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!

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?

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.

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?

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?

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?

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?

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