Bizarre Watches and How They Work

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

• 0:01Speaker 00

  Hello. Welcome to The Rest Is Science. I'm Hannah Fry.

• 0:03Speaker 01

  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.

• 0:17Speaker 00

  Yes.

• 0:18Speaker 01

  Today, you don't know what I'm bringing. You never know.

• 0:21Speaker 00

  I don't.

• 0:21Speaker 01

  I often don't know until 30 minutes before, and I'm like, aw crud. Luckily, I've got all this stuff around here I can show off. Today, we're gonna have a great time, because I'm gonna 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.

• 0:44Speaker 00

  Okay. Oh, my gosh. I have a secret obsession with the history of timekeeping. And I'm excited. I'm excited.

• 0:53Speaker 01

  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, watches that are a little bit silly. I can't afford to just get like, you know, handmade, beautiful, 300 jewel watches.

• 1:14Speaker 00

  But if you are listening, Rolex.

• 1:15Speaker 01

  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 is. It says now.

• 1:35Speaker 00

  Helpful, useful. Does it change?

• 1:38Speaker 01

  Yeah. Oh, and it says on the back, it says Steel Time Back. I guess that's the brand that made it. I got this up 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:OW. So what time is it? Oh, it's now. And in a way, you know, that's a good thing to know. Like-

• 2:06Speaker 00

  I sort of wanted you to be able to scroll the dial forward, and then it say the future.

• 2:12Speaker 01

  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.

• 2:29Speaker 00

  You know, it's sort of the most philosophically elegant watch there is, you know?

• 2:34Speaker 01

  Yeah.

• 2:34Speaker 00

  All you have is now.

• 2:36Speaker 01

  It's not functional. It has a crown on it, but you can't turn it. You can'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, right now, it's now. I have a feeling that in an hour, it'll still be now.

• 3:02Speaker 00

  This episode is brought to you by Cancer Research UK.

• 3:05Speaker 01

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  For more information about Cancer Research UK, their research, breakthroughs, and how you can support them, visit cancerresearchuk.org/RestIsScience.

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  Observe the North American dad. 50s, great polo collection. He enters his vehicle information on Carvana. An offer appears in minutes. Remarkable. He squints, reads it again, smiles and says, dang, that's a good offer. The highest form of approval. No haggling, no hassle. No one called him boss. He's still on the couch. Astonishing. Sell your car today on carvana.com. Pickup fees may apply.

• 4:42Speaker 03

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• 5:14Speaker 01

  These are the kinds of watches I collect, okay?

• 5:17Speaker 00

  It's sort of like a dad joke, but in watch form.

• 5:20Speaker 01

  That's what it is. Yeah, I'll give you another example. If you give me 10 seconds.

• 5:26Speaker 00

  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.

• 5:57Speaker 01

  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

• 6:39Speaker 01

  domestic chemical terrorism in America. There's a whole documentary on Netflix about it.

• 6:44Speaker 00

  Sorry, did you say it's a cookbook?

• 6:46Speaker 01

  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 Osho, 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.

• 7:31Speaker 00

  I don't understand. I don't understand. I have lots of questions. Who published it? It wasn't actually him?

• 7:39Speaker 01

  Yes, it was.

• 7:40Speaker 00

  How long ago is this guy? I've never heard of this guy. Also, what's it got to do with watches? I'm not sure I understand.

• 7:45Speaker 01

  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.

• 7:58Speaker 00

  I see. Or, I've got a really nice book on numbers. It's the square root of 4 to 4,000 decimal places.

• 8:07Speaker 01

  Yes, exactly. 2.00000. 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 exactly 4.

• 8:18Speaker 00

  They're checked. What's his name? No Show? How'd you spell it?

• 8:22Speaker 01

  Osho. O-S-H-O. I've read a lot of Osho's 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.

• 8:41Speaker 00

  Right. I've never come across this guy.

• 8:44Speaker 01

  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 Philosophers 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 pi. 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 face's

• 9:30Speaker 01

  circle, and there's like a string that you could wrap from 12 around, you would hit one radian at 57.3 degrees. That's not normally where there's a numeral on a watch. But because it takes 2 pi radian to go all the way around a circle, it takes 1 pi diameter, but it takes 2 pi radii, that means that you go all the way around, you're at 2 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 2, 3, 4, 5, and then 6. And then there's a little bit of change, since 2 pi is required to go around.

• 10:12Speaker 00

  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 around the outside, how many multiples of the minute hand you have traversed in that moment.

• 10:34Speaker 01

  Yeah, exactly. And so a quarter of the way around a circle means that you're a quarter of 2 pi around. So you're pi over 2, you're half pi, radians around the circle. And then they divide that further to give you where 1, 2, 3 o'clock should be. So this watch needs batteries. Right now, it says that it's, it basically says that it's 125, or in radians, it is 5 pi over 6 past pi over 6.

• 11:09Speaker 00

  I can't tell you how much I want that.

• 11:11Speaker 01

  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.

• 11:18Speaker 01

  How many radians go around a circle? I mean, if you wear it every day, you never forget, but still. It's it's a good little cheat sheet.

• 11:25Speaker 00

  I like that. Who made it? The retired, the out of work philosophers club.

• 11:29Speaker 01

  The unemployed philosophers guild. They they make a lot of famous stuff, including they made slippers that have Sigmund Freud's face on them and they're called Freudian slippers.

• 11:41Speaker 00

  Freudian slippers. I, 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.

• 11:56Speaker 01

  Exactly, exactly. They're they're they're pretty great. I've got a few other things from them. I'll show some other day. This is a a bit of a bummer that 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?

• 12:13Speaker 00

  Okay, the numbers are backwards.

• 12:14Speaker 01

  That's right. Yeah. Instead of going clockwise around, one, two, three, four, five, six, seven, 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 the numerals are still written normally. But they go around the watch the wrong way.

• 12:39Speaker 00

  So three o'clock looks like nine o'clock.

• 12:41Speaker 01

  Yeah, and this is, if you if you're 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 the only backwards watch I have. There's a different one. 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 it's got ink, our octopus mascot. It's amazing how quickly you you adapt to counterclockwise clocks and and watches. It's just you. 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.

• 13:26Speaker 01

  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.

• 13:33Speaker 00

  Really? Well, so you can glance at, if you've been wearing it for a while, you can glance at backwards watch and be like, yeah, got it.

• 13:38Speaker 01

  Yes, yes. For for for me at least, it it generates this feeling of counterclockwise is how time moves. And so if the if the hour hand is between the eight and the nine, I know that it's approaching the the the eight. I know that it's not coming up to the nine. It's it's going. Wait, sorry, I'm I'm confusing myself now.

• 14:05Speaker 00

  You've spent too much time working switching between clockwise and counterclockwise watches in your life.

• 14:11Speaker 01

  I really have. But you know, you know that if you see the hand between the seven and the eight, that it's climbing counterclockwise towards the eight.

• 14:22Speaker 00

  Rather than clockwise towards the seven.

• 14:24Speaker 01

  It's like an idea of motion that that is what comes over you. Whew, I haven't worn this watch in a long time.

• 14:32Speaker 00

  Honestly, Michael, I hate it.

• 14:36Speaker 00

  The other one's great. That one I hate it. Don't want it.

• 14:38Speaker 01

  All right. Well, now, how about this? This is this is a really unique piece. It's a good conversation piece. It's an Apple watch.

• 14:48Speaker 00

  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 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 on the back?

• 15:20Speaker 01

  Not much. It says stainless steel back, contemporary design, Japan movement.

• 15:27Speaker 00

  Yeah, it's I I strongly suspect that is not actually made by. It's not an official Apple piece of merchandise.

• 15:35Speaker 01

  Well, you would be wrong.

• 15:36Speaker 00

  No.

• 15:37Speaker 01

  This was an actual watch made by Apple. It is a 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.

• 16:09Speaker 01

  So these are not very expensive. They might be expensive now as people like kind of learn that this existed.

• 16:15Speaker 00

  They probably are, especially after this podcast.

• 16:18Speaker 01

  So the the the design is very like Memphis. If you're familiar with the that 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.

• 16:38Speaker 00

  Hold on, how long have you had it? Have you had it since the original time?

• 16:42Speaker 01

  Uh, no, no, no, no. I got it. My wife got it for me as a birthday gift. I told her, I I only got it three years ago.

• 16:50Speaker 00

  Okay, they're about 400 quid. That is that is a great, A, a great birthday present and B, a great watch. I that one I like.

• 16:59Speaker 01

  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, um, yeah, it was only about 100 bucks when my wife got it. So I guess it's also an investment, huh?

• 17:17Speaker 00

  Hey, look, four times is quadrupled in value over the space of of of a couple of years. It's better than Apple stock.

• 17:26Speaker 01

  Maybe, maybe. Now, now I've got two more to show you. One, this one I I really love. It's a little bit dirty because it's been, again, I 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

• 17:47Speaker 01

  a typical like 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 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 that little ball protrudes a little bit above the watch face.

• 18:33Speaker 01

  So you can be blind and tell the time. Or you can just not have to look your eyes down at your watch, you know, if it feels rude.

• 18:39Speaker 00

  It's absolutely perfect for people who work in pitch blackness.

• 18:42Speaker 01

  Yeah, or if you work in pitch darkness, you don't want to illuminate something. You can just feel what time it is.

• 18:47Speaker 00

  A burglar, for instance.

• 18:49Speaker 01

  A burg- it's perfect for committing crimes and being on time while you do it. So obviously, these magnets move around at the correct speeds so that the ball is always being pulled to represent the correct hour and minute.

• 19:02Speaker 00

  Well, how else are you going to meet your getaway car? This is, you've you've you've accidentally chanced upon something here.

• 19:08Speaker 01

  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, watch that minute hand.

• 19:22Speaker 01

  See that? It moves around.

• 19:23Speaker 00

  Oh, that is satisfying.

• 19:25Speaker 01

  And then the hour, the hour hand there, I I 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.

• 19:38Speaker 00

  Yeah, you know what? That is actually, that's really satisfying. I like that one.

• 19:41Speaker 01

  And and these balls, you can touch them. And if they get moved out of the way, no problem, just let go and it'll stick, they'll stick back on the magnet.

• 19:48Speaker 00

  So I'm going to give you a ranking at the end of this of all of these watches. I hope you I hope you're okay with that.

• 19:53Speaker 01

  Yeah, I'm okay with that. So here's the final entry. This final entry is a Sturmansky watch. It's the watch I've been wearing this entire time. Ta-da. 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.

• 20:12Speaker 00

  Hold on a second then. So when you're looking at this where it would be pointing at three o'clock, for example, you are actually looking at six o'clock.

• 20:22Speaker 01

  That's correct. And instead of six 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.

• 20:30Speaker 00

  Okay, hold on. Does the minute still sweep around? Sorry, I'm I'm just realized I'm holding my daughter's pen.

• 20:36Speaker 01

  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 a like a keychain holding this fuzzy little ball. Not just any bobble, it is a cute little pillow for an elf, for a for a fairy.

• 20:51Speaker 00

  I'm an extremely important professional woman, okay? And this is the statuary that I choose. Okay, but I wonder what the minute hands is doing. Is the minute hand still doing one entire sweep?

• 21:00Speaker 01

  Yes, the minute hand goes around once an hour.

• 21:03Speaker 00

  Oh, no, no, I don't like it. So you're you're having to sort of translate half of an original system and half of a new system when you're reading it.

• 21:13Speaker 01

  But it's easy because you look at it and you go, okay, like right now, this 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 we're how many minutes past? We're like 20, 23, 24 minutes past one or 13. Okay. 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 you 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.

• 21:53Speaker 00

  Okay, so you've shown me five in total. Is that correct?

• 21:57Speaker 01

  One, two, three, four, five. There's one more piece of this that I want to show. And this is, my 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.

• 22:31Speaker 00

  And then the Russian in 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?

• 22:46Speaker 01

  Yeah, yeah, I'll hold them up.

• 22:48Speaker 00

  Okay, thank you. Right, which way around do you want it? Do you want the ones I hate the most first?

• 22:53Speaker 01

  Yes, I want the bottom first.

• 22:56Speaker 00

  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.

• 23:06Speaker 01

  Yep, okay.

• 23:07Speaker 00

  I think that does something horrible to my brain, and I never want to see it again.

• 23:12Speaker 01

  That's a valid answer, but I'm going to strong disagree on that. Okay, next.

• 23:17Speaker 00

  Okay, one up from the backwards clock. It's just, it's just suddenly swapped places. It's only now swapped places with the 24-hour watch, because it had the commemoration of space event on the back, is the Now watch, which I kind of like, but it's sort of a one-time thing.

• 23:38Speaker 01

  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.

• 23:45Speaker 00

  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.

• 23:53Speaker 01

  Isn't it? There's some poetry to that.

• 23:56Speaker 00

  There's some poetry in that. Okay, so next up, I'm afraid, is the 24-hour clock for the same reason as the 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.

• 24:09Speaker 01

  It's not transparent. It wouldn't work.

• 24:11Speaker 00

  It's not transparent. Okay, just one up from that is the Pi 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 radiance and 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.

• 24:44Speaker 01

  That is true. It's the first regular watch.

• 24:47Speaker 00

  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 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 and it goes back down to the bottom.

• 25:15Speaker 01

  No, it's great. It's great. And the problem with all of these, except for the Stromanski, 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.

• 25:31Speaker 00

  Okay, fine, it can come third. That was wonderful. Thank you. I appreciated that little insight into the things on Michael's wrists. Shall we have a little break, and then we can come to some questions?

• 25:43Speaker 01

  Let's do it. I can't wait. All right, see you guys after the break.

• 25:53Speaker 04

  What are you doing on the Fourth 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?

• 26:03Speaker 05

  We have four weekend live shows for you all from your favourite Goldhanger podcasts.

• 26:09Speaker 00

  Hello, all ship. I'm going to be there with Tom Holland, talking about the most scandalous housewives of Regency England.

• 26:15Speaker 04

  And I'm going to be sitting down with the wonderful Anita Anand, my co-host on the Empire Pod, to talk about the history of modern Iran with the absolutely brilliant Ali Ansari. Dominic and I will be telling a thrilling Victorian adventure on the Friday night to kick things off.

• 26:31Speaker 06

  And it's not just us. Mary Beard is coming, Stanley Tucci's coming. You really couldn't ask for a better guest list, unless you were on it.

• 26:38Speaker 05

  If you want to join us, head to southbankcentre.co.uk for the full line-up. Buy your ticket now.

• 26:44Speaker 04

  See you there. See you there.

• 26:57Speaker 01

  This episode is brought to you by Cancer Research UK.

• 26:59Speaker 00

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• 28:31Speaker 00

  Okay, we're back. Shall we do some questions?

• 28:33Speaker 01

  Let's do some questions. And this one came in through email from Beau De Narius, who says, "Basian 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 judgements spring to mind."

• 29:00Speaker 00

  Yeah, okay, excellent question, Beau. I think probably, let me first tell you a little bit about Bayesian 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.

• 29:19Speaker 01

  Yeah.

• 29:20Speaker 00

  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 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, he was a man of the church, and he would write these letters of like 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.

• 30:04Speaker 00

  There's a table behind you, okay? 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.

• 30:15Speaker 01

  It's going to stay on the table. Okay.

• 30:16Speaker 00

  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.

• 30:54Speaker 01

  Okay.

• 30:55Speaker 00

  So as you throw one over your shoulder, you say, your friend says, okay, the bag that you have just thrown is to the northwest of your red beanbag.

• 31:07Speaker 01

  Okay.

• 31:08Speaker 00

  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. In the beginning, you've got no idea where it is. But after you've thrown five, 10, 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.

• 31:48Speaker 01

  Yeah, right, right.

• 31:49Speaker 00

  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 beanbag, 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, it's sort of in the south middle of the table.

• 32:11Speaker 00

  And what Bayes realised 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, right? That essentially is Bayesian thinking.

• 32:33Speaker 00

  Has that made sense? I'm not sure. Was that okay? Should I do it again?

• 32:35Speaker 01

  Yeah, no, that makes that makes sense. That makes sense. So here's my question, though. This this whole thing requires that you have a friend who does know where the red beanbag is.

• 32:44Speaker 00

  Yes.

• 32:45Speaker 01

  What if you what if no one knows where it is?

• 32:47Speaker 00

  So there is lots of evidence that this is the way that our brains work all the time. And this is the reason why visual 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 too, right, on the outside of my my face and body, that are transmitting information. So in that situation, it's like my eyes, your hands, your ears,

• 33:31Speaker 00

  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 of 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.

• 34:13Speaker 01

  Yeah.

• 34:13Speaker 00

  Your brain is 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.

• 34:23Speaker 01

  Right, right. Okay, so I'm gonna ask a question because I 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 like way of thinking is to say, well, on the next flip, it's gonna be it's gonna be either heads or tails, 50 50 still. But the the Bayesian answer would be, no, your coin is probably not fair.

• 34:54Speaker 00

  Right. I think the key thing that is different to classic probability of like, count it up, divide it by, you know, whatever, it's 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 confirms your ideas about what it expects it to be almost all of the time, there's still enough doubt in your in your kind of your your 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.

• 35:34Speaker 01

  Got it.

• 35:35Speaker 00

  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.

• 35:50Speaker 01

  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.

• 36:08Speaker 00

  There is an equation, and it's like, it's almost laughably simple, this equation. Honestly, this, I think the thing about Bayes, right, that in fact, actually, the book that I'm writing at the moment is basically about Bayes. Although I will never sell it that way. I say it's a book about doubt.

• 36:26Speaker 01

  I hear about this all the time from Nate Silver.

• 36:28Speaker 00

  Yeah.

• 36:29Speaker 01

  He's he always mentions like, well, from a Bayesian perspective. And I'm like, what do you mean?

• 36:33Speaker 00

  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.

• 36:42Speaker 01

  I see. I see. Because he also talks about priors a lot.

• 36:46Speaker 00

  Right. So prior is your is your best guess right now, and then you update it.

• 36:53Speaker 01

  Got it.

• 36:53Speaker 00

  I mean, really, all of the evidence is pointing towards your brain being this phenomenal Bayesian machine.

• 37:02Speaker 01

  Right.

• 37:03Speaker 00

  That is, that has hypotheses, that updates it with the evidence, and then comes up with this sort of constructed, but with room for uncertainty version of reality, right? It's it's amazing. The thing is, the the question that Beau asks is really interesting because if your brain is perfectly Bayesian, why do people do irrational things? When they're in love, when they're angry, when they're full of anxiety, when when, you know, all of these different types of 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?

• 37:48Speaker 00

  You hear, this is sort of ancient brain, you know, you're like, whatever, let's go back to hunter gatherer world. And you hear a rustle in the in in the bushes.

• 37:59Speaker 00

  You could say that your prior, your your existing understanding of the situation is, okay, that's very unlikely to be a tiger. Let's analyze all of the evidence and the data. Let's say the the probability of there being a tiger in this area at this time of day, blah, blah, blah, blah, blah, blah. You could do a whole calculation. And you could say, okay, now I've heard a rustle, I'll update my understanding and conclude that it's not a tiger.

• 38:25Speaker 01

  Yeah.

• 38:25Speaker 00

  That's sort of like a naive way to to interpret what the the Bayesian formulation of that question would be. But in reality, like, that would lose you, 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 weighting your sort of prior belief that there could be tigers at any corner. So 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.

• 39:09Speaker 00

  And if you are expecting there to be a tiger at any moment in time, you're still doing Bayesian updating.

• 39:14Speaker 01

  Yeah.

• 39:14Speaker 00

  Still kind of, you're still doing the same thing. You're still assessing the information and 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.

• 39:30Speaker 01

  Yeah, right. And and that is a smart thing to do because we evolved to survive, not calculate the truth.

• 39:39Speaker 00

  Right.

• 39:40Speaker 01

  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 been already been waiting in line for an hour, stay in line, because your identity is now wrapped up in in achieving this finally. You've 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.

• 40:09Speaker 00

  I mean, I 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.

• 40:22Speaker 01

  Right.

• 40:23Speaker 00

  Right? We might have Bayesian brains, but we're not these, we're not data crunchers naturally. We're not like, there might be a mathematical formulation that can explain how our brains are working, but we're not maths 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 like, 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 fit the world they find themselves in.

• 41:00Speaker 01

  Very true.

• 41:00Speaker 00

  Okay. Should we do our next question?

• 41:02Speaker 01

  Yeah, let's do the next question.

• 41:03Speaker 00

  Right, this is for.

• 41:06Speaker 00

  What I really love about this is how obvious it is, which questions are for you, which ones are for me, even before we've assigned them. Okay, this is from Vitor 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 favourite syllogism?"

• 41:28Speaker 01

  Mmm, I'll leave it as an exercise to the listener to find the error in that syllogism about the cheese, but my favourite is kind of similar. It's, I don't know if it's similar, but here's my favourite. I'll just get right into it. My favourite 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.

• 42:08Speaker 00

  No thing.

• 42:09Speaker 01

  But when I say "a ham sandwich is better than nothing," I mean a ham sandwich is better than an absence of things.

• 42:16Speaker 00

  Mm-hmm.

• 42:17Speaker 01

  However, it's the same, it's the same word, "nothing."

• 42:20Speaker 00

  It's a little cheeky little wordplay.

• 42:22Speaker 01

  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 that, those two different meanings of "nothing," and how from them we can construct all of the cardinal numbers.

• 42:43Speaker 00

  Mm-hmm, that's good. I like that. I'm trying to think if I have any.

• 42:47Speaker 01

  Yeah, do you have one?

• 42:48Speaker 00

  Let me see. There's one, there is one that's similar to your ham sandwich one, which is, "I am, I'm a nobody. Nobody is perfect, therefore, I am perfect."

• 42:59Speaker 01

  Nice, yeah. Again, words for "nothing" or "no thing," "nobody,"

• 43:06Speaker 00

  Yeah.

• 43:06Speaker 01

  "no one" can lead us to these really funny conclusions. I like that. "I'm a nobody, and nobody's perfect." You'd agree with both of them. "I'm a nobody, and nobody's perfect." Okay, so far, so good. Therefore, if I'm nobody and nobody is perfect, then I must be perfect. Nice.

• 43:23Speaker 00

  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?

• 44:04Speaker 00

  But I think that actually, this is the trick, this is the trick that actually gets used quite often. It's like, "sensible thing, sensible thing." Completely wild, strange connection. "Sensible thing, sensible thing." 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.

• 44:25Speaker 01

  Yes, yes, yes. They do happen all the time, especially in commercials and in like influencers selling a product. They're like, "Look, you gotta do this, you gotta do that." Therefore, and then the answer does not follow logically, and not in a funny way, like the ham sandwich one, in 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.

• 44:53Speaker 00

  And yeah, it's just a bunch of words, exactly. All right, should we do the last question?

• 44:58Speaker 01

  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 realise 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?"

• 45:22Speaker 00

  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 dyscalculia, which is like a real, genuine thing. So people talk a lot about, maths 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, or 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

• 46:05Speaker 00

  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.

• 46:20Speaker 01

  Yep, yep.

• 46:21Speaker 00

  So you can do this, but not just that, when you ask people sort of rough calculations, like what is 10% of 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 dyscalculia essentially struggle for that reason, right? So 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

• 47:05Speaker 00

  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.

• 47:41Speaker 01

  Huh.

• 47:42Speaker 00

  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.

• 48:02Speaker 01

  Huh.

• 48:03Speaker 00

  And it is so innately connected to mathematical ability, like you would not believe.

• 48:10Speaker 01

  Really? But which way does the causation go?

• 48:14Speaker 00

  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 ends up becoming true. It's a self fulfilling prophecy.

• 48:35Speaker 01

  Yeah, and it feels like it's true all the time, but it's so especially true for doing mathematics.

• 48:41Speaker 00

  It's so especially true for mathematics. And the thing about this is that maths anxiety and self-efficacy in maths 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 maths question, and half the people get easy questions, and half the people get actually secretly impossible questions.

• 49:15Speaker 01

  Oh.

• 49:16Speaker 00

  So they're set with tasks that they literally are not able to do.

• 49:19Speaker 01

  Yeah.

• 49:20Speaker 00

  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 Western, 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."

• 49:48Speaker 01

  Yeah, yeah.

• 49:50Speaker 00

  If it's an easier question, they're 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.

• 50:17Speaker 01

  Oh, wow. So the ones with easy problems are like, no thanks.

• 50:20Speaker 00

  Yeah, you give them these questions like, yeah, I mean, sure, I can do another one if I want to. 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.

• 50:32Speaker 01

  Wow.

• 50:33Speaker 00

  Because they culturally know that this is hard, but they also know that it's achievable.

• 50:38Speaker 01

  Right.

• 50:39Speaker 00

  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-efficacy is 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 GCSE maths despite all my efforts. I only got a C. I know what my difficulty was. I know what I couldn't do. My brain is just instinctively less able to do it.

• 51:23Speaker 00

  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, right? That is what you want, somebody who is unwilling to stop until they get to the bottom of something.

• 51:46Speaker 01

  That is such a perfect way to put it, Hannah, that a mathematician is the one asking why. If you're getting As in those kind of classes, then you're going to be a fantastic 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've 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.

• 52:23Speaker 00

  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.

• 52:42Speaker 01

  Yeah.

• 52:43Speaker 00

  Believe in yourselves more. That makes it sound really simple.

• 52:47Speaker 01

  Yeah, it's, guys, come on.

• 52:48Speaker 00

  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.

• 53:00Speaker 01

  Yeah.

• 53:01Speaker 00

  Right, now that we've fixed the maths education system, we have got to the bottom of our brains.

• 53:07Speaker 01

  We know where ham sandwiches fall in the hierarchy.

• 53:11Speaker 00

  And can sort of tell the time with one of your watches.

• 53:15Speaker 01

  Well, with, yeah, with only, the only one that's running.

• 53:19Speaker 00

  I think that brings us to the end of this episode. But as ever, please do send us in your questions, [email protected]. 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.

• 53:39Speaker 01

  Yeah, please do that.

• 53:41Speaker 00

  We will see you next week.

• 53:43Speaker 01

  See you later.

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