Maths is full of cool theorems. The Pigeonhole Principle is one of my favourites because of the fact that it is so powerful and quite tricky to prove, yet so intuitive and easy to understand. Before I can talk about it though, I need to introduce you to the world of mathematical functions. Functions In maths, a function is a ‘mapping’ from one ‘space’ to another. The ones that people are used to seeing are things like f(x) = x2 […]
In high school, I remember thinking how our grading system was a total farce. We weren’t graded on ‘results’, allegedly. Instead, our teachers gave us a grading based on our ‘effort’. There were 5 grades in total: C – Commendable G – Good S – Satisfactory D – Disappointing U – Unsatisfactory To me this was complete nonsense, because effort is not observable! What the teachers did was to look at the end product, and use that to infer some […]
Yum. Breakfast is my favourite meal of the day. And hopefully, you should all know by now that skipping it is not a good idea. Breakfast cereals are big business – other than toast, cereals are by far the most common way to start the day. But how nutritious are these cereals? I decided to find out. I managed to collect nutritional information for 117 of the major branded cereals in the UK. After whacking them into a great big […]
Pythagoras’ theorem is one of the beauties of mathematics. Something so simple as being able to work out sides of a right angled triangle has had pretty much unlimited use in practical engineering as well as very theoretical linear algebra and calculus. For those of you less mathematically inclined, I’ll explain briefly what the theorem says and then show you a nice real-world application of it. The Theorem If your years of mathematics are long gone and forgotten, then Pythagoras’ […]
Labour economists devote much of their time to looking at what factors affect wages. The classic regressions they run show that you are likely to have a higher wage if you’ve been to school for more years and if you have more work experience. This seems pretty intuitive and obvious. They’ve also looked at how IQ/intelligence affects wages. The general consensus is the common sense one – you earn more if you’re smarter. Again, this makes sense intuitively. There’s a […]
‘Pupillary Distance’ is an ophthalmic term. It means, quite simply, the distance between your pupils. If you wear glasses, then you may remember the optician putting a strange metal frame on you and rotating some markers on the top of it before you have a pair made. This is how they measure your pupillary distance (hereafter, ‘PD’). The PD is an important measurement, because the curvature of the lens must be centred around your pupil in order for you to […]
Back when the Ultimate Fighting Championship (UFC) was in its infancy, there were very few rules. Ex-presidential candidate John McCain actually described it as the human equivalent of a cock fight, and to be fair to him, the lack of rules made for a rather unsavoury spectacle in some cases. One of the most notable cases in question happened in UFC 4, when strikes to the groin were completely legal. It saw Keith Hackney punch Joe Son (in the photo) […]
What are ‘sunk costs’? ‘Sunk cost’ is a term commonly used in economics. It refers to a cost that you or a firm might incur which is irretrievable – you can’t get it back. Suppose you own a large cheese company which has a cheese factory. You want to build an extension to your factory after a bumper year of exotic cheese sales (sorry, it’s lunchtime). If you bought some steel girders for £100,000 to lay some sort of framework […]
Well, the World Cup has been and gone. Enthralling as always, this time the tournament proved to be more of a tactical battle. Although I felt Germany deserved to win, Spain did manage to stamp their authority and lose their ‘perennial underachiever’ status. Let’s look back at my prior predictions to compare them to what really happened… 1. Team that completely meets expectations Prediction: Democratic People’s Republic of Korea (North Korea) No surprise that I was spot-on here. […]
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 […]
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 […]
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 […]