Author Archives: blueocean

How many games are there in a tournament?

In keeping with the football spirit, I’m going to use the format of the FIFA World Cup as an example to show you how to calculate the total number of matches/games played in a tournament. There are two cases that we need to consider: 1. The league stage – where every team plays every other team in a group 2. The knockout stage, which follows a structure like that shown in the picture above, until one team is declared the […]

5 alternative World Cup predictions

It’s less than a week to go until the start of the 2010 FIFA Football World Cup – the second biggest sporting event in the world, after the Olympics. As always, before any sort of tournament, there will be predictions, wagers, speculation etc. on matters such as who will win, who will score the most goals, and so on. Whilst all that is very entertaining, it gets a little boring after the same things are said by 100 different sports […]

Mouse activity

I discovered a neat bit of software last week. It’s called IOGraph and you can download it here for Windows, OSX or Linux. If you leave it running in the background, it will trace your mouse movements. It will also put a ‘blob’ where your mouse movement comes to a stop. The bigger the dot, the more time the mouse has been left in that position. Although the intention for it was to be an artistic application, I had a […]

Who should you vote for? Download my Election Model!

I’m sure you know that next Thursday, the UK is going to have a general election. And I’m also pretty sure that you’re sick of hearing about it all over the media. Random interviews with MPs spewing out generic garbage litter the news channels. It’s worse than a playground squabble. Something that is as important as you helping to decide the future of the UK has, as usual, been trivialised into some X Factor-esque popularity contest. I know what my […]

Daniel Kahneman, Loss Aversion and a video

Out of all of the various areas and branches of economics, none has captured my interest more than ‘behavioural economics’. This studies the links between psychology and economics to try to discover more about how the individual thinks when faced with decisions. It brings to light the irrationality of the human being, and the flaws of many classical economic models, which assume rational behaviour at all times. Israeli psychologist Daniel Kahneman was one of the pioneers of this field of […]

Dutch Auction Shops

Japan have been struggling for some time with poor aggregate demand in their economy. The interest rate has been near zero (and actually zero at some points) for a very long time to try and stimulate borrowing and investment. I saw an interesting programme on NHK World (Japanese news channel) a few weeks ago. It was about consumption and consumer attitudes in Japan. Lots of things both surprised and intrigued me, such as the fact that the youth of Japan […]

Cost Curves and a Nice Proof

As I like to do before getting down to some hardcore maths, I’m going to take an artistic break and present to you a Haiku that I wrote a couple of days ago: The flower withers Petal falls on wilted earth New shoot takes its place There, that’s enough of the artsy fartsy stuff for now. What’s all this about? I will firstly explain briefly what cost curves are, and why they look like they do. I will then go […]

Top 20 Favourite Games of All Time

In the world of digital entertainment, some games have transcended the boundaries and managed to create artistic, intelligent and immersive experiences that cannot be matched. I thought I’d sit down and think about the computer games that have had the biggest impact – on me and the gaming world. Here are my top 20 games of all time. 20. Worms: Armageddon (PC – 1999) Probably the most innovative multiplayer strategy game ever made. The Worms series throws teams of up […]

Present Discounted Value

Before we get down to the maths, let me digress to explain why there is a still from BBC’s motoring magazine Top Gear at the top of this page. In the last few series of the show, I have noticed an interesting tendency for BBC to include attractive women in the camera shot whilst the presenters are sitting in the foreground. The image above shows a prime example of this. Whether this is a conscious attempt at subliminal messaging targeted […]

Cycle your way to musical theory

Modes. They seem to be difficult for many musicians to get the hang of. Fortunately, I’ve found that the easiest way to understand them and to explain them lies in a nice bit of maths. A quick note on Cycles Cycles are a neat piece of mathematics, lying as a part of permutations within the realms of combinatorics and algebra. Despite its simple nature, it has very powerful applications. Let me give you a short introduction. A permutation of a […]

Why I love… Elasto Mania

Elasto Mania became a cult classic game around 8 years ago when I was in high school. It swept our school network (and many others) like a class A drug – you know it will suck you into its world, but the draw of being there is too strong to resist. Not that I have any experience with narcotics, mind. It was created by independent Hungarian developer Balázs Rózsa in 2000 – someone who surely has earned the respect of […]

Mathematical Music

Maths and music. Probably my two favourite subjects, and yet, two things that are often considered as mutually exclusive. But this is very, very far from the truth. Much research has been done to show that logicians and mathematicians are often very talented musicians. History also supports this fact (I have linked to a couple of interesting articles at the end of this one that go into more detail about this). There are more direct mathematical links to be found […]