From the post: I’ll tell you a secret: when I read a statistical statement I often wonder whether it’s a temporal statement or an ensemble statement. Do you do that too? Take this headline for example: “Young black people nine times more likely to be jailed than young white people” from The Guardian. I won’t talk about why this might be, that’s not the point of this post. My point, as usual, is about time versus ensembles. If you read the Guardian article, you’ll find that the headline is an ensemble statement. It’s supposed to convey that the proportion of the ensemble of black people under the age of 18 in the UK who were in jail (in a broad sense) when statistics were collected was nine times higher (0.09%) than the corresponding figure for white people (0.01%). It would be a temporal statement if it meant that your friend David, who is black, spent around 142 hours in jail before he turned 18, whereas your friend Luigi, who is white, spent only around 16 hours in jail before he turned 18. It obviously doesn’t mean that, but — perhaps less obviously — it also doesn’t mean that when David was born he was in any meaningful way 9 times more likely than Luigi to be in jail before they turned 18 — what happens along a single life path over time is not reflected by these aggregate figures. The word “likely” does not specify whether the probabilities it reflects are relative frequencies in an ensemble or in time. Such unspecific language is problematic when only one interpretation is correct. So: people’s experiences of the penal system are best not talked about in probabilistic terms. Let’s generalize this recommendation: we shouldn’t talk about anything in probabilistic terms unless we’re convinced that the time and ensemble interpretations of what we’re saying are equivalent. Nassim Taleb, in his latest book, put it laconically as “no probability without ergodicity.” It’s not just this one example — lots of statistical statements are phrased in probabilistic language, with the implicit (and often false) assumption that ensemble-interpretations and temporal interpretations of that language will be equivalent. That assumption is called the “ergodic hypothesis.” In the guardian example, just reading the headline and then wrongly assuming ergodicity can quite easily lead to horrendous misinterpretations, so let’s watch our language, seriously.