## Quick question

The discussion about the density Hales-Jewett theorem is now getting quite long. What do you think we should do about it?

We could continue with the discussion just as it is, or we could summarize it and start again, or we could summarize each thread and continue with lots of separate discussions, one for each thread. What do you think would be best? I don’t promise to do what the majority says, but I will be interested to know what the majority opinion is.

Update: I have gone with the majority, but the vote was close, so as a small compromise the discussion is not divided into “lots of separate discussions” but only three. I hope this will make the discussion easier to follow without making it too fragmented. Technically the polls have not closed: there is still a chance to register a vote to show your approval or disapproval of this decision. Thanks to all those who have already voted: maybe the wisdom of crowds could be incorporated into mathematical research somehow …

`Take Our Poll`

### 16 Responses to “Quick question”

1. Kevembuangga Says:

Reasons for my vote (start ONE new post)
– continuing the same post will ultimately break some browsers limits.
– splitting the thread in multiple topics will damage the continuity.

What you would really need is something which will look like this TiddlyDesktop with some extra functionalities about multiple threading of ideas, concurrent updates and distributed repositories.
Not yet there…

2. Tom Says:

The commenting really needs to support threading, otherwise following the discussions is going to get very hard, very quickly.

3. Tom Says:

http://disqus.com/ may offer a powerful enough solution to have a deeply nested and in depth discussion.

4. Jason Dyer Says:

If we want to go multi-thread, we can probably stick with just three, since we’re tackling what seems like three problems now:

Quasirandomness (or however you want to describe the approach to the primary problem)
Modifying Sperner (producing a new proof and/or modifying to help with k>2)
Upper and lower bounds

5. Tyler Neylon Says:

For future discussions of this type, it might be useful to use a wiki platform, similar to wikipedia.

This has several advantages – contributors can preview and edit their own comments in case of typo’s and updates, anyone can start a new thread on a page of its own, embedded links to other comments are do-able, as well as adding a reference section. You can also still use inline latex notation, and user signatures with each section to maintain attribution for each comment (which would also be recorded in the page’s history anyway).

If this idea is interesting, I’d be happy to help set up something like this or volunteer my math site as a host wiki.

6. Kevembuangga Says:

@Tyler Neylon

Yes, some kind of beefed up Wiki, see the discussion at Nathaniel Thurston’s blog

7. Terence Tao Says:

Tim, if it simplifies life any, I would be willing to host one of the threads (presumably the lower/upper bounds thread) on my own blog.

To continue our comment numbering system, perhaps we could allocate to each thread a hundred numbers (200-299, 300-399, etc.) with the understanding that threads would be closed and moved to new threads before that limit is reached. (And if not, we could always improvise with decimals (299.1, 299.2, etc.) if necessary.)

8. Kristal Cantwell Says:

I voted for multiple new threads with summary. It seems the best system. When there are multiple topics it seems best to separate them
rather than trying to summarize each topic and start again.

Kristal

9. Nathaniel Thurston Says:

I voted for one new post, to keep the threads interconnected. However, I think it would be better to move to a blog that supports threaded comments (such as Geeklog). I could set one up and host it if needed. I wouldn’t favor a wiki just yet, as it seems likely to fragment the discussion too much.

10. gowers Says:

I’m in a bit of a hurry now, but here, just to make the discussion more concrete, is a list off the top of my head of what some of the threads are.

Upper and lower bounds for $c_n$.

Trying to find different proofs of Sperner’s theorem with better chances of generalizing to density Hales-Jewett.

Obstructions to uniformity and density arguments.

Is there a new regularity lemma that would work inside the is-disjoint-from graph?

General discussion of strategies for proving the theorem.

Using Szemerédi’s original proof as a model.

Some of the above are connected, and some of them (such as e.g. the Sperner thread) could be split into further subthreads (e.g. pair removal, pushing slices around, etc.).

So two questions here. First, what should the threads be if we split into threads? Secondly, who’s prepared to write summaries? (I’m happy to do some of them — it’s probably fairly obvious which ones I feel most involved with.)

Terry, that’s a kind offer, which sounds like a good idea.

11. Terence Tao Says:

I think the pace of new comments will probably slow down a bit from its current intensity, and so I would favour relatively few new posts in order to retain some residual benefit from cross-fertilisation. For instance, I could combine “upper and lower bounds for c_n” with “Other proof strategies, including those based on Szemeredi’s arguments” in a single post on my blog. “General strategies” sounds like a topic that should belong in every thread.

It seems abundantly clear that polymath2 will be hosted on something other than a wordpress blog, but I think we should keep polymath1 in the current setup, clunky as it is.

12. Andrew Stacey Says:

Have you not considered a maths-enabled forum? Wouldn’t that make threading and starting discussions much easier? Also, you can have more than one administrator making that aspect of it also simpler. On a good forum, cross-posting is possible so the structure can be quite complicated without losing sight of how things link together.

13. gowers Says:

Andrew: it was one of the first things I thought of, but I’ve had a look on the web and not found anything that’s obviously easy to set up and also easy to write maths in in the way that a WordPress blog is. Tom, I looked into Disqus and was tempted, but there seem to be concerns about losing all one’s comments up to now, and about moving the entire hosting to another site. There does seem to exist a threading plugin for WordPress but it didn’t look all that easy to get going.

I’ve been surprised at how much I value the rather strange and artificial linear structure that’s been imposed on the discussion so far. So I think I agree with Terry that if we do what the majority want and split into multiple threads, then the multiplicity should be small. I suggest just three, which one could loosely think of as regularity and triangle removal methods, density methods, and purely combinatorial methods. Into the first thread would go the discussion of Sperner, thoughts about possible regularity lemmas, triangle removal, etc. Into the second would go obstructions to uniformity, attempts to define quasirandomness for combinatorial lines, etc. And into the third would go upper and lower bounds for small $n$, Szemerédi’s proof, etc. I’m happy to write a summary for the first, Terry has offered to do one for the third, and we can probably cobble something together for the second by cutting and pasting from existing comments (though maybe it would be better to tidy things up more. Maybe someone else feels like doing it.

14. Upper and lower bounds for the density Hales-Jewett problem « What’s new Says:

[…] in future projects of this type, we will use a platform that allows for comment threading; see this post for further discussion.) Possibly related posts: (automatically generated)Dedekind CompletionFCC […]

15. Nathaniel Thurston Says:

A friend pointed me at the gitit wiki, available from http://johnmacfarlane.net/tools.html .
I haven’t yet had a chance to test it personally, but the author claims it can do LaTeX. I’m planning to investigate further.

16. Andrew Stacey Says:

Regarding math-enabled forums, I agree that there’s nothing obvious out there. However, I got the impression from your Tricki posts that you have access to one or two hackers so the following might be plausible.

WordPress do a forum software called bbpress. They allege that it is simple to align it to a wordpress blog and make the two work nicely together. Thus you can have blog posts followed by forum discussions. From reading the documentation it seems as though it is not hard to adapt a wordpress plugin to a bbpress one – though it does seem as though a little adaptation is needed. I suspect that this really would not be hard to do, particularly for someone already familiar with the system (unlike me).

In addition, since wordpress does seem to be the blog-of-choice for mathematicians at the moment, it would be rendering a huge service to adapt the latex plugin to bbpress. I don’t know whether math-enabled forums are a Good Thing or not, but it might be worth doing the experiment.

The bbpress website is at:

http://bbpress.org/