## Archive for the ‘Uncategorized’ Category

### Holding a country to ransom

October 15, 2013

Here is a quick thought about the mathematics of the US shutdown, not to be taken too seriously (the thought I mean — the shutdown obviously is to be taken seriously). It’s for the benefit of anyone who is puzzled that the Tea Party can have such a large influence, and more generally how a political system can be stable when almost nobody likes it. I’m going to prove that in a country of $n$ people, it is possible to devise a democratic system in which $n^\alpha$ of those people control the decisions, where $\alpha=\log 2/\log 3$. For example, in a population of 100,000,000, all you need is a band of fanatics with about 112,000 people — or approximately 0.1% of the population. Although we do not have such a system and the distribution is unlikely, the systems and distributions we do have still allow a minority to have undue influence, and for similar reasons. What I’m about to describe is the extreme case.
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### Another test

April 2, 2013

This time I want to test whether I can have polls where the results are not visible until the poll closes. So if you have a few seconds to vote, that would be very helpful. If the facility works, then my next post will include some secret ballots.

### An experiment concerning mathematical writing

March 25, 2013

Update: comments on this post are now closed, since my latest post would compromise any further contributions to the experiment.

Most of this post consists of write-ups of proofs of five simple propositions about metric spaces. There are three write-ups per proof, and I would be very grateful for any comments that you might have. If you would like to participate in the experiment, then please state your level of mathematical experience (the main thing I need to know is whether you yourself have studied the basic theory of metric spaces) and then make any comments/observations you wish on the write-ups. The more you say, the more useful it will be (within reason). I am particularly interested in comparisons and preferences. For each proof, the order of the three write-ups has been chosen randomly and independently.

It would also be useful if you could rate each of the 15 write-ups for clarity and style. So that everyone rates in the same way, I suggest the following rating systems.

Clarity.

-2 very hard to understand
-1 hard to understand
0 neither particularly hard nor particularly easy
1 easy to understand
2 very easy to understand

Style.

0 neither badly written nor well written
1 well written
2 very well written

I stress that ratings should not be regarded as a substitute for comments and observations, or vice versa. What I really need is both comments and numerical ratings.

I do not want people to be influenced by the answers that other people give, so all comments on this post will go to my moderation queue. When I have enough data for the experiment, probably in a week or so, I will publish all the comments (unless for some reason you specifically request that your comment should not be published).

The more people who participate, the more reliable the results of the experiment will be. I realize that it may take a little time, so thank you very much in advance to everybody who agrees to help. (Update 26th March: I now have over 30 responses; they have been very helpful indeed, so I am extremely grateful for those. If they keep coming in at a similar rate over the next few days it will be wonderful.)
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### Test

March 24, 2013

I am testing the WordPress feature that allows me to moderate all comments before allowing them to appear. This has nothing to do with the discussion on the last post. Rather, I want to be sure that the feature works before my next post, where it will be important for people to comment without seeing what others have said. So if someone could make a quick comment on this post, that would be helpful. Once I’m sure the feature is working, I’ll put up the post for which it matters.

In an ideal world, I would use the feature just for that post. However, as far as I can tell, my only options are allowing all comments, moderating all comments, or disabling comments completely on individual posts. Sending comments to the moderation queue on a post-by-post basis doesn’t seem to be possible, but if anyone knows a way, then I’d be very pleased to hear about it. Assuming there isn’t a way, then for a short while, all comments on this blog will be moderated, but I will try to approve comments on other posts regularly, so I hope this won’t be too annoying.

Update. Good job I did this test. I changed the relevant setting but didn’t click “Save settings”. Hence the three comments below.

Further update. OK, now it seems to be working just fine. Many thanks to those who sent test comments. I’ll put up the new post later this evening (British time).

### A more formal statement about mathematical publishing

February 8, 2012

A group of mathematicians have been putting together a statement that explains some of the background to, and reasons for, the Elsevier boycott. This statement, which has been signed by 34 mathematicians (we are confident that many more would be happy to endorse it, but we had to stop somewhere), is now ready for release. If you are interested in reading it, then click here.
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### Abstract thoughts about online review systems

February 2, 2012

As many people have pointed out, to get to a new and better system for dealing with mathematical papers, a positive strategy of actually setting up a new system might work rather better than complaining about the current system. Or rather, since it seems unlikely that one can simply invent ex nihilo a system that’s satisfactory in all respects, one should set up systems (in the plural) and see which ones work and catch on.

I’ve already had a go at suggesting a system, back in this post and this post. Another system that has been advocated, which I also like the sound of, is free-floating “evaluation boards” that offer their stamps of approval to papers that are on the arXiv. (I associate this idea with Andrew Stacey, though I think that in this area there are several good ideas that have been had independently by several people.) But instead of discussing particular systems, which runs the risk that one ends up arguing about incidental details, I want to try to adopt a more “axiomatic” approach, and think about what it is that we want these new systems to do. Once we’re clear on that, we have a more straightforward problem to solve: how do we achieve most efficiently what we want to achieve?
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### AV vs FPTP — a supplementary post

April 29, 2011

In this post (the first past the previous one) I want to consider some further arguments, most of which have arisen from the interesting comments I have received. You’ll have to be pretty interested in voting theory to have waded through my earlier post and still want more, but NO2AVers who are looking for ammunition may find some here (as long as they are selective about which arguments they go for).

I have also written a shorter post on AV versus FPTP. I plan to post it at the weekend (when people are less distracted by the Royal Wedding, though perhaps the audience for that is rather different from the audience for this). (more…)

### Status update

November 30, 2010

I would not normally edit my own Wikipedia page, but there was an inaccuracy I felt strongly about. I hope that Quomodocumque will understand.

### EDP14 — strategic questions

April 25, 2010

In this post I want to take the following attitude. Although there are several promising approaches to solving EDP, I am going to concentrate just on the representation-of-diagonals idea and pretend that that is the problem. That is, I want to pretend that the main problem we are trying to solve is not a problem about discrepancy of $\pm 1$ sequences in HAPs but the following question instead.

Problem. Is it true that for every positive constant $C$ there exists a diagonal matrix with trace at least $C$ that can be expressed as a linear combination of the form $\sum_i\lambda_i P_i\otimes Q_i$ with $\sum_i|\lambda_i|=1$ and each $P_i$ and $Q_i$ the characteristic function of a homogeneous arithmetic progression?

There are other equivalent ways of formulating this problem, but I’ll stick with this one for now. Incidentally, $P_i\otimes Q_i$ can be thought of as notation for the characteristic function of $P_i\times Q_i$.

In this post I want to try to encourage a certain stepping back. Our general problem is to construct something with some rather delicate properties. We don’t really know how to go about it. In that kind of situation, what is one to do? Does one wait to be struck suddenly by a brilliant idea? Or is there a way of searching systematically? Of course, I very much hope it will be the latter, or at least nearer to the latter. (more…)

### Wiles meets his match

December 20, 2009

A brief return to the theme of mathematics in literature: I can’t resist sharing what is, by a long way, the silliest piece of fictional mathematics I have ever come across. It comes in “The Girl Who Played With Fire,” by the late Stieg Larsson, translated (not very well) by someone called Reg Keeling. Here is a little piece of advice for any author who wants to incorporate mathematics into a novel. If you don’t want what you write to be risibly unrealistic, it is not enough to read popular science books: you must also run what you write past a mathematician.

And here is the passage in question. (more…)