Coincidences

Although we know that the probability of an unspecified “unexpected” event is rather high, given how many possible events can occur, it is still interesting to note them. There is probably an evolutionary reason why probability is so unintuitive to us. Perhaps being curious about coincidences had substantial survival value in the past.

Here are two that have occurred to me recently.

1) Just over a week ago I wandered into the Mechanics Institute Chess Club (apparently the oldest in the US) in downtown San Francisco.There were just a few players sitting around casually on a Sunday afternoon, with no events scheduled. Then in walked someone I haven’t had any contact with for 25 years, whom I knew from playing against in the schools tournaments in Christchurch and at the Canterbury Chess Club, who later became NZ champion. Now that is a coincidence – he works for Google in Sydney and was in SF for a conference. Neither of us has played competitively for many times longer than our competitive chess career lasted. Playing a few games with the newfangled clock (3 minutes per player, plus 2 second increment per move) was a fun way to spend an hour.

2) This is close enough to true, and doesn’t change the essential mathematics. I know someone who has been married twice, each time to someone with the same birthday. How likely is that? This is different from the famous “birthday problem”. Suppose that everything is uniformly randomly chosen, and I have $latex k$ acquaintances who are in a position to marry and whom I know well enough that I would hear about such a coincidence. Let $latex n$ be the number of days in a year. The probability that one of these acquaintances fails to have such a coincidence is $latex 1-1/n$, so the probability that some succeeds is $latex 1 – (1-1/n)^k$. Let $latex c$ be a number between $latex 0$ and $latex 1$ that represents our threshold for incredulity – if an event has probability less than $latex c$, I will be surprised to see it, and otherwise not. Thus we should be surprised if $latex (1-1/n)^k > 1-c$. Reasonable values for $latex n,k,c$ are $latex 365, 100, 0.01$, but since $latex (364/365)^{100} = 0.76$, we should not be surprised. Analytically, the inequality $latex (1-1/n)^k > 1 – c$ can be approximately solved via making the approximation $latex (1-1/n)^k = exp(k log(1-1/n) approx exp(-k/n) approx 1 – k/n$. Thus I expect to need $latex k < cn$ in order to be surprised: the number of acquaintances should scale linearly with $latex n$, which clearly doesn’t have to measure days. So if I only care about which month the person is born in, I will never be surprised, but if I care about the hour and have fewer than about 80 acquaintances, very likely I will be surprised. The original case of a day shows that if I have more than 4 acquaintances, I should not be surprised.

Suppose everyone in the world is my acquaintance. How precise could we be about the birthday without being surprised? Now $latex k$ is of the order of 5 billion, so with the same value of $latex c$, $latex n$ should be about 500 billion. That means we can slice up a year into milliseconds and such a coincidence event would not be at all strange.

Au revoir Berkeley

I will be leaving later this week after 2 months here. I will miss the lack of rain and the relaxed lifestyle and high education level off campus (not having to teach or listen to colleagues in meetings certainly helps – I suppose sabbaticals are supposed to be better than “real life”). Yesterday I saw two full large shelves of mathematics books, many very high level, in a used bookstore, something impossible to find at home. Not to mention a shop selling only dog collars, nurses on strike, the local street people, poor roads, compostable plates and forks.

Two interesting Berkeley institutions are worth mentioning. The Berkeley Math Circle has been running for over 15 years, modelled on East European practice and driven by dedicated people such as Zvezdelina Stankova. It is tempting to try to replicate something like this at home, starting small of course. The Simons Institute for Theory of Computing is up and running, and promises to be a great venue for collaboration.

Trying out new social media

I have been posting to this blog for well over 5 years now, and the silence is deafening, as I almost never receive any comments. It seems that this phenomenon is common. In an attempt to have a bit more conversation (without being overwhelmed) I am going to try using Google+ systematically, in addition to this blog. I think Twitter is still a step too far for me, because I don’t understand how to deal with the deluge of tweets.

This article seems a useful one for researchers new to social media.

Reverse liaison

As I understand it, many languages are pronounced “incorrectly” in such a way as to make it easier. Liaison in French is very common: saying “les amis” without pronouncing the final “s” of “les” would require a pause or glottal stop. I have just noticed that it is very common in American English to do the reverse in some situations, and I have absolutely no idea why. I have heard many people pronounce phrases like “get off” with a glottal stop instead of the “t” of “get”, and also words like “button” have a break between the two “t”s. This seems very weird – why pronounce words in a nonstandard way when that makes it harder to say, not to mention ugly-sounding? I first noticed it in an episode of Dora the Explorer several years ago, and assumed it was an idiosyncrasy of the voice actor in question. But it seems to be very common, and I even heard a reporter on National Public Radio doing it today.

What theory accounts for this illogical and inefficient behaviour? Wikipedia tells us that it is not confined to the US, which I had known for much longer, having as a child seen too many TV programmes involving Cockney characters.

Three (plus two) months in Berkeley

In late 2009 I started writing the post below:

I have spent 3 months in Berkeley, California as part of a sabbatical, although not affiliated formally with the university. The university, despite recent budget worries, is still very impressive, and the town is comfortable (if expensive) to live in.

The Computer Science Theory Lunch and seminars in the Wozniak Lounge in Soda Hall were enjoyable and informative. A particularly interesting talk was Why Sex? by Adi Livnat (view the associated paper). I am still on the mailing list for seminars, and this year they have some very interesting-sounding ones.

Now I am back in Berkeley, this time visiting officially (thanks to my excellent host Elchanan Mossel).
I gave a talk in the Probability seminar in the Statistics Department. This was a daunting task, given the kind of speakers they normally get. It was a good experience for me (not sure about the audience). One of the best-known people in that department is David Aldous (who, I think, attended my talk). He has some really interesting stuff on his website. I found this interview with Persi Diaconis very worthwhile.

Theory Lunch is still going on, and I have been to a talk by Shayan Oveis Gharan on the Asymmetric Travelling Salesman Problem. There is a joint Berkeley-Stanford series of talks on Data, Inference, and Society, and so far I have heard Jon Kleinberg (Cornell) on algorithmic detection of memorable phrases and Randall Lewis (Google) on the near-impossibility of measuring the returns to advertising. Further afield, a public talk by Craig Venter on synthetic life was held in a very small room (appalling organization – didn’t they think he might be a popular speaker) and was alternately incomprehensible and inspiring (I guess I should have studied some biology). There are so many interesting talks, I wouldn’t have enough time to get any work done if I went to all of them.

I do have worries about the state of Californian public finances and the impact it may have on the university system. But that’s still very good from what I have seen.

Flajolet memorial volume of CPC

The journal Combinatorics, Probability and Computing (obviously, since the publisher is Cambridge University Press, it doesn’t use the “Oxford comma”) will publish a special issue dedicated to Philippe Flajolet, whose early death in 2011 shocked, although perhaps didn’t surprise, the Analysis of Algorithms community.

I have submitted a paper, and judging from one I have been asked to referee, the standard will be high. Philippe’s own research work and encouragement of others were an inspiration to the entire community, and I am sure everyone wants to submit something approaching his standards.

Academic stereotypes

I just read a New York Times article about Paul Frampton, a physicist who ran into major trouble in “real life”. I would have had trouble inventing such a character, but on reflection, I can’t say that I am all that surprised that one exists.