Is anything truly random?

This BBC podcast is supported by ads outside the UK. Hello, I'm Brian Cox. I'm Robin Ince and we're back for a new series of The Infinite Monkey Cage. We have our 201st extravaganza where we're going to talk about how animals emote when around trains and tunnels or something like that. I'm not entirely...

We're doing one on potatoes. Of course we're doing one on potatoes. You love potatoes. I know, but... Yeah, you love chips, you love mash. I'll only enjoy it if it's got curry sauce on it. We've always got techno fossils, moths versus butterflies, and a history of light. Listen on bbc.com or...

wherever you get your podcasts. So these are our photon detectors and these are just counting how many photons they see every second. You're listening to CrowdScience from the BBC World Service, the show that asks some of the smartest scientists in the world to explain the nature of reality, preferably using lasers. And so when we turn the laser on, we'll start to see...

Lots of counts now on the detectors as they're starting to detect photons. And if it makes cool noises, well, that's even better. If the photon arrives at detector A, the computer will make a particular noise. And if it arrives at detector B, it will make a different frequency tone. So we'll actually be able to hear this. And so this is something that you guys have jimmied up so that you can demonstrate this for crowd size. Yeah, exactly. Yeah, yeah. I'm Anna Jagatia, and for this episode...

I've travelled to Geneva in Switzerland to meet some physicists to help me understand a particular behaviour of quantum particles that is really hard to get your head around. In fact, you could say it's impossible. If I gave you... you wouldn't be able to guess. It's not just because you haven't figured it out yet. No, it's fundamentally no one can tell you. And we've ended up in a strange place because we didn't originally set out to investigate fundamental mysteries of the universe.

The email that started this whole thing off was actually about interior design, which sounds like an unlikely journey. But that's the great thing about working on CrowdScience. You just can't predict where listener questions will take you. And this week, our listener is Dorit, a Canadian currently living in Austria. My question is, is anything really random? And what is randomness?

What has got you thinking about randomness? We are renovating a house and the plan for one of the bathrooms was a floor with... tiles that have a very slight color difference and that they could just be distributed randomly. And so we instructed the tiler, who just is super smart and experienced and skilled. And we just thought, well, we don't have to plan the precise floor design with him because it's random.

And then we had several back and forth with him that he kept on sending us photos and we would come see and we'd say, but this is completely not random. This is a pattern. And what was the sort of response from the Tyler? Was he confused? Was he frustrated or like, how did he take it? I think he thought we were idiots. Initially, actually, we were, I think, being kind of arrogant and thought, oh, he just doesn't understand what randomness means.

But then we started thinking, well maybe just what is random to him is not random to us. And you actually, when you emailed us, you attached some pictures to kind of illustrate this. So we're looking now at a picture, which is like a sketch that presumably you said, look, this is what random looks like. And you've shaded in some of the tiles. Yes, because once we thought, oh.

you know, we understand what randomness is. We'll sort it out. But you still end up with patterns. I mean, I can see patterns in that now. Exactly. That's the thing. In the end, yes, it has... what look like patterns that's right so what are you hoping that we will find out in this show i hope that you will find a solution as to how we should tile our bathroom floor So, Dorit wants us to help her decorate her bathroom. But to do that, we need to generate a truly random pattern.

And to work out whether that's even physically possible, we have to understand what randomness actually is. You might think you have an intuitive sense of whether something is random or not, but as Dorit learned for herself, After her fiasco with the Tyler, that only gets you so far. If this home improvement project is going to succeed, we need to seek the help of a certified professional. A mathematician.

This is Hugo Dumenil-Copin, a professor at the University of Geneva and winner of the Fields Medal for his work on probability. It's the most prestigious award you can get in mathematics. I'm going to ask you. He's like, I thought that was the one asking questions. And fittingly for an expert on probability whose office is on the top floor of an old bank, Hugo asks me to toss an imaginary coin 25 times.

head, tails, head, tails. You do whatever you want. I will not look at it, but you write here. But I have to do it in my head. I can't actually use it. You just do exactly as you want. You are not allowed to use an actual coin. You have to email. Imagine that you are doing this. That sounds deceptively easy. The idea is that I try and come up with a random sequence of 25 coin flips, heads and tails, that resembles what would happen if I really did toss a coin.

I just write down whatever pops into my mind. Until I get to 25. So I'm going to try to guess what you wrote. Okay, and every single time you will let me know if I'm right or if I'm wrong. Okay. Wow, this is like a magic trick. Well, there is no magic. Only probability. Yeah. So the first one, don't worry, I will not always guess right. Okay. The first one is a head. Yes. Okay.

So I would say the second one is a tail. No. Okay, so I'm wrong on this one. So the third one is a tail. Yes. The fourth one is a head. Yes. Hugo is uncannily good at guessing what's on my piece of paper. Then head. Yeah. Then the tail. Yes. So I try to guess what you came up with. And you agree that if you would have been truly random every single time, I had one chance out of two, right? I'm guessing right.

But I got it wrong out of 25 times. I got it wrong six times. Not roughly 12. I might have seven here. Hang on. One, two, three, four, five, six. Seven times. So again, I don't know how to count. Ah, yes, indeed. This is a classic case of mathematicians marking their own homework. OK, perhaps he's not quite as good as he thinks he is, but seven wrong out of 25...

is still pretty good. So clearly what I wrote down can't have been very random. So what happened, I mean, my rule was very simple if you want to play at home, is that we have a tendency to think that things should not repeat. so we are going to not put enough things in a row so we are going to change between tail and head way too often and here you did it really a lot and what i was doing is just every single time i was changing i thought that's what

It was a very simple rule. But you see, it works extremely well. So you made way too many changes and way too few two tails in a row or two heads in a row. The second thing here that I could see... is that you did not put four head or four tail in a row. Exactly for this reason, right? I mean, at the end, how likely it is to have four tail or four head in a row. Out of 25...

it's very likely, in fact. There is maybe one chance out of six or something like that that you would not see four tails or four heads in a row. In a string of 25. If you go to a string of 100, for instance, you will typically see seven heads or seven tails in a row. So we would never think that. I think if we would have more time and I would ask 100. For sure, you would never put seven in a row. It would look so weird. So that's my point that the brain is extremely bad at producing randomness.

Hugo's magic trick, or demonstration of probability, shows us that our intuition about randomness is often totally wrong, which explains why in the parable of Dorit and the Tyler, both parties were doomed to fail. It would have been really difficult for either of them to make up a pattern that really was random. But this brings us to another weird thing about randomness. Even if one of them had come up with something genuinely random, it probably wouldn't have looked random to the other.

It's actually very difficult to make something that looks random. The human brain in general is set up to look for patterns in things. a cognitive neuroscientist at the National Institute of Mental Health in Maryland in the United States. I think this is actually a great example of how much work our brain, especially our visual brain, is doing in the background just for the everyday act of seeing.

From our perspective, we open our eyes and we just see a coherent world and we go about our day. But that's actually not what's going on. So, you know, the input that the eye receives are these very noisy patterns of light. So, you know, there's no structure there. It's flickering. It's changing constantly. It's very overwhelming.

And so our brain does this enormous computational feat. Every second, it's organizing and sorting and grouping this information and making it make sense so that we can get on with our day. Okay, that's really interesting, but how does that sort of relate to seeing patterns in bathroom tiles?

Yes. So if you're trying to organize things of different shades, so I think the tiles are kind of monochrome, different grays and that kind of thing. If you put things next to each other, your visual brain is trying to group these things to just make structure out of the noisy input that they are.

gets. So for example, things that we think are just out there in the world, like edges and the boundaries of what an object is. So if you think about your coffee cup in the morning, your brain actually has to do a lot of work to segment what's your coffee cup and what's the

background visually and one of the ways it does that is by looking at grouping things so proximity what's close together what's the same color because if your coffee cup is blue and there's other bits of blue from the visual information it's more likely to be part of the same object so this

kind of grouping that the brain does is related to this because if you're trying to make tiles look random you have like a limited number of color tiles and you you place them in different orders if there's any structure at all your brain will seize on that and the more limited your palate is the easier it's going to be for

your brain to make grouping things out of it. What Susan is saying is the brain is constantly trying to generate order out of chaos. So when you show it actual chaos, it has a hard time recognizing it. I think what this means for Dorit is that she should give up on trying to create a bathroom floor that looks random, because it never will.

Instead, we'll have to come up with a way of arranging the tiles that we can say with 100% certainty genuinely is random, and that way there can't be any arguments. But that's the thing. Does true randomness... actually exist. I think that's what we need to work out next.

Hello, I'm Brian Cox. I'm Robin Ince, and we're back for a new series of The Infinite Monkey Cage. We have our 201st extravaganza, where we're going to talk about how animals emote when around trains and tunnels, or something like that. I'm not entirely...

We're doing one on potatoes. Of course we're doing one on potatoes. You love potatoes. I know, but... Yeah, you love chips, you love mash. I'll only enjoy it if it's got curry sauce on it. We've always got techno fossils, moths versus butterflies, and a history of light. Listen on bbc.com or... wherever you get your podcasts. You're listening to CrowdScience from the BBC World Service, the show that investigates the questions behind your random shower thoughts. Sometimes literally, it turns out.

I'm Anand Jagatia, and to continue our quest to help listener Dorit tile her bathroom floor, we need to define what randomness actually is. Randomness is what cannot be predicted. Here to help out again is our friendly mathematician Hugo Dumenil-Copin. What I mean by what cannot be predicted is... things that cannot be predicted by any means, even with the most delicate machines, even with the most precise theories, there will be zero way of predicting things.

Earlier in the show, Hugo had me flipping an imaginary coin, and you'll remember that my pathetic human brain struggled to come up with a sequence that looked genuinely random. That's why we flip real coins to decide which team goes first in a sports game, or in my case, who has to do the washing up. Because a real coin toss is random. It can't be predicted. Right?

A coin toss, if you have a very high frequency camera and that it is measuring exactly how the coin is starting from your hand, and if it has all the information on the distance, blah, blah, blah, it will be able to predict. If it falls on tail or head. So if you knew everything about the weight of the coin, the pressure of the air, the temperature, the force, the angle, blah, blah, blah, blah. In theory, you could predict it. It looks random to us.

It's sufficiently complex to predict that humans cannot do it, and therefore we call it random. But it's not a true randomness. It's kind of apparent randomness. just out of our lack of being able to predict. So to answer one of Dorit's questions, this is what we mean by a truly random event, something that can't be predicted even in principle. Of course, as humans, we can't predict with certainty which way a coin will fall but a coin flip is essentially just a mechanical system.

We have laws of physics that describe how systems like this behave. So in theory, if you knew everything about it and you had a good enough computer, the outcome of a coin toss would be entirely predictable. And if that's true, then the behaviour of weather systems, people, or the entire universe might be predictable if you could know the position and properties of every force and particle in existence.

which would mean not only that nothing is random, but that everything that happens is inevitable. The question is, do we actually live in a deterministic universe like that one? Or do we live in a universe where randomness exists and where Dorit can be happy with her bathroom floor? Well, to find out, let's head across town to another part of Geneva.

where I'm about to meet some quantum physicists. When we told them about Dorit's question, they said they'd be able to build something that would settle things once and for all. So I'm Tiff Bridges. I work at the University of Geneva where I'm a researcher in quantum physics. And we have come to a lab station where you've hooked up loads of very exciting looking equipment to explain...

Something that is actually random, genuinely, truly random. Yeah. Okay, so what are we looking at here? What are all these wires and cubes and prisms and lasers? So here we've got our laser.

that comes out of this fiber here so this wire that's coming out of what looks like a computer tower you're transmitting lasers through that exactly this is uh just like standard telecom fiber that transmits laser light through very similar to what's used in all telecom industries nowadays wow that's really cool okay so light

going through a wire, being shone through this thing directly into what looks like a glass cube. Exactly. What is special about this glass cube? So this cube is what we call a 50-50 beam splitter, and it's a bit like a mirror in a way. but 50% of the time it will transmit the light going on it, and 50% of the time it will reflect it.

Okay, so for every photon that comes from out of this laser, 50% of the time it will just go straight through the glass and into this detector, which is directly opposite the beam. And 50% of the time it will be reflected and be diverted into this. other detector which we can see on the right of the cube exactly and that's that's random is it so whether it goes straight or turns to the right is completely random that is completely random and so

This is light, but how will we know whether the photon has ended up at detector A or detector B? So detector A, when there's a photon that's incident on this one, the computer will play one tone. And with detector B, whenever it sees a photon... computer will play another tone. Cool okay well should we turn the sound on and see what we can hear? Sure let's do it.

And so every time you hear the note change, that means that the photon is arriving in a different one of the detectors? Exactly. So a different photon has been either transmitted or reflected. It's kind of like an experiment I did earlier with heads or tails, that there's two options and that it's either one or the other and...

I tried to create a random sequence, but this is actually truly a random sequence. Exactly. So it's exactly the same concept. You're getting either heads or tails. You're getting here detector one or detector two. But exactly, it's completely randomness. It's intrinsically random. I should say that this laser emits an unimaginably large number of photons every second, but the team here have slowed it all down so that we can hear a steady stream of them. And there you have it.

But how do we know it's really random? And if it is...

Why? So what you heard is a process within quantum physics. This is TIFF's colleague Nicola Brunner. So quantum physics is the theory that describes the world of particles, of atoms, and also photons, so those particles of light that you heard before. And so quantum physics has this very astonishing property that... it features intrinsic randomness. So there are processes within quantum theory that must be random. And that's in contrast to classical physics, where the laws are deterministic.

why doesn't the photon just do the same thing every time? Right. So according to quantum physics, the state of the photon after passing through that beam splitter will be in a superposition. So it will be... at the same time going through straight and being reflected. But it's not one or the other, it's both at the same time. This is what quantum physics tell us. This is like an object, a photon here, being in two places at the same time.

So this would be a property that we usually associate to a wave. A wave can split in half into equal halves at a beam splitter. A photon, we think of it as a particle. It should, in principle, go either left or right. Now, a photon is a quantum particle, so it has this property that it can behave as a wave and as a particle at the same time. This is not an easy thing to conceptualise, but let's give it a go. A wave is like ripples on a pond, all spread out and able to split apart and recombine.

A particle is more like a marble, a single object in a specific place. A quantum particle, however, has both properties, at least until you measure it. you put the detector and you ask the photon did you go straight or were you reflected and so then the photon will actually localize in one of these two places.

And that is the moment that is truly random. So it's not just like we've looked at loads of photons and we can't see a pattern. It's just that we think that that's sort of baked into the structure of reality. Yes, that's right. Okay. This is, in fact, one of the most mysterious aspects of quantum physics. What is exactly happening at this moment when we measure the photon?

So that is a process that we still don't really understand. But what we understand about it is that it must be fundamentally random. The point is that if it wouldn't, if it would be deterministic somehow, then it would lead to very implausible consequences in physics, like communication at infinite speed.

And communication at infinite speed is incompatible with the famous theory of relativity by Albert Einstein. And this would enable dramatic things like... traveling to the past and kill your grandparents. OK, so even as implausible as it sounds that something can exist in two places at once and that we only know where it is or it only is in one place once we look.

that's less implausible than that, you know, time runs in all different directions and anything can travel faster than the speed of light. And I'm my own grandfather, etc. Right, right. Okay, so we've sort of learned in this show that randomness is about not being able to predict something.

And so predicting something is about sort of saying, OK, based on what's happening now, I can tell what will happen in the future. But because the photon is in two states or two places at once before you look... It's like there is no future to be able to say until you look. So it's meaningless to say. What will it be like when I look? Because nothing has happened until you look. Right. Is that right? Yeah, that's correct. So it means that the world is fundamentally indeterministic.

So, Dorit, I think we're finally in a position to answer your questions. It's really hard to come up with something that's truly random, and it's definitely beyond the ability of the human brain. Your brain is going to see patterns in everything anyway, even if they're not really there. But there are things in nature that really are random.

The fundamental particles that make up matter like photons can behave in ways that are intrinsically unpredictable. Our best theories of physics state that there are situations where it is impossible to know the outcome.

There's something a bit strange about all of this, though. If, as Nicolas said, the universe is fundamentally indeterministic at the level of these particles, how come anything exists that isn't random? In randomness... There's a lot of order, in fact. Here's Hugo Dumenil-Copa again. There are rules that are telling us what happens when you repeat.

an experiment several times. If you toss 1000 coins, roughly half of them will fall on tail half of them on head of course you can end up with only tails but this is a tiny tiny probability so little that it will never happen anywhere in the universe so there's something interesting going on here with numbers that if you have one or two for example atoms or you have like one particle it may behave in a truly random way

But once you have enough atoms to, for example, make a coin or to make a human, all the randomness will kind of obey these rules that means that it's very predictable. So my atoms are here and they're not sort of spread all over the universe at this moment in time. Yeah, maybe an analogy to keep in mind is that a priori, small atoms can actually teleport in close distances, you know, because it behaves at random.

So in some sense, you could imagine that if you run into this wall just next to us, you will be able to cross it. There is, in fact, a small probability that this will happen. But this probability is so, so small because all these atoms collectively, in some sense, order emerges from the fact that there are so many. Even if each one behaves randomly, there are so many that the whole body, your body, my body, is behaving in a kind of deterministic fashion. So if we run into this wall...

I can tell you, unfortunately, we will not cross it. In fact, there is a small probability we will, but it's so, so small that you would need many, many, many parallel universes and many, many tries. to manage to cross. And when I'm saying that, it's really a huge number. Please do not try at all to do that. Good advice from a trained professional there.

And speaking of advice, Dorit, here's how our experts would go about tiling your bathroom floor in a random pattern. This is what a mathematician would do. Here it's a two outcome thing, so what could have been done is simply... To throw a coin. Nice and simple, just toss a coin to decide which tile to pick. It's not truly random, but it's probably good enough.

here's how a neuroscientist would tackle it. I think the first thing I would do, sadly, is to buy some new tiles. So I would introduce some more variants into this. So the more differences you have between the tiles... the easier it's going to be to make something that still looks random. And here's what a quantum physicist would do. Well, she should buy a quantum random number generator. Okay. And a very patient plumber.

I think her plumbers and tilers have lost patience now with them because they've been asked to do this too many times. A quantum plumber. A quantum tiger. So there you go, Dorit. We would love to know which of those solutions you end up choosing. Thank you for a brilliant question and over to you for the credits. That's it for this episode of CrowdScience from the BBC World Service. The question was for me, Dorit in Austria. The presenter was Anand Jagatia and the producer was Ben Motley.

If you've got any random questions that you'd like the team to answer, you can email them to crowdscience at bbc.co.uk. Thanks for listening. Hello, I'm Brian Cox. I'm Robin Ince and we're back for a new series of The Infinite Monkey Cage. We have our 201st extravaganza where we're going to talk about how animals emote when around trains and tunnels or something like that. I'm not entirely...

We're doing one on potatoes. Of course we're doing one on potatoes. You love potatoes. I know, but... Yeah, you love chips, you love mash. I'll only enjoy it if it's got curry sauce on it. We've always got techno fossils, moths versus butterflies, and a history of light. Listen on bbc.com or... wherever you get your podcasts.