Bizarre Watches and How They Work

21:57Michael Stevens:and it's a cool reminder of human space history. 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? 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.

22:36Okay. I think that does something horrible to my brain and I never want to see it again.

22:43Michael Stevens: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 suddenly swap places. It's only now swap places with the 24-hour watch because I had the commemoration of a space event on the back is the now watch, which 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.

23:23Isn'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 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.

24:14Michael Stevens:That is true. It's 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 And 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.

24:50Michael Stevens: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. OK, 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 alright see you guys after the break

25:40I'm 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 Anand, my co-host on the Empire Pod, to talk about the history of modern Iran with the absolutely brilliant Ali Ansari.

25:55Michael Stevens: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 Tucci's coming. You really couldn't ask for a better guest list unless you were on it. If you want to join us, head to southbankcenter.co.uk for the full lineup. Buy your tickets now. See you there. See you there.

26:38Michael Stevens:for it. Ready to make anything online make sense? There's no place like Chrome. Check responses set up required compatibility and availability varies 18 plus.

26:54Michael Stevens:Okay, we're back. Should we do some questions? Let's do some questions. This one came in through email from Beau 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, 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 yeah okay um and uh 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 um the original bayesian theorem uh the original formulation for it wasn't Bayes himself.

28:03It 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. 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.

28:38Michael Stevens:It's going to stay on the table. Okay. 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 to-do service, 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.

29:17Okay. 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.

29:30Michael Stevens: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. In the beginning, 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.

30:11Michael Stevens:Yeah, right, right. Likewise, if half of your throws are landing to the east of the red bean bag and half of them are landing to the west of your red bean bag then you'll probably know that your red bean bag 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 bean bag is in this example is sort of in the south middle of the table. and what they realize 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 has that made sense i'm not sure was that okay should i do it again yeah no that makes that That makes sense.

31:00Michael Stevens:That makes sense. So here's my question, though. This whole thing requires that you have a friend who does know where the red beanbag 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 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 light in it, nothing. And it's only my senses, and your senses too, right, on the outside of my face and body that are transmitting information.

31:50So 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.

32:36Your 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.

32:47Michael Stevens: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 a hundred 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 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, divide it by, you know, whatever is 50%, 50 % is that with Bayesian thinking, you are never absolutely sure.

33:32There 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 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 got it 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.

34:11We need to update our understanding of the world.

34:14Michael Stevens: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 Bayes, 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. I hear about this all the time from Nate Silver.

34:51Yeah.

34:52Michael Stevens: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 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?

35:36It's amazing. The thing is, the question that Bo asks is really interesting because if your brain is perfectly based on, why do people do irrational 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 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 probability of there being a tiger in this area at this time of day 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 okay yeah That's sort of like a naive way to interpret what the Bayesian formulation of that question would be.

36:55But in reality, like that would lead you to die. OK, so if instead your fear in that environment is like, OK, 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 and if you are expecting there to be a tiger at any moment in time you're still doing bayesian updating. You're still kind of, 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.

37:47But you're just doing it in a slightly different way than a cold, emotionless calculation.

37:53Michael Stevens:Yeah, right. And that is a smart thing to do because we evolved to survive, not calculate the truth. Right. It 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.

38:36I 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 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.

39:23Michael Stevens:Very true. OK, should we do the next question? Yeah, let's do the next question. Right. This is from... 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? I'll leave it as an exercise to the listener to find the error in that syllogism about the cheese.

40:00Michael Stevens:But my favorite is kind of similar. It's, well, 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. Nothing. But when I say a ham sandwich is better than nothing, I mean a ham sandwich is better than an absence of things. Mm-hmm. However, it's the same word, nothing.

40:43Michael Stevens: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 that, 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, I'm a nobody. Nobody is perfect.

41:20Therefore, I'm perfect.

41:22Michael Stevens:Nice. Yeah. Again, words for nothing or no thing. Nobody. Yeah. 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. 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.

42:10every family is different therefore you choose your family or something basically it was like sensible thing sensible thing your soul ah selects your family before you were born right and it was like okay sorry sorry you just could we just go back to that but i think 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.

42:49Michael Stevens: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, Or, 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. 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.

43:25Michael Stevens: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 dyscalculate, 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.

44:11And 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 if you give a number line from from zero to one trillion and you ask people to mark a billion on 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 but not just that when you ask people sort of rough calculations like what is 10 % of 56 or whatever it might be.

44:54There 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 discalculate 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 uh 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 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 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.

46:04Huh. 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. Huh. And it is so innately connected to mathematical ability like you would not believe. Really?

46:34Michael Stevens:But which way does 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 thing starts in your head, it 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 math anxiety and self-efficacy in math is cultural. And there are so many amazing experiments that really demonstrate this.

47:19So 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 uh half the people get easy questions and half the people get actually secretly impossible questions oh so they're set with tasks that they literally are not able to do yeah 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.

48:04That 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.

48:12Michael Stevens:Yeah, yeah. 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 uh from asia particularly from um south korea and singapore which regularly are the number one in the world for uh 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 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 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 to to really focus more on this particular problem and that is definitely something i think that ends up um i see it over and over and over again in schools particularly in girls right self-efficacy 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 um i should just say actually i mean even in the this question charlotte that you wrote right uh i did gcse math despite all my efforts i only got a c i i know what my difficulty was i know what I couldn't do.

49:43My 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, right? That is what you want. Somebody who is unwilling to stop until they get to the bottom of something.

50:10Michael Stevens: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 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 and so yeah 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 um yeah and it's unfortunate that we 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 much harder than that it's so much harder than that but yeah it's it's a real shame it's a real shame that this this happens and um there's 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 um fix the math education system we have uh got to the bottom of our brains we know uh where ham sandwiches fall in the hierarchy.

51:35And can sort of tell the time with one of your watches.

51:39Michael Stevens:Well, with only, yeah, 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 is 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 night time. Do whatever you want with it. Yeah. Yeah, please do that. We will see you next week. See you later.