## DAY 106: The Fall

November 1st, 2014 § 0 comments

Which, of course, means any number of things – Americans find themselves thinking about what we call autumn. I, of tripping on North London’s uneven pavements and banging/bruising the head, the knees, or whatever – I could refer you back by now to half a dozen places in these records where I’ve done myself some such mischief and bored you with my confessions on the subject; and last Monday there I was again, flat on my face, relying on the kindness of strangers, taken into the Whittington’s A&E which mercifully Jeremy Corbyn and his gallant campaigners have kept alive. O felix culpa, I don’t think.

While for the declining band of Christians,

Masaccio

it (the fall, are you still with me?) relates to apples and expulsion from the garden. To use James Joyce’s memorable word (and if you’ve chosen it as your memorable word with your bank, I take off my hat to you): ‘The fall (bababadalgharaghtakamminarronnkonnbronntonner-ronntuonnthunn

nuk!) of a once wallstrait oldparr is retaled early in bed and lateron life down through all christian minstrelsy.’ It occurred to me to wonder how this might translate into Mandarin Chinese (see post 88).

At the movies

I had a few friends around to watch Dreyer’s The Passion of Jeanne D’Arc (on Youtube, piped into the TV via an HDMI cable). After about an hour it became clear that they were getting restless and the endless close-ups of Falconetti’s tearful face were becoming repetitive; didn’t I have anything with more sex, say featuring Delphine Seyrig? Cue Chantal Akerman’s 1975 3 1/4-hour feminist masterpiece of potato-peeling and prostitution Jeanne Dielman, 23 quai du Commerce, 1080 Bruxelles. (Pedantic niggle here: Wikipedia’s imitated pronunciation for the title reads [ʒɔ̃ dilmɑ̃ vɛ̃ tʁwa ke dy kɔmeʁs mil katʁəvɛ̃ bʁysɛl]. I can’t begin to point out how many trivial mistakes there are here, I hope they aren’t usually this bad. I had thought that in Belgium 80 was not katʁəvɛ̃ but witɑ̃t, but that’s Switzerland and Val d’Aosta.) Anyway, we got out the beer, chips and mayonnaise and began the streaming. The movie ties for 35th place in the BFI’s all-time great list with Metropolis, Psycho, and Sátántangó, and you should probably watch all four in succession to see what was in the BFI judges’ ‘mind’ when they made their list. With Sátántangó running at seven hours, you’re in for a long night.

You asked: 1. What’s the probability that two randomly chosen natural numbers are coprime?

Answer: Well, for a start, the probability that they (call them Marty and Brenda) are not both divisible by 2 is 3/4, obviously; so the prob that they don’t have common factor 2 or 3 is 3/4.8/9. And for 2, 3 or 5 it’s 3/4.8/9.24/25.

So, extrapolating, the probability that they don’t have 2, 3, 5, or any other prime p as a common factor is $\prod_{p=2}^\infty(1-\frac{1}{p^2})\$

Taking the product, of course, over all primes p. This, I suppose, should be enough, but I hear some of you asking what it looks like to three decimal places. For which, as you can see, the obvious thing is to invert it so that  the factors turn into

$(1-\frac{1}{p^2})^{-1}=\sum_{i=0}^{\infty}\frac{1}{p^{2i}}$

The product of all of these, by a  few rather trivial manipulations which I don’t want to bore you with, is the sum

$\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}=1.64493$

and the inverse – the probability we were after – is 0.60793.

For those who really want to be kept up at night: You check into Hilbert’s hotel, They sell lottery tickets for \$1; each ticket has six random natural numbers. The house pays if all six are coprime. What ought you to expect if you win?

2. All this crystallography is all very well, but can it help us in the fight against malaria?

Answer: There is an answer to this, and I don’t suppose you’re surprised to hear it contains the name ‘Gates’. The claim (it’s all over the internet, but that doesn’t mean you have to believe it) is that all insects have a universal receptor called OR83b; and if it’s disabled, they can’t smell anything, and so – if they are mosquitoes – can’t find humans to infect with malaria, dengue fever, chikugunya et al. [Is this blog getting obsessed with mosquito-borne diseases?] Hence, you find its crystal structure (I mean that of OR83b), zap it and cripple the insect. Thus it was that, in a typical crystallographer’s voyage of discovery, ‘short, bristle-covered antennae from Anopheles gambiae – the mosquito culpable for transmitting malaria in Africa – arrived at Filippo Mancia’s lab [courtesy of Mr Gates and Melinda (I suppose)] inside a small brown box’, ready for analysis of the OR83b. How (I and Bruno Latour would ask) did insects manage to smell anything before the social construction of this molecule?

More seriously, if Gates and his friends do declare a war on mosquitoes and disable their sense of smell, how do we know that attacking the sense of smell of mosquitoes wouldn’t disable that of really cool insects which we love like bees? Think twice before you open that Pandora’s box, I say.

How can I have been dabbling in poetry for so long without coming across Regina Derieva,

whose fascinating life you can look up online? And now it’s too late; Russian, Jewish, Christian, not allowed Israeli nationality so lived on the West Bank; died in Stockholm in 2013 and buried next to Nobel. (Can this be true?)

I’d dearly love to post a bilingual English/Russian poem; but the web publishers seem peculiarly bad about such things. Why? Anyway, here’s one in English, I’ll add one in Russian if there’s a huge demand.

I may have played too much of Pete Seeger’s offerings already; but it’s still a temptation, and so appropriate, to have the Weavers reunited and singing ‘Get up and Go

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