Archive for the ‘General’ Category

If politicians were mathematicians

May 9, 2010

Before I start, let me get one thing over and done with: I fully admit that professional mathematicians are as capable as anyone else of making stupid collective decisions.

But I don’t want to imagine what the world would be like if it were run by mathematical researchers. I just wonder how much difference it would make if politicians understood enough mathematics to be able to understand an argument of more than one sentence. Or to put it more accurately, what would it be like if the following rules of political life were no longer accepted?

1. An argument that is slightly complicated but correct is trumped by an argument that is punchy, amusing, and wrong.

2. If option A is better than B in some respects and worse in others, then instead of weighing up the pros and cons, you decide which side you are on and then just mention the pros of the option you prefer and the cons of the other option.

3. If option A is better than B in every respect, but your party supports B, then you support B.

4. If one of your political opponents points out a flaw in your argument, then count to ten and repeat the flawed argument.

If that were the case, then one consequence would be that one could advocate new ways of doing politics and have them discussed seriously. In this post, I would like to mention a few ideas that would be dismissed as utter lunacy by any politician. But perhaps people who read this blog would be prepared to engage with them properly and weigh up the pros and cons. I’m sure there are cons — but I don’t think the ideas are utter lunacy. (more…)

Is the British voting system fair?

May 3, 2010

At the last general election, the percentages of votes and numbers of seats in parliament for the three main parties in Britain were as follows: Labour, 35.3% of votes, 356 seats; Conservatives, 32.3% of votes, 198 seats; Liberal Democrats, 22.1% of votes, 62 seats. In the election coming up on the 6th May, there is a distinct possibility of some quite bizarre outcomes. For example, if some recent polls give a true picture of how people will vote (which is of course far from certain), then there is a good chance that the Liberal Democrats will get more votes than Labour, but well under half the number of seats. It is also a commonplace that the Conservatives will need a higher percentage of votes than Labour to become the party with the largest number of seats. In the past there have been occasions where the party with the largest number of votes has lost the election. (Much of what I am saying applies equally to the system for electing a US president, but I shall stick with the British system in this post.)

Supporters of the first-past-the-post system argue, correctly, that it makes it much more likely that one party will have an absolute majority. They also argue, much more controversially, that this is a good idea. However, regardless of outcome of that argument, there can be no doubt that it has the potential to lead to anomalous results, and this potential has been thrown into sharp focus in the last week or two because it has a good chance of being realized. Here I would like to discuss whether it is correct to describe these anomalies as unfair. (more…)

Swine flu and British public health policy

June 5, 2009

One of my children has just recovered from swine flu, as a result of which I now have a clearer idea of what British policy is towards outbreaks. Much of it was perfectly sensible, but not quite all. Since there’s a small amount of mathematics involved, and since I wanted to get this off my chest, I thought I’d blog about it.

The good part was that everyone who had been in close contact with the child who had swine flu was immediately put on Tamiflu, which seems to have stopped any of the rest of us getting it. (It’s now been long enough that we can be almost certain of this.) The less good part was the piece of advice that I mainly want to discuss. The main question I had was, of course, to what extent I and my family should avoid contact with other people. The advice I was given, which, it was made clear to me, was the official policy and not just the whim of the public health official I spoke to, was that we should continue to lead our lives as normal for as long as we did not show any symptoms. (more…)

When normality is abnormal

May 9, 2009

Suppose you were reading a novel, or watching a play or film, that included a fictional mathematician …

My guess is that the moment you read the two words “fictional mathematician” a second or two ago, your mind leapt ahead and you had a pretty good idea of what he—yes he, since even if there are female fictional mathematicians out there, femaleness is unlikely to be part of your instant and not fully conscious reaction to the phrase—was like: a social misfit who is prone to flashes of extraordinary insight that completely baffle everybody else, or perhaps a social misfit who would like to have those flashes but doesn’t and goes mad instead, or perhaps a social misfit who does have the insights but with madness the huge price he has to pay.

So here is a question: is there any example of a mathematician in literature, theatre or cinema who is a fairly normal person socially, and pretty good at maths but not astoundingly so? Some examples that do not work are Uncle Petros, from Uncle Petros and Goldbach’s Conjecture, both the father and the daughter in Proof, and Will from Good Will Hunting: they’re all either ridiculously good at maths (usually without having to do all that routine stuff like learning the proof of Schur’s lemma, or the open mapping theorem, or the Gram-Schmidt orthogonalization process etc.) or mad, or both. I also don’t count characters if they are colleagues of a crazy genius and their main role in the book/play/film is to marvel at how clever the crazy genius is. Let’s say that the character has to be the main one, or at least the main mathematical one. (more…)

General news—February 2008

February 1, 2008

Not entirely surprisingly, my hibernation is going to go on for longer than I had hoped. The reason for this is quite simple: there is a major push to get the Princeton Companion to Mathematics finished within the next couple of months or so, and if I spend time blogging then it won’t happen. There has also been a delay with the Tricks Wiki, but that may be less severe because I am not the main bottleneck for that (though there are a few things I need to do before it can be up and running). This term I am giving a first course on probability. I had planned a few blog entries on that too, and I hope I’ll have time for some in due course.

General news — December 2007

December 19, 2007

As I predicted in an earlier post, my rate of posting has (temporarily) gone right down. This is partly for the reasons I said—I am very busy with a final push to finish the Princeton Companion to Mathematics, and busy in general—but also for another reason. I was going to keep personal matters rigorously excluded from this blog but since my secret is out (see the comments on Examples First II on November 17th) I may as well also mention that I have a five-week-old son, Octave, who doesn’t leave much time for blogging given that my other commitments won’t go away. So this isn’t a proper post but just a way of saying that my blog hasn’t died: it’s just hibernating. Meanwhile, I can at least briefly mention that a “Tricki”—that is, a Wiki-style website devoted to theorem-proving techniques—will almost certainly exist in the near future. Remarkably, my earlier post on this idea led to an offer of technical help that will be enough to turn it from a fantasy into a reality. And that’s saying something, since my own technical ability in this area is basically zero. I’ve seen a prototype and it looks great. Probably we’ll get a small site up and running and I’ll then ask for comments about how it could be improved before we throw it open. (We still haven’t decided what policy to adopt about who can edit what, but we are actively thinking about it.) And that’s it from me until 2008.

About this blog

September 15, 2007

As I mentioned in my first post, I am very busy at the moment, so my rate of posting will soon go right down, probably until about February. However, I wanted to have at least one post that had mathematical content (as opposed to remarks about the presentation of mathematics) since I hope that in the end that will be the main focus of the blog. So the post about cubics is supposed to be more representative of what this blog is about. Thanks to all who have contributed so far. Although I had read about the power of blogs it nevertheless came as a surprise to see from the stats how many more visits a blog gets than a homepage, and also to discover how easy it is to get useful advice. I’ve even had a serious offer of technical help with setting up new wiki-style websites, so there’s a good chance that some of those ideas will actually be realized.


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