Author: Brendon Brewer

What Experts Do and Don’t Know

Some recent political events, from the result of the Brexit referendum to the nomination of Donald Trump as the Republican candidate in the US election, have been described in terms of clashes between the views of two tribes of people, often described as experts or elites and those who trust them on one side, and ordinary people on the other. While one may argue for one side or another on these specific issues, or have a preference for the views of experts or ordinary people in general, reflexively taking sides on this basis is neither principled nor likely to lead to correct judgments. Personally, I have a Bachelor’s degree in physics and applied mathematics, a PhD in astrophysics, and an academic career in statistics. I know what it’s like to be an expert in a couple of small areas, and how easy it is to imagine myself as one in other areas. Many of my friends are smart academics, and usually fall on the expert side of the discourse. I understand their frustration and anger …

The Mathematics of Happiness

If you could choose between these two possible lives, which would you prefer? (1) You struggle through difficulties, challenges, and a fair amount of misery for 60 years, after which you emerge wise and content. You die at age 80. (2) You spend the first 60 years indulging in relatively shallow pleasures. At age 60, you develop a chronic health condition where you can no longer do many things you enjoy, and you spend the last 20 years of your life regretting that you didn’t do anything very meaningful with the first 60. A conundrum along these lines came up during a recent episode of Sam Harris’s podcast [1], with guest Jonathan Haidt. I am a big fan of these two — their recent books, Waking Up and The Righteous Mind by Harris and Haidt respectively, were both life-changing for me, so I had been looking forward to the episode for a long time. In the podcast (starting at 1:30:48), Haidt used an example like the one above to argue that utilitarian conceptions of the …

Unscrambling the Second Law of Thermodynamics

The second law of thermodynamics surely qualifies as one of the most talked-about principles in all of physics. Depending on who you ask, it is either incredibly mysterious or fairly mundane. Some physicists think the second law is connected to fundamental ideas such as time and the origin of the universe,1 yet it is also an aspect of everyday experiences, such as how a morning cup of coffee cools down, or the fact that you cannot unscramble an egg. The second law has even been invoked by rock band Muse to explain why, in their view, economic growth cannot continue for much longer.2 However, trying to find a clear explanation of what the second law actually is (and why it is true) can be a frustrating experience. I first encountered the second law as a teenager, while reading an issue of the fundamentalist Christian magazine Creation, given to me by my grandmother. Since the article’s author wanted to argue against biological evolution, it claimed that the second law of thermodynamics implies evolution is impossible. Its …

The Great Statistical Schism

What is probability? This sounds like a discussion question for a philosophy class, one of those questions that’s fun to think about but that doesn’t have many practical consequences. Surprisingly, this is not the case. As it turns out, different answers to this question lead to completely different views of how to do statistics and data analysis in practice. In the early 20th century, this led to a split in the field of statistics, with intense debates taking place about whose methods and ways of thinking were better. Unfortunately, the wrong side won the debate and their ideas still dominate mainstream statistics, a situation which has exacerbated the reproducibility crises affecting science today [1]. Here’s a common, standard statistical inference problem. An old drug successfully treats 70% of patients. To test a new drug, researchers give it to 100 patients, 83 of whom recover. Based on this evidence, how certain should we be that the new drug is worse than, identical to, or better than the old one? If you think it is legitimate to …