The Better Letter: Math Mandate

We should all be able to agree on a math mandate.

According to the most recent information from Secretary of State Antony Blinken, U.S. and coalition forces have evacuated approximately 82,300 people out of Kabul, Afghanistan since August 14. According to the Biden administration’s analysis, between 500 and 1,500 Americans seeking evacuation remain in the country. Blinken said the administration has been “aggressively” reaching out to about 1,000 contacts who may be Americans, but noted some may no longer be in the country, have chosen to stay, or erroneously claimed to be American. The U.S. Embassy in Kabul issued an alert Wednesday night advising U.S. citizens to avoid traveling to the airport — or “leave immediately” — due to “security threats outside the gates.” 

Those threats proved all too real yesterday.

An American defeat became a retreat became a debacle and then a tragedy. Allowing anti-American jihadists time and space to operate in a country controlled by an anti-American jihadist regime will lead to terrorism against Americans. Beyond that obvious reality, it’s way too early for me to do more than note my devout wish that things will get better there, and soon. May God bless the families of the fallen, who “gave the last full measure of devotion.” 

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Math Mandate 

We are all prone to innumeracy, which is “the mathematical counterpart of illiteracy,” according to Douglas Hofstadter. It describes “a person’s inability to make sense of the numbers that run their lives.” Although Hofstadter coined the term, mathematician John Allen Paulos popularized the concept with his book, Innumeracy: Mathematical Illiteracy and Its Consequences. While illiteracy strikes mostly the uneducated, we are all prone to innumeracy. More students find math their most difficult subject than any other.

We’re even worse at probability.

If a weather forecaster says that there is an 80 percent chance of rain and it remains sunny, instead of determining if it rains 80 out of every 100 times within an adequately sized sample of times when his or her forecast called for an 80 percent chance of rain, we race to conclude — perhaps based upon that single instance — that the forecaster isn’t any good. Data trumps our lyin’ eyes, but we don’t routinely see it.

This problem was addressed during a discussion between two of the world’s leading thinkers about decision-making under uncertainty, Nassim Taleb and Daniel Kahneman. Throughout the conversation, Kahneman evaluates Taleb’s ideas through the lens of psychology and often highlights the contrasts. 

When someone in the audience asked why it is so difficult for people generally to compute and deal with probabilities, Kahneman offers an interesting answer. He did not point to innumeracy. Instead, he said, “to compute probabilities you need to keep several possibilities in your mind at once. It’s difficult for most people. Typically, we have a single story with a theme. People have a sense of propensity, that the system is more likely to do one thing than the other, but it’s quite different from the probabilities where you have to think of two possibilities and weigh their relative chances of happening.”

We prefer to think linearly, manufacturing a storyline, in effect, with a beginning, middle, and end. That’s why we are so susceptible to the “narrative fallacy.” We inherently prefer stories to data. Contingencies and (often random) consequences don’t correspond to the way we like to see the world. We are — pretty much all the time — either looking backward and creating a pattern to fit events and constructing a story that explains what happened along with what caused it to happen, fitting what we see or assume we see into a preconceived narrative, or both.

Carleton Young is all but forgotten except for his immortal turn as the newspaper editor in The Man Who Shot Liberty Valance, in which his most famous line is truer today than the day he shot the scene. When the legend and the facts are at odds, “Print the legend.” 

In politics, as in life, people choose their loyalties early. Once that happens, little will change them – even extensive and expensive campaigns of “education.” Multiple studies dating well before any effective vaccines were developed consistently found that 35 percent of Americans were unlikely and 20 percent highly unlikely to take any vaccine to combat Covid-19. That stance is a matter of tribe and conviction rather than information — true or false — about the vaccines themselves.

Dealing effectively with math and probabilities demands that we recognize the power of the random and the contingent. No matter how good a story we have concocted with respect to what we expect to happen, no matter how careful our analysis, stuff happens that can and often does mess up and with our hopes, dreams, and schemes. 

For example, most people would consider it an unlikely coincidence if any two people would share the same birthday in a room with 23 people in it. People would generally look at it like this: since one would need 366 people (in a non-leap year) in a room to be certain of finding two people with the same birthday, then it seems to make sense that there is only a 6.28 percent chance of that happening with only 23 people in a room (23 divided by 366). However, 99 percent probability is actually reached with just 57 people in a room and 50 percent probability exists with only 23 people (see more on the “birthday problem” here).

In the investment world, we intuitively tend to think that if we start with $1,000 and suffer a 50 percent loss on Day 1 but make 50 percent back on Day 2 (day-to-day volatility being exceptionally high), we’re back to even. However, were that to happen, our $1,000 would be reduced to a mere $750 (more on the “arithmetic of loss” here). Similarly, a sum of money growing at 8 percent simple interest for ten years is the same as 6 percent (6.054 percent to be exact) compounded over that same period. Most of us have trouble thinking in those terms.

These examples are pretty (pardon the pun) simple. When things get more complicated we can really go off the rails, especially when the answer seems straightforward. To illustrate, if you have two children and one of them is a boy born on a Tuesday, what is the probability you have two boys? If you do not answer 13/27 or 0.481 — as opposed to the intuitive 1/2 – you’re wrong (to find out why, go here).

The inherent biases we suffer make matters worse. For example, we’re all prone to the gambler’s fallacy. We tend to think that randomness is somehow self-correcting (the idea that if a fair coin is fairly tossed nine times in a row and it comes up heads each time, tails is more likely on the tenth toss). However, as the SEC-required commercial disclaimer takes pains to point out, past performance is not indicative of future results. On the tenth toss, the probability remains 50 percent.

The conjunction fallacy is another common problem whereby we see the conjunction of two events as being more likely than either of the events individually. Consider the following typical example. A group of people was asked if it was more probable that Linda was a bank teller or a bank teller active in the feminist movement from the following data points. “Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.” Fully 85 percent of respondents chose the latter, even though the probability of two things happening together can never be greater than that of the events occurring individually.

Now suppose that Company X has a workforce that is only 20 percent female. The base-rate fallacy might suggest that the company is discriminatory. But further analysis is required. If the applicant pool was only 10 percent female, Company X might actually have an exemplary record of hiring women. If you want to learn more in this area, you might start with this paper on teaching statistics.

In his famous 1974 Caltech commencement address, the great physicist (but general creep) Richard Feynman talked about the scientific method as the best means to achieve progress. Even so, notice what he emphasizes: “The first principle is that you must not fool yourself – and you are the easiest person to fool.” The examples above make Feynman’s point. It’s easy to fool ourselves, especially when we want to be fooled – we all really like to be right and have a vested interest in our supposed rightness. If we are going to be data-driven (and that’s a very good thing), we need to check our work and our biases very carefully anyway, and especially because we’re bad at math generally and are especially poor at probability.

Our current news cycle is full of related examples.

Let’s start with an easy one. Anecdotes – even a lot of anecdotes – are not data.

It’s also possible to misuse or misinterpret data.

The described tweet is accurate but deceptive. It’s an example of Simpson’s Paradox – a statistical phenomenon where an association between two variables in a population emerges, disappears, or reverses when the population is divided into subpopulations. As noted, a large percentage increase from a low baseline looks like a big number while a smaller percentage increase from a much higher baseline is a much bigger deal overall.* 

new CDC study looking at 43,000 infections in Los Angeles County found that, in late July, the COVID-19 hospitalization rate among unvaccinated people was more than 29 times that of fully vaccinated people. The report also determined infection rates to be about five times higher among the unvaccinated. Notwithstanding the tweet highlighted above, it should be obvious to everyone that they ought to be vaccinated.

We live in a time and a place where everything seems in dispute. We all ought to be able to agree, if we’re extremely optimistic, on a math mandate. We should strive to check and re-check our work — with help as necessary — to avoid the mathematical errors and misconceptions to which we are all so prone. No matter how poor we are at dealing with mathematical concepts, they remain largely objective and fixable.


* Simpson’s Paradox isn’t really as counterintuitive as you might think. For example, David Justice outhit Derek Jeter in both 1995 (.253 to .250) and 1996 (.321 to .314) while only hitting .270 combined for the two years, far below Jeter’s .310. Jeter played only a few games in 1995 before becoming the starting shortstop for the Yankees and winning the Rookie of the Year award in 1996. Justice, on the other hand, played far fewer games in 1996 compared to 1995 due to injury.

Totally Worth It 

On February 5, 1777, George Washington ordered the entire Continental Army inoculated against smallpox to counter both the fear of and the disease itself.

I heard the Goat Rodeo – Yo-Yo Ma, Stuart Duncan, Edgar Meyer, and Chris Thile – in concert last weekend. They were amazing. Among the songs they played was the surprising and lovely “Waltz Whitman.” 

Beatlemania began in earnest 58 years ago, on August 23, 1963, when the upstart band released “She Loves You,” which remains the band’s best-selling single in the United Kingdom.

New Jersey is the diner capital of the world. The oldest and best in the Garden State is the Summit Diner. Ernest Hemingway ate there and it could be the source of the “Cheeseburger!” sketch on Saturday Night Live.

I have eaten there dozens of times and it’s great.

Here is the best thing I read or saw this week. The best-written. The best start. The best interview. The best lede. The least surprising. The most ironic. The most impressive. The most inevitable. The most insightful. The most inspiring. The most promising. The most helpful. The most hopeful. The most chilling. The most dreadful. The most disgusting. The most tragic. The most efficient. The most amazing. The craziest. The creepiest. The stupidest. The silliest. The subtlest. The saddest. The nicest.

Rolling Stones drummer Charlie Watts died this week at the age of 80. Rock historian Jack Hamilton wrote the best piece on the band’s longtime heartbeat.

“[Watts] wouldn’t have been anyone’s pick for the world’s most technically accomplished drummer. His chops were fine but unremarkable; his sense of time would never be mistaken for a metronome. It speaks to the wonder of music, and rock ’n’ roll music in particular, that these objective shortcomings were, in fact, crucial to what made him so great. … You can’t learn to play music like this; you’re born with those ears or you’re not. No one will ever play drums like Charlie Watts, the perfect drummer in what was, once upon a time, the perfect band.”

John Pierce is an attorney who represents many January 6 insurrectionists. Last week he tweeted, “The entire 82nd Airborne couldn't make me get an experimental government vaccine stuck in my arm.” Today, he is non-responsive and on a ventilator due to Covid-19. 

Feel free to contact me via rpseawright [at] gmail [dot] com or on Twitter (@rpseawright) and let me know what you like, what you don’t like, what you’d like to see changed, and what you’d add. Don’t forget to subscribe and share.

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Beauty will change the world. This week, I’ll give beauty (and Bach) the last word.

Don’t forget to turn up the volume.

Thanks for reading.

Issue 76 (August 27, 2021)