Everything Everywhere Daily: History, Science, Geography & More - Innumeracy

Episode Date: August 13, 2022

Over the last several centuries, there has been a concerted effort to raise literacy rates around the world. For the most part, although there is still work to be done, we’ve done a pretty good job. The vast majority of people around the world know how to read and write. While literacy has improved, despite our world becoming ever more dependent on technology, overall mathematical literacy has not improved. Learn more about numeracy, or mathematical literacy, on this episode of Everything Everywhere Daily. Subscribe to the podcast!  https://link.chtbl.com/EverythingEverywhere?sid=ShowNotes -------------------------------- Executive Producer: Darcy Adams Associate Producers: Peter Bennett & Thor Thomsen   Become a supporter on Patreon: https://www.patreon.com/everythingeverywhere Update your podcast app at newpodcastapps.com Search Past Episodes at fathom.fm Discord Server: https://discord.gg/UkRUJFh Instagram: https://www.instagram.com/everythingeverywhere/ Facebook: https://www.facebook.com/EverythingEverywhere Twitter: https://twitter.com/everywheretrip Website: https://everything-everywhere.com/everything-everywhere-daily-podcast/ Everything Everywhere is an Airwave Media podcast." or "Everything Everywhere is part of the Airwave Media podcast network Please contact [e-mail] to advertise on Everything Everywhere. Learn more about your ad choices. Visit megaphone.fm/adchoices

Over the last several centuries, there has been a concerted effort to raise literacy rates around the world. For the most part, although there is still work to be done, we've done a pretty good job. The vast majority of people on this planet know how to read and write. While literacy has improved, despite our world becoming ever more dependent upon technology, overall mathematical literacy has not improved. Learn more about numeracy or mathematical literacy on this episode of Everything Everywhere Daily. What if your perceptions about the past, were wrong. ThruLine is a podcast that takes you back in time to uncover the parts of the story

that may have gone unnoticed. It effectively turned day into night. And how it shaped the world now. Time travel with us every week on the ThruLine podcast from NPR. In the 1980s, the fast food chain A&W was competing with a much larger fast food chain McDonald's. One of the most popular McDonald's hamburgers was, both now and then, the quarter-pounder. A&W thought that they came up with a great idea to compete with McDonald's quarter-pounder. They introduced a hamburger with a third-pound patty instead of a quarter-pound patty for the same price, and it beat the quarter-pounder in blind taste tests. A&W was sure that they had a winner on their hands. However, the A&W third-pound burger wasn't the success that they had hoped. A&W conducted customer surveys to find out why people didn't

like the new burger. The owner of A.N.W. at that time, Alfred Taubman, wrote about what they found in his book, Threshold resistance. Quote, more than half of the participants in the Yanklevich focus groups questioned the price of our burger. Why, they asked, should we pay the same amount for a third of a pound of meat as we do for a quarter pound of meat at McDonald's? You're overcharging us. Honestly, people thought that a third pound was less than a quarter pound, because, after all, three is less than four. End quote. This case is the poster child for what has been dubbed enumeracy, the mathematical equivalent of illiteracy. In numeracy isn't necessarily the inability to do basic arithmetic or multiplication.

Rather, it's an inability to understand and reason using basic mathematical concepts and logic. It doesn't really have anything to do with how well you did in math class or the highest level of mathematics that you took. What I want to do in this episode is go over some of the biggest mistakes people make with math. Some of these you might have seen before, and some you might be guilty of yourself. And the first has to do with really large numbers. Most people don't have a problem with numbers that are on a human scale. Things that are counted in the dozens, hundreds, or even thousands are numbers that we can grasp.

Most of us can intuitively understand the difference between a thousand dollars and ten thousand dollars. However, there are many things in science or economics where we encounter numbers in the billions, trillions, or even greater. and most people don't even know what septillions, quadrillions, or octillions even are. Numbers at this scale are difficult for people to grasp intuitively. One helpful way to grasp this scale is to think about how long a million, billion, and trillion seconds are. One million seconds will pass in 12 days. One billion seconds will pass in 32 years. And one trillion seconds will take 31,688 years.

Scientists and mathematicians have developed an easy way to express these numbers using what's known as scientific notation. Scientific notation is based on 10 raised to the power of something. The number that it's raised to, aka the exponent, is just the number of zeros. For example, a million is 10 to the 6th, as 1 million has 6 zeros. A billion is 10 to the 9th. If you wanted to express the number of humans on Earth, it would be 8 times 10 to the 9th, or 8 times a billion, or 8 billion. With this, we can easily express huge numbers without making our eyes bleed looking at a ton of zeros. The diameter of Earth in meters is 12.7 times 10 to the 6, or 12.7 million meters or 12,700 kilometers.

The diameter of the observable universe is 8.8 times 10 to the 26 meters. I don't even know the name of a number that big, and I really don't need to know, because it doesn't matter. You can also express incredibly small numbers the exact same way by making the exponent negative. One hundredth is 10 to the minus 2. The diameter of an atom is approximately 10 to the minus 10 or 1 tenth of a nanometer. As handy as scientific notation is for really big and really small numbers, most people don't understand it. So you will very seldom see it used in public discourse. The inability to conceptualize big numbers also leads to problems when it comes to statistics and probability.

For example, there is a dating company called E-Harmony. They claim that their service makes a match with members every 14 minutes. They phrase it this way because it makes it seem like you might only be 14 minutes away from finding true love. Assuming that this number is correct, it really doesn't tell us anything because we don't know how many people are signed up for the E-Harmony service. The most recent public number I could find was that there were 10 million people who were actively using their service today. With one match every 14 minutes, that would mean the system only makes approximately 103 matches per day or about 37,542 per year, out of a population of 10 million. So, in an average year, only 0.4% of the members of E-Harmony will find a match. That isn't nearly as exciting or hopeful as one every 14 minutes.

Another example of making numbers look good is with pharmaceutical products. Let's say a certain pharmaceutical product claimed that if you took their drug, your risk of dying from a certain type of cancer would be reduced by 10%. 10% isn't something to sneeze at, so that sounds like a pretty good thing. However, those numbers cited will almost always cite relative risk, not absolute risk. That 10% reduction doesn't tell you the absolute risk before the drug was taken. If the odds of dying from a particular cancer is one in 100,000, then even assuming the data on the drug is correct, the odds would now be one in 110,000.

The odds have gone from minuscule to still pretty minuscule. Almost all pharmaceutical efficacy percentages are reported as relative risks, but they never say that explicitly because most people will think that it's really absolute risk. Speaking of odds, I'd like to propose a hypothetical game. In this game, we will flip a coin. If the coin comes up heads, you give me a dollar. and if the coin comes up tails, I'll give you 98 cents. Given the way I just proposed the game,

you would probably be smart if you declined to play. You are clearly going to lose in the long run. Yet, that game I just proposed is basically every game at a casino, except they usually pay much less than 98 cents. The cards, the dice, and the spinning wheels are all designed to obfuscate the fact that the house has an edge. The more you play, the greater the odds are that the house will come out ahead. Casinos will feed this irrationality when they can.

For example, many roulette tables will have a digital display showing what the last several numbers and colors to come up were. They make no claims regarding what this information means, but it's really encouraging what is known as the gambler's fallacy. If you see that red has come up five times in a row, then surely you must say, black is now due. In reality, it doesn't matter what happened in the past. If red comes up five times in a row, then the odds of it coming up again are exactly the same as if black had come up five times in a row previously. Odds and probability come up in a lot more situations than just casinos. Let's suppose that the weather forecast for the weekend calls for a 50% chance of rain on Saturday and a 50% chance of rain on Sunday. What are the odds that it will rain at some point over the weekend?

Now, if you're really enumerate, you would say that the odds are 100%, because 50% and you're 50%, plus 50% equals 100%. But this is obviously wrong. If each day were independent of each other, the odds of it raining on either of the two days would be 75%. That would be the odds of getting at least one head to come up on two consecutive

coin flips. However, the real answer is, we don't know. And the reason we don't know is that the weather isn't like a coin flip. The odds of rain on two consecutive days are not independent of each other. One storm cloud might pass over near midnight on Sunday morning, in which case the forecast could be for the same event split into two days. Or it could be two separate events separated by almost 48 hours.

Another area where people are confused by probability is elections. Let's say there are two candidates. Candidate A is polling at 52 percent and candidate B is polling at 48 percent. Many people think that because the polling results are published in percentages, they are the same as the odds of winning, and they're not. If the polling is consistent and there's little variance, someone polling at 52% might just have an 80 to 90% chance of winning. Also, when political polling is conducted, it is always given with a margin of error. Most people ignore the margin of error and take the number at face value. However, the errors are there for a reason. If there's a 3% margin of error and two candidates are within 3% of each other, then it's basically a statistical dead heat.

Risk assessment is also an area where people don't think mathematically. People tend to inflate the risk of dramatic low probability events which appear on the news and underestimate the risks of more probable yet commonplace events. A good example of this is the risk assessment people have with terrorism. Thousands, if not millions of people have canceled or changed their travel plans because of the threat of terrorism. Yet, the odds of being a victim of a terrorist attack while traveling are extremely low and are dwarfed by many other things. One thing that few people worry about is actually the biggest single killer of travelers, automobile accidents. You are hundreds of times more likely to be involved in an automobile accident than you are in a terrorist attack. Yet, no one seems worried about it.

I'll end by noting something that many people also completely misjudge the odds of, coincidences. A coincidence is by definition a low probability event. However, certain coincidences aren't that improbable. For example, if you have a group of 25 people, the odds are better than 50% that at least two of them will share the same birthday. It doesn't seem like it because we think of someone having the same birthday as us, but with any two people, it's more probable than not. Coincidences happen all the time.

Predicting any particular coincidence before it happens is improbable, but pointing one out after the fact isn't that big of a deal because the universe of possible coincidences is extremely large. Humans like to find patterns, so there is a tendency to try to find reasons why coincidences occurred, even if there wasn't anything that was the cause. Not accepting coincidences can lead to conspiracy theories in pseudoscience, trying to find underlying reasons to explain something that doesn't actually require explanations. In numeracy isn't as obvious as illiteracy. but it is far more prevalent.

It isn't just something that affects regular people either. You can often see evidence of it in news reports and even in academic research papers. Almost 40 years after A&W failed with the launch of their third pound burger, they reintroduced it in 2021. This time, however, they changed their marketing. Instead of calling it the third pound burger, they change the name to the three-ninth pound burger. Everything Everywhere Daily is an Airwave Media podcast.

The executive producer is Darcy Adams. The associate producers are Thor Thompson and Peter Bennett. Today's review comes from listener Dave from Keeney, Alaska, over at Apple Podcasts in the United States. He writes, Easily one of the best podcasts I've found. I've listened to every episode, and they are all great. It is rare to find a podcast where every episode is interesting, but this is that podcast. Thank you for the great show.

Well, thank you, Dave, and welcome to the Completionist Club. I've actually been to a part of your Neck of the Woods. I've been to the Kenai Peninsula and Kenai Fjord National Park, but never got all the way down to the town of Kenai itself. But I am glad to know that I do have people listening in the 49th state. Remember, if you leave a review or send a boostogram, you two can have it read on the show. In the 1980s, ANW launched an advertising campaign to promote a new third-pound burger. It was bigger and beefier than the competition's puny quarter-pound option. And the price was the same.

So how come nobody bought it? Turns out Americans are just terrible at math, like really bad. Everybody thought that one-third was smaller than one-quarter because, you know, four is bigger than three. The whole thing went down in history as a huge marketing fail. And we've spent the last 40 years crunching the numbers. Our best mathematicians working day in and day out, trying to crack the uncrackable cone, solving the insolvable. equation to claw our way back from this embarrassing episode.

And we've done it. Introducing the ANW3 Knightsberger. It's bigger. Genius.