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okay today's video is about annoying puzzles and i want to start with what i think is possibly the most annoying puzzle in the world so it's a simple enough question just imagine the department for transport is looking at a road layout and they've got two different possibilities for the road layout and they're trying to figure out which one is going to cause the fewest accidents so let me just set out the possibilities okay this is road layout a this is road layout b okay very easy now both of them are predicted to have a certain number of major accidents major accidents this is going to put people in hospital we're talking broken bones you know serious stuff there's also a certain number of minor accidents that might just be like a bit of first aid you might need to see a doctor cut some scrapes that sort of thing okay it's really simple each of these different road layouts is going to cause a certain number of major and minor road accidents and i just want you to fill in this gap here so here we go two thousand one thousand sixteen now what goes here to make these two schemes equivalent it feels like eight doesn't it feel like eight doesn't it feel like eight so this puzzle comes from shane frederick who's a behavioral economist psychologist at yale university yale university they're smart at yale university and he asked a whole bunch of yale university students what the answer was and the most common number was a bit more than a quarter of them said eight the next most common answer was 32 and the next most common answer was if i remember rightly 1016. let's have a think about what's going on here road layout a is going to cause 2 000 major accidents this is people in hospital oh and 16 people with bumps and bruises okay so why do we even care about this rollout b is going to cause only a thousand major accidents so that's much better so how many minor accidents would make it equivalent to to road layout a and the reason this is annoying question is because there's no there is no right answer but it's got to be like a lot it's got to be many thousands surely many thousands because these are trivial accidents and these are substantial and a very small number of people in shade frederick's survey did say a hundred thousand a million and there's no right answer but it's gotta be something like that but so many just like you brady the majority of people all the the largest minority of people uh more than a quarter of people said oh we think that the correct answer is eight and when you look at this you your mind is wanting you to say eight right because it's like it just puts everything in the same proportion right same you've been asked make these the same that's the same this is a an example it's quite a quite a fascinating example quite a complicated example of something that shane frederick studies which he calls cognitive reflection problems and they were made famous by the psychologist daniel kahneman in his book thinking fast and slow but this one is not in thinking fast and slow so this one is this has barely seen the light of day and i find it fascinating but um another example this one's made very famous by thinking fast and slow is a bat and a ball together cost a dollar ten and the bat costs a dollar more than the ball so how much does the bat cost you may well have heard this before a lot of people have uh and instinctively you just think well it's a dollar right because because the bat costs a dollar more than the the ball how much does they cost a dollar ten together so it's like a dollar and but that's not right because that's 90 cents and in fact the correct answer is the ball costs five cents the bat costs a dollar and five cents but people leap to the wrong answer um you want more oh yeah this is a classic easier in the time of coronavirus imagine a lake that is filling with lily pads has his patch of lily pads on the lake and the patch doubles in size every day and after 48 days the lake is completely covered so the question is on what day out of the 48 days on what day is the lake half covered and people often go oh well 48 divided by two um it's 24 or they'll they'll sort of plot some kind of curve in their mind and they'll say oh maybe it's like 32 or something but of course the actual answer is 47 days because the patch is doubling in size every day so it's half full the day before you get to 48 that's what exponential growth uh looks like and we've kind of found that the hard way now why do people get these things wrong why do people mess these cognitive reflection tests up why don't people look at this and go there is no right answer but it's got to be something like 10 000 or 100 000 or a million the reason it's annoying is we don't even have the information we need to give the correct answer but what we do know is it can't possibly be eight why can't it be eight because because to look at that if you look at major accidents it looks like road a is twice as dangerous as we could be yeah so we remember what we've been asked we're being asked to make these two equivalent we're being asked to uh to say well how many minor accidents would it be for for road layout b to be the equivalent of road layout a so well the answer is well it's the same as how many minor accidents are the equivalent of 16 minor accidents plus a thousand extra major accidents right and the answer is well we don't know but it's got to be it's got to be at least a thousand and sixteen it's a bit apples and oranges though isn't it because like what's a what's a major accident worth yeah yeah exactly there's there's no answer to the question which is why i say it's the most annoying question in the world but you don't look at it and go oh there's not enough there's not enough information we need we need an exchange rate of major to minor accidents what you do is you look at it you go eight i mean you might not but an awful lot of very smart students at yale university immediately said eight a whole other bunch not quite as many said 32 and another bunch not quite as many said a thousand and sixteen a thousand and sixteen is maybe just about right if you say well we're just going to count accidents and we can't compare them but really the answer's got to be you know a lot way way more than a thousand and sixteen you know what the problem with that question is you straight away forget what you're trying to solve you don't you you forget the question but that's it that's interesting though isn't it because it's you know i told you i told you the story we're trying to compare these layouts we're trying to figure out you know which which layout which i know what's the equivalent of the two layouts and you daniel kahneman often says when we're given a difficult question we often substitute an easy question and we don't notice that that's what we've that's that's exactly what i did because i thought there was a solution i contrived a question in my head that had a solution yes absolutely and eight looks about right i mean you're absolutely right brady eight is the of course it's eight of course it's eight but of course it's not eight it's not even close to eight so why do i find these cognitive reflection um problems interesting it's because my own interest is in how we think about statistical claims in the news now when people see a claim on social media they see it on twitter on facebook they see a newspaper headline they see a talking head on tv how do we think about those claims how do we process them and uh it's tempting as a nerd to go straight to you know the technical details have they confused correlation and causation you know have they um is it within the margin of error all the sort of statistical questions you might ask um but actually very often what's getting between us and the truth is our own tendency to leap to conclusions just as you saw this and they thought eight that sounds about right very often we see somebody talking and we very quickly go yeah that can't be right that's just fake news what would you expect you know from those guys or instead they go oh yeah yeah that sounds right this goes to prove i was i was right all along i always knew that this government was you know was full of rogues and villains and and they can't be trusted with anything i you know i was having this argument with my friends in the pub last night in the pub i remember the pub um i was having this argument with my friends last night and this proves i was right and we leap in with this emotional reaction it was a really interesting study published i think about a year ago by gordon pennycook and a bunch of other psychologists and gordon penny cook is interested in fake news and why fake news spreads and why people spread misinformation what they found was you could take a bunch of people who were say die hard trump supporters and show them a ridiculous claim like 500 migrant caravans have been intercepted at the mexican border wearing suicide vests you know if you show them that claim in the wild they might well click on it they might well amplify it like it share it and you ask them and they'll say yeah yeah that that is the kind of thing i might share if you instead go just wait a moment how likely do you think that claim is to be true there's no judgment do you think that claim is likely to be true about 90 of them will go actually yeah that can't like why would they be wearing suicide vests why would why would migrant it doesn't make any sense none of this makes any sense and so they're able to see despite the fact they have a strong you know view of the world we all have strong views of the world they're able to see that that can't be true and yet at the same time in a moment of distraction a moment of inattention they would they admit that they would retweet it they would amplify it and i think i personally wouldn't be amplifying stuff about migrant caravans in suicide vests but we all have stuff that we see that we we are tempted to retweet because it fits our biases i can give you an example um a few years ago i saw a graph about support for same-sex marriage personally um i think that's great news more americans in favor of uh equal rights for everybody great and i retweeted this graph which i think was from a the washington post or a perfectly decent source and i tweeted it because of my emotional reaction like oh that looks right great tweet 150 000 followers the very first reply was tim have you looked at the axes on that graph and i hadn't and actually it was a mess it was they'd done that thing where the the opinion polls the questions have been asked um different distances apart so maybe 10 years would pass and then they'd ask it twice within one year and they were all equally spread the whole thing was a mess i should have clipped it for my bad data visualization file but instead i was amplifying it to all of my followers on twitter because it just seemed like the kind of thing that should be true and i wanted it to be true and i wanted to to share the news just like this seems like it should be eight i love these puzzles because i you know i love being tricked and falling over my you know my own feet mentally i love watching other people get tricked by funny little puzzles but there's something deeper going on here when we're reading the newspapers looking at social media we shouldn't be just accepting or rejecting things because they feel right because they fit our view of the world you only need to notice your own emotions count to three have a little think and that is a way to stop yourself spreading misinformation if you enjoyed this why not check out tim harford's book how to make the world add up it's also out in america under a different title the data detective or the data detective if that's how you like to say it there are links in the description and if you like puzzles why not check out today's episode sponsor brilliant they've got a site bursting with puzzles quizzes interactive courses like the ones you can see on screen now all superbly designed to guide you through the wonderful worlds of mathematics computers science all sorts of other stuff this scientific thinking course already has my mind buzzing or why not up your game with some statistics it's like a fully equipped gym for your brain you can get 20 off a premium subscription by going to brilliant.org and adding that slash number file again brilliant.org number five i had some delicious toast one bit with peanut butter and a different beer with cheese because you know living the dream