[Note: I post my monthly newsletters to the blog with a one month delay. If you’d like to get them when they’re first shared, join my mailing list.]

Hello everyone, and welcome to the month of May! When I lived in Oxford, they celebrated May Day by singing madrigals and dancing around maypoles. When I lived in Berlin, they celebrated it by chanting workers’ slogans and setting cars on fire. Here in Vancouver, May is starting with fair weather and I’m about to go for a hike.
 
At the start of April, I wrapped up my winter session of online classes and I ended the month by announcing my summer class. Starting at the beginning of June, I’m offering a course that focuses on philosophy written in the last one hundred years. “How Should We Live? Answers from the Modern World” confronts the distinctive challenge of finding meaning in a world shaped by secularism, pluralism, and change, and explores some of the ways that older traditions have been given fresh meaning in this modern context.
 
You can choose between three weekly class times: Wednesdays or Thursdays at 11am Pacific/2pm Eastern/7pm UK & Ireland/8pm Europe or on Wednesdays at 6pm Pacific/9pm Eastern. We’ll have a first introductory session on June 1/2 and then meet weekly for 75 minutes until August 10/11. Each weekly session is accompanied by a video lecture and a short reading guide.
 
The course fee is $349 CAD, which works out to about $275 USD, £215, or €255. I want to make sure everyone has a chance to experience the course before making a firm commitment, so I offer a no-questions-asked money-back guarantee up to the start of the second full week of class.
 
In surveys from past courses, 76% of respondents describe the courses as “excellent value for money.” That said, I realize not everyone can afford a course at this price. I want to make philosophy accessible to as many people as possible, so I also offer a limited number of pay-what-you-can spots for those who can’t afford the full course fee. Just let me know if you’d like to exercise this option.
 
And if you expect to be in Vancouver in late May, I’d love to discuss philosophy with you in person! I’m offering my first in-person course at the end of May, a weekend intensive called “The Story of Your Life: Life and Narrative.” The course explores the relationship between a life as lived and the stories we tell about it. We’ll investigate whether and in what way the shape of a life and the shape of a narrative coincide. Email me if you’d like to learn more.
 
In other philosophy news, the last week of April was a busy one. I gave two talks, one to the British Wittgenstein Society and the other to the Environmental Managers Association of British Columbia—two organizations whose only common feature is that they both have “British” in the title. A recording of the first talk, on Wittgenstein and existentialism, is now available on the BWS website. The second talk, on existential anxiety in a time of environmental change, was a fun opportunity to bring philosophy to a broader audience. I also do birthday parties.
 
April tends to be a rainy month in Vancouver but up in the mountains that rain still falls as snow. I managed to get away from my work in mid-April for a beautiful day of snowshoeing up to Hollyburn Mountain with a terrific view over the city.

(The following mini-essay is a bit longer than the norm for my monthly newsletters. Reading it will take you around five to ten minutes.)

The meaning of life in one simple equation

The question of how we should live is subtle and complex. It doesn’t seem like the kind of thing that can get boiled down to a mathematical formula. But try this one on for size:

That formula is called Bayes’ Theorem. It plays an important role in probability theory. I learned it in high school. You might have done too. But I only learned much later that some people see in it a profound and important source of life guidance.

Bayes’ Theorem, or more precisely Bayesian updating, was on my mind a lot during and after my jury duty in late March. (By the way, I wrote a short article about my experience, which should be published in the Globe and Mail newspaper next weekend.) I found myself thinking that a crash course in critical thinking could be a helpful prerequisite to jury duty.

I’ll explain how Bayesian updating might be put to use in a jury context first, and then say a bit about its applicability to life more generally. I’ll give an example of Bayesian updating without unpacking the equation itself. If you’re curious about the math, you can find a short explainer here.

Bayesian updating for jurors

The role of a juror is to assess and weigh evidence. Over the course of a trial, the jury is presented with a bundle of evidence in the form of sworn testimony and physical exhibits. The prosecution and defense agree on what the evidence is—and it’s to the judge to determine what gets to count as evidence and what should be excluded—but they present the jury with different arguments about what that evidence shows. The prosecution tries to persuade the jury that the evidence is proof of guilt. The defense tries to persuade the jury that the evidence fails to establish the burden of proof required for a guilty verdict.

As a juror, then, your job is to determine what the evidence you see is evidence for and how strong that evidence is. Bayesian updating can help you do that.

Suppose you’re a juror in a trial in which Annie is accused of having stolen a cookie from the cookie jar. (The trial I served in wasn’t about cookie larceny but this is a family-friendly newsletter and some of the details of that case were decidedly not family friendly.) One piece of evidence you encounter in the trial is a trail of cookie crumbs leading from the cookie jar to Annie’s bedroom. The prosecution claims this evidence clearly points to Annie’s guilt. In her defense, Annie claims the dog took the cookie and carried it off to her room, sprinkling crumbs as it went.

Here we have two stories, both of which could be true. So surely we have reasonable doubt here and Annie gets off the hook? Perhaps, but not so fast. Let’s first consider how strong the evidence of the crumbs is. Here’s where Bayesian updating can help us.

Let’s suppose that, up to this point in the trial, you’re on the fence as to Annie’s guilt: you think there’s an even 50/50 chance that she’s guilty as charged. This is the prior probability you assign to Annie’s guilt—that is, your assessment of the situation prior to this new piece of evidence.

Next, you want to consider the two rival stories. Story A is that Annie stole the cookie. Story B is that the dog stole the cookie. Our natural tendency is to consider how likely each of these stories is in light of the evidence. And since both stories line up with the evidence, we might be inclined to find them equally likely.

Bayes’ Theorem instructs us instead to ask the converse question: how likely is it that we would encounter this evidence if each given story were true? Suppose, to begin with, that Annie stole the cookie. How likely is it in that case that we might expect to find a trail of cookie crumbs leading from the cookie jar to Annie’s bedroom? If Annie knows she’s not to eat the cookie, she’d likely take it to her bedroom where she could enjoy it hidden from view. So let’s assign a probability of 80% to the proposition that there would be a trail of crumbs leading to Annie’s bedroom if story A were true.

Now suppose that the dog stole the cookie. If story B were true, how likely is it that we’d find a trail of crumbs leading to Annie’s bedroom? Well, the dog might have taken the cookie to Annie’s bedroom. It’s not impossible, but it’s unlikely—why would the dog take the cookie there rather than somewhere else? Let’s say there’s just a 10% chance that the dog would take the cookie to Annie’s bedroom.

So now we have a rough picture of the strength of the evidence. We’ve determined that this evidence is 80% likely if story A is true and 10% likely if story B is true. That means that, when we’re presented with the evidence of the trail of cookie crumbs, we should say that it strengthens our confidence in story A over story B by a multiple of 8, since 80% is eight times 10%.

Now return to our prior probability: those 50/50 odds we’d assigned to Annie’s guilt. If this new evidence has a strength factor of 8, that means we should revise our prior probability accordingly. Our updated probability should reflect that new evidence and we should now think the odds are eight-to-one that Annie is guilty.

Bayesian updating for life

Bayes’ Theorem is a method for aligning your beliefs with your evidence. In Bayesian language, the theorem teaches us how to “update our priors” in the light of new evidence—that is, how new evidence should affect our beliefs. Since we form beliefs based on evidence in all walks of life—in fact, all of our beliefs have some basis in evidence, however tenuous—it has application well beyond the context of a jury trial.

And it’s not just that Bayes’ Theorem can be widely applied. Some argue forcefully that it should be widely applied. Bayes’ Theorem is a critical tool in helping us to overcome irrational thinking.

To begin with, humans are just naturally bad at thinking with probabilities. People’s intuitions are a surprisingly good guide when making eyeball judgments of raw quantities—in guessing the number of jellybeans in a jar, for instance. But intuitions go wildly askew when people make judgments about probabilities. Even trained doctors tend to underestimate the probability of false positives in diagnostic tests by a wide margin. So learning how to reason probabilistically helps us with a natural blind spot.

More important, we have a strong tendency not to think of our beliefs in terms of probabilities. When people adopt beliefs, they tend to treat them as possessions and guard them jealously. The well-studied phenomenon of confirmation bias exposes our tendency to seek out evidence that supports our prior beliefs and to impatiently brush aside evidence that conflicts with our beliefs. If you pay any attention to politics, you’ll recognize what I’m talking about.

Imagine treating your beliefs not as certainties that must be defended against attack but as probabilities. Suppose I reckon that I’m 80% confident in my belief that such-and-such policy is the best approach to immigration in my country or that I’m 70% confident that such-and-such career move will best help me realize my goals. Then I can take on new considerations that might strengthen or weaken my confidence in these beliefs without having to take an all-or-nothing defensive attitude toward them. Loosening my identification with my beliefs and treating them probabilistically strengthens my meta-cognitive skills—that is, my ability to reflect on my own thinking and to examine it critically.

A community devoted to thinking more rationally has taken Bayesian reasoning as its lodestar. They cluster in forums like LessWrong and the Center for Applied Rationality. (LessWrong in particular has a reputation for attracting empathy-challenged young white men so follow this lead with due caution. You can read a fascinating critical profile of the movement in this New Yorker article.) They view Bayesian reasoning and the mindset it promotes—open, rational, mindful of biases—as a full-fledged guide to living well.

Sages and mystics of many stripes have claimed that the secret to life lies in hidden in some unexpected place. An equation from probability theory devised by an eighteenth-century statistician is certainly not the least unusual.