A ‘derivative’ is the rate of change of a slope on a graph. If you had a graph of time (seconds) and distance (metres), the shape of the line tells you something about the speed (metres per second). If the line is straight, your speed is constant. If the line is curved, your speed is changing. A derivative measures the slope of the curve at an exac

Imagine you do some study to test some hypothesis – we won’t say what it is yet – and you get a p-value of 0.02. How likely is it that your hypothesis is true? It’s an annoying fact that a large number of people who definitely should know better would say that the probability is 98 per cent. The chance of seeing those results by chance is one in fi

Pascal’s Triangle is only one way of working out the probability of seeing some number of outcomes, although it’s a very neat way. In situations where there are two possible outcomes, like flipping a coin, it’s called a ‘binomial distribution’.

Life isn’t chess, a game of perfect information, one that can in theory be ‘solved’. It’s poker, a game where you’re trying to make the best decisions using the limited information you have.

probability ‘is an expression of our lack of knowledge about the world’.43

But the point is that when you’re trying to work out how likely something is, what we need to talk about is the number of outcomes – the number of outcomes that result in whatever it is you’re talking about, and the total number of possible outcomes. This was, I think it’s fair to say, the first real formalisation of the idea of ‘probability’.

And we’re Bayesian at a deeper level, too. Our brains, our perception, seem to work by predicting the world – prior probabilities – and updating those predictions with information from our senses: new data. Our conscious experience of the world can be best described as our priors. I predict, therefore I am.

Jeffreys himself wrote: ‘[E]very scientific advance involves a transition from complete ignorance, through a stage of partial knowledge based on evidence becoming gradually more conclusive, to the stage of practical certainty.’ The uncertain parts of science, he said, are ‘the most interesting part’.96

‘Necessarily,’ wrote David Howie, a historian of statistics, ‘these inferences were tentative. They were advanced not with certainty but with degrees of confidence that were updated or modified to account for new information.’95 That is: they were done in a Bayesian fashion. Each time Jeffreys got new information, he updated his prior confidence in