J curve?

As highlighted in a recent issue of Prospect magazine, and noted in passing by me, everyone is going on about this “J-curve” book that a chap called Ian Bremmer has written. In it, Bremmer argues that you lose stability in the first place but then gain openness in time when a state moves from closed to open (such as Iraq, say, is doing).</p.

The point being: isn’t this just another way of saying that things get worse before they get better?

The J-curve is, as I understand it, a very well known economics phenomenon and has been applied extensively to post-Communist countries and their transitions to democracy. Why this Bremmer book is so popular, then, when it’s clearly a bit of a re-hash (at least, so far as I can tell through reviews having not read it), I don’t know.


Ban the freesheets

I was pleased to see Stef argue, in the del.icio.us links column to the right, for the banning of freesheet newspapers in London, on the back of a Council’s decision to do the same.

Stef’s exact words were:

Shame it is for the waste that it causes on the ground as opposed to the mushing of the mind it causes.

I agree with the latter but not with the former: even though I’m not much of an environmentalist, I can’t see how printing nearly 750,000 newspapers a day, the majority of which end up on the floor or on the floors of buses, can in any way help the environment.

And, whatever you do, don’t get me started on the content of these papers. Seriously, if people want to pass time on their way home, I’d rather they all just listened to music on their mobile phones. If you knew me, you’d understand the force of the statement I’ve just made…

Guess who

Which organisation might the following contributors to the bbc‘s Have Your Say (yes, I know) be describing?

[It] is far to [sic] pro-government and unaccountable to the people who pay [for it] – the public. It does not allow anywhere near a level playing field politically.

[It] is biased and a complete and utter puppet for the Blair government, choosing to opt out of anything controversial.

[It is] too liberal and always jumping on the latest politically-correct bandwagon that rumbles along (MMCC, racism, islamaphobia, etc).

[A] UK propoganda chanell [sic] to which I am forced to subscribe, [sic] it should be privatised and sold off immediately.

That last one should give it away, but for those of you who haven’t got it yet, see here.

Remarkable, isn’t it? Most of the reasons stated above are precisely the opposite of the reasons I’ve criticised the self-same organisation before (e.g. here and here). I know that people will have their say, but it does rather remind you of the famous Abraham Lincoln quote, doesn’t it?

Right person, wrong subject no. 4: Richard Branson

Typical: you wait months for the next instalment in this feature, and two come along at once!

Today’s expert speaking in a field totally unrelated to their field of expertise is Richard Branson. The entrepreneur is annoyed that a takeover bid he was looking to orchestrate is being scuppered by Rupert Murdoch; which leads him to comment on, erm, the state of and prospects for the UK’s democracy:

The Government’s job is to stop too much dominance in the media ending up in one person’s hands… All of us in this room know that governments are scared stiff of (Rupert) Murdoch…

[If Murdoch’s newspapers] come out in favour of a particular political party, the election is likely to be won by that particular party… If you then tag on ITV to that as well, basically we have got rid of democracy in this country [my emphasis].


Bias at the BBC?

I’m no fan of the British Broadcasting Corporation (bbc), and neither am I a conspiracy theorist about its political leanings. I have detected, however, on previous occasions — like others — a noticable bias in its coverage of particular events.

Which is what makes this response to accusations of bias from the Director of News at the BBC, Helen Boaden, interesting.

Both Andrew Marr and Jeff Randall have made comments about the bbc being biased, and both have been dismissed by Roaden for basing their conclusion “on anecdote and attitude rather than evidence”. She then bases, in part, her own belief that the bbc is not biased on, erm, anecdote and attitude as follows:

When I first joined the BBC I asked a very experienced and subtle journalist what was meant by BBC impartiality. “It means we don’t take sides,” he said. “We don’t take sides either explicitly or implicitly. We test all opinion toughly but fairly and we let the audience make up their own minds.”

Interesting stuff. But what’s really interesting are the areas in which Boaden suggests bias:

According to the Mail on Sunday, and other recent press reports, we have admitted that we are an organisation of trendy, left-leaning liberals who are anti-American, biased against Christianity, in favour of multiculturalism, and staffed by people who wouldn’t know an unbiased fact if it hit them on the head.

Now, I’m happy to accept this isn’t an exhaustive list of potential bbc biases, but there does seem to be one big one missing, doesn’t there?

On mathematics journalism revisited

Some time ago, news was delivered on progress made in two of the seven million-dollar questions posed by the Clay Institute: the Riemann hypothesis and the Poincaré conjecture — the second of which looks like it has now been solved. The coverage of the news at that time unfortunately proves the points I have made over the last two posts (here and here), and it is worth seeing why that is the case.

It shouldn’t be a surprise to see that the standard of writing at the Guardian concerning the Riemann hypothesis was nothing short of mind-bogglingly ridiculous, being as it was a very bad attempt at making maths seem relevant. Under the headline

Maths holy grail could bring disaster for internet

the writer (no less than the then science editor, Tim Radford) wrote:

Mathematicians could be on the verge of solving two separate million dollar problems. If they are right — still a big if — and somebody really has cracked the so-called Riemann hypothesis, financial disaster might follow. Suddenly all cryptic codes could be breakable. No internet transaction would be safe. On the other hand, if somebody has already sorted out the so-called Poincaré conjecture, then scientists will understand something profound about the nature of spacetime.”

Given the fact that the Riemann problem certainly hadn’t been solved — a fact generally accepted within the wider mathematical community at the time — it was clearly a bit silly to concentrate on the implications of a proof of the Riemann hypothesis for the rest of the article. The only conclusion to be drawn is that someone at the Guardian obviously had a bit of time to spare and a big space in the paper on their hands. That the writer then went on to say that the Poincare conjectureé is “almost mind-numbing” can only be described as ironic in at least two senses. It certainly wasn’t mind-numbing according to the Guardian‘s recent hyperbole.

The proof of the Poincaré conjecture looked at the time like it may be the real thing and has indeed proved to be so. At Not Even Wrong, Peter Woit wrote an interesting post concerning the possible proof at the time, with excellent links to conferences and lecture courses that were discussing the possible breakthrough. It’s not often you get to see things like this and some of the resources, which include hand-written notes taken during a lecture by the author of the proof talking about his work, are worth a look, even if you know you won’t understand it (I certainly don’t have a clue).

To leave this subject for the moment, it is worth noting Woit’s comments on the Guardian article mentioned above:

For a really dumb news article about this, go [to the article] (no, proving the Riemann hypothesis won’t bring down the internet, and Perelman’s Poincaré proof won’t explain the nature of the universe).

I couldn’t have put it better myself.

On mathematics journalism

A topologist is one who doesn’t know the difference between a doughnut and a coffee cup.

— John Kelley

The recent news concerning Grigory Perelman, the aloof Russian mathematician who has solved the Poincaré conjecture but turned down both the Fields Medal [1] and the Clay Institute’s $1m dollar prize, has put mathematics on the front pages. It is certainly an interesting story and one, given the mathematical significance of the Poincaré conjecture, which deserves the attention it is receiving. The nature of that attention, however, is the subject of this post, for the telling of the story of Perelman’s reluctance to receive the prizes for his work is an unfortunate example of poor journalism.

In order to explain this point, I would like to highlight two recent articles published on the topic of Perelman: the Guardian article entitled Meet the cleverest man in the world (who’s going to say no to a $1m prize) and the New York Times piece entitled Elusive Proof, Elusive Prover: A New Mathematical Mystery.

The very headlines of the pieces provide a neat indication of the approach each newspaper takes to reporting the Perelman news. For whilst the New York Times provides an interesting overview of what the Poincaré conjecture is, what its relevance to the “real world” is, who the mathematicians are that have previously worked on the problem, what is known of Perelman himself and finally information relating to his recent proof, the Guardian opts for a different approach as demonstrated in the opening paragraphs of the article below:

He is possibly the cleverest person on the planet: an enigmatic and reclusive genius who shocked the academic world with his claim to have solved one of the hardest problems in maths. He is tipped to win a “maths Nobel” for his work on possible shapes of the universe. But rumours are rife that the brilliant Russian mathematician will spurn the greatest accolade his peers can bestow.

… [E]ven by the standards of troubled maths virtuosos such as John Nash, portrayed in the film A Beautiful Mind, Dr Perelman is described as “unconventional”.

This is, as is the rest of the article, hyperbole and nonsense of the highest order, which contrasts poorly with the opening of the New York Times article as follows:

Three years ago, a Russian mathematician by the name of Grigory Perelman… announced that he had solved a famous and intractable mathematical problem, known as the Poincaré conjecture, about the nature of space.

After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Dr. Perelman disappeared back into the Russian woods in the spring of 2003, leaving the world’s mathematicians to pick up the pieces and decide if he was right.

Now they say they have finished his work, and the evidence is circulating among scholars in the form of three book-length papers with about 1,000 pages of dense mathematics and prose between them.

The difference in style is clear and one that is re-iterated in the first quotations from other mathematicians each article chooses to employ:

I just don’t see him turning up in a stretch limo with four over-endowed women and waving his cheque in the air. It’s not his style. — used in the Guardian

It’s really a great moment in mathematics… It could have happened 100 years from now, or never. — used in the New York Times

The approaches couldn’t be more different.

It is likely that the Guardian chooses to write on this topic in such a manner in order to make the subject of maths and the people that do it more interesting and accessible for its readers. For example, the article regularly refers to “Prof Du Sautoy” and “Prof Hitchin” when these mathematicians provide useful sound bites for the article as if calling them “Prof” instead of “Professor” makes them more human. What the article actually achieves, however, is a condescension that should not only offend the mathematics community it undermines by writing about in this way, but also the readers of the Guardian for whom the editors have chosen an inappropriate approach to the subject. The choice of the editors of the New York Times is by far the most commendable.

The quotation cited at the start of this post is a fun comment on the way topologists see the world through the tool of mathematics. It is also, however, a neat summation of the way in which journalists often feel they need to approach the subject of mathematics in order to be able to report it. That the Guardian felt it necessary to report the news of Perelman’s actions in the manner highlighted above is revealing of the general public’s relationship with the subject of maths, which is something I will consider another time. On its own, however, the Guardian‘s is an approach that I can only commend as poor journalism.

[1] — the maths equivalent of the Nobel Prize, as it is now always referred to. The significant difference between a Fields Medal and a Nobel Prize is that the Fields Medal is presented to mathematicians up to the age of 40 and not only recognises the work the winner has done to date but highlights the promise of things to come, whereas the Nobel Prize is always presented for work completed, often many years before.

Radical syllogisms

A syllogism is defined as a formal deductive argument made up of a major premise, a minor premise and a conclusion which follows the two. For example:

All men are mortal [the major premise] and Socrates is a man [minor premise]. Therefore Socrates is mortal [the conclusion].

Common mistakes can occur with syllogisms — mistakes that are created by introducing indefinite or arguable terms (“some”, “should” etc.). For example:

Some cats are black [major] and some black things are television [minor]. Therefore some cats are television [conclusion] [1].

In this case, the introduction of the word “some” creates the illogical conclusion.

Although this is interesting in itself, I’m afraid this Friday afternoon discussion of the finer points of syllogisms isn’t for its own sake. For whilst reading the letters page in today’s Metro (an admittedly easy target), I came across the following:

I note with interest the remarks by John Reid that we all have a part to play in the fight against the new breed of terrorist. Whilst I am happy to accept my civil responsibilities, I’d like to suggest something a bit radical.

My mind was racing: what could the letter writer (one Ken Levy from NW1) possible go on to suggest? Surely not something as radical as norm? Alas, no:

The Government should bring home all of our troops currently in Iraq.

Ah, I wasn’t expecting that. For what Mr Levy has done is provide his very own illogical conclusion to an implied major and minor premise — namely that Britain is currently under threat [major] and the British army can protect us against threats [minor].

Alas, this is not just a common syllogical mistake, but one informed by Mr Levy’s clear disagreement with the British government’s involvement in Iraq! How do I know this? Because Mr Levy concludes his triumphantly illogical conclusion with the following:

That way the troops could do the job they are supposed to do: protect Britain and its people, rather than protect the ego trip Blair and Bush are on.

That Mr Levy makes a mistake often made by those employing syllogisms is excusable. That he thinks Blair and Bush are simply protecting their egos, by continuing to support the development of civil society and democracy in a country that has suffered at the hands of a disgusting authoritarian dictator, however, is unacceptable.

Unfortunately, only one of these faults can be corrected by a quick lesson in grammar.

[1] — both examples taken from Wikipedia

President in swearing shock

No stranger to mangling his words, George W. Bush shocked the world yesterday by making a statement many thought was to the point and without obfuscation:

The irony is, what they really need to do is to get Syria to get Hezbollah to stop doing this shit, and it’s over.

When asked why he thought it necessary to swear, Mr Bush probably would have replied: “Hey, I’m not the only one“.

Quotation of the week

The letters page of The Sun isn’t normally a cause for celebration. However, today’s “txt” of one Andy Kerr of Essex to this most cherished of British newspapers surprised me with its style, wit and insight:

The Church [sic] wants us to take The Da Vinci Code with a pinch of salt. That’s just how I take the Bible.

What a magnificent sentiment — and all in less than 180 characters!