Graeme Archer's Diary: Brownian motion

Every undergraduate statistician – and, I think, every City trader – is familiar with the concept of Brownian motion: the random, aimless, jittering path taken by particles suspended in a fluid; a completely random walk, where the direction taken at time t isn’t deterministically predictive of the path to be taken one step into the future. It’s called “Brownian” after the botanist Robert Brown, who noticed, in 1827, that particles in the cell-fluid of pollen suspended in water moved in such a random path.

I can’t think why the concept of a random walk, with no deterministic path clear to an observer, no obvious ultimate destination and no idea about which way to turn next – I can’t think why, as I say, it should seem so fitting that such aimless dithering should be labeled “Brownian” – can you?

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Am I a one-man Twilight Zone? Whenever I leave the country, some annoying event seems to fall on the party. I set off for Verona last Monday morning, the sun was shining, we were 10 points ahead, Hain had just resigned and the net was closing in on Harman, Alexander et al. Then Derek Conway’s sons pop up, and Brown must be gripping his sides in glee at this “Get out of jail” card handed him. (I’m using “jail” metaphorically, Mr Brown – don’t be too gleeful).

I don’t know what annoys me more: that Mr Conway’s family funding arrangements have given our opponents some sticky mud to fling at us, or that his No.1 son does his best to live up to every toe-curling stereotype about homosexual men known to the tabloids. The result of all that expensive public school education appears to be a man who throws “F*** Off I’m Rich” parties in B-list London nightclubs. All funded with public money. I dunno. Maybe I was wrong about Section 28 after all.

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You’ll know that the centre-left administration of Romano Prodi lost a vote of confidence in Italy recently, leaving the door open for a comeback for everyone’s favourite Man In A Bandana, Silvio Berlusconi. My favourite quote in the Italian newspaper I struggled with last Wednesday morning: “Prodi gone. Berlusconi not yet back. Enjoy these small comforts while we can”.

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OK, so statistical reasoning is probably a wee bit more to the forefront of my mind than it is to anyone normal, but with my first day of jury service starting tomorrow, it’s rarely felt more relevant. I remembered a chapter discussing the arguments around jury composition in Ian Hacking’s book The Taming of Chance, so I took myself back to it this week for some revision.

Have you ever wondered why we use a random selection of twelve citizens to serve on our juries, accepting a verdict when ten of those twelve agree? Why not 40 jurors, or a requirement for a simple majority? The French mathematician Condorcet, in 1785, held that the desire for uniformity in a selection of twelve citizens was untenable. Though it was then the requirement in England, Condorcet concluded that English juries proceeded by a sort of majoritarian bullying, and that it was better to allow a system which could produce a verdict even in the face of a non-unanimous vote. While he would would have preferred 30 jurors, he also concluded that a 10:2 majority would be sufficient. In fact the French code of 1808 allowed a simple majority (7:5) verdict, albeit with a second-level vote by five judges if that were the result.

This bothered Laplace, who used some simple reasoning in 1815 – based on some dodgy assumptions (the most specious being that the a priori probability of a defendant’s guilt is 50%) – to show that the probability of a mistaken verdict from a system of 12 jurors is vanishingly small if they split 12:0; but is about 30% if they split 7:5. Ostrogradsky – a St Petersburg mathematician – refined Laplace’s assumptions, most notably by allowing a common interval of reliability for each juror, from which he derived a probability of jury error, if that jury splits 7:5, as 0.1%. I’m still thinking through their reasoning, but I hope that Ostrogradsky is closer to the truth! Wish me luck tomorrow.

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Judith arrives from Philadelphia and we give her the Friday Night In Hackney treatment – no kebabs and no Home Secretaries. On Saturday she takes a train from St Pancras and so we all tube it round to have a butcher’s at the new station. Goodness: it is amazing. Alright, the world’s longest champagne bar turns out to be what we used to call a railway platform – but we treat ourselves to a glass anyway, and enjoy the thrill of seeing the Eurostar pull out right next to us. I'm feeling like an extra in a '40s film noir and tremble with joy at the TARDIS-like groans of the train picking up speed. Turning round I can see the tower of the old Midland Grand hotel through the far corner of the steel and glass ceiling. It is stunningly beautiful. Did you know that Gilbert Scott, the architect, also designed the Victorian renovations for the University of Glasgow? Any former Glasgow student cannot help but be struck by the similarity of the two buildings, and remember the story that the architect originally submitted the Grand Hotel design to Glasgow, but that the university senate turned it down on the grounds that it was “too fussy”. Glasgow’s loss, and quite definitely London’s gain.

Readers interested in St Pancras might enjoy Oberon Houston's piece.