h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: A Collatz Conjecture Zinger - A87739212
Author: smallfrey - U13668064

The article is a bit technical, but it should be readable by anyone with the standard mathematical background.

Thanks for submitting this, smallfrey.

I'm afraid there are a number of problems with it.

Entries in h2g2 are intended for an intelligent reader who has no knowledge of the subject. They are not intended to have every piece of information about the subject known to man, but instead should lead the reader from knowing nothing to having a reasonable understanding of what the subject is all about.

We already have an entry on the Collatz Conjecture: A565788. It explains the whole thing in a very clear and simple way.

Your entry provides a lot more information, but it is not presented in any coherent way - it seems to be just a big list of topics to do with the subject.

Perhaps you could rewrite this to be more in line with our approach. Try and build on the existing entry, rather than repeating the information in it. Explain what avenues have been explored, say whether anyone is close to solving the conjecture, but don't assume that the reader understands everything you say. Keep it simple.



3. You seem to present a lot of different things about the collatz conjecture without explaining what they are for, why people might be interested in them.

Can I just add to Gnomon's comments? I am the least knowledgeable person when it comes to mathematics, but occasionally I might wish to find an article which explains a concept or a phrase to me. eg if I'd come across it in something else I was reading. So an introductory paragraph, aimed at the likes of me for instance, would define the term, where it might come in useful, where it is used and when it was first thought about would be excellent. I see that Gnomon has this at the foot of his Entry, but it seems that there is more to say? If so, bear me in mind in your introduction and interested mathematics students in the following paragraphs.

It's great to see you submitting this, and I do hope we can eventually have this in a form which is published in the Guide! Good luck, and thanks.


Lanzababy.

First of all, I really like the current 3n+1 Problem entry. It gives a brief summary of what the Collatz conjecture is, gives some links to technical articles, and conveys some of the wonder and mystery of the problem at the end. But no, at this level, I can't expand on the current article. (We've been down this road before, but I thought I'd try again. I was hoping that the new h2g2 would become a little more technical.) I suppose that part of the problem is that the Collatz conjecture is not easily popularized. (Even general relatively is more easily popularized than the Collatz conjecture; Stephen Hawkings managed to do this.) As to what the Collatz problem is (it concerns many things such as stochastic processes, Diophantine equations, etc.), it mainly concerns factorization of what Belaga calls Collatz numbers (numbers of the form 2^(K+L)-3^K). You can't really even say what the Collatz conjecture is about without getting technical. That's why I started with Bohm and Sontacchi's result (showing the relevance of Collatz numbers to cycles), introduced the algorithm for finding all cycles in the 3n+c sequence, and mentioned the mapping of these cycles to the different c values. Parity vectors were essential to quantifying the number of interrelated cycles. The gist of the article is that a Poisson probability distribution can be used to model the number of cycles (something that should be of interest to anyone). Associated cycles were used to improve the data fit. To the layman, the expected number of cycles may be the ultimate zinger. (All that is left other than cycles is whether the sequence is unbounded for some initial n values.)

Some of the entries I've written have got quite technical, but they all start out with a simple statement of what you're trying to achieve in the entry and explain topics in a simple way.

Have a look at:

A964956 Diophantine Equations
A43825827 Mathematical Knots
A3251693 Curved Space and the Fate of the Universe (an introduction to non-Euclidean geometry)

I suppose the article could be salvaged if you were at all interested (it certainly wouldn't be a concise one-pager after all the explaining). I don't know how it could be integrated with your article. The reason I bother you folks with this is that the article is not up the standards of the mathematical journals (no new proofs, just empirical results). In fact, you could say that all I've done is look at Belaga's table (all 10,000+ pages of it) and done some elementary data analysis. Do you think it is worth the trouble, or should we just forget about it?

I don't really understand your article, so I can't say whether it is worthwhile doing work on it or not.

I took the article out of peer review as it would require major revisions. Thanks for your time and consideration.