The Rest Is Science - Hannah Ranks Michael's Bizarre Watches

Episode Date: August 19, 2026

Michael Stevens keeps a small museum of unusual timepieces on his desk: a clock that runs backwards, a watch built to be read in complete darkness, and one whose entire face simply says "now." Each is a miniature experiment in the psychology of time, and each reveals something surprising about how our perception of time shapes the way we understand uncertainty and the world around us. The conversation then turns to logic and reasoning: how we make judgements, why we get things wrong, and whether thinking more carefully can help us make better sense of reality. It ends with your questions, including why so many of us are convinced we're simply "not maths people”. Is that belief itself, rather than any innate ability, the real source of our mathematical failure? ------------------- For more information about Cancer Research UK, their research, breakthroughs and how you can support them, visit ⁠https://www.cancerresearchuk.org/our-research/rest-is-science Cancer Research UK is a registered charity in England and Wales (1089464), Scotland (SC041666), the Isle of Man (1103) and Jersey (247). A company limited by guarantee. Registered company in England and Wales (4325234) and the Isle of Man (5713F). Registered address: 2 Redman Place, London, E20 1JQ. ------------------- Find The Rest Is Science all over the internet by ⁠⁠clicking here.⁠⁠ ------------------- Video Producer: Adam Thornton + Oli Oakley + Jack Meek Animator: Sam Benson Video & Social: Bex Tyrrell Assistant Producer: Lucy Lipscombe Producer: Simona Rata Senior Producer: Lauren Armstrong-Carter Chief Digital Officer: Samuel Oakley Exec Producer: Neil Fearn Learn more about your ad choices. Visit podcastchoices.com/adchoices

Hello, welcome to The Rest of Science. I'm Hannah Fry. And I've got a lamp above me that I just hit with my hand. My name, though, is Michael Stevens. Welcome. This is Field Notes today where we show off some loot, some bounty from our adventures, both real and cognitive. Yes. Today, you don't know what I'm bringing. You never know.

I don't. I often don't know until 30 minutes before. And I'm like, oh, crud. Luckily, I've got all this stuff around here I can show off. Today, we're going to have a great. time because I'm going to show you some watches, some timekeeping devices from my collection, not all of them, but some that I think are relevant to you and the show. Okay. Oh my gosh. I have a secret obsession with the history of timekeeping and I am excited. I'm excited.

Okay. First of all, it's not a secret. Your obsession with timekeeping. And two, the watches we're looking at today are Not so much, like, orological masterpieces. They are novelty watches. Okay. Watches that are a little bit silly. I can't afford to just get, like, you know, handmade, beautiful 300 jewel watches. But if you are listening, Rolex. Yeah, we would love to.

And we will talk about them and the process and how great they are for our richest listeners. But most of my watches are like this one. Okay. It's a little silicone-strapped white watch. And if you look at it, it tells you what the time. time is. It says now. Helpful. Useful. Does it change? Yeah. Oh, and it says on the back, it says steal time back. I guess that's the brand that made it. I got this many, many years ago. So for those of you listening, the watch face looks like it should have workings inside of it,

but instead the face just has written as though it was a digital watch in that kind of like seven-segment display. It just says now, N-O-W. So what time is it? Oh, it's now. And in a way, you know, that's a good thing to know. I sort of wanted you to be able to scroll the dial forward and then it say the future. Oh, no, because it's never going to be the future, Hannah. This watch tells the truth. It will never be tomorrow. Because as soon as the next day comes, it's today.

Tomorrow's always out of reach. The past is always out of reach. All we have is what this watch can give you, which is to tell you that it's now. You know, it's sort of the most philosophically elegant watch there is, you know? Yeah. All you have is now. It's not functional. It has a crown on it, but you can't turn it.

You can't, it doesn't, it doesn't move at all. It doesn't even, like, move as a joke. But it is funny. It's fun to have on. And people don't notice until you go, well, let's see. Okay, it's right now, it's now. I have a feeling that in an hour it'll still be now. This episode is brought to you by Cancer.

Research UK. Do you remember when we discussed why feet are so weird? Well, one particular footbone holds an even stranger surprise. It's helping shape our understanding of cancer timelines. And for that, we're going to need to go all the way back before Neanderthals even existed to a 1.7 million-year-old footbone. Researchers have identified a tumor in it in the oldest known example of cancer in people. Which really shows that cancer is far from a modern disease. Beating a disease so deeply rooted in our biology won't happen overnight. But today, Cancer Research, UK scientists are discovering incredible ways to turn our biology against cancer. In fact, Cancer Research UK has helped double UK cancer survival over the past 50 years.

And their world-class research is driving even more discoveries to tackle over 200 types of cancer. For more information about Cancer Research UK, their research, breakthroughs and how you can support them, visitcounterresearch.uk.org forward slash rested science. Real Canadian Superstore has everything you need this back-to-school season. Save on lunchbox savers like Ziggy's sliced deli-meat products for always 375. And get life brand pure Vita shampoo or conditioner for $8 each. At Real Canadian Superstore, when you're ready, we're ready with a whole world and more. Get your tickets now for the dog stars. It's no surprise how fast civilization can disappear.

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Okay, tough guy. And Guy Pearce. Arm up! The Dog Stars, directed by Ridley Scott. In theaters, August 28th. Get tickets now. These are the kinds of watches I collect, okay? It's sort of like a dad joke, but in watchful.

That's what it is. Yeah, I'll give you another example. If you give me 10 seconds, these are my favorite bits of the podcast when we get to see an unshielded view of Michael's room and wall of strange and obscure objects. In the back there, there's like a miniature table and chairs. There's a doll's head just floating on a shelf.

There's, what else have we got? there's like some strange puzzles. Hello, there he is. And there's Michael Stevens right there. There's some ducks sitting on a sofa. So, okay, I found it. This is another example of the kinds of things I collect. They fit different genres of item.

Like, it's a watch. It's a book. But it's never a expensive thing. It's a weird thing. So when it comes to books, I probably own maybe two books that actually have some kind of value. The rest of them are books like this one I found at the thrift shop next door. This is written by Osho, the guru, who if you know anything about Osho, you'll know that his followers eventually poisoned the water supply in their municipality in Oregon. So it's like one of the only instances of domestic chemical terrorism in America.

There's a whole documentary on Netflix about it. Sorry, did you say it's a cookbook? It's not a cookbook. It's called no book. And you go, what does that mean? It's a hardcover book. It's got a picture of Osho, the guru, there on the front. And when you look inside, this is what you get.

You get a picture of OSHA, another picture. You get a cover title page. And then the whole book is just blank. Every page is blank. That's what he has to teach you. But yet it does mean something at the very end. It ends with what I could say, I have told you. What I could not say, I have given you.

So I guess it's supposed to be like a meditation aid where you're like, oh, yeah, sometimes talking just gets in the way of understanding. I don't understand. I don't understand. I have lots of questions. Who published it? It wasn't actually him? Yes, it was. How long ago is this guy?

I've never heard of this guy. Also, what has it got to do with watches? I'm not sure I understand. Oh, it's just to show that my versions of things that I collect are always goofy things. It's like, oh, I've got a really nice book. Every page is blank. I see. Or I've got a really nice book on numbers.

It's the square root of four to 4,000 decimal places. Yes, exactly. 2.000-000-0-0-0, and there's like hundreds of pages of those zeros. just to make sure you know that even 10,000 places in, it's still, it's still exactly four. They checked. What's his name, No Show? How did you spell it? O-Show.

O-S-H-O. I've read a lot of O-S-H-O. Actual Books about reality, meditation, because I think I just wanted to get into the minds of the people who eventually decided that their commune needed to commit chemical terrorism. Right. I've never come across this guy. Okay, let's go back to watches. This watch I really love, and it actually comes in really handy. It is from, I'm pretty sure, yep, it's from the Unemployed Philosopher's Guild.

And instead of having 1 to 12, it uses the watch face as a circle, and it gives you radians. So up at the top, we have 2 pi, and at 3 o'clock we have pi over 2, down at 6 o'clock we have pie. So what this is showing you is how many radii of this watch face could fit around the circumference. That's what a radian is. A radian is equal to 57.3 degrees. So if you imagine taking the radius of this circle,

the watch faces circle, and there was like a string that you could wrap from 12 around, you would hit one radian at 57.3. three degrees. That's not normally where there's a numeral on a watch. But because it takes two pi radian to go all the way around a circle, it takes one pi diameter, but it takes two pi radii. That means that you go all the way around, you're at two pi. That's where the 12 would be. And it also shows you whole number radians. Like if you look closely, they do show you where one radian is. And then they show you two, three, four, five, and then six. And then there's a little

bit of change since two pie is required to go around. Of course, because zero's at the top. Okay, yeah, I love that so much. I love that so much. Essentially, it's saying that if the minute hand is sort of your unit length, it tells you, it tells you around the outside how many, how many multiples of the minute hand you have traversed in that moment. Yeah, exactly. And so, So a quarter of the way around a circle means that you're a quarter of two pi around. So you're pie over two, your half pi, radians around the circle. And then they divide that further to give you where one, two, three o'clock should be. So this watch needs batteries.

Right now it says that it's, it basically says that it's 1.25. Or in radians, it is 5 pi over six past pi over six. I can't tell you how much I want that. It's really good. It's a good conversation starter. And it's also just good to reference when you're like, oh, wait a second. How many radians go around a circle? I mean, if you wear it every day, you never forget.

But still, it's a good little cheat sheet. I like that. Who made it the retired, the Out of Work Philosophers Club? The Unemployed Philosopher's Guild, they make a lot of famous stuff, including they made slippers that have Sigman Freud. face on them and they're called Freudian slippers. Freudian slippers. Do you know what?

A friend of mine who was studying philosophy at university, that is what I gave her for Christmas. I got a pair of slippers and I hand stitched the word Freud onto them. They have got a very similar sense of humor to me. Exactly. Exactly. They're pretty great. I've got a few other things from them. I'll show some other day.

This is a bit of a bummer. The batteries in these watches have all run out. So you'll have to just believe me on this one. What do you notice is weird about this watch? Okay, the numbers are backwards. That's right. Yeah, instead of going clockwise around, 1, 2, 3, 4, 5, 6, 7, and so on, the numbers go counterclockwise. If this watch were running, you would see that the second hand goes counterclockwise.

And so does the minute hand and so does the hour hand. So it's a reverse watch. It's not for looking into a mirror because the numerals are still written normally. but they go around the watch the wrong way. So three o'clock looks like nine o'clock. Yeah. And this is, if you're just listening, it's an orange watch that says curiosity box on it

because we made this watch and it was in a box years ago. It's not the only backwards watch I have. There's a different one that I didn't really like the look of it. So I was like, let's make one that I'm more aesthetically pleased by. There's the back of it. It's got ink our octopus mask. got. It's amazing how quickly you adapt to counterclockwise clocks and watches. It's just you start to understand, oh, we're moving this way. So when it's, when it looks like it's 35 past the hour,

it's actually still not yet 30 because it's working its way, the minute hand's working its way to the bottom. And you get really into it. And then when you go back to a normal watch, you're like confused and you have to relearn how to tell time. Really? Well, so you can glance at it. If you've been wearing it for a while, you can glance at a backwards watch and be like, yeah, got it. Yes, yes. For me at least, it generates this feeling of counterclockwise is how time moves. And so if the hour hand is between the eight and the nine, I know that it's approaching the eight. I know that it's not coming up to the nine. It's going, wait, sorry, I'm confusing myself now. You've spent too much time switching between clockwise and counts clockwise watches in your life.

I really have. But you know that if you see the hand between the seven and the eight, that it's climbing counterclockwise towards the eight. Rather than clockwise towards the start. It's like an idea of motion that is what comes over you. I haven't worn this watch in a long time. I want to see Michael, I hate it. The other one's great.

That one, I hate it. Don't want it. All right. Well, now how about this? This is a really unique piece. It's a good conversation piece. It's an Apple Watch. I should tell people who are listening to this only.

Michael is holding up to the camera. An Apple Watch, if Apple made watches around maybe 1989, it has the original Apple logo with the graded colors from green all the way through to blue. The minute hand is a red stick. The second hand is a squiggly yellow line and the hour hand is a green triangle. Hang on, what's up in the back? Not much. It says stainless steel back, contemporary design, Japan movement.

Yeah. I strongly suspect that is not actually made by, it's not an official. piece of merchandise. Well, you would be wrong. No. This was an actual watch made by Apple. It is a quartz movement watch that they made in 1995, 20 years before what we today call an Apple Watch. They called this an Apple Watch.

It was a free gift that you could get if you bought Microsoft System 7.5. You had an option. You could either choose to get a copy of Conflict Catcher 3, which was some software, or you could get an Apple Watch. And that's what they called it. They said, this is an Apple Watch. And I have one. So these are not very expensive.

They might be expensive now, as people I kind of learn that this existed. They probably are, especially after this podcast. So the design is very like Memphis, if you're familiar with that group. So it's got this brilliant 90s geometric, bright-colored look. And it came with a black silicone strap that had rotted away.

So I've replaced it with a metal strap, a metal band that belonged to a watch my grandfather owned. Hold on. How long have you had it? Have you had it since the original time? No. No, no, no. I got it.

My wife got it for me as a birthday gift. I told her, I only got it three years ago. Okay. They're about 400 quidge. That is a great, A, a great birthday present. And B, a great watch. That one I like. It's a special piece of history.

And again, it's a funny thing. And people will be like, what is that? You're like, it's an Apple Watch. And no one thinks that it was made by Apple, the company. But it really was. And it was officially offered by them. And, yeah, it was only about $100 when my wife got it. So I guess it's also an investment, huh?

Hey, look, four times is quadrupled in value over the space of a couple of years. It's better than Apple's stock. Maybe. Maybe. Now, now I've got two more to show you. This one I really love. It's a little bit dirty because it's been, again, I've just been wearing sort of like one everyday watch. But this is a, it's not a braille watch.

It's a tactile watch. So if you look at this, you'll see that it's got a typical watch face that's a circle. But there's a groove in the middle that's like a little circle. And there's a ball bearing stuck in that groove. And that ball bearing is stuck on a magnet. So if I push it out of the way, I can roll it back and forth in the groove. But it'll eventually get caught back on where that magnet is. Okay?

And then along the edge, there's a groove that also has a ball bearing stuck in it. And if I push with my finger, that ball bearing becomes loose. And now it's rolling around in that groove around the edge of the watch, but it will get caught on the magnet. So the little one is the hour hand, and that big one is the minute hand. So you can tell what time it is without looking at your watch. you feel how that little ball protrudes a little bit above the watch face. So you can be blind until the time. Or you can just not have to look your eyes down at your watch, you know, if it feels rude.

It's absolutely perfect for people who work in pitch blackness. Yeah. Or if you work in pitch darkness, you don't want to illuminate something. You can just feel what time it is. A burglar, for instance. It's perfect for committing crimes and being on time while you do it. So obviously these magnets move around at the correct speed. so that the ball is always being pulled

to represent the correct hour and minute. Well, how else are you going to meet your getaway car? This is, you've, you've accidentally chanced upon something here. I'm just realizing I can probably, oh yeah, here we go. I apologize for all the dust in the grooves. I should have cleaned this before the episode. But if I turn the crown, watch that minute hand. See that? It moves around.

Oh, that is satisfying. And then the hour hand there, so I misspoke. The outside groove is the hour hand and see how turning causes them to move at different speeds around the watch connected to magnets. Yeah, you know what? That's really satisfying. I like that one. And these balls, you can touch them. And if they get moved out of the way, no problem, just let go and they'll stick back on the magnet. So I'm going to give you a ranking at the end of this of all of these watches. I hope you're okay with that. Yeah, I'm okay with that. So here's the final entry. This final entry is a Sturmanski watch. It's the watch I've been wearing this entire time. Tadda. And it's a Russian watch that, first of all, I love because it's a 24-hour watch. Instead of having 12 at the top, you've got 24 at the top. Hold on a second then. So when you're looking at this, where it would be pointing at 3 o'clock, for example, you are actually looking at 6 o'clock. That's correct. And instead of 6 o'clock being at the bottom, 12 o'clock noon is at the bottom. So the hour hand only goes around the face once in a day.

Okay. Hold on. Does the minute still sweep around? Sorry, I'm just realized I'm holding my daughter's pen. Oh, that is so cute. You should say more. It's a, it's like a lavender pencil with a happy face star on the top with like a keychain holding this fuzzy little ball. Not just any bobble. It is a cute little pillow for an elf, for a fairy. I'm an extremely important professional woman, okay? And this is the stationary that I choose. Okay, but I wonder what the minute hands is doing. Is the minute hand still doing one entire sweep? Yes. The minute hand goes around once an hour.

Oh, no, no, I don't like it. So you're having to sort of translate half of an original system and half of a new system when you're reading it. But it's easy because you look at it and you go, okay, like right now, this is actually set to the correct time. So we're kind of doxing ourselves on how long it takes for these episodes to be recorded and then released. It is the 31st right now. And as you can see, we are just past 13 on the hour hand. So it's 13. And then where how many minutes passed?

We're like 23, 24 minutes past one or 13. I'm happy to look at it myself because when I hold it up to the screen, I'm seeing a mirror reversed image. But you just need to kind of relearn where the hours are. But really, it's got numerals on it, so you just go, oh, it's 1324. You know, it's not that hard. Okay. So you've shown me five in total. Is that correct?

One, two, three, four, five. There's one more piece of this that I want to show. And this is my favorite part is that it is actually a commemorative watch that commemorates Alexei Leonov's first spacewalk, the first human spacewalk in 1965. I'm trying to move this around to not catch the glare, but it's got an engraving on the back. I'm not sure if this is called engraving. I don't know enough about metalwork, but it's got a depiction of a human doing a spacewalk outside of that module.

And it's a cool reminder of human space history. And then the Russian and the side. Yeah, nice. Okay, you know what, that's bumped it up a little bit. I'll let it go up one place. I'll let it go up one place. Okay, I've got my ranking. Do you want to hear my ranking?

Yeah, yeah. I'll hold them up. Okay, thank you. Right. Which way around do you want it? Do you want the ones I hate the most first? Yes, I want the bottom first. Okay, here we go.

All right. In reverse order. Okay, right at the bottom, because I think that this is an abomination and should not exist, is the red backwards clock. Yeah. Okay. I think that does something horrible to my brain, and I never want to see it again. That's a valid answer, but I'm going to strong disagree on that.

Okay, next. Okay, one up from the backwards clock, it's just, it's just suddenly swap places. It's only now, swap places with the 24-hour watch because I had the commemoration of space event on the back, is the now watch, which I, you know, I kind of like, but it's sort of a one-time thing. It's kind of impractical. And then, yeah, if you wear it too many days in a row, people start to be like, oh, gee, it's like a thing rather than just a joke. He's the now watch guy. Something ironic about how a now watch is a joke that only works once and once only

and never again. Isn't it? There's some poetry to that. There's some poetry in that. Okay. So next up, I'm afraid, is the 24-hour clock for the same reason as a backwards clock, but it gets one extra place purely for the back. I think maybe you should wear it backwards next time, okay, if you really want to.

It's not transparent. It wouldn't work. It's not transparent. Okay. Just one up from that is the pie. clock, which I am inherently drawn to purely because of my status as a mathematician. I like it from the outside. It actually tells the time, sort of, kind of.

But, you know, it's good for learning radians. Yes. Not much more. One up from that is the Apple Watch. This is the first one of all of the others that gives you an actual, accurate representation of what the time really is without confusing you. So that is what gave it number two position. It is true.

the first regular watch. It's the first one that tells the time. And then number one, purely for my ambitious hopes to become a master criminal in future, it's the magnet, it's the magnet watch. I enjoy that one greatly. That one's very good. As long as you don't tell me that it actually runs backwards or, you know, upside down or inverted or you have to do some complex calculation to convert the time into the real time

once you've done that, in which case I hate it again. It goes back down to the bottom. No, it's great. It's great. And the problem with all of these, except for the Stramansky, is that they're battery powered. And so I have to keep replacing their batteries. This one is one of those. You wind it, but it also winds itself. It's self-winding through the motion of my hand. So I can wear this one every day and never worry about it. Okay, fine. It can come third. That was wonderful. Thank you. I appreciated that little insight into the things on Michael's wrists. Should we have a little break and then we can come to some questions? Let's do it. I can't wait. All right. See you guys. after the break.

What are you doing on the 4th of September? Oh, you're still free? Why? Haven't you heard that me and me? Are all going to be at the South Bank Centre? We have full weekend live shows for you all from your favourite gold hanger podcasts. Hello, all you're going to be there with Tom Holland talking about the most scandalous housewives of Regency England.

And I'm going to be sitting down with the wonderful Anita, Anna, my co-host on The Empire Pod. to talk about the history of modern Iran with the absolutely brilliant Ali Ansari. And Dominic and I will be telling a thrilling Victorian adventure on the Friday night to kick things off. And it's not just us. Mary Beard is coming. Stanley Toucci's coming. You really couldn't ask for a better guess list, unless you were on it. If you want to join us, head to southbank centre.co.com.uk for the full line-up and buy your tickets now. See you there. See that. This episode is brought to you by Cancer Research UK.

When we talk about beating cancer, we often focus a lot on survival, and that can mean overlooking impacts that last long after treatment ends. Yeah, for example, take cancers in children and young people. The treatments themselves can be incredibly harsh. They can cause lifelong side effects like infertility or hearing loss. And Cancer Resets UK is working to change that, because young people, they should be able to grow up hearing the voices of the people that they love and living their lives to the fullest. That's right. And one clinical trial led by Cancer Research UK showed that giving another drug,

alongside chemotherapy, nearly halved the number of children losing their hearing. And today, the treatment combination is being used by doctors across the world. For more information about Cancer Research UK, their research and breakthroughs, and how you can support them, visit cancerresearchuk.org

slash rest is science. At IKEA, we make things just for college, Like the Rosenmandel blackout curtains in gray. They say you can't put a price on sleep, but we did for the low low price of $49. Why are you in my room? Shh, go back to sleep. You have a big exam tomorrow.

Shop back to school at IKEA. Okay, we're back. Should we do some questions? Let's do some questions. This one came in through email from Bo DeNarius, who says, Bayesian reasoning is awesome. But how often do our emotions, good or bad, mess up our ability to properly use it? Some examples, being head over heels in love leading to overly optimistic probabilities.

Anger making us resist contradictory evidence or disgust, skewing risk judgments spring to mind. Yeah. Okay. Excellent question, Bo. I think probably let me first tell you a little bit about Beijing reasoning what it is and where it comes from because you will hear a lot of people, myself included,

act as though this is like a magical formula that solves everything in the universe and that's sort of like the one formula to rule them all. Yeah, okay. And when you actually hear what it is or what it does, it sounds so absurdly simple

that it doesn't make any sense that it should possibly be that powerful. So the original the original Bayesian theorem, the original formulation for it, wasn't Bayes himself. It was many years later that it was then attributed to Bayes. But Bayes was this, he was a reverend who was a man of the church. And he would write these letters of mathematical thinking to various people. And in one of these letters, he imagined a situation, which I think is the best explanation of this.

So, okay, I want you to imagine that you are sitting, with your back to a table. There's a table behind you. And onto the table, you throw a red ball. Let's say a beanbag, actually, so that you know that it's going to land on the table. It's going to stay on the table. Right.

You chuck it over your shoulder and it lands on the table. Now, at this point, you've got no idea where it is on the table, right? The table is essentially like a square, a 2D surface, and it's somewhere in that 2D surface, right? A friend is playing this game with you. So as you chuck successive beanbags over your shoulder, they are going to tell you a little piece of information. So your red one is on the table. You are now going to throw over your shoulder a series of blue beanbags.

And what happens as you throw them over your shoulder? You have a friend there who will tell you where the blue beanbags land, but only with respect to your red one. Okay. So as you throw one over your shoulder, you say that your friend says, okay, the, bag that you have just thrown is to the northwest of your red beanbag. Okay. You throw another one and they say, oh, now it's to the northeast of your beanbag. And you carry on throwing, carry on throwing, carry on throwing.

And every time, every new beanbag that you throw, your friend will tell you where it is in relation to your beanbag. Here's the thing. Every new piece of information tells you a bit more about your red beanbag. you've got no idea where it is. But after you've thrown five, ten, whatever beanbags, if all of them are landing north of your beanbag, of your red beanbag, you're like, okay, actually, I've got quite a lot of information here

that tells me that probably the red one is somewhere on the south side of the table. Yeah, right, right. Likewise, if half of your throws are landing to the east of the red beanbag and half of them are landing to the west of your red bean bag, then you'll probably know that your red beanbag is somewhere in the middle of the table. So as you do this, you can come up with this guess as to where your red beanbag is, in this example, is sort of at the south middle of the table. And what Bayes realized then is that even though you have never been told, this is where the red beanbag has landed, you can infer that information by taking successive pieces of information and updating what you believe at every moment in time. That essentially is Bayesian thinking.

Has that made sense? I'm not sure. Was that okay? Should I do it again? Yeah, no, that makes sense. That makes sense. So here's my question, though. This whole thing requires that you have a friend who does know where the red bean bag is. Yes. What if no one knows where it is? So there is lots of evidence that this is the way that our brains work all the time.

And this is the reason why visually, illusions, auditory illusions and so on, end up working. Because right now, I have a belief about the state of the world. But my skull is like this locked off black box with no sound in it, no, no light in it, nothing. And it's only my senses, and your senses do, right, on the outside of my face and body that are transmitting information. So in that situation, it's like my eyes, your hands, your ears are like the friend giving you little updates. And your brain is putting all of that information together to try and work out what the real picture is. So right now I'm sitting in this room and given everything that I know, all of the past and all the future,

the context and so on, I have a belief that there is a door to my right hand side. And as I sort of look over at it, it's like, oh, okay, well, my brain is adding more information and my belief that there's a door there is extremely strong. But if I showed you a picture, one of the classic, you know, visual illusions about, I don't know, like a strawberry, which has got a shadow over it and you think the strawberry is red,

but actually it's blue. Yeah. Your brain is like assuming, your brain is like, okay, given all of this information, I believe that the strawberry is red, even though the strawberry isn't actually red. Right, right. Okay, so I'm going to ask a question

because I hear about Bayesian reasoning all the time. I feel like I've also heard it described as a like, if you've got a coin and you flip it 100 times and you get heads every single time, an old school way of thinking is to say, well, on the next flip, it's going to be either heads or tails, 50-50 still. But the Bayesian answer would be, no, your coin is probably not fair.

Right. I think the key thing that is different to classic probability of like count it up divided by, you know, whatever is 50%, 50%, is that with Bayesian thinking, you are never absolutely sure. There is always room for doubt, always room for doubt. Even if you go through the world and the world confirms your ideas about what it expects it to be almost all over the time, there's still enough doubt in your kind of your, your, you know, picture of reality. When you walk down an escalator and you think, expect it to be moving and it isn't, your brain does a little jump. It's sort of correcting its own version of reality. Got it. Sort of expecting it to move. And then the evidence from your input says that it isn't, so you're kind of, you have to update. And that little jump that you get, the little jolt that

you get is your Bayesian brain being like, okay, but we made a prediction. It didn't turn out to be right. We need to update our understanding of the world. So then how is this made formal? Like, it feels like it's a lot of like, well, the vibe is like maybe, you know, the really smart person would say that, oh, my beanbag's probably down below. How is this? Because probabilities are so, you know, you take the outcomes, you divide by the blah, blah, blah. There is an equation. And it's like, it's almost laughably simple, this equation. Honestly, I think the thing about Bates, right? In fact, actually, the book that I'm writing at the moment is basically about Bates. Although I will never sell it that way. I say it's a book about doubt. I hear about this all the time from Nate Silver. Yeah. He always mentions like, well, from a Bayesian perspective. And I'm like, what do you mean?

Yeah. It means that you're never certain. You're always collecting evidence. And you're always updating your current best guess. That's what it means. I see. I see. Because he also talks about priors a lot.

Right. So prior is your best guess right now. And then you update it. Got it. I mean, really, all of the evidence is pointing towards your brain being this phenomenal Bayesian machine. Right. That is, that has hypotheses, that updates it with the evidence, and then comes up with this sort of constructed, with room for uncertainty version of reality, right? It's amazing. The thing is, the question that Boe asks is really interesting because if your brain is perfectly beige and why do people do a rational thing? things, when they're in love, when they're angry, when they're full of anxiety, when, you know, all of these different types of moments.

And it's true, people are irrational in love, right? They're irrational when angry. But actually, if you buy into the Bayesian brain hypothesis, then it's still, there's still a way to argue this through because, okay, so let me give you an example, right? You hear, this is sort of ancient brain, you know, you're like, whatever, let's go back to a hunter-gatherer world and you hear a rustle in the in in the bushes um you could say that your prior your your existing understanding of the situation is okay that's very unlikely to be a tiger uh let's analyze all of the evidence and the data um let's say uh the the the the probability of there being a tiger in this area at this time of day a blah blah blah blah blah blah blah blah You could do a whole calculation, and you could say, okay, now I've heard a Russell, I'll update my understanding and conclude that it's not a tiger.

Yeah. That's sort of like a naive way to interpret what the Bayesian formulation of that question would be. But in reality, like that would lead you to die. Okay. So if instead your fear in that environment is like, okay, I really, really do not want to be eaten by a tiger, what you're doing then is you are really heavily waiting your sort of prior belief that there could be tigers at any corner. So all you're doing is you're tweaking how much the new evidence counts

versus how much your existing belief about the situation counts. And if you are expecting there to be a tiger at any moment in time, you're still doing Bayesian updating. Yeah. You're still doing the same thing. You're still assessing the information and sort of drawing conclusions based on the evidence as it comes in. But you're just doing it in a slightly different way than a cold, emotionless calculation. Yeah, right.

And that is a smart thing to do because we evolved to survive, not calculate the truth. Right. That makes me think of this, I think it was like a tweet or something I read years ago. that was like, the sunk cost fallacy is not a fallacy at all. Like, if you've already been waiting in line for an hour, stay in line. Because your identity is now wrapped up in achieving this finally. You've become an hour more of a person who's in this line. Like, it's not irrational to stick with it.

It's not a sunk cost. It is who you are now. I mean, I couldn't agree with you more. I couldn't agree with you more. I think where it goes wrong, question mark, is that I just, you know, as you said, we are not, we're not statistical machines. Right. We might have Bayesian brains, but we're not these, we're not data crunches naturally. We're not like, there might be a mathematical formulation that can explain how our brains are working, but we're not math engines.

And so I think sometimes we end up making calculations in a world that wasn't really. designed for us essentially, right? You know, anxiety and love and anger and all of these things. I think we're making calculations based on ancient biological Bayesian systems that don't necessarily feel the world they find themselves in. Very true. Okay. Should you do your next question? Yeah, let's do the next question.

Right. This is for... What I really love about this is how obvious it is, which questions are for you or which ones are for me, even before... Even before we've assigned them. Okay, this is from Vittor Guidoni. Swiss cheese has holes. So the more cheese you have, the more holes you have.

However, the more holes you have, the less cheese you have. So logically, of course, the more cheese you have, the less cheese you have. What's your favorite, syllogism? Mm-hmm. I'll leave it as an exercise to the listener to find the error in that syllogism about the cheese. But my favorite is kind of similar. I don't know if it's similar, but here's my favorite. I'll just get right into it.

My favorite is, nothing is better than God. A ham sandwich is better than nothing. Therefore, a ham sandwich is better than God. Now, what's going on there is two different meanings of the word nothing. In the first case, when I say nothing is better than God, I mean there is no object better than him. No thing. But when I say a ham sandwich is better than nothing. Nothing, I mean a ham sandwich is better than an absence of things.

Mm-hmm. However, it's the same, it's the same word, nothing. It's a little cheeky little wordplay. So, okay, nothing's better than God. That means I put nothing above God because nothing is better than God. But a ham sandwich is better than nothing. Well, then, you know, God's here below nothing in ham sandwiches. I love that.

I did a whole short about those two different meanings of nothing and how from them we can construct all of the cardinal numbers. Mm-hmm. That was good. I like that. I'm trying to think if I have any. Yeah, do you have one? Let me see.

There is one that's similar to your ham sandwich one, which is I am a nobody. Nobody is perfect. Therefore, I'm perfect. Nice. Yeah. Again, words for nothing or no thing. Nobody? Yeah.

No one can lead us to these really funny conclusive. I like that. I'm a nobody and nobody's perfect. You'd agree with both of them. I'm a nobody. Yeah. And nobody's perfect. Okay, so far so good. Therefore, if I'm nobody and nobody is perfect, then I must be perfect. Nice. I remember I once a very long time ago, and I won't go into the reasons why, but I once interacted with someone who was in a very strange cult. And I was having a chat with them about their life's philosophy. And they basically, did a version of this. I can't remember it perfectly, but it was something like everybody is shaped by their family. Every family is different.

Therefore, you choose your family or something. Basically, it was like, sensible thing, sensible thing. Your soul selects your family before you were born, right? And it was like, okay, sorry, sorry, can we just go back to that? But I think actually this is the trick. This is the trick that actually gets used quite often. And it's like, sensible thing, sensible thing, completely wild, strange connection. Right, right, right.

And you're left being like, okay, sorry, can we just, sorry, can we, there was a bit that you missed there, which didn't make any logical sense whatsoever. Yes, yes, yes. They do happen all the time, especially in commercials and in like influencers selling a product. They're like, look, you got to do this, you got to do that, therefore. And then the answer does not follow logically. And not in a funny way, like the ham sandwich one, and more of a like, wait, that's just disconnected. But it's got the structure of a syllogism.

So it smacks of reasonableness. And yet it's just a bunch of words. And yet it's just a bunch of words, exactly. All right. Should we do the last question? Last question was emailed in by Charlotte. Hello, Hannah and Michael. I did GCSE maths.

And despite all my efforts, I only got a C. My science grades weren't much higher. As I get older, I realize my difficulty was due to being bogged down in the, But Why? My question is this. Are there just some brains that are more or less able to instinctively interpret maths? Okay. Thank you for saying maths there. I appreciated it. Right. So the answer is sort of yes and sort of no, I think. There is something called Discalcula, which is like a real genuine thing.

So people talk a lot about math teachers especially talk a lot about number sense. So this idea that you just have a working sense of how big or small numbers are. And that is definitely better in some people than others. You could put mathematicians in MRI scanners. Actually, mathematicians don't necessarily have that great a number sense. It's more, you know, you don't end up working with numbers that often. But an example of this is I think we've spoken about before. if you give a number line from zero to one trillion

and you ask people to mark a billion on the line, a lot of people, especially those who don't have a great number sense, will put it somewhere in the middle of the line below. It's about halfway. When actually it's a thousandth of the way along, it's essentially still at zero. Yeah, yeah. So you can do this,

but not just that when you ask people sort of rough calculations, like what is 10% to 56 or whatever it might be. There are some people who just are quicker and better at it than others. And that is because of a particular fold that happens in the brain that lights up more in people who are better at this than others.

And people who have discalcula essentially struggle for that reason, right? It's like a physical difference in the brain. There's also one of the things that makes people naturally better at mathematics than others is that it takes a lot of working memory

to be a good mathematician. So if you think about, especially if you're doing like a complex calculation, you've got to like move things around, you've got to like flip things upside down, you've got to like bring in other things, you've got to be like, wait, why are we carrying a one? What's going, what was the point of this?

What were we doing this for again? So people who have slightly better working memories do tend to be better mathematicians. But I think and I think also a lot of the evidence suggests that actually a great part, a really significant element of being good at maths or not comes down to something that is called self-efficacy. And this essentially, it's kind of like self-confidence, but it's different because with self-efficacy, it's measurable and changeable. So self-efficacy is essentially how likely you believe you are to be able to complete a following.

task. And it is so innately connected to mathematical ability like you would not believe. Really? But which way is the causation go? If you believe that you're going to fail, you almost certainly will. If you believe that you can do it, you almost certainly can. And this is why maths anxiety is such a real thing, because as soon as that kind of that thing starts in your head, it actually actually ends up becoming true. It's a self- fulfilling prophecy. Yeah, and it feels like it's true all the time, but it's so especially true for doing mathematics.

It's so especially true for mathematics. And the thing about this is that mass anxiety and self-efficacy in math is cultural. And there are so many amazing experiments that really demonstrate this. So one of them that I really like, one of the things that demonstrates this really clearly, is you take students from around the world

and you give them a math question and half the people get easy questions and half the people get actually secretly impossible questions so they're set with tasks that they literally are not able to do and then after they finish that question you say okay or after they've kind of come to the end of the time whatever it might be you say to them hey do you want to do another one would you like to do another question and pretty much without fail,

the kids from the Western world say, the ones who had the impossible question are like, no, thanks, I don't want to. That sounds horrific. I did not enjoy this. This is a comment on my own intelligence and ability. I do not want to go anywhere near it. Yeah, yeah.

If it's an easier question, then more likely to say, yeah, yeah, yeah, I'd like to do it, right? So the kids from a Western world, if they believe that they will be able to do the next thing, they're like, yeah, okay, fine. You take kids from Asia, particularly from South Korea and Singapore, which regularly are the number one in the world

for scores at school. The results completely flip over. Oh, wow. So the ones with easy problems are like, no thanks. Yeah, you give them these questions like, yeah, I mean, sure, I can do another one for a lot more T. But you give them an impossible question and the number of kids who say,

I would like to do another one goes up, not down. Wow. Because they culturally know that this is hard, but they also know that it's achievable. Right. And so their attitude is, ah, okay, I didn't get that last one. It means I need to try harder. It means I need to put more work in. It means I need to really focus more on this particular problem.

And that is definitely something I think that ends up, I see it over and over and over again in schools. particularly in girls, right? Self-Africacy has a particular problem in girls that as soon as you start to believe that you can't do it, it ends up becoming true. I should just say, actually, I mean, even in this question, Charlotte, that you wrote, right? I did GCSEMAS, despite all my efforts, I only got to see. I know what my difficulty was. I know what I couldn't do. My brain is just instinctively less able to do it. I can hear it in your voice, right?

I can hear it in the writing. It's exactly the same thing as I'm already describing because I would say that somebody who continually questions but why is absolutely grade A mathematician material. That is what you want, somebody who is unwilling to stop until they get to the bottom of something. That is such a perfect way to put it, Hannah, that a mathematician is the one asking why.

If you're getting A's in those kind of classes, then you're going to be a fantastic number. number cruncher. Oh, that's great. Because that's what math was. I mean, at least for me in America in high school and college, it was if you memorize the formulas, you would get the right answers. But if you were still struggling with how do we define a limit, you're going to get a D in the class. You got to just accept it. And so I think you're right. I think the skill, the interest in why, is what really makes a mathematician. Absolutely. It's the difference between instrumental learning.

where you're just learning the rules without the reasons so you can apply it, which is what you have to do for exams. And then relational understanding, which is like, I want to pull this apart and get to the bottom of it. Yeah, and it's unfortunate that we test one, but care about the other. Yeah. Believe in yourselves more. I know it makes it sound really simple.

Yeah, it's, guys, come on. It's so much harder than that. It's so much harder than that. But, yeah, it's a real shame. It's a real shame that this happens. and there's a number of people around the world, really brilliant people who are trying to change it. Yeah.

Right. Now that we fix the maths education system, we have got to the bottom of our brains. We know where ham sandwiches fall in the hierarchy. And can sort of tell the time with one of your watches. Well, with only the only one that's running. I think that brings us to the end of this episode. But as ever, please do.

send us in your questions, the rest of science at goalhanger.com, comment on this video, share it, like it, subscribe to it, send it to your friends, transcribe it and print it on paper and stick it around your room so you can read it at nighttime. Do whatever you want with it. Yeah, please do that. We will see you next week. See you later. Real Canadian Superstore has everything you need this back-to-school season. Save on lunchbox savers like Ziggy's sliced delimie-meat products for always 375. and get Life Brand Pure Vita shampoo or conditioner for $8 each. At Real Canadian Superstore, when you're ready, we're ready.

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