Why Your Brain Sees Patterns in Chaos

0:00This episode is brought to you by Cancer Research UK. Dinosaurs walked the earth 180 million years ago. But, you know, cancer was part of their story too. Scientists have found tumors in ancient fossils. Well, that is part of the reason why cancer is a big, big part of our story, right? It's the other side of evolution. It's the most complex disease that we face. There are more than 200 types of cancer in total, each with distinct characteristics, challenges and mysteries. And that complexity demands scale. Cancer Research UK is the world's largest charitable funder of cancer research, with more than 4 ,000 scientists, doctors and nurses working across more than 20 countries in the search for answers, and then sharing their discoveries beyond borders.

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1:20Hello and welcome to The Rest is Science with me, Hannah Fry. And me, Michael Stevens. Okay, Michael, I've brought a present for you. I see them on the table. The potential to be a very good present indeed. I've got some scratch cards. Do you have a preference? Oh, there's different kinds. There is different kinds. You didn't just get two of the same? No. So this one is just a straight up top prize of 5 ,000. Boring. This one I think is a more interesting choice. Would you rather have 20 ,000 pounds a month for five years or 300 ,000 pounds? I'd rather have the 20 ,000. I think I'm more likely to win a smaller prize.

1:50Oh, okay. So here is one. Smaller top prize. 5 ,000 pounds top prize on this one. So is this the one you won? No. Because that one only cost one pound. So you got to also spend more. You're more likely to win. So give me that 20 ,000 a month for five years. Because it's five pounds. I agree this is the best one, by the way. I agree this is the best one. Can I scratch this now or should we do it later? Because let's wait. Let's wait, right? Because I want to know what the chance of both of us. I've got three games on mine. Yeah, I don't think it works like that. All right. We'll have to find out.

2:24We'll have to find out. But funny enough, randomness might lead us there. Look, hey, that's what I call a hook and tease. Yeah. If we're talking about randomness, we should probably define it, right? Yeah. I'll throw one out there. I like to just say randomness is a property something has that makes it unpredictable and lacking in identifiable, recognizable patterns. Where you don't know the outcomes in advance. When you don't know the outcomes in advance, you cannot predict them. and you can't even find them when you look at past data, you say, this seems quite random. Although I also think that to add to that, I don't think that that means that something being random is necessarily interesting.

3:07I mean, statisticians love the idea of a weighted coin, right? But like, let's say that somehow I managed to trick this coin so that it landed heads 99 % of the time and then do 100 throws. The results would technically be random, but it would be like heads, heads, heads, heads, heads, heads, there'd probably be one, maybe a couple of tails in there somewhere. Yeah. But where they appear, we wouldn't be able to predict. Agree. I think that's a really great difference to point out, that randomness doesn't mean equal probability. Absolutely. You do have the other end of the spectrum, right? Like if you have a completely fair coin, then you can't tell where any heads or tails will be.

3:42Like it'll be kind of all over the place. And I think that when people talk about purely random, that's sort of what they mean. But really, they're talking about where every possibility is equally likely to come up. That's right. That's really what they mean, because they will say, oh, well, that doesn't look very random. And it's like, well, that'll happen sometimes. Yeah. Randomly. Yeah. Because a weighted coin that heads 99.9 % of the time, it's still random which one it lands on. But what do they call it when there's an equal chance of all the options? like pi for example so the digits after the decimal place in pi well we think that there's an equal chance of every digit to come up and if it does it's called a normal number if you know just as likely to get a two as a four as a you know as a six as an eight whatever and every combination every two combinations so your 22 is like is a 83 or whatever and as far as we've checked which by the way is very very very very far after the decimal point in pi i would say frankly too far i know people worship pi too far we haven't even started it's so long i there will never be far into pi no but we've checked and what have we found we found so far that it looks like it's normal it's normal so you're i mean at the moment we have checked so far into pi but basically if you wanted to measure the radius of the entire universe you could do it you know to the level of accuracy that was way beyond the width of an atom oh yeah to measure the universe you only need pi to like seven digits max hardly any you need hardly any yeah i think i think seven might even be too many but we know it to seven trillion at least yeah um i'm still going how many how many digits of pi do you know um competition yes we can i think you'll win i think i can so do you want to go first go on then we'll take it in turn shall we okay okay okay i like that all right 3.1.4.1.5.9.2.6.

5:48I'm out. I'm out. 3.141592653589793. Once you get to, I think it's like the 760 second digits from there, it goes 999999. How many nines is that? I think it's six in a row. Six in a row. Right, which is like, well, that feels unlike, that feels pretty random. Oh, this is the Feynman point. This is the Feynman. I've heard about this. Yeah, Feynman would always say that what he wanted to do was to memorize the digits of pi all the way up to 762, and then just say 909, 999, and so on. And so on. Wasn't he a clever guy? He was. Okay, so this is the other end of the spectrum, right? The digits of pi are the other end of the spectrum in terms of the random sequence.

6:29It's not random. They're random and potentially normal. Yes. Well, okay, we should be careful, though, because they're not actually random because pi is a particular number. That's true. I can predict what it'll be. It'll be the ratio between a circumference and a diameter of a circle. Exactly. But they have all the characteristics of a random sequence. So, you know, this infinite sequence in pi where the digits are distributed uniformly, right? First of all, I want to throw in another definition of randomness that I really like, but then I got a question about it. And the definition is that when something is random, it takes longer to describe to someone over the phone.

7:07So imagine that I flipped a coin 100 times and it landed heads every time. I could quickly tell my friend, dude, I rolled a coin 100 times. I got heads every time. Bye. Completely predictable, completely ordered. Exactly. The results of those flips were random. Let's say it was just weird luck. However, that string of digits is easy to communicate. Easy to communicate. So is it still random? So, OK, there's two slightly different things going on here, right? Yeah, there are, aren't there? Yeah, two subtly different things. So one of them is about whether or not the next thing that's going to happen can be predetermined, whether it's predictable, essentially, right?

7:45Whether this outcome is determined in advance. That's randomness. But then there's also the other thing here, which is like the opportunity for surprise, as it were, right? because you could have it's kind of going back to that spectrum of like a very ordered sequence easy to communicate a very unordered sequence where you know like taking a chunk of the digits of pi is really difficult to communicate i mean that if you were saying that down the phone you would have to literally read them out one by one by one yeah right if i flipped a coin and i got a more typical distribution i couldn't just call my friend and say oh they were all heads i'd have to be like, dude, OK, there were two heads, tails, heads.

8:26I'd basically have to just read the whole thing and it would take a long time. That string of digits is more random. It's less predictable and there aren't a lot of patterns in it. Well, I don't know if it's more random, right? But I think it has, well, it's what the information theorists call more entropy. It's more chaotic. OK, so then there's a difference between being random and being high entropy absolutely so being random is about whether or not you can tell the next thing that's going to happen in advance and having high entropy is about like the number of opportunities for surprise so like in an alphabet you know if i if i had some scrabble tiles something that was low entropy would be aaa right perfectly ordered right nothing interesting going on something that was high entropy would be like you know t g d p l w like no no discernible patterns for you to latch onto there's two things that are going on here right so one of them is is randomness and that's whether or not the next thing in the sequence is predictable and it doesn't matter whether it's very very likely to be heads or equally likely to be heads and tails it's still whether you or not you can absolutely say for certain what it's going to be in advance but then there's this other thing that's going on, which is that we sort of have a spectrum of chaos here.

9:41So at one end, you've got something that's perfectly ordered. Heads, heads, heads, heads, heads, heads, heads, heads, heads, heads, really boring. And then the other end, you've got something that is perfectly messy, right? There's no structure or pattern that you can latch onto. And at the one end, you're going to be able to communicate that down the phone extremely quickly and easily. It's just always. And at the other end, you're gonna have to read out the entire thing. There's no way that you can compress that message. Yeah, that's a very important distinction to make. The difference between randomness, meaning can't predict it, and how disordered is the result that we got from a random, unpredictable process.

10:18You can throw Scrabble tiles on the ground, and it is possible that they'll land in a way that spells a sentence. That would be highly ordered. But if they just look like a mess, it's very unordered. And I think it's important to point out, and this will keep Keep us in the topic of randomness, but it's important to point out that this is starting to feel a little bit subjective. Yeah. Because what do you mean it looks messy? What I mean is there's a lot of ways Scrabble tiles thrown on the floor can look messy. There's a lot of ways, but there's like only one way they can fall on the ground and spell out how I was born.

10:55Yeah. All right. And so the fewer different ways something can be arranged to look the way it does, the higher the entropy. Yeah, absolutely. Richard Feynman had a quote that I actually wrote in my notes. We measure disorder by the number of ways the insides can be arranged so that from the outside it looks the same. Oh, that's so good. Yeah. He really was smart, wasn't he? Flip a coin a hundred times and get heads the whole time. There's only one way you could get heads every time. But how many ways are there to get something that's really hard to communicate on the phone? Most of them. A bunch.

11:32A lot, a lot, a lot. That has low entropy. Yeah, I like this idea of the distinction between randomness and disorder, which is what we're really ultimately talking about here. You know, the other thing about the throwing those scrabble tiles on the floor and getting a sentence that spells out the way that you were born is that that's you imparting meaning onto what is essentially a random sequence. Because if you carried on going forever, if you chucked, you know, scrabble tiles on the floor over and over and over and over again, eventually you would end up with something that told the story of your birth and your death.

12:06Well, right. But like, let's just imagine that the universe is really huge. like infinite, and that there are intelligent civilizations that number almost infinite as well, then the chances that I could throw Scrabble tiles on the ground and some alien somewhere could look and go, that's how I was born, using its language becomes higher and higher. So whether something is disordered really depends on the context that they're looking from. Have you read The Library of Babel by Jorge Borges? Yeah, I have. Oh my God, I love it so much. I love it so much. But he had this, it's a really short story, it's only like three pages or something.

12:49But he had this idea that there was a fictional library, a kind of infinite library, where every single possible combination of letters on a page existed within the books within this library. So that in theory, you could go in, I mean spaces are included right you could go in and you could go to some shelf in this library pull a book off flick to a page and it just say nothing on the page at all apart from your name it was right written in the middle but there would also be a page somewhere in that library where your name would be written vertically right and another one diagonally and another one where it was just your name over and over and over again every possible combination of a way to write your name must appear within that library but the sort of twist on this story is that even though that might be true because as you said the number of ways to order letters on a page the number of ways to order scrabble tiles is so gigantically massive what this means is your experience of going into the library is that you pull out a book you open a page it's junk another page it's junk another page it's junk so he has these librarians wandering around this this infinite library looking for meaning and essentially finding nothing for you know there's there's one person who has spent 10 years and found half a sentence right someone found the word it's a dog or whatever even that's hard to believe even that's hard to believe even though every single sentence possible is in that library your likelihood of finding one of them in your lifetime it's got to be close to zero.

14:26It's not zero. It's not zero. Do you know that someone made this? Someone made a digital version? Yeah, I talked about it in my video Messages for the Future. And I got to speak to the guy who made it. And he told me how he coded the site to work. Because yes, it contains every combination of letters, including spaces, up to a certain number of characters. He only did every possible page, right? rather than every possible book. It's not every possible book, but it also doesn't exist on a server, like every combination. Instead, it's coded within numbers. He did a mathematical trick, basically.

15:02That's right. You can search and it will find anything you search in the library of Babel. Because we already know they're out there. In theory, they already exist. But what he managed to do was to create a way that he can order them and allow you to search them. Right. So if I looked up your name, I would find it on a certain page in a certain book in a certain volume in a certain wing. But then if anyone else looked up your name, it would be in that same spot. So he's cataloged everything that's ever been said and everything that still hasn't been said. It is a little bit scary. It's really scary.

15:36But I also think that what this demonstrates is just how like how difficult we find it to conceive of these worlds, right, of randomness, of combinations. I think that we are just really, really bad at having intuition for what randomness looks like. We really are. You said something that I want to get back to, which is that the librarians in the library of Babel are looking for meaning. What is meaning? Is it meaning something that we effectively create because the universe doesn't provide it? Yeah, I might not totally agree with that yet. But I think I will say this, that to me, meaning is what happens when information is discarded, but can be put back in.

16:22Meaning is what happens when information is discarded, but not lost. Go on. OK, so let's just talk about someone's name. Right. Like the name Hannah Fry means something. It means you. It means your life story. it means a lot. It means a lot to different people. But I don't have to refer to you by describing everything about you and everything that you've done and where you are right now. I can just say your name. If someone goes, oh, who'd you see today? I don't have to be like, I saw the woman who was born in this town. And it'd go on and on. I can just say Hannah. A lot of information has been discarded.

17:02I'm not mentioning a lot of stuff. And yet I am. It's like, you know, it kind of goes back to that idea of like, Like how quickly can you communicate something around the phone? I'm compressing everything you represent into a single name. When we ask what something means, we're asking what information has been discarded. Right. Okay. You're asking for the invisible thing that you're no longer directly communicating, but that is common shared agreement. I heard what you said, but what did you not say? Because that's what you meant. But then here's, I'm going to go back to what I said before, that meaning is something that we create right because the universe doesn't provide it and i actually i want to double down on that because the thing is the words hannah fry they might mean something now right they might have a shared meaning between people who are my family or whatever right now but this is something that only has existed for the briefest flicker of time and will quite soon cease to exist right like in a hundred years maybe less it will have no longer any meaning whatsoever in the same way as like Ignatius spelling, you know, or whatever.

18:10It doesn't have any meaning to anyone. That means a lot to me. That was my father's name. How dare you? And so, yeah, I think that actually meaning is something that we are creating, that we are putting on top of the randomness that already exists. Not only are we creating meaning, it is what we do. I think our niche as a species is that we create meaning. We discard information to save time, to solve problems. It's all what cognition really is. And I think we make meaning just like bees make honey. We take stuff, we take information from the universe, just like bees take nectar, and we go, eh, this could be sweeter.

18:55And we discard a bunch of stuff. The bees dry out that nectar until they've just got this really, really sweet honey. And we take in all this information and we discard stuff until we've just got this meaningful thing. I really like that idea. I really like that idea. I think we can go further with it. So I'm going to pause for a break. And when we come back, we're going to see if there are other ways to make meaning from randomness and disorder.

19:27This episode is brought to you by Cancer Research UK, who over the past 50 years have helped double cancer survival in the UK. You might have heard of BRCA genes. These are the ones that made headlines when Angelina Jolie revealed that she carried a faulty version. Yeah, BRCA genes are part of our DNA. They help to repair cells and keep them healthy. The risk comes when BRCA genes are faulty. And about 1 in 400 people inherit a faulty version, increasing the risk of some cancers. Yeah, now this discovery came from Cancer Research UK scientists who came across the BRCA1 and BRCA2 genes, a breakthrough that changed how doctors prevent, diagnose and treat cancer.

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22:05welcome back we are talking randomness we are talking meaning we're talking disorder and chaos all of the sweet easy subjects for today it's been so random i think i was thinking about that during the break i went to the bathroom and i was thinking i was like yep i think people use the word random nowadays in the right way they're saying look i couldn't have predicted it i didn't know that guy would be at the party so he was a rando yeah that one i don't mind is when people say oh i just crashed my car i'm so random that's the one that bothers me it's like no no no no no you can't you can't retrospectively apply a person who talks like that is someone that i would predict would be in a car accident it's not random that's actually my natural voice oh so you're just like putting on this this one is the fake one i'm from essex you know come on okay we agree then that the there's a lot of disorder there's a lot of uncertainty but the thing is i think science is really really very good at taking that uncertainty and using it for our own advantage give me an example all right one of my favorite stories is back in like the 1700s there was a lot of woo woo in medicine right even like official hospitals had a lot of crazy, crazy stuff going on.

23:25What wasn't woo-woo back then? I mean, mathematics, thank you. There's a lot of good mathematics in the 1700s. But anyway, one of the most amazing bits of woo-woo was this thing called Perkins Metallic Tractors. You come across these? No. Basically, there were these little rods and they had pointy ends. And what you would do is you would go around to somebody who was like not feeling very well and you would point the rods over the bit of their body that was hurting. And then technically, if you stood there for about 20 minutes, They could draw out the noxious electrical fluids. I think people were quite into electricity at the time.

23:57And they sold for an absolute fortune. Old Georgie Washington, he had a set. Everyone was like fully bought into them. And then there was this guy called John Haygarth. And he was like, I think this is not, something's not right here. So what he did is he went away and he made some little wooden versions of these tractors. And he painted them to look like the original. And then he went into a hospital and he was like, OK, there's lots of people here, right? If I try this on a number of different people and I won't tell them, sometimes I'm going to use the real tractors. Sometimes I'm going to randomly assign the other ones, the wooden ones, and I'll see who ends up getting better.

24:34And he went around and he collected all the data, wiggling these little sticks in front of people and demonstrated that the real ones had made no difference whatsoever. Whether he was wiggling the metal sticks, the really expensive tractors, or these little wooden toothpicks that he mocked up at home didn't make any difference. But what he was effectively doing there was he was using the kind of randomness, the disorder of the universe to his own advantage to kind of prove that there was nothing special about these tractors. That's right. He found their meaning or lack thereof by randomly applying them.

25:11Was it like double blind? Did the users not even know whether they had the real things or not? No, because he was the user. So no. So he knew. He knew. He knew. But it was a bit later on. I mean, it was like the 1940s when controlled trials, random controlled trials. So he was one of the first on record to be doing this kind of a random trial to find whether there's meaning or not. Exactly. Exactly. Did he look at the outcomes of people that he didn't do any of the treatments to? No, this is like early doors, right? So for that stuff, for it to be properly, the point at which it became the new gold standard, that was the treatment of TB in the 1940s.

25:52And then there was a particular drug, it was called streptomycin. And people weren't sure whether it was actually making a difference or not. Because of course, you give a drug to some people with TB and they get better. You give it to other people with TB, and they don't get better. And it's really difficult to kind of hone in on precisely the role of the drug in all of that. So that was when they did it absolutely properly. They deliberately withheld the drug from a randomly selected group of individuals who had TB in order to work out whether it was the drug that was making the difference or it was just randomness.

26:23Yeah, right. Because there could even be a placebo effect where whether it's real medicine or not, just the fact that a doctor cares enough to give you attention can affect how your body heals, how it reacts, what symptoms you have. And it's only by harnessing randomness and disorder, by doing it on multiple people, that you can start to separate out some of these effects. To separate out the meaning. The meaning, exactly. Meaning can even emerge from randomness. I think my favorite example is Ziff's Law. Yeah. Ziff's Law is this really bizarre phenomenon that we've observed in every known language.

27:01We've observed this in craters on the moon. I'll describe it using language. So in languages, there are words that are used more than others. And you can rank how often a word is used. So in English, it's the word the. The second most used word, as it turns out, will be used about half as often as the most used word. Really? I'm not done yet. Okay. The third most used word will show up in texts a third as often as the number one. The fourth, a quarter as much. The fifth, a fifth as much. And so on. Really? All the way down. I did a video about this and I just, I said, well, Vsauce is my YouTube channel.

27:41I'll check the word sauce. And I don't remember the exact number, but sauce was like the 5 ,000th most used word in English. And it showed up one 5 ,000th as often as the word the. In the Gutenberg corpus and in Google's corpus. I was like, this is incredible. And so what's going on, right? Yeah. Yeah, I mean, that sort of feels like it's not random. That feels like it's an imparted pattern. Maybe it's put in there by human minds. No, because we see this in craters as well. Crater size and location, it follows Ziff's law. The most common size shows up a certain amount of time. The next most common shows up half as often as the most common.

28:19And it's incredible. But then later, it was found that Ziff's law is also obeyed by random typing on a keyboard. No. Yep. That just a monkey slapping a keyboard is going to also create a language that follows Ziff's law. Wait, so hold on, hold on, hold on, though. What are you counting? What counts as the most common thing there? Like a combination of letters? You just treat it like they're words and you say, what's the most common word? Which means letters that are separated by spaces. What's the most common word that the monkey's typing? And then you look and they're going to follow the same pattern.

28:57and that is because the space bar is what defines a word ending and beginning. The space bar is one of the keys. So imagine a keyboard that just had letters and a space bar. It's got 27 buttons. Eventually, you're going to hit the space bar and that makes shorter words more likely than longer ones. A longer word means that you've gone a long time without hitting the space bar. It's much less likely. And how much less likely? You can look at the math behind it and it just forms that exact same shape. So actually what Zipp's law is doing there is that it's like this inherent pattern that appears when things are generated effectively at random.