’ll report it to the mods for you).

Also you said that your friend’s brother wrote it. Now you are claiming you wrote it. Why?

How much did you pay them to publish this without reviewing it?

Now that we have established that you haven’t presented your proof, will you do so now please.

Things are quite completed . So I've got a person who is interested in the proof rather than the background story. So if you want to answer I expect a polite one if you dont want to do so please don't fill the string with unnecessary comments. It's a science forum and I believe that you should be more interested in the proof rather than who wrote it using which program at what time at which place and bla bla bla.This is the last time I'm giving you a polite reply . You wanna be a part the  give relevant answers or else feel free to get engaged in some other work.

1 hour ago, Ghideon said:

Thanks for the clarification, we are discussing the Time dilation paper.

Is the version of the Time Dilation paper you attached to this topic the same version you sent to IJISRT? If so, how come the paper is ready to be published? The paper has quality issues.

And by the way this is how a normal human being (science enthusiast talks. Learn to be polite.

Thank you

4 minutes ago, Carrock said:

It seems to be the sort of paid for journal which 'reviews' papers and always passes them.

I couldn't find anything specifically dodgy, but at less than one citation per paper it's not exactly a prestigious journal.

Ok thanks I agree with that. Can you please suggest some good journals ? (Polite request) please

I can attempt to get it reviewed a 1000 times if you all say so. Just tell me how

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22 minutes ago, Antony Howard Stark said:

Ok thanks I agree with that. Can you please suggest some good journals ? (Polite request) please

I can attempt to get it reviewed a 1000 times if you all say so. Just tell me how

There have been some excellent suggestions earlier in the thread. I can't improve on those.

However, it's worth emphasising that if you come up with a valid proof of anything on this forum, and someone copies it, you can easily prove prior publication. That's what really counts in science and maths.

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Ok I'll check them out by night.

By the way thanks for the suggestion.

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36 minutes ago, Antony Howard Stark said:

Ok thanks I agree with that. Can you please suggest some good journals ? (Polite request) please

I can attempt to get it reviewed a 1000 times if you all say so. Just tell me how

I am curious why you are discussing your paper about relativity in regard to the Collatz Conjecture. I wonder if you would be able to explain this please.

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Moderator Note

Since the OP has decided to discuss other subjects, and they are available in another thread, there is no reason to keep this open.