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

Episode Date: November 7, 2021

2,500 years ago, the Greek philosopher Zeno posed a question. If you want wanted to travel from one place to another, you first have to go half the distance, then you have to go half the distance again, and then again. You can do this infinitely and never reach your goal. This was one of the first paradoxes known to history. Since then, there have been many many others, which often leave people scratching their heads. Learn more about your ad choices. Visit megaphone.fm/adchoices

2,500 years ago, the Greek philosopher Zeno posited a quandary. If you wanted to travel from one place to another, you first have to go half the distance. Then you have to go half the distance again, and then half again. You can do this indefinitely, and never reach your goal. This was one of the first paradoxes known to history. Since then, there have been many others which often leave people scratching their heads. Learn more about paradoxes, and how to resolve some of them, on this episode of Everything Everywhere Daily. Do you ever climb into bed, ready to sleep, only to have your mind

start racing the moment your head hits the pillow? Thoughts bouncing around, replaying the day, or jumping ahead to tomorrow? That is exactly why Catherine Nicolai created Nothing Much Happens. Each episode is a gentle, cozy bedtime story where, well, nothing much happens. No drama, no tension, nothing you need to follow closely. Just soft narration, calming repetition, and soothing sensory details designed to help your mind slow down and your body relax. It's not about entertainment, it's about rest. And millions of listeners around the world use it every night to quiet their thoughts and finally fall asleep. If you've ever struggled to shut your brain off at night, this might be exactly what you've

been missing. You can listen to Nothing Much Happens wherever you get your podcasts. Episodes are every Monday and Thursday. A paradox is something which is contradictory or something which appears to be contradictory. Paradoxes appear in many different areas, including logic, mathematics, physics, economics, psychology, and politics. So let's just jump right in and talk about the most basic form of paradox, a logical paradox. The most basic of that would be what's called the liar's paradox. The liar's paradox would be the following statement. I always lie. If in fact I always lie, then that statement is true. And if it's true, then I don't always lie,

which makes the statement false. The statement is self-contradictory. There are many different ways to state the liar's paradox, but in the end, it's all pretty much the same. Another similar logic paradox was put forward by the British logician Bertrand Russell called the barber paradox, and it goes like this. In a town, there is a single barber. The barber shaves all those, and only those who do not shave themselves. The question then is, who shaves the barber? If the barber shaves himself, then he isn't the barber. If he doesn't shave himself, then he has to be shaved by the barber, who is himself? This is a self-referential paradox, and most logical paradoxes, even the liar's paradox, are of that type.

Another great paradox is called the surprise test paradox. Suppose a teacher tells you that the beginning of class on someday next week, you will get a surprise test. You figure that the test can't come on Friday, because if it hasn't happened through Thursday, you know it will be on Friday and then it won't be a surprise. Having eliminated Friday, you realize that it also can come on Thursday. Because if it hasn't come by Wednesday, you know it will be Thursday, and then it won't be a surprise. And you can do this for all the other days of the week and conclude that you will not,

in fact, get the test. But then, the teacher gives you the test on Wednesday, which is a surprise. You've all probably heard of the question proposed what would happen if an immovable object collided with an irresistible force. This isn't so much a paradox as it's a definitional issue. If there is such a thing as an immovable object, then there can't be such a thing as an irresistible force, and vice versa. Definitional paradoxes are easy to create. For example, what would happen if the tallest person in the world met someone taller? Well, then that person wouldn't be the tallest person in the world. The statement simply contradicts itself. My favorite type of paradox are mathematical paradoxes. They often are true,

but they don't seem like they're true at first glance. I previously did an entire episode on the Monty Hall problem, which is often called the Monty Hall paradox. This actually was a huge debate that are raged in mathematical circles. The paradox is that there are three doors, and there's a prize behind one of the doors. If you select one door, and the host opens up a door with no prize behind it, should you switch doors have given the choice?

And the answer is, yes, and I did an episode explaining everything, so I'll refer you to that. Another mathematical paradox is one that you might have encountered before, and it states that the number, point-99-99-9-9-9-9-repeating, is equal to the number one. Many people have a hard time getting their heads around this, but it's true.

And the reason it's true is that it's impossible to come up with a number between 0.999 repeating and 1. If they were different numbers, then there has to be some number between them. Likewise, you could have a definite solution to an infinite sum of numbers. Add up the following infinite list of numbers. 1 plus 1⁄2th, plus 1⁄2th, plus 1.6th, etc. What does that add up to? You might say that it's impossible to know because there's no last number. However, we do know the answer, and it's two. The reason why we know it's two is the same reason why 0.999 repeating is equal to 1. No matter how close you want to get to 2, the infinite sum can

always get closer. I bring this up because of the next paradox which I mentioned in the introduction, Xenos paradox. This is one of the oldest paradoxes known, and it can be stated. several different ways. Let's assume you want to move two meters. First, you have to move one meter, then you have to move a half a meter, then a fourth of a meter, etc. According to Zeno, you could never reach your goal because you have to travel an infinite number of distances each half the length of the previous one. The secret to resolving Zenos paradox is that it's mathematically the same thing as the infinite sum that I just mentioned earlier. However, there is also a physical resolution of the paradox. In reality, you can't keep going down in distance forever.

There's a minimum distance in the universe called the plonk length. Once you get down to that distance, you can't go any further. Likewise, there's a plonk time, which is the smallest unit of time. There are several interesting statistical paradoxes. One is called the false positive or the rare disease paradox. Suppose you have a rare disease that affects one out of every 10,000 people. And suppose a test is developed that is 99% accurate. If you test positive for the disease, what are the odds that you have?

the disease. Now, you might think the answer is 99% because that's what the accuracy of the test is, but it's not. Let's say you have a population of 100 million people. In that population, 10,000 people will have the disease. When those 10,000 people are tested, 99% or 9,900 will have a positive test, and 100 people will have a false negative. For the rest of the population, because it's 99% accurate, 98,990,100,100 people will return a negative result. However, for 1% of the population, or 99,900 people will show a false positive result. That means a 1,9,800 people will get a positive test result, but for only 9,900, or about 1%, will it actually be correct.

That means, of the people who get a positive test result, 99% of them would not have the disease. This statistical paradox occurs when the odds of the disease are much less than the accuracy of the test. Another interesting statistical paradox is Simpson's paradox. Simpson's paradox is that trends amongst groups can disappear when the groups are combined. For example, in a recent election in the state of Wisconsin, there was an issue comparing the education systems of Wisconsin and Texas. The argument was made that Wisconsin had a better educational system because it had higher average test scores than Texas. However, when they looked into the data, they found something interesting. When they looked at racial subgroups, Texas performed better

in every single one. Black students in Texas perform better than in Wisconsin. Latino students in Texas performed better, Asian students scored better, and white students scored better. Both of the claims were true. Wisconsin did score better. overall, but Texas did score better in every subgroup. How is that possible? It has to do with the size of the groups in each state and the fact that they had different average scores. This can manifest itself in baseball batting averages, admission rates to colleges, and other areas. There's another paradox called the Will Rogers Paradox. He first raised it as a joke when he said, quote, when the Okies left Oklahoma and moved to California, they raised the average intelligence

level in both states. While this was a joke, such a statement can statistically be true. Let's say you took the smallest person on a basketball team and put them with a group of horse jockeys. Removing the smallest person from a basketball team would increase the average height, and adding them to a group of smaller people would increase their average height as well. One of the favorite paradoxes of movies in science fiction are time travel paradoxes, the most well-known of which is the grandfather paradox. Let's assume you go back in time and kill your grandfather when he was a child. You would never be born, which means you wouldn't be around to go back in time to kill your grandfather.

And there are all sorts of time travel paradoxes which have been used as plot devices in many movies. And this is why we can't have nice things like time travel. There are several things called paradoxes in the physical world which really aren't paradoxes per se. One is the potato paradox. Let's say a farmer has a hundred pounds of potatoes and the potatoes are not. 99% water and 1% solids. The farmer leaves them in the sun until the water level goes down to only 98% water. When he weighs the 98% water potatoes, it now weighs 50 pounds, having lost half of its weight.

How is that possible? In the initial weight, 1% of the 100 pounds was solid, or 1 pound. The weight of the solids doesn't change after the potatoes dry. The new ratio is too solid to 98 water, or alternatively, one solid, to 49 water. If the solid remains one pound, the water has to weigh 49 pounds for a total of 50 pounds. Hence, going from 99 to 98% water will drop its weight in half. In nutrition, there was something called the French and Israeli paradoxes. Researchers in the 60s thought that saturated fat caused heart disease, but France consumed high levels of saturated fat and had low heart disease.

Likewise, Israel had low levels of saturated fat consumption and high heart disease. The answer, of course, is that there is no paradox in such cases. The assumptions are usually just wrong, and that's what's been discovered about saturated fat since then. Voting has many paradoxes. Arrow's paradox is proven by Nobel Prize winning economist Kenneth Arrow. He showed that no ranked voting system with three or more choices can always accurately reflect voters' desires.

This is because voting, unlike mathematics, isn't true. transitive. Theno's paradox states that most polls show that Americans have low approval for Congress as a body, yet most individual members of Congress have very high rates of re-election. The apportionment of representatives also has several paradoxes. One is called the Alabama paradox. It was discovered in 1880 that increasing the size of the House of Representatives would actually have decreased the number of representatives in Alabama by one. Likewise, there's the New State Paradox, when Oklahoma was added as a state, New York lost a seat and Maine gained one, even though the total size of the house increased. There are dozens and dozens of paradoxes, both literal and figurative. Sometimes

they are a true paradox. Other times, they are just a puzzle waiting to be figured out to make sense. The associate producers of Everything Everywhere Daily are Thor Thompson and Peter Bennett. Today's review comes from listener Guisa 1981 on Apple Podcasts in Canada. They write, A new favorite. Original topics that are superbly summarized and delivered. I've been binge listening to this podcast for a couple of days. Well, done, sir. Well, thank you, Guisa, 1981.

It's always a comfort to know that you've become binge-worthy. Remember, if you leave a review or send a question, you two can have it read in the show.