Tuesday, 23 November 2010

Advice to a First Year Me

The first, and I think most important, thing that you need to know is that research is *hard*. Really, really hard. You've done an undergraduate degree already, and that probably wasn't hard. You probably sat in lectures following everything the lecturer said, and the longest you've ever been stuck on an exercise is probably measured in minutes, or at worst hours.

Research is not like that. You will spend months thinking about things and getting nowhere. You may think you've understood that, but read it again, and try to actually understand what it means, I do literally mean months, and I do literally mean nowhere.

Your progress will come in fits and starts, and the fits and starts will be separated by long periods of nothing. Months of nothing is hard work emotionally. Almost everyone I know who has done a PhD in maths has complained at some point about the long periods of nothing. This even includes those people who I actually have managed to give this advice to before they started, and it even includes myself, after having given out this advice. You will be depressed because you don't feel like you're achieving anything. Don't worry, this is normal!

The following is approximately a graph of my perceived progress so far in my PhD thesis. the time axis doesn't have a scale, but it is roughly linear, and spans 3 years. Note that the flat bits really are genuinely flat and, if I'm perfectly honest, the spikes probably aren't quite spiky enough.

Note that I'm *not* saying that the time spent doing nothing is literally wasted. Obviously you need to check which ways of proving something don't work before you can find the ones that do, and, perhaps more subtly, there are so many hidden connections buried in mathematics that any time at all spent reading any mathematics is quite likely to turn out to be useful to you one day (I'll have an example of this in another post I'm preparing for later in the week). But it sure doesn't feel like that when you're going through the periods of nothing.

You are now hitting your limits. You are going to be doing something that is genuinely hard work. This is going to feel like hard work. Be ready for it.

Thursday, 18 November 2010

Report: To reduce immigration, you have to prevent people coming into the country

The Migration Advisory Committee reported today, after having been tasked to determine:
at what levels should limits on Tier 1 and Tier 2 of the Points Based
System be set for their first full year of operation in 2011/12, in order to contribute to achieving the Government’s aim of reducing net migration to an annual level of tens of thousands by the end of this Parliament, and taking into account social and public service impacts as well as economic impacts?
Oddly enough, they seem to have decided that if we want to reduce the number of foreigners coming into the country, we need to reduce the number of foreigners coming into the country.

They weren't, of course, tasked to try and find out if reducing the number of foreigners coming into the country was a good idea. Mostly because it obviously isn't. Even if you are willing to ignore the benefits to the immigrants themselves. I mean, even David Cameron could work that out.

I've read the first twenty pages or so of the report, and some of the relevant data. I have a few comments below the fold. But just remember, this report was commissioned in order to decide how to reduce immigration. They decided it should be done by reducing immigration. They were not asked to decide whether reducing immigration is a good idea, mostly because they wouldn't have been able to pretend that it was.

Wednesday, 17 November 2010

University is not about learning

With a generous hat tip to Robin Hanson for the title, and to just about every blog on the planet for the link, I'm going to quote the following paragraph from this article, from a man who writes other people's assignments for a living:
I've written toward a master's degree in cognitive psychology, a Ph.D. in sociology, and a handful of postgraduate credits in international diplomacy. I've worked on bachelor's degrees in hospitality, business administration, and accounting. I've written for courses in history, cinema, labor relations, pharmacology, theology, sports management, maritime security, airline services, sustainability, municipal budgeting, marketing, philosophy, ethics, Eastern religion, postmodern architecture, anthropology, literature, and public administration. I've attended three dozen online universities. I've completed 12 graduate theses of 50 pages or more. All for someone else.
Now, let's say university actually was about learning, let's say the reason that people got degrees was because they came out with useful skills at the end of them and let's say that unversity grades were  good measure of people's skill at the subjects in which they get their degrees. Is it really likely that any one person could be good at all of those things? Good enough to get a high-level - graduate level, in fact - degree in all of those things?

No, university, like all places where people get educational labels, is a signalling game (I think Paul Graham is probably more accurate on what school is about). I've been meaning to write about this for a while, and might finally get round to it soon, but I just thought this quote was too much to pass up.

Thursday, 11 November 2010

This blog post is not self-referential

This sentence would like you to read the list of self-referential sentences which you can find here. This sentence would like to acknowledge that it was stolen from the aforementioned list of sentences, except it wasn't, so it can't. This one wasn't either. Exactly one of the final two sentences in this paragraph were stolen from that article. Thit sentence is not self-referential, because 'thit' is not a word.

If this sentence is false, then so is the Riemann Hypothesis. This sentence really likes that last one. The next sentence is false. The previous sentence is true. This is the sentence which asks "Were either of those previous two sentences self-referential?". This is the sentence after the previous one. I thought about writing this sentence, but then decided not to. Is this sentence self-referential? Is this one? This? ...?

This sentence is about the story "This is the title of this story, which is also found several times in the story itself", by David Moser. This one isn't about the David Moser story mentioned in the previous sentence. This sentence contains a hidden review of the aforementioned story. That last sentence didn't do what it said, but this one does, it's funny.

All self-referential sentences are just silly, including this one.

Thursday, 4 November 2010

Turing Test

Randall Munroe seems to be under the impression that building spam bots which could fool a Turing Test would be cool because then you'd get fewer annoying comments on blogs. I can't help but feel that there might be some slightly more serious implications...

Tuesday, 2 November 2010

Rounding to the nearest penny

Just seen this (linked from Marginal Revolution). A doughnut shop in the US is getting rid of pennies - and intends to round their customers' orders to the nearest penny (rather than taking the, presumably more popular route, of always rounding up). The bizarre part about this story is... why on Earth wouldn't they just change their prices so that they were all integer multiples of $0.05 in the first place?

Why aren't all journals open access?

Here is the way the current system of academic publishing works, as far as I can tell: universities employ researchers who do original research, and produce journal papers; universities employ researchers who do peer-review, and make sure journal papers are up to standard; journals employ editors, who put the content together, and organise the referees; universities pay large amounts of money to journals in order to be allowed to read the articles.

Now, as you can see all of the money in the system comes from the universities. Universities pay the wages of the researchers and the reviewers directly, and they pay the wages of the editors indirectly (through journal subscriptions). So, here's an idea; why don't the universities club together to buy the journals, employ the editors directly, and publish all the content for free?

Note that buying the journals doesn't cost the universities (as a group) anything in the long-run, as the entire current value of the journal companies comes from the amount of money they expect to be paid in journal subscriptions by universities in the future. And there's no need for the journals to charge "submission fees", as those were all being paid by the universities in the first place: they can just come out of the communal pot.

So far as I can see, there is literally no downside to this - assuming coordination can be achieved, you have the same universities paying the same amount of money to the same people to produce the same articles, but the articles are now all available open-access. I admit that "assuming coordination can be achieved" is a fairly hefty assumption, but given the massive upsides, why isn't anyone at least suggesting this sort of approach?

There seems to be a general trend towards open-access publishing anyway, which is a Good Thing, but I don't undestand why this model isn't a strict Pareto improvement on the current system.

Thursday, 28 October 2010

The Prisoners and the Chessboard Solution

 Two weeks ago, I posted the following puzzle:

So, the evil guy who kidnaps people and sets them bizarre mathematical tasks which they have to complete or be executed has kidnapped you and your friend Bob. He sets you the following bizarre mathematical task:

I will take you into a room in which there is a chessboard. There is a coin on every one of the squares of this chessboard, showing either heads or tails. I will then tell you which one of the squares has the key to the door of the prison under it. After this, you will be allowed to turn over exactly one of the 64 coins and then be escorted from the room.

Immediately after this, Bob will be brought in, and will be asked to find the key. If he can locate it you're both free to use it to unlock the prison and leave. If not, you'll both be eaten by rabid wildebeest.

You and Bob are free to discuss a strategy before you are taken into the room with the chessboard - what should you do?

Adrianna emailed me a (sort of) solution less than a few hours later. I've posted my solution (and hers) below the fold).

Tuesday, 26 October 2010

The next number in the sequence

We'll start today's post with what I think is a relatively easy set of puzzles. What is the next number in each of the following sequences?

a. 1 2 3 4 5 6 7 8 9 10 11 12
b. 1 1 2 3 5 8 13 21
c. 8 8,000,000,000 8,000,000,008
d. 31 28 31 30 31 30 31 31 30 31
e. 3 1 4 1 5
f. 1 11 21 1112 3112 211312 312213 212223
g. 1 1 4 1 9 2 16 3 25 5 36 8 49 13

Saturday, 23 October 2010

Iterated Prisoner's Dilemma

Just a little note to say that we're running an Iterated Prisoner's Dilemma competition in our department. If anyone is reading this, and would like to enter a strategy, they're more than welcome. I've already written a description of the tournament, which you can find here, so I'm not going to write it again.

Incidentally, while writing that website, I decided I should probably put something on my academic page, you can read what I decided to write here - I'll be updating it with a few bits and bobs that I've done over the past few years (mostly the outreach stuff I've done) as soon as I get back from Jamaica. If it looks familiar, that's because it looks exactly like Andy's academic homepage - thanks for the template Andy!

Wednesday, 20 October 2010

Toy Boat, Big Whip, Piano Panier

I learned a long time ago that one of the hardest Tongue Twisters in the English language is "toy boat". If you're a native speaker and you don't trust me, try it - say "toy boat" quickly and repeatedly. If you're not a native speaker, go find one and get them to say it - you'll be pleasantly amused by their difficulty.

Other examples of this phenomenon in English are "big whip" and "unique New York", although this latter is far too contrived for my liking - the beauty of "toy boat" is that it's a phrase that you've undoubtedly said at some point in the past without realising it's potential for short-circuiting your voicebox.

Since I discovered this weird phenomenon - not just that "toy boat" makes for a ridiculously good tongue twister, but also that non-native speakers never seem to have any difficulty with it, I've been on the hunt for something similar in other languages. So far, I've found "piano panier". If you're a native French speaker, try it. If you're not (but speak good enough French to give it a go), just see how easy it is. I've yet to get any examples in other languages, but that's probably at least in part because I haven't asked enough people.

I'm also very intrigued as to why there is such a difference. Do our brains actually process speech in foreign languages fundamentally differently? Is it just that I pronounce "piano panier" so badly that I don't come across the same difficulty as a native speaker would? Are there any serious linguists out there who would be interested in studying this phenomenon?

Monday, 18 October 2010

Optical illusions

The BBC has this article about optical illusions which we were discussing in the pub after the seminar today. I thought this would be a good chance to share one of my favourites. Have a look at the picture below:

The blue squares on the top in the left-hand picture are the same colour as the yellow squares on the top in the right-hand picture.
Don't believe me?

That grey line is the same colour all the way along. If you still don't believe me, use some sort of graphics programme and determine what the colours are for yourself.

I can't remember where I downloaded these pictures from, it was ages ago - if anyone knows who this illusion was made by, I'll put in  link.

If you want some more illusions, have a look here I particularly recommend the break of the curveball and the color dove, but the whole site is full of pretty awesome stuff.

Thursday, 14 October 2010

The Prisoners and the Chessboard

There's a long tradition in mathematics of puzzles in which someone asks some prisoners to perform some bizarre task. Usually, if they can't complete the task, they are to be executed. Here is one of my favourite examples of the genre (which I only heard for the first time relatively recently).

So, the evil guy who kidnaps people and sets them bizarre mathematical tasks which they have to complete or be executed has kidnapped you and your friend Bob. He sets you the following bizarre mathematical task:

I will take you into a room in which there is a chessboard. There is a coin on every one of the squares of this chessboard, showing either heads or tails. I will then tell you which one of the squares has the key to the door of the prison under it. After this, you will be allowed to turn over exactly one of the 64 coins and then be escorted from the room.

Immediately after this, Bob will be brought in, and will be asked to find the key. If he can locate it you're both free to use it to unlock the prison and leave. If not, you'll both be eaten by rabid wildebeest.

You and Bob are free to discuss a strategy before you are taken into the room with the chessboard - what should you do?

Wednesday, 29 September 2010

Unit Fail in the Evening Standard

From an article by Anthony Hilton in the Evening Standard today:

It is very difficult to believe that the capitalist system has been seriously improved by the arrival of computers able to trade in a microsecond and to exploit movements in share prices visible for just that amount of time.
It is even harder to believe that it will be improved further when the next generation of technology — including that of the stock exchange itself — will increase the available buying and selling speeds to milliseconds — millionths of a second.
Do they even employ any copy editors any more? And why would you pay this guy to comment on this sort of thing?

Wednesday, 15 September 2010

What is the most commonly Mispelt word on the internet?

I've wondered about this before, and finally got around to doing some research last night. For a measure of how often a word is mispelled on the internet, let's use this: the ratio of the number of times the correct spelling appears to the number of times the misspelling appears. I'm not quite sure what to do if there is more than one common way in which a given word is misspelt - probably take the ratio of the correct spelling to the sum of the incorrect spellings.

Anyway, here's my first few attempts:
definitely: definately - 96,900,000: 13,500,000 = 7.18:1
separate: seperate - 172,000,000: 12,200,000 = 14.10:1
accommodation: accomodation 98,400,000: 12,600,000: 7.81:1
So, after my first few tries, the old perennial "definately" seemed to be doing well.

The two people I've discussed this with both suggested having a look at the number of hits for "teh" vs "the", which I did the ratios are:
the: teh - 11,910,000,000: 23,000,000 = 517.8:1
The most interesting thing about this fact is that "the" appears in more than 12 *billion" webpages. That means that there is now almost certainly more than two webpages in the google index for every person on Earth. The fact that "the" is so common makes it nearly impossible for the typos to overwhelm the people getting it right.

Anyway, the best I've been able to do so far is the following:
Gauge: guage - 33,100,000: 11,200,000 = 2.96:1
I got pretty excited by the number of hits for the word "miniscule", but it appears that the consensus is that that's an acceptable spelling these days, so you don't get points for that (I'm not quite sure what rules I'm using on what makes a spelling count as "acceptable", but I'm sure there are some). 

Anyone beat 2.96? 

EDIT (16/9)
As Adrianna points out, I had managed to fail to misspell two of the words in my original post - now corrected. She also suggests "occurring", as a candidate, which is a new clear winner:
Occurring: occuring/ocurring = 49,900,000:22,300,000+22,100,000 = 1.12:1
Notice that either of these individual misspellings would already have been winning on its own. Note also that for some reason this word is much more commonly misspelled than either "occurred" or "occurrence".
So - new challenge - can anyone get a ratio below 1?

Thursday, 2 September 2010

Monty Hall, Monty Hell and Tuesday's Boy

Consider the following problem (which I've quoted from the wikipedia page):
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
 Well. Is it?

Tuesday, 31 August 2010

Asymmetric walking

When I walk from Mile End Road to Sainsbury's, I almost always walk in through the front entrance. When I leave, I leave by the side entrance. This despite the fact that I walk past the side entrance on the way in.

When I walk into university, I usually do so via Mile End Road and the little bridge you can just about make out on the map. When I walk home from university, I do so via Hamlet's Way and (sometimes) the park.

View Larger Map
As you can see, there is little to choose between these two alternatives in terms of distance (actually, there's probably more to choose between them than I would have guessed - the park seems to win quite clearly) but it seems that there is a pretty regular bias that makes me choose one in one direction and one in the other. There are several other places where I've noticed this phenomenon.

Now, I know that there are lots of situations in which the fastest way from A to B is not the fastest way from B to A, even when walking, but I pretty sure this doesn't explain what's going on here. There's some sort of heuristic governing my decisions, and I can't quite work out what it is. It seems to be something like "if you know you need to turn, do so early". Why am I doing this? Does anyone else do the same thing? Have other, more bizarre heuristics?

Sunday, 15 August 2010

Tube or False (or just nonsense)

There is a new advertising campaign on the London Underground... I'm not entirely sure what it's advertising, as everyone who sees the posters is already on the Tube and presumably already aware that it exists. Anyway, the campaign is entitled Tube or False, and consists of 8 statements about the system for us to guess whether they are true or false.

One of these is:
Every week, our escalators travel the equivalent of 2 times round the world. 
I'll post a spoiler under the fold, but pause for a second to decide if you think that's plausible.

Saturday, 14 August 2010

The Handshaking Lemma

Professor Geoffrey Beattie of the University of Manchester has given us mathematical formula for the perfect handshake. For some reason, all of the articles which contain said formula seem to include it as a picture, rather than writing it out in words, so I'll do the same thing (mostly because I don't know how or if it's possible to get LaTeX to work in blogger... does wordpress do it?

Just in case you're wondering what all those symbols mean...

(e) is eye contact (1=none; 5=direct); 
(ve) is verbal greeting (1=totally inappropriate; 5=totally appropriate); 
(d) is Duchenne smile - smiling in eyes and mouth, plus symmetry on both sides of face, and slower offset (1=totally non-Duchenne smile (false smile); 5=totally Duchenne); 
(cg) completeness of grip (1=very incomplete; 5=full); 
(dr) is dryness of hand (1=damp; 5=dry); 
(s) is strength (1= weak; 5=strong); 
(p) is position of hand (1=back towards own body; 5=other person's bodily zone); 
(vi) is vigour (1=too low/too high; 5=mid) 
(t) is temperature of hands (1=too cold/too hot; 5=mid); 
(te) is texture of hands (5=mid; 1=too rough/too smooth); 
(c) is control (1=low; 5=high); 
(du) is duration (1= brief; 5=long).

Wednesday, 11 August 2010

A Tiling Problem

A while ago, Andy and I were at a maths challenge. There were a few problems with the answers we'd been given to the questions. Andy has already documented one of them, I'm going to comment on the other.

Here's a tiling pattern (imagine, if you will, that it was drawn by someone more competent than me, so all three polygons are regular every time they occur):

Now imagine that we use this pattern to tile the entire plane - so that we can ignore what happens at the boundary. The question is: what is the ratio of hexagons to squares to triangles in the final tiling (actually, the question was "what is the ratio of squares to triangles?", but you might as well do all three). The answer is probably not what you think immediately.

Friday, 6 August 2010

Not from The Onion

Stolen directly from Marginal Revolution, but how can I not share this?

Japanese macaques will completely flip out when presented with flying squirrels, a new study in monkey-antagonism has found. The research could pave the way for advanced methods of enraging monkeys.

 I'm not quite sure why Tyler didn't list it under "not from the Onion"

PS - I'll write the stuff about the inefficiency of queues when I get round to it - very possibly in the next week or so.

Thursday, 29 July 2010


I have two things to say about queues today. The second one is inspired by Steven Landsburg, and I was reminded of it by the fact that I spent 40 minutes of today standing in a queue to get on the London Eye. Time which was essentially deadweight loss to the world.

The first is simpler, and I was inspired to write it by AJ Jacobs. AJ Jacobs is the author of The Year of Living Biblically, and I'm currently reading his new book "My Experimental Life". He's one of those journalists, who does crazy things and writes about them (he claims because he has nothing interesting in his past to write about - although why he can't just make stuff up like everyone else, I don't know). Anyway, the chapter of the book I was just reading is called The Rationality Project. Jacobs, having read Predictably Irrational and Nudge (but no doubt not having actually read Tversky and Kahneman) decides to rid himself of all of his irrational biases. He fails in funny ways, of course, and has a few interesting things to say along the way.

Anyway, at the end of the chapter he has a few points to make. Things he does differently since spending a month trying to be as rational as possible. Some of these are sensible: "I read menus from the bottom up" (because they are designed to be read from the top down - and are carefully designed to 'nudge' you into buying whatever the restaurant wants you to buy that day); "I spend a few minutes each week reading Michelle Malkin's conservative musings" (because he disagrees strongly with Michell Malkin, and only reading things by people you agree with is a sure way never to change your mind).

The one that I take issue with is this: "I make a note every time I'm in a fast moving grocery line". Now, the idea behind this is obvious:
We all are predisposed to notice and remember the bad stuff... when we're on a checkout line behind an eighty-two year old man paying with a sack of pennies and nickels.
But it's a really, really bad example to choose of this particular phenomenon because we actually do spend more time in slow-moving queues than in fast-moving queues. This is obvious once you think about it: slow-moving queues move slower! So if all queues were the same length, but with random speeds (which were impossible to predict before you join) you would still spend most of your time in slow-moving queues. You're just as likely to choose a fast queue, but every time you do choose a fast queue, you get to the front of it quicker.

If you want to avoid believing in the signficance of random events, you should make a note of every time you take your umbrella out and it does rain (or choose not to take it and it doesn't). You should remember every time you have a really strong feeling that you're about to get a phonecall from your grandmother and then you don't, or every time you meet someone who doesn't share your birthday.

I said I had two things to say about queues, but it's late, and I've spent longer than I expected writing about that one. I'll do the other one tomorrow.

Tuesday, 6 July 2010

Things I wish I'd read earlier: I Pencil

I'm going to start an occasional series in which I'll post links to several articles and books that I wish I'd read earlier (or if they're in copyright, links to somewhere you can buy them). Mostly because if you're reading this, and you haven't read them, you're probably going to enjoy them.

Also, I kind of plan to post something sometime about what I think they should teach in schools (and which parts of the current curriculum they could afford to miss out) and I think most of this belongs there.

I Pencil

I think by the time I finished school, I had just about heard of the Invisible Hand, but I'd never been taught about it, and didn't *really* understand what it meant. The genealogy of a pencil is an incredibly powerful illustration of what it means. I challenge anyone to read it and not be amazed by the power of the price system (why don't more people cite *that* as a proof of God's existence?). The fact that I can walk into a shop whenever I want a loaf of bread and be sure that I'll find one on a shelf really is a miracle - everyone should be reminded of that every now and then.

Monday, 5 July 2010

How not to draw a graph

The Daily Mail had an article earlier this year reporting some research which stated that people are happy at the age of 15, gradually drop off in satisfaction until the age of 45, then get happier again until a peak at 74. There are a few potential problems I can see with the research (asking people to self-report on their happiness has always seemed pretty dodgy, and have they properly controlled for some years just being less happy than others?) But that's not the issue here. The issue is the "graph" they used to illustrate the research.

Let's have a look at it:
Yes, really. That is a genuine graph directly from the website (in fact, that picture is being hosted on their website, I couldn't be bothered to download it). Look at the scale... The horizontal axis doesn't have one! The distance from 15-40 is the same as the distance from 40-50! Why would anyone make the graph look like that? Would they really be unable to make the same point using a graph with sensible axes?

Let's have a look:
That doesn't really look any less impressive (apart from the fact that I drew it in about 10 minutes in GIMP, and the Daily Mail hires qualified graphics people), and the patterns are still pretty clear. The slight upward trend in the 40's starts before 46 (but that's also true on the Mail's original) and the *massive* peak at 74 does start to look a bit suspicious... could it be a small-numbers effect?

Why did the Mail choose to go with the inumerate version? Apart from the obvious, I genuinely can't see how theirs is better than mine on any dimension, and it's pretty obvious in which ways it's worse.

HT to Dave in the comments at BishopBlog

Sunday, 4 July 2010

Non-news story of the week: Union demands higher pay for its members

The National Union of Teachers has complained that teaching assistants have been used instead of teachers to look after classes full of kids. This has resulted in job opportunities for supply teachers (who are members of the National Union of Teachers) dropping significantly.

I can barely imagine a purer example of what unions are really all about: cartels formed by workers to artificially drive up wages. Using teaching assistants to look after a classroom is not only a Bad Thing, it is also illegal (presumably thanks to the efforts of organisations like the NUT). Unless teaching assistants are capable of looking after a classroom full of kids, why would anyone bother with a law like that?

Unions tend to put themselves forward as defending some sort of moral principle (even when they're supporting laws which ban people from hiring low-skilled workers). It can hardly be a coincidence that their moral principles always happen to coincide with the interests of their members...

Saturday, 3 July 2010

'Minor Delays'

I have spent a long time wondering exactly what is meant by 'minor delays' on the Tube. They have a fixed amount of track, and a fixed number of trains running on it. The only way for their to be delays is for the trains to slow down... how is it possible that 'a customer incident' which happened over an hour ago is still causing the trains to run slower?

I can just about see why there are delays at peak times (the trains run slower because they spend longer in each station) but how do 'delays' propogate through the system? I can see how there might be bunching, but 'delays' (or is that what they mean by delays?)?

Thursday, 1 July 2010

Equal Prize Money at Wimbledon

People have been going on (again) about equal prize money at Wimbledon. Lots of people have been saying (again) that it is right that pize money is now equal. Lots of people have then been responding (again) by saying that this is silly because the men play 5 sets while the women play only 3.

No-one seems to have noticed (again) that the prize money for the junior section is even less than the prize money for the women... how can this be fair? They play the same number of sets!

And the prize money for the World Tiddlywinks Championship (spot the familiar face, for those at QM...) is even lower!

In fact, the prize money for the annual 'working at MacDonalds for 40 hours a week' championship would barely pay for Andy Murray's chicken baguettes, and yet no tennis player would dream of playing 40 hours in the entire two weeks of Wimbledon - how can this be fair? The '5 sets' crowd seem to adhere to some bizarrely warped form of the Labour Theory of Value (inasmuch as they have any principle at all) - why not insist on equal prize money for burger flippers?

Seriously, how can anyone possibly imagine that the prize money for a tennis tournament is proportionate to the amount of work put in, or that the prize money for two entirely different tennis tournaments should necessarily be the same?

I am not an economist, so I don't want to try to explain how the prize money *is* determined. All I know is that neither the "equal prize money" crowd nor the "but they play 5 sets" crowd has captured the full story.

Wednesday, 23 June 2010

Bridge Probability

I've been re-reading Victor Mollo's classic bridge book 'Card Play Technique: the art of being lucky'. I've come, once again, to the sections about probabilities that I just can't get my head round. Consider the following passage:
If the Ace of Clubs is right, all is well. If not, the contract will depend on guessing the diamonds. How then, should we set about it? The man in the street will draw trumps quickly, sway in his chair slowly and mutter something like: "Well, it's six of one and half a dozen of the other".
But is it?
To the expert there is a vital difference between the Club and the Diamond positions. The latter will be the subject of guesswork. The former lends itslef only to prayer. The Club must be played first, and the reason is that it will provide a clue to the Diamonds.
If East has the Ace of Clubs, West will be credited with the Ace of Diamonds.
There is similar reasoning throughout the book, just one hand later:
West has pleaded guilty to 7 points hearts and to the King of Diamonds: 10 in total. East has only 3. It is more likely that the defender's high-card strength will be divided between them 10-5 than 12-3. Therefore the best chance is to play East for the King of Clubs.
I just can't believe that this reasoning is valid. The deck doesn't know which cards we assign points to, so it is no more likely to put the Ace of Clubs in a different hand to the Ace of Diamonds than it is to put, say, the Three of Clubs in a different hand to the Ace of Diamonds. Similarly, while it is true that a 10-5 distribution is more likely, a priori, than a 12-3 distribution, surely this ceases to be the case when you've alread placed the remaining points 10-3 (assuming that the principle of Vacant Spaces doesn't come into play - ie, every player has followed with a small card to each of his partner's honours).

To repeat: the deck doesn't know which cards we assign points to!

Maybe this sort of reasoning is a useful shortcut to some valid reasoning, or maybe I'm missing something (I certainly hope so). Can anyone shed any light?

Tuesday, 22 June 2010

What's wrong with "sell"?

There are a *lot* of adverts on the TV right now for services like MazumaMobile, mobilephoneXchange and various others. There is also CashMyGold and PostalGold and no doubt many others. These are all companies to which you can sell your goods. The one thing that all of their adverts have in common (apart from being insanely annoying) is that none of them use the word "sell". I really can't understand why.

The most commonly used wording seems to be informing people that they can "exchange" their goods for cash. We already have a perfectly good word which means almost exactly "exchange for cash". Why don't these adverts use it? Because it would remind people that there are various other routes through which they could sell their gold/old phone/whatever? Because the word "sell" is unsavoury?

NB - Mazuma goes even further, suggesting that they can 'magic' your phone into cash... imagine that!

Monday, 21 June 2010

Whacky Formula: The Happiest Day of the Year

You might think that all the Irish people you saw smiling last Friday were just experiencing some good old-fashioned Schadenfreude at the abysmal perfomance of the England football team, but no, they'd probably been reading the Examiner. If they had, they'd've found out that Dr. Cliff Arnall has some 'research' explaining why June 18 is the happiest day of the year. He has a formula, in fact, for telling us exactly how happy every day of the year is.
The ex-Cardiff University lecturer’s complicated formula is: O + (N x S) + Cpm/T + He.
My, that does look complicated... what on earth could it all mean? Luckily there's an explanation for the formula in the article (although no explanation for why (N x S) is in brackets. You can read it below the fold.

Sunday, 20 June 2010

Pinker vs. Greenfield: is facebook rotting your brain?

I read two articles in the last week by leading intellectuals about what effect mass media have on the brain. One of them was Steven Pinker: Mind Over Mass Media. Pinker's conclusion:
The new media have caught on for a reason. Knowledge is increasing exponentially; human brainpower and waking hours are not. Fortunately, the Internet and information technologies are helping us manage, search and retrieve our collective intellectual output at different scales, from Twitter and previews to e-books and online encyclopedias. Far from making us stupid, these technologies are the only things that will keep us smart.
In a fairly scholarly article for Edge, Pinker cites evidence from cognitive science, psychology and neuroscience. He explains the bias that causes people to believe that mass media is damaging our brains:
As with primitive peoples who believe that eating fierce animals will make them fierce, they assume that watching quick cuts in rock videos turns your mental life into quick cuts or that reading bullet points and Twitter postings turns your thoughts into bullet points and Twitter postings
He pithily ridicules the notion that "changing our brains" is a bad thing:
Yes, every time we learn a fact or skill the wiring of the brain changes; it's not as if the information is stored in the pancreas
The other article I read was an interview with Baroness Greenfield, with the headline Facebook Addicts Can't Relate, Greenfield is worried about the effect social media is having on a generation that is growing up with it as a regular means of communication:
If you are not rehearsing looking someone in the eye in three dimensions, but instead you have 900 friends on Facebook ... one does question what kind of relationship they might be having,
In defence of her position that facebook might be contributing to rising levels of ADD (how can a diagnosis that didn't exist 30 years ago be rising?) she cites... erm... some studies that haven't actually been done:
Perhaps it's mandating a shorter attention span. I'm not saying it is but I'm saying, 'Wouldn't it be worth exploring?'
Of course it would be worth exploring.. but what is the point in encouraging sensationalist and uninformed scare stories in the press until it has been explored? She also warns us (somewhat ungrammatically) to be careful before we ignore her non-argument:
We are being complacent in the extreme if you just dismiss me as a whingeing, middle-aged Luddite.
Indeed... I'm not quite sure on what planet 59 qualifies as 'middle-aged' (the average age is still less than 80). But she's right, it would be silly to dismiss her fears because of her age, or her lack of fluency with the relevant technology. Dismissing them because they have absolutely no evidence to support them on the other hand...

I'll let you draw your own conclusions on which of the two articles I was most impressed by.

Friday, 18 June 2010

Reasons to be a Republican

Surely you can't give any sort of power, even figurehead-style can-only-use-it-in-an-emergency power to a guy who is capable of saying stuff like this:
Nature has been completely objectified — ‘She’ has become an ‘it’ — and we are persuaded to concentrate on the material aspect of reality that fits within Galileo’s scheme
“It is no good just fixing the pump and not the well,” he said. Talk of an “environmental crisis” or of a “financial crisis” was actually describing “the outward consequences of a deep, inner crisis of the soul”. 
Seriously. They guy picked Galileo as a general-purpose scapegoat for what's wrong with our world. Could he be less suitable to govern?

Thursday, 17 June 2010

Conjunction Fallacy

There's a sign that's just appeared in the changing rooms of Barts pool:
Please be aware that these areas are cleaned by male or female staff.
So not those hermaphrodite staff they use at Guy's and Thomas' then...

The "Forced to Deny" Files

The Metro settles the eternal question: is there life after death?. There is, and you can even be forced to deny things there....
Russell Crowe has been forced to deny that he's not dead
In other words 'someone said Russel Crowe was dead, they were wrong'. Gotta love 'forced to deny'.

HT (as they say) to @andydrizen

Wednesday, 16 June 2010

The wisdom to accept the things I cannot change

There are several 'life lessons' that I've picked up from playing bridge. Some of them are incredibly obvious in hindsight. Some of them less so. This is one of the more obvious in hindsight, but also one of the more important, so I think I'll start with it.

It is fairly common when playing bridge to reason thusly: in order to make this contract, I need West to hold the King of Diamonds. If West holds the King of Diamonds, then he can't hold the Ace of Spades. Therefore, I'll assume East holds the Ace of Spades and play accordingly (an example).

Tuesday, 15 June 2010

Blogging vs. Talking

There are several occasions when I've started writing a blog post about a story, realised halfway through that the point that I was trying to make was nonsense, and stopped. Note that if I was intending to write a blog post, this means that I had already thought about the issue for some fairly significant period of time. Somehow, writing it down allows me to see where I was going wrong.

I'm not sure if its writing things down, or just the process of articulating them that enables me to change my mind, however, I am fairly sure I change my mind about things less often in conversation than I do when writing blog posts about them. This can't be because I spend more time thinking about something before I say in than I do before I decide to blog about them: I write maybe 3 blog posts a week, I have several hundred conversations. I have a few explanations below the fold.

Monday, 14 June 2010

The Economist can't think of any good arguments against trading organs

People have probably already seen the new posters for The Economist, frankly, I don't think any of the three issues they've picked are particularly interesting debates (should drugs be legalised, should prisoners be allowed to vote and should we allow trade in human organs). As far as I can see, all three are pretty much a slam dunk for the yes side. Anyway, it appears that, at least for the organ trading argument that the Economist agrees with me. Let's have a look at their 'against' arguments (you can see the poster here).
1. The British Medical Association says that allowing organs to be traded would put pressure on poorer people to sell.
Well.. yes, and allowing cars to be traded probably puts pressure on poorer people to sell. I have no idea why this is supposed to be a bad thing. Does the BMA have some reason to believe that poorer people would prefer having two functioning kidneys to money? That they should prefer this? Is there any particular reason we should believe the BMA is likely to have anything interesting to say about the question (they're medics, not economists or ethicists)
2. There are alternatives to a trade in organs. Countries in which people's consent to donating their organs is assumed unless they opt out have shorter waiting lists. 
Again, I have no idea why anyone would think this was an argument against allowing a trade in organs. Countries in which a trade in organs is allowed (ie, Iran) have even shorter waiting lists (ie, they don't have any).

There are alternatives to most things, the question is which alternative is best. (I would think presumed consent is even more of a slam-dunk than allowing trade in organs, except there's remarkably little evidence that it actually increases donations).
3. Legalising the trade in organs would turn the human body into a commodity. That is taking free markets too far.
To paraphrase "If we legalised trade in organs, then trade in organs would be legal. This is bad. Ner ner ner ner". This just doesn't even begin to be an argument against anything.

I'm not very surprised that the Economist agrees with me about legalising trade in organs, but surely they could have tried a bit harder to come up with some argument against? Or is it just that there aren't any?

Tuesday, 8 June 2010

Inadvertent Accuracy

Horrible article in the Telegraph, but with a great opening paragraph:
It is not necessary to be a conspiracy theorist to recognise that the General Medical Council's recent ruling to strike professors Andrew Wakefield and John Walker-Smith off the register had the fingerprints of the medical establishment all over it. 
Well... no, it's not. The medical establishment has struck off a doctor who performed unethical experiments on kids then misreported the results to make money out of them. That's pretty much what the medical establishment is for. Of course, I'm not entirely sure that's what Le Fanu means...

Correlations vs. Causation.

A while ago, I said I'd write a post with my favourite "things which are correlated". Well, now I've finally figured out how to do page-breaks, I guess it makes sense to write it now. Here are my favourites. Any suggestions as to why they might be correlated? (answers below the fold)
  1. Countries which put Fluoride in the water have much higher cancer rates than countries which don't.
  2. Schoolchildren's shoe size is very strongly correlated with their performance on spelling tests.
  3. The number of shark attacks on a given day is strongly correlated with ice cream sales.
  4. You are much more likely to wake up dehydrated if you sleep on a sofa than if you sleep on a bed.
  5. The number of prostitutes working in a city is positively correlated with the number of policemen.

Wednesday, 2 June 2010

Druids Demonstrate Regression to the Mean perfectly

I once heard of an experiment that a friend of mine (an anti-speed camera campaigner) used to do when he was giving a presentation. He would get everyone in the room to randomly generate a 2-digit number (not sure how, exactly, maybe he used to carry some sort of 10-sided dice with him). He would then give everyone who rolled more than 80 a big picture of a speed camera and got them to generate a second set of numbers. Lo and behold, only a small fraction (on average around 1/5) of those carrying speed camera signs had high levels of deaths. The speed cameras had worked!

This is the purest way I've ever seen to explain the phenomenon of 'regression to the mean'. It's a well-known phenomenon, and explains a lot of things, from why test scores at the worst schools tend to improve the next year, through why patients who visit a homeopath seem to feel better, to the Sports Illustrated Jinx.

However, the Austrian motorway authority seems never to have heard of it. They recently asked some druids to reduce the number of fatalities at a few accident blackspots by burying some magnetic slates. The results were a roaring success:
Austrian motorway authority ASFINAG said it was sceptical at first and kept the project a secret. But it went public after the druids’ efforts cut the number of deaths at the notorious crash site from six a year to zero in two years.
I don't think there's much more to say.

Sunday, 30 May 2010

Why is the suicide rate so low at Foxconn.

Foxconn is a chinese company that you may have heard a lot about recently. There has, according to the BBC been "a string" of suicides there recently. According to the Times there is a "spiralling suicide crisis". Reuters says there has been "a spate of employee deaths".

10 people have committed suicide this year at a particular Foxconn factory in China (where a lot of parts for the iphone are made, apparently, which I think is why this is supposed to be a news story). The factory employs 300,000 people. I make that a suicide rate of (approximately) 7 people per 100,000 per year. The suicide rate in China is about 13 people per 100,000 per year. In other words, working for Foxconn cuts your chance of committing suicide almost in half!

How is it possible for every single person everywhere in the world's media to have gotten this story exactly backwards? There are a lot of very clever people suggesting "explanations" for the suicide rate at Foxconn. Unfortunately, they're trying to explain why it's so high, when they should be doing the opposite! This should lead us to seriously doubt these people's 'explanations' when the phenomena they're describing happen to be real. If your theory can explain anything, it has no explanatory power at all.

However, I think the main story here is how this became a story. What is going on? Why did someone decide to report the suicide rate at Foxconn instead of, say, the suicide rate among Tesco employees (another company which employs around 300,000 people, at least in the UK). And how did no-one notice that what they were reporting was in no way interesting.

Saturday, 29 May 2010

Deadweight Loss

I'm currently reading Joel Waldfogel's book "Scroogenomics". In it, he expands on some of the points made in his classic research paper "The Deadweight Loss of Christmas". The basic premise is that people (especially distant relatives) don't know what you want as well as you do, so any gifts they buy you are less desirable to you than anything you could have bought yourself with the money. He has plenty of facts and figures to back up this eminently plausible theory, and I think a serious point to make.

However, he does have at least one minor slip. In describing what deadweight loss is, he says the following:
If a dollar disappears from my pocket and appears in yours, it's a loss to me, but it's not a deadweight loss to society. If you take my dollar and destroy it lightling your Cohiba, then it's a deadweight loss.
This isn't quite right, for the simple reason that dollars only have purely symbolic value. Burning a dollar bill is a genuine loss of $1 to the burner, but can't possibly make society as a whole worse off... you can't eat money. So who benefits? As the wikipedia article on burning money explains, everyone. Burning a banknote has a (very) slightly deflationary effect, so makes all of the money in everyone else's pocket worth slightly more.

I first encountered this idea in Steve Lansburg's excellent Armchair economist, and it seems to be pretty standard fayre in economics literature, so how did Waldfogel miss it? Or did he think that burning money seemed more wasteful than any other genuine example of a deadweight loss, so sacrificed accuracy for impact?

Monday, 24 May 2010

What exactly are confidence intervals?

So, a friend (who would probably prefer to remain nameless) is currently looking for jobs in finance, and sent me some sample interview questions that they like to ask people. One of them is the following:
A drug trial gives the result that the drug works better than the
placebo, with 95% confidence. What exactly does this statement mean? What further assumptions are needed to be able to deduce that the probability of the drug working is actually 95%?
Now, I wasn't entirely sure I knew the answer to this question. I thought I did, but despite having studied rather a lot of statistics, I don't think anyone ever actually told me what a 95% confidence interval was, so I did what everyone does faced with such a situation, and checked the wikipedia article. Wikipedia is singularly confusing on the matter, but it gives the answer as roughly the following.

Thursday, 20 May 2010

My Favourite Limericks (of which precisely one is actually a limerick)

Here's the actual limerick:

There was a young man from place B
Who satisfied Predicate P,
He performed action A,
In adjective way,
Resulting in Consequence C.

Tuesday, 18 May 2010

Wikipedia can't add up

Have a look at this list of best-selling books. In particular, look at the Harry Potter books. There is one Harry Potter book in the list of best-selling books. Harry Potter and the Deathly Hallows, which has sold approximately 44 million copies. Harry Potter is also listed as the best-selling series of all time, with 400 million total copies sold.

In order to see why there is a problem with this, you just need to know that there are 7 Harry Potter books, and understand the Pigeonhole Principle.

There is a (sort of) explanation of the problem in the 'talk' page of the wikipedia article, but the inconsistency remains on the initial page. This actually highlights a fairly major problem with wikipedia's epistemology. The inconsistency has to remain because there's no 'credible source' for the figures for the other individual books. So even though everyone knows that the article is wrong, it can't be corrected because this would constitute 'original research'. Hmm... just how credible does a 'credible source' have to be? Will a mathematical proof do?

How to sample randomly

I was once told that 'duration of unemployment' figures were collected in the following way: people were telephoned at random during the day. If they answered, they were asked if they were unemployed. If they said yes, they were asked for how long they had been unemployed. Before you read any further, can you see what is horribly, horribly wrong with this method of data collection? (There are several things wrong with it, but one of them renders it entirely useless)

Before I give you the answer, a brief detour. When I was at school, I did a piece of statistics coursework (I think it was for GCSE's) in which I compared the average sentence length in a French text to an English text. I can't remember exactly which texts I chose, I think it was newspapers of 'equivalent' quality, but that's largely irrelevant. In order to estimate the average length of sentences in each text, I adopted the following method: pick a word uniformly at random from the text and count the number of words in the sentence containing it.

I had collected around 100 sentence lengths before I noticed the utter ridiculousness of this method. In case anyone hasn't spotted it yet, this 'random sampling' is guaranteed to massively overestimate the average sentence length in any given document, as the probability of any given sentence being chosen is in direct proportion to its length.

Consider the following passage:

"The quick brown fox jumps over the lazy dog whilst the five boxing wizards jump quickly over my lovely sphinx of quartz. Jesus wept"

 If we pick a few random words from this and compute the 'average' sentence length of the sentences that contain them, we're going to come up with something very close to 20 (if we pick every single word, we'll get 20.3333)  The actual average sentence length is 12.

Now, if you didn't immediately spot that this was the key problem with the method of collecting unemployment data I mentioned in the first paragraph (there are problems with telephone polls in general, of course, but they are essentially insignificant compared to the problem with the sampling method), this should make you worry about how easy it is to slip *exceedingly* dodgy statistics past people who aren't paying attention. I'll post a few examples of my favourite 'correlated for spurious reasons' statistics in another post later this week.

As an aside - if you do actually collect the data in the way suggested, you can presumably still get some information about the distribution you're studying - what's your best estimator for the mean? And what assumptions do you have to make about how the data are distributed?

Saturday, 15 May 2010

Why don't we sample more?

Steve Landsburg recently blogged about a maths professor who weeds out 'unlucky' applicants by randomly rejecting half of the resumes he gets sent. Now, this is unusual, in that it is a random sampling method which significantly *reduces* the average quality of the applicant that gets hired.

There are a *lot* of situations in which random sampling would reduce workload whilst having no effect whatsoever on effectiveness. I'll start with one of the simplest and least controversial (and one that I have the most personal experience with). Students regularly submit 10 or more pieces of coursework for each course in a university semester. Every question is then marked, and the papers returned to the students. Assuming (which is probably not entirely accurate) that the courseworks are solely intended as a normative assessment of student performance, surely it would be massively more efficient to sample questions at random and mark those, rather than marking the entire paper. The expected mark for any given student is the same - only the variance goes up.

There are a few situations in which students suffer as a result of this. Say there's a pass mark of 40, and you have to pass every coursework, now someone who answers exactly 40% of the questions right in each coursework expects to fail (although they do expect to get an average mark of 40). Similarly, there are situations in which students benefit from this (pass mark of 40, answer exactly 39% of the questions correctly, you now have a non-zero chance of passing). On the whole, I would expect these things to cancel out, and that no one student knows their mark accurately enough to know whether they would benefit or lose out from this policy being enacted.

So why isn't this done more? I've heard from a few lecturers who've tried it, and it went down horribly with the students, who perceive it as 'unfair'. Apparently there were several comments along the lines of 'what if you only mark the questions I did badly?'. I guess this is some sort of loss aversion - it is quite obviously equally likely that we only mark the questions you did well!

Yvain has an article about a similar example from education - in which students are reluctant to guess answers to true/false questions with a penalty of 50% of a point for a wrong answer for some inexplicable reason. Again,  random sampling is a massive net win.

Another example is public transport. No-one every pays to get on the 25 bus. This is because it is extremely rare for anyone to check whether you've paid or not and the penalties just aren't high enough to make it worthwhile paying given how rare the checks are. There are two obvious solutions to this problem: you could either do twice as many checks (thus requiring you to hire twice as many people to do the checking, and inconvenience twice as many people whilst checking) or you could double the fine. I've no idea why they don't take the second option.

How about voting? Instead of counting all of the votes in a general election, why not shake the votes up in a big bowl and count, say, the first 10,000 for any given seat? I can't be bothered to crunch the numbers, but I'm pretty sure the probability of error would be down below 1% - and errors would only occur in seats which were closely contested - where errors are not so important anyway, as the people obviously don't have a clear preference between the candidates.

Most of the examples I can think of exploit the same principle as the public transport idea above - when committing some transgression, your expected utility is the utility of cheating minus the disutility of punishment times the chance of getting caught. Since it's expensive to increase the chance of getting caught, there are a lot of situations in which I think it would be a net win to decrease this and increase the size of the punishment. Why not check half as many tax returns and double the fine for misfiling? Have half as many speed cameras and double the fine for speeding (speed cameras aren't expensive, so this might not be a net win)?

There are dozens of examples - and I don't think that the people in charge have sat down and done the relevant calculation in all cases. Are people just afraid of randomness? Afraid of seeming 'arbitrary'? Afraid of letting people 'get away with' committing crimes - assuming the only legitimate purpose of the criminal justice system is deterrence, this shouldn't be an issue. Maybe there's legitimate concerns that a 'random sampling' approach to some of these problems would be more subject to corruption - but we can just check a few of the samplers at random, and have massive fines for people doing it corruptly!

The law of large numbers is a powerful and important mathematical theorem. Why don't we exploit it better?

Friday, 14 May 2010

Lucozade Sport Lite: the Low Energy Energy Drink!

I just saw an advert for Lucozade Sport Lite. Yes. Seriously. This is an energy drink which contains only 50 calories. But don't worry:
Lucozade Sport Lite contains electrolytes and fluid which help to keep you hydrated
Hmm... a fluid which helps keep you hydrated, I wonder what other things there might be that fit that description....

The website really is excellent though - it actually include a section entitled 'how do I use it?'. Erm... put it in your mouth and swallow?

Wednesday, 12 May 2010

Gladwell on probability

There's quite a nice list of random quotes from Malcolm Gladwell in an interview for this Sunday's Observer.

However, one of them seems to show some misunderstanding of probability:
History suggests that there is almost exactly a 50% chance that any piece of information a spy gives you is true. We would be as well off getting rid of the secret service and flipping coins.
Now if the first part of this sentence is true (which I have no reason to doubt) the second part most definitely does not follow. This is (tangentially) related to a discussion that's been going on at Peter Cameron's blog about probability. Unless spies only ever make statements about things where your prior was already 50%, a 50% accuracy rate could be incredibly useful.

Eg, let's say we're trying to find out where a particular terrorist group has their headquarters. To start with, our probabilities are essentially uniformly distributed across the whole of the world. Our spy comes up to us and says 'the HQ is at number 32 Barkston Gardens, Earl's Court, London'. This information is far from useless - in fact, if we have more than one spy coincide on the same piece of information then we're in business, and can find the location pretty quickly.

Of course, I think Gladwell's '50%' is actually just a proxy for 'exactly as true as you'd expect if they were generating their statements at random', but that's not *quite* the same thing

Tuesday, 11 May 2010

Whacky World Cup Formula: Germany will win

According to this article from the Telegraph (which, incidentally, is a carbon copy of the article in various other news sources from around the world - I assume it's lifted directly from a wire service, but who knows?) Germany are definitely going to win this year's world cup. How do we know this? Trigonometry!
The scientist has written a formula based on trigonometry which analyses all Germany's results from previous World Cups and predicts a winner for this year's tournament.

Having won the World Cup three times, in 1954, 1974 and 1990, Germany's average finishing place at previous tournaments is 3.7 and Prof Tolan says his formula shows this will be Germany's year to lift the trophy. 
Unfortunately, Metin Tolan doesn't show his work, so we can't see quite how he came up with this ridiculous conclusion. It's hard to see why any team with an average finish of 3.7 (whatever that means) would expect to finish in position 1. It's also really, really hard to see how a formula which appears to be essentially some sort of regression/reformulation of the law of averages could be 'based on trigonometry'.

We do get some indication of his track record:
Prof Tolan already predicted Germany would win the last World Cup, which they hosted in 2006,
So he may be displaying a tiny bit of overconfidence in his predicition to say:

"Nobody can beat us this year and you can already put the champagne on ice."

However, my favourite part of the article is the end, in which Tolan demonstrates that he doesn't understand basic game theory or probability, with regard to penalty shoot-outs:
"The weakest kicker should take the first penalty, then the second-weakest and so on," he said. "Then you have the greatest chance of scoring as many goals as possible."
Now this is quite clearly the exact opposite of the truth. I can't even be bothered to crunch any numbers, because it only takes a few seconds of thought to see that if one side follows the good professor's advice whilst the other uses the more sensible plan of doing the exact opposite, the latter side will win before things have even gotten started - the better players on Tolan's team literally won't get a kick.

I'm not quite sure why people who seem to have perfectly respectable research careers get inolved in this sort of thing. I would suggest it was for the money, but he did the same thing 4 years ago... is it just that some people can't resist having their name in the paper?

Tuesday, 4 May 2010

What You Can't Say in Harvard

Paul Graham  is one of my new favourite authors, and What You Can't Say is one of my favourite among his essays*. He discusses the idea that there are almost certainly several things which happen to be true, but which we can't refer to in polite society. I want to write about recent example of the sort of topic that appears to be taboo in modern western academia. To quote Graham:
What can't we say? One way to find these ideas is simply to look at things people do say, and get in trouble for.
That seems like a perfect introduction for this story which, if it weren't true, would strike me as utterly implausible. A Harvard Law student wrote a perfectly reasonable email to a friend, about six months ago, in which she stated that she could not "absolutely rule out the possibility that African Americans are, on average, genetically predisposed to be less intelligent." She was roundly condemned by the Harvard Black Law Students Association, and the Dean of Harvard Law.

Now... I'm going to take a risk and say that I can't 'absolutely rule out' the possibility that African Americans are genetically predisposed to be less intelligent than non-African Americans either (although Stephanie Grace is much better informed on this topic than I am).  Presumably, though, there is no a priori reason to assume that the intelligence of the two groups is the same - African Americans, for example, are clearly genetically predisposed to run faster (I'll give anyone 50-1 on a white man winning Olympic gold before 2020!), why should intelligence have a smaller genetic component than running speed? 
What is much more disturbing is the reaction from the Dean of Harvard Law:
I am writing this morning to address an email message in which one of our students suggested that black people are genetically inferior to white people.
Firstly, she doesn't appear to have read the email in question. The student actually suggested that she wasn't convinced either way by the evidence. Secondly, and more worryingly, the Dean of Harvard Law is equating 'more intelligent' with 'superior'. She seems to be worryingly close to implying that *if* it turned out that black people were genetically predisposed to be less intelligent than white people (which is it at least a logical possibility) then this would somehow vindicate racism. And even closer to implying that stupid people (who definitely *do* exist) are somehow less worthy than intelligent people.

It is very dangerous to attach moral weight to issues of scientific fact. There is always the danger that you might be wrong.This is an issue that Pinker comes back to again and again - there are a list of supposedly morally charged issues of scientific fact in the preface to "What's your Dangerous Idea?" If you are wrong about any of these issues, are you willing to bite the moral bullet?

Does the Dean of Harvard Law really believe that racism is wrong because race differences in intelligence are negligible? Or does she believe it is wrong because a person's worth isn't related to their intelligence, or any other trait they may have, but a fundamental part of being human?

This might just turn out to be another one of those cases where reality is the Least Convenient Possible World. I'm willing to countenance that possibility and still condemn racism. So is Stephanie Grace (I'm charitably assuming her apology is a political necessity, rather than a genuine retraction of her commitment to scientific integrity). Is Dean Minow? 

* Although Why Nerds are Unpopular has some important insights, and contains several ideas which make you go 'I wish I'd thought of that first' - or, more precisely, that 'I wish I'd managed to formulate so clearly first': 
It's important for nerds to realize, too, that school is not life. School is a strange, artificial thing, half sterile and half feral. It's all-encompassing, like life, but it isn't the real thing. It's only temporary, and if you look, you can see beyond it even while you're still in it.

Wednesday, 28 April 2010

The Great (Train) Toilet Conundrum

I'm sure I'm not the first person to wonder about this, but why do they have three buttons to operate the door on a train toilet? There's an 'open door' button, a 'close door' button and a 'lock door' button. So... who exactly is there out there that wants to go inside the train toilet, close the door, but not lock it? I am struggling to think of a single scenario in which that particular option would be useful.

Presumably it would be just as easy to design the buttons so that the 'close' button also automatically locks the door, so someone, somewhere made a conscious decision not to do this. Any suggestions why?

Addendum (05/05): After dicussing this with Andy at lunch, we came up with one plausible(ish) explanation for why someone might decide to do this: if the button automatically locked the door, then pressing the button on the way out with have undesirable consequences. Of course, there are about a thousand ways these undesirable consequences could be avoided, and none of them seem as undesirable as the current worst-case scenario, but it is at least a plausible way in which someone might have stumbled across such crappy design.

Monday, 26 April 2010

Completely Inane Newspaper Stories Part IV: Dogs again

According to this shocking piece in the Salisbury Journal:

POLICE in Ringwood are investigating the circumstances surrounding an injury to a dog’s nose.

Well, what more is there to say? You can read the article for yourself if you want more details. Do remember to read the comments (incidentally, this reminds of this recipe for salted water that Steve Landsburg linked to a couple of months ago (again, read the comments).

Saturday, 20 March 2010

Forced to Deny

The phrase "forced to deny" currently has 155 hits in the Google News search and just over 15 million hits on the web more generally. It's a massively overused cliched phrase, but that is by far the least worst thing about it: it is completely meaningless. Just look at it again, what does it actually say? It says that someone, somewhere, accused someone of something. How is that news? There was a minor variant of this in the John Terry story I wrote about yesterday (in which it was reported as news that John Terry was forced to take a breathalyser test after being in a traffic accident). Let's just take a few examples of the phrase from my Google News search, and look at what they actually say:

Sir Alex Ferguson forced to deny Red Knights claims he wants part of £1.5bn Manchester United takeover bid

Or, in other words, someone somewhere said that Alex Ferguson wants to join in the Red Knights attempt to buy out the Glazer's share in Manchester United. Alex Ferguson said he doesn't. There isn't really any evidence in the story that he does, apart from the fact that he used to be friends with some people who are involved. But he was 'forced to deny' claims, so apparently that's news. 

That's from the Mail, as are most of the hits for 'forced to deny' in the first few pages of news, but then there's this from the Financial Times:

Allies of Gordon Brown were yesterday forced to deny that the UK prime minister "bullies" staff

Right. How does that say anything more than 'someone accused Gordon Brown of bullying staff'? What exactly does it mean to force someone to deny something? Is it enough to simply accuse them of it? Or do you have some evidence? Credibility? A column in a national newspaper? 

There are plenty of others. The family of Samil Saheed 'forced to deny' that they were involved in his kidnapping. David Cameron's wife 'forced to deny' that she once voted Labour. And many more. 

In almost all cases, the allegations that people have been 'forced to deny' have themselves been made by the newspapers. This is the media at it's worst. Not only do they report non-stories on flimsy evidence, they then report the fact that someone reported it!

Friday, 19 March 2010

Completely Inane Newspaper Stories Part III: John Terry didn't drink and drive

I know I haven't done one of these for a while, and I know I said I'd avoid celebrity stories, but I just couldn't resist this: on the front page(!) of yesterday's Guardian, we had the following dramatic piece of news:

John Terry in more trouble after hitting Chelsea steward with car

Sounds pretty drastic, especially as it was considered important enough to make the front page of a generally reasonably respectable national newspaper. Let's look at some of the details:
"Terry was then questioned and breathalysed by police in the small hours after accidentally running over a Chelsea steward as he left Stamford Bridge."
Oh, so it was an accident, that's less exciting that it could have been. Presumably the steward is badly injured though? Or Terry drove off without trying to help him? Also, he was breathalysed: presumably the reason we are being told this is because he had been drinking and not, say, because police always breathalyse anyone that was involved in any sort of accident, especially if they're John Terry. Surely there must be *some* reason that this story is more interesting that, say the legal status of mephodrone, the entire Nigerian cabinet being sacked or how election campaigns are run. All of which were relegated to the inside of the paper. Well, let's look at some details:
"Terry and his wife Toni..., were oblivious to the accident until he was contacted by the club on returning home"
So, hardly a hit and run.
"Surrey police breathalysed the player, who was found to be within the legal alcohol limit... He hadn't had a single drop to drink"
So, not a drink driving incident (and the fact that he was forced to take a breathalsyer test is about as interesting as telling us that he was forced to give his name to the police, or that he was forced to turn the key in his ignition before car would start).
Rowley said: "Contrary to media reports I did not suffer a broken leg. It is badly bruised.
So, not even a broken bone. Surely there must be *some* reason that this story is news (and some justification for the claim that Terry is in "further trouble" - at least Terry must be to blame for the incident
, right. Well, I'll leave Rowley with the last word on that:
"It wasn't his fault at all, it was a complete accident."
So, a complete non-story, and it makes the front page of the Guardian. Bring back dog x-rays, all is forgiven.

Friday, 12 March 2010

QMUL sells quackery: The Correspondence

Edit (Mar 13): Just got a very nice reply from Charlotte. Says she was busy last week, but would like to meet in person to discuss this at some point. I'll try to arrange a meeting for sometime next week and report back here.

I wrote about this at the weekend. QMUL  sells homeopathy, and actively advertises it in the reception of the gym. I don't think they should, and would like to find out why they do.
So, on Monday, I sent the email below to Charlotte Kendrick, the manager of QMotion, who I was advised by Simon Levey was probably the person to contact about this. In retrospect, I regret the tone of the email. It is both unnecessarily confrontational and overbearingly condescending (as well as quite officious). I haven't yet had a reply, but I'm not altogether surprised. I've also sent the following message today, requesting a reply in slightly more temperate language:

Today's message:
Dear Charlotte,

I'd like to apologise for the tone of my last email: it was unnecessarily confrontational, especially as I have no idea how much involvement you personally had with the decision to allow homeopaths to use university facilities. However, this is an important issue that I feel quite strongly about, and I would appreciate a reply. If you're not the person I should be contacting about this, please let me know who is, and I'll start bothering them instead.

Monday's (heat of the moment) message. Note the particularly cringe-y "I don't mean to be patronising" - it's almost completely impossible to either say or write those words without a. being patronising and b. sounding like a dick. (even if I did genuinely mean them).
Dear Charlotte,

I am a member of the QMotion gym, and a PhD student in the maths department at Queen Mary University. I was somewhat surprised, and frankly quite disappointed, when I noticed the other day that QMotion allows a homeopath to use their treatment rooms once a week, and actively advertises homeopathy as a 'safe and gentle form of complimentary (sic) medicine' which 'can be used to treat most diseases'. Homeopathy is an anti-scientific and ineffective medicine, which has been shown time and time again to perform no better than a placebo in randomised controlled trials (I'm more than willing to provide citations for this if you need them). I don't think that QMotion should be encouraging its use and I was told that you were probably the person to contact about this.

I suggest that the relationship between QMotion and Surrey Homeopathy for Health be ended as soon as possible, and if this is not to be done, would at least like an explanation as to why you (or whoever is in charge of these decisions) consider it appropriate to continue to associate the name of the Student Union (and by extension the University) with a treatment which has absolutely no credible theory to support it and no evidence whatever for its efficacy.


PS - I don't mean to be patronising, but in my experience many people simply aren't aware of quite how ridiculous the rationale behind homeopathy is. In case you're one of those people, here's a good explanation (written by Matt Parker, who also works in the maths department) http://timesonline.typepad.com/science/2010/01/homeopathy-by-the-mindboggling-numbers.html

PPS - I have already written about this on my blog (http://eucalculia.blogspot.com) and will probably post some/all of any reply you send me there. Hope you don't have a problem with this.

Saturday, 6 March 2010

QMUL sells quackery

Just noticed this one my way out of the gym today:
Homeopathy is a safe and natural form of complementary medicine, which has helped many people suffering from all varieties of ailments to regain and retain their health and wellbeing. The Homeopath will look at each patient individually in an attempt to discover the core reasons for their problem and choose specific remedies to change the soil within the person from which the disease stems.
Now, I'm not entirely sure who gets to decide what services are and aren't offered at QMotion - I imagine it's probably owned by the Students Union, and I'm currently trying to figure out who I should complain to. I don't see how the university can possibly justify advertising medicine which just doesn't work. I'm mostly too shocked about this to write anything particularly incisive right now (and anyone reading this is fully aware that homeopathy just doesn't work anyway), but I am genuinely going to try my best to figure out who I should complain to, and how to get these people out of the university-owned gym.

Incidentally, they claim to 'treat' IBS, hayfever, and a long list of other named diseases on the literature that's available inside the gym (and on this page, they appear to be specifically claiming to be able to cure them). I thought homeopaths were banned from claiming to cure specific diseases?

Thursday, 18 February 2010

Bloody Mary at the SE Frisbee Regionals

I played in the South Eastern University Regionals Ulitmate Fribsee tournament last weekend for the Queen Mary "Bloody Mary" team. I woke up on Monday morning more sore than I can ever remember being, but had a great time, and I've decided to write "the report" for the weekend. It's pretty long, so I've put most of it below the fold: if you don't want to read that far, here's a summary: we finished 10th, out of 23, after being seeded 23rd, with only 6 players, finished second in a 3 pint challenge, and partied at least as hard as any of the other teams. All in all, a pretty awesome weekend.

Incidentally, this is all pretty much steam-of-consciousness, and I can't be bothered to edit it, so please forgive any typos/spelling errors/factual inaccuracies/blatant lies. Names have *not* been changed to protect the innocent!

Click here to read the rest