Simpson’s Paradox

People can often get things very wrong when they try to read advanced material from a field before they understand the basics, and this matters today because so many people – often driven by a distrust of science and medicine – insist on “doing their own research”. Working out cause and effect from simple statistical data can seem easy, straightforward and intuitive, but it’s not. Continue reading

The Art of Human Rationality

For anyone who wants to believe that the Apollo moon landings were faked, or that MMR vaccine causes autism, or even that we’re ruled by lizard people, an internet search will quickly oblige your curiosity with plenty of sophisticated arguments – not to mention a supportive community of other believers – to permit you to believe what you sought to. But if you’d like to figure out what’s actually true, this strategy is rather poor. Continue reading

Social Networks and Nuclear Physics

A chain reaction is a phenomenon that happens when one event can cause similar events to occur. The main thing that the outcomes of these chain reaction phenomena all depend on critically on is the answer to one question: how many additional events does each event cause on average? The outcome of a chain reaction can be dramatically different depending on this number. Continue reading

The Quick Draw Game – Part 2 – Exploration and Exploitation

In Quick Draw you don’t actually have five seconds to draw the chosen subject, because you have to use part of the five seconds to decide how you’re going to draw it. The most important skill in the game is deciding how much of the five seconds you spend thinking about what you’re going to draw, and how much you spend actually drawing. Making this decision involves solving a problem known as the exploration/exploitation tradeoff. Continue reading


Welcome to Rational Numbers. My name is James Kay.

I’m a PhD candidate in the faculty of applied science at the University of British Columbia. My academic research is in the field of materials science, but I’m also interested more generally in science, mathematics, philosophy, rationality, games and probability theory. Rational Numbers is my way to share ideas about all these topics. Continue reading