Tag: numeracy

How to board an airplane?

MIKE

Everyone knows how to board an airplane, back to front. It’s logical. Back to front means that if someone is taking their time in seat 21C the person in 20A can still seat themselves.

Physicist Jason Steffen built a computer model to see how much faster back to front was relative to front to back. He was shocked. The difference was minimal. Hmm, Steffen scowled at his code, is there a better way?

What if instead of 30 to 1 or 1 to 30, a plane boarded everyone in row 30, then rows 1, 2, 3…. That might work right? The folks in row 30 would have time to stow and seat without holding anyone up.

That kinda works. Steffen’s code continued and compared the 30, 1, 2…29 option to the 1, 2,…30 option. The code noted the faster sequence, and switched around two more numbers. Again it kept the faster option and computed another switcheroo. The fastest boarding process turned out to be boarding every other row.

“It turns the boarding process from a serial process, where one person gets to their place, puts their luggage away, and sits down into a parallel process where you send in fifteen people, say in all the even rows, and they all put their luggage away and sit down at the same time. And then you send in the next group of people.” – Jason Steffen, August 2021

Steffen’s code was a Markov Chain Monte Carlo, a way to solve problems through computer code and exploration. But like wet bias or wait times, ideal solutions may not be the best.

One problem with Steffen’s method is when people travel in groups, especially families. Another obstacle is the culture of air travel, there’s some established norms. Further confounding the case is an airline’s incentives. Faster turns do matter, but relative to upgrades how much does saving time save the company?

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A landmark numbers walk

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We tend to remember more when things are connected. We tend to remember more when there is a story.

For instance, about 1,000 ants equal the length of one beetle. Rather, one Beetle, 1,000 of which lined end to end equal about the length of Central Park. Imagine that. One-thousand VW bugs lined up along the length of Central Park with one-thousand ants lined up along each bug.

Now another step, 1,000 Central Parks is about the width of Australia, ten of which is about the length of the equator.

That’s a nice story and it gives us some Landmark Numbers.

“What I mean by landmark numbers is something that sticks in your brain, you don’t set out to memorize it but it sticks in your brain as a reference point. It becomes a ready reference for you to relate to. These are numbers where, if you have them ready, they help you make yardstick comparisons of the things you hear about. It’s something where you hear a number on the news you go: ‘Hold on.That’s not a big number because it compares to this landmark number in some way.'” – Andrew Elliott, Talks at Google, December 2018

Another landmark number is 4 million. That’s about the number of Americans of any single age. That’s via Tim Harford.

Landmark numbers fit nicely with Maxims for thinking analytically. Richard Zeckhauser suggests that simple cases, extremes, and everyday analogues help us think better. A basic understanding needs context though, and landmark numbers provide just that.

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Similar to Landmark Numbers is thinking like Fermi.

Fermi questions, answers, and landmarks

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A Fermi question is something like, How many rolls of toilet paper do the residents of Columbus Ohio use in a week? Fermi questions are silly but embody some serious thought. Namely, how do we think about the world?

There’s some fun little math behind a Fermi question but the hardest part is often the start. For instance, how many people live in Columbus Ohio? Tim Harford knows. Rather, Tim Harford has a suggestion.

“Andrew Elliott—an entrepreneur who likes the question so much he published a book with the title Is That a Big Number?—suggests that we should all carry a few ‘landmark numbers’.”

Landmark numbers are figures we can use to guide our thoughts about the world. For instance, there are about four million Americans at any age under sixty. New York City has a population of about nine million. Columbus Ohio has a population of about one million. This is actually quite helpful just for a start.

Using a Zeckhauser maxim, “when you are having trouble getting your thinking straight, go to a simple case.” If every resident of Columbus Ohio used half a roll a week, how many rolls of toilet paper would they use? That’s easy! We have a million people, each uses half a roll, and that’s 500,000 rolls per week. No wonder we had a shortage.

Tsk tsk, Enrico Fermi would scold us. You can do better. And indeed we can. That is the point of thinking about Fermi questions. We can do better and even if we make a mistake, even if we make a few mistakes, we can still very likely be right. The reason is because of the random walk nature of our guesses. Some of our guesses will be too high (Columbus actually has 898,000 residents) and some will be too low, but overall these kinda-sorta balance out and that puts us in the right ballpark. Not only that, but making additional steps doesn’t necessarily mean additional steps in error. That, and more examples are here.

Good decision making takes nouns and verbs. We’ve got good verbs like inversion, mean reversion, extreme examples, and such. Landmark numbers give us a few nouns to work with too.

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The very good Fermi book inspired this post: Fermi Knowledge.

Numeracy at Best Buy

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We note that numeracy is important but it is hard to box in what numeracy is and how to use it well. Generally it is this idea that numbers explain some parts of the world well and we should use those numbers in a world full of people.

Yes?

Maybe an example will help:

“The Best Buy Geek Squad was reporting the mean (repair time) to their customers. A customer walks in to get their computer fixed, the part is on backorder, and the Geek Squad would quote the mean time to repair the computer. Of course, that means plenty of people’s repairs were not the average amount of time. So they changed and reported the 95th percentile time. They ranked the past times and now quote that to the customer – which is what people want!” – Elea Feit, March 2018

Like wet bias, maybe we can’t handle the truth. Or rather, maybe the way we see the world makes more sense one way rather than another.

One thing people are pretty bad at is randomness. We use stories to connect actions to events. Another thing we tend to miss is thinking that what did happen was the only thing that could have happened. It’s not.

We work around this through design. For instance, we know innovation is important but without separate metrics and incentives it’s less likely to happen. Put another way, it’s the framing stupid.

Wet bias makes sense. Being less honest than possible also makes sense. Quoting average waits may be more accurate but it’s less valuable.

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Design and framing were two of my favorite ideas. For the ideas vitamin-style in a daily email drip, buy the email-drip on Gumroad. Find it on Amazon too.

A confusing life expectancy calculation

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“Statisticians are sometimes dismissed as bean counters. The sneering term is misleading as well as unfair. Most of the concepts that matter in policy are not like beans; they are not merely difficult to count, but difficult to define…the truth is more subtle yet in some ways easier: our confusion often lies less in numbers than in words.” – Tim Harford, The Data Detective, 2021

One of Harford’s goals is to help people understand the world more as it is and less as they wish it. Harford kindly covers ideas like base rates, sampling bias, and algorithm associations.

That last one has some quite funny anecdotes. For instance, one AI system was trained to distinguish healthy skin from cancerous skin. Crunching and comparing over and over are two things computers do really well, so this seemed a good fit. And it was! The AI categorized correctly. But computer code is like a mango slicer – it has a singular use. In the case of the skin cancer, what the AI “learned” was that if a ruler was present it was cancer.

That’s funny.

But also not. One economic principle that’s going to affect (is affect_ing_) work is the idea that as something gets cheaper it’s used more. LEDs and cameras are two recent examples, name an electronic product that does not have one of those. Data too, is going to be part of our lives more, and Harford wants us to think about the numbers a bit more. For instance, what does “life expectancy” mean?

“They take the relative risk at every age and they integrate it. They ask, if the relative risk this year stayed constant forever, how long would someone born today live? That’s where we lost a year, but that’s assuming Covid stays and the year we just had gets repeated .” – Adi Wyner, Wharton Moneyball, July 2021

This isn’t the only way to calculate life expectancy, but it was the way that lead to headlines like, “US Life Expectancy in 2020 Saw Biggest Drop Since WWII, With Virus Mostly to Blame”. That’s true, but is that how most people understood it?

Most of what happens, and Harford starts his book on this idea, is that we think fast. “Biggest drop”, “WWII”, and “Virus” are all oh-boy-this-is-bad bits of information. But we dig in to what the words really mean and things look a little better.

Our tendency to think fast doesn’t have to be a hinderance. We can use this tendency to be more numerate. Books like Harford’s bump up (be Bayesian baby) these ideas. Riddles like: most British men live past the average age help too. A steady dose of numeracy uses the availability heuristic for our own good.

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Not into the book thing? Harford has great podcast that cover these ideas. Wharton Moneyball is another with more of a sport’s bent. Gambling podcasts too cover these ideas. As Tyler Cowen said, it’s not that these things are VERY IMPORTANT but that if we see them more we update our mental toolboxes so they are marginally more important.

A confusing life expectancy calculation

MIKE

“Statisticians are sometimes dismissed as bean counters. The sneering term is misleading as well as unfair. Most of the concepts that matter in policy are not like beans; they are not merely difficult to count, but difficult to define…the truth is more subtle yet in some ways easier: our confusion often lies less in numbers than in words.” – Tim Harford, The Data Detective, 2021

One of Harford’s goals is to help people understand the world more as it is and less as they wish it. Harford kindly covers ideas like base rates, sampling bias, and algorithm associations.

That last one has some quite funny anecdotes. For instance, one AI system was trained to distinguish healthy skin from cancerous skin. Crunching and comparing are two things computers do really well, so this seemed a good fit. And it was! The AI (read: computer code) categorized correctly. But computer code is like a mango slicer – it has a singular use. In the case of the skin cancer, what the AI “learned” was that if a ruler was present it was cancer.

That’s funny.

But also not. One economic principle that’s going to affect (is affect_ing_) work is the idea that as something gets cheaper it’s used more. LEDs and cameras are two recent examples. Data too, is going to be part of our lives more, and Harford wants us to think about the numbers a bit more. For instance, what does “life expectancy” mean?

“They take the relative risk at every age and they integrate it. They ask, if the relative risk this year stayed constant forever, how long would someone born today live? That’s where we lost a year, but that’s assuming Covid stays and the year we just had gets repeated .” – Adi Wyner, Wharton Moneyball, July 2021

This isn’t the only way to calculate life expectancy, but it was the way that lead to headlines like, “US Life Expectancy in 2020 Saw Biggest Drop Since WWII, With Virus Mostly to Blame”. That’s true, but is that how most people understood it? Does if this previous year repeated forever seem like a good conditional?

Most of what happens, and Harford starts his book on this idea, is that we think fast. But we can use this tendency to being more numerate. Books like Harford’s bump up (Bayesian baby) these ideas. Riddles like: most British men live past the average age help too. A steady dose of numeracy uses the availability heuristic for our own good.

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Not into the book thing? Harford has great podcast that cover these ideas. Wharton Moneyball is another with more of a sport’s bent. Gambling podcasts too cover these ideas. As Tyler Cowen said, it’s not that these things are VERY IMPORTANT but that if we see them more we update our mental toolboxes so they are marginally more important.

Numeracy + Psychology

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One of the consistent behavioral psychology findings is the framing effect. People judge what is pointed out and consider the number attached to it. Two out of every three dentists approve chewing no-sugar gum. Sure, but do they caveat that with increased flossing? Heck, no one cares. The thinking goes that if it was flossing that was important someone would have mentioned it.

This effect is most often seen in medical communication and Matt Yglesias captures it perfectly here:

https://twitter.com/mattyglesias/status/1361266437130706945?s=20

But that headline is good. It’s salient – 4 people. It’s got friction. The real surprise is that they didn’t say ‘warn’ rather than ‘said’.

This kind of psycho-logic-magic needs countered with another kind of psycho-logic-magic.

We can assume two things work: (1) that people pay attention to and value what someone points out to them. This is normal, helpful, and completely understandable. It works. Most things that most people say are relevant to our lives. (2) that new news works. Different is interesting. This is also, normally helpful and understandable.

Here’s the pitch. This is the angle, the message. Here’s the psycho-logic-magic for vaccine interventions: opportunity cost.

If you’re pro-vaccine point out all the things that will be back to normal once people get it. Grandparents will visit grandchildren. Sports will resume. Christmas won’t be cancelled. Freedom and fellowship. Dining out and date nights. Cruise ships and college trips. Find whatever people value and point it out. People do not consider the opportunity cost unless it is explicit.

Closing note: if SkininTheGame is the ultimate signal, my wife had her second dose last weekend.

What the mean age means.

MIKE6 Comments

The Math of Life and Death is a good addition to the when are we ever going to use this collection of popular science books. With numeracy being so important in life, a regular diet of these ideas keeps someone mentally fit. Consider the story of student loans as one example.

Often the mathematical manuscripts show mean and median differing in network systems like in the case of income or the social graph. Or, how much Bill Gates skews average wealth but not legs.

Kip Yates reminds us of other instances.

“However, ecological fallacies can be more subtle than this. Perhaps it would surprise you to know that despite having a mean life expectancy of just 78.8 years, the majority of British males will live longer than the overall population life expectancy of eighty-one years. At first this statement seems contradictory, but it is due to a discrepancy in the statistics we use to summarize the data. The small, but significant, number of people who die young brings down the mean age of death (the typically quoted life expectancy in which everyone’s age at death is added together and then divided by the total number of people). Surprisingly, these early deaths take the mean well below the median (the age that falls exactly in the middle: as many people die before this age as after). The median age of death for UK males is eighty-two, meaning that half of them will be at least this age when they die.”

Kip Yates

Numeracy is becoming more important because we are generating more data. Luckily, we don’t have to become mathematicians but we do have to see if ideas pass the sniff test. We have to think about how survivor explains sampling, and consider gambling parlays. We have to be mathematically minded.

The Vaccine Friendship Paradox

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One non-intuitive concept, at least in scale, is the network. Like average numbers, it takes some work to construct the correct conclusions. Graph, chart, and count the way that people interact, decide, and connect and there will be patterns. It’s network effects which fuel companies like Instagram and create the increasing returns economy.

Networks, as Nicholas Christakis notes, are agnostic. They spread whatever they are seeded with, whether real viruses like Ebola or WOW viruses like corrupted blood. The question then is; How and what to seed a network with?

Eric Bradlow wondered about Covid vaccines on Wharton Moneyball:

“We study diffusion of products all the time. In theory, you want to observe the social graph. In marketing the question is: Who do you give the free product to? This is standard network analysis and with that data you could do a smarter initial seeding (of a vaccine).”

Is there more bang for the buck if one person gets the vaccine rather than another?

Yes, though it’s not intuitive.

As the Friendship Paradox video shows, we aren’t all connected to the same number of friends. Some people have more, some have fewer friends and to wisely allocate a scare resource (like with marathon slots) it takes some small adjustments.

Christakis has spent a lot of time mapping networks and noted that across cultures, space, and time most human networks look the same. Some people are more connected than others. A few have hundred of connections and hundreds have a few.

It’s important for Christakis because like Bradlow, he works with a diffusion problem. Rather than marketing products though, it’s about sharing vaccines and vitamins. The thinking for both goes like this, if you can share something that works with the right person then they will share the benefits of that with the rest of their network.

But how do you pick the right person? Christakis shared this tip: “Go into a village and pick people at random. Have them suggest their friends and vaccinate their friends rather than the originals.”

Most networks are like the Curb Your Enthusiasm network (via Funkhauser).

curb_your_enthusiasm_-_season_9_-_network_graph

Randomly enter that network and you could get anyone but then ask for that person’s friend and more often than not you’ll get Larry. He’s the hub. He’s the super spreader. He’s who to vaccinate or market to.

It’s a neat bit of math. Rather than random choice, ask one question to improve the odds of an idea, movement, or effect catching on.

While there’s nothing on networks, my latests pay-what-you-want is on Tyler Cowen’s ideas about decision making. One idea is ‘meta-rationality’ or knowing when you don’t know AND knowing where or who to go to to find out. 

Large N Small p

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Is it more likely for an infected football player to transmit a disease to their teammates or their competition? Adi Wyner:

"I would expect intrateam transmission by far. Not only huddle time, but the time on the bench, in the locker room, and while they travel. It’s a small chance of any given pairing but it’s lots of pairs. Anytime you multiply a large number by small odds you get a large number."

That’s via Wharton Moneyball and demonstrates the large N, small p principle. It’s the idea behind TikTok too. Ben Thompson said:

"What’s interesting thinking about Quibi and TikTok is that Quibi was such an arrogant idea, that professionally produced content is always going to be better. Are we sure about that? The vast majority of TikTok is garbage and that’s always the case with user generated content. But as it turns out, .1% of a massive, massive amount of content is super compelling. You find that one-percent not by being a picker, you find it by sourcing it."

Large N, small p is why something is always happening.