Considering the Alternative

If you were faced with a choice, and receiving $100 was one option, would you choose it? If the other choice was to receive $1000, you probably wouldn’t; if the alternative was getting kicked in the shin, you’d probably take the hundred bucks. In decision making, different options can not be rationally evaluated on their own, only compared to each other. What’s important are the differences between the expected outcomes of the choices. The best choice is the one that tends to produce the best outcome relative to the other options. Continue reading

Probability and Logic

The type of probability theory that dominates most of the sciences is called frequentism, but this version of probability is based on a mistaken idea about the nature of randomness. Another interpretation of probability, Bayesian probability, not only corresponds better with people’s intuitive concept of chance, but can also be interpreted as a logic that is consistent with the laws of probability. Continue reading

Evidence and Beliefs

Evidence is the connection between our beliefs and the real world; it is how information flows and spreads through relationships of cause and effect. When information from the world reaches our senses and arrives in our brains, its patterns are analyzed. In this way our brains build up a representation of the patterns of the world. To borrow Alfred Korzybski’s famous map/territory metaphor, evidence is what connects the “map” in your head with the “territory” in the real world. Continue reading


Research in several academic fields, especially in the last few decades, has given us a new perspective on our own minds. These are the fields at the confluence of science and philosophy: fields like experimental psychology, probability theory, decision theory, information theory and artificial intelligence. In these disciplines we have begun to examine human reasoning and knowledge itself, and to attempt to explain how they work. Here we have developed powerful tools for understanding our world. Rationality is about applying these tools to our thoughts and actions in order to systematically optimize our lives and our world. 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