{"id":9740,"date":"2023-11-05T01:44:00","date_gmt":"2023-11-05T01:44:00","guid":{"rendered":"https:\/\/zoominfinancial.com\/business\/the-simple-maths-puzzle-that-shows-us-how-to-separate-fact-from-fiction\/"},"modified":"2023-11-05T01:44:00","modified_gmt":"2023-11-05T01:44:00","slug":"the-simple-maths-puzzle-that-shows-us-how-to-separate-fact-from-fiction","status":"publish","type":"post","link":"https:\/\/zoominfinancial.com\/?p=9740","title":{"rendered":"The simple maths puzzle that shows us how to separate fact from fiction"},"content":{"rendered":"<div>\n<p>Unlock the Editor\u2019s Digest for free<\/p>\n<p class=\"article__content-sign-up-topic-description\"><span>Roula Khalaf, Editor of the FT, selects her favourite stories in this weekly newsletter.<\/span><\/p>\n<p><iframe class=\"article__content-sign-up-iframe close\" scrolling=\"no\" id=\"signUpIframe\" data-prev-url=\"\/register\/in-article-sign-up?ft-content-uuid=222fed3d-b2c1-4e27-81ae-3600bc4d4647\"><\/iframe><\/div>\n<div id=\"article-body\">\n<p>For certain kinds of questions, there are answers that are simple, elegant and wrong. Take the most famous example of the genre, the \u201cbat and ball\u201d question: if a bat and a ball together cost $1.10, and the bat costs a dollar more than the ball, how much does the ball cost ?<\/p>\n<p>This is known as a cognitive reflection problem, because it\u2019s designed to be a test of your ability to stop and think rather than a test of sophisticated maths. There\u2019s a tempting wrong answer: 10 cents. But a moment\u2019s reflection says that can\u2019t be right: if the ball costs 10 cents, then the bat costs $1.10 and the two together don\u2019t cost $1.10. Something doesn\u2019t add up.<\/p>\n<p>The bat and ball problem was developed by the behavioural economist Shane Frederick of Yale University and made famous by Nobel laureate Daniel Kahneman in his book <em>Thinking, Fast and Slow<\/em>. It\u2019s an elegant illustration of Kahneman\u2019s model of the human mind, which is that we have two modes of thinking. There\u2019s a fast, intuitive processing system, which solves many problems with graceful ease but can also be lured into error, and there\u2019s a slower, more effortful logic module, which can grind out the right answer when it must.<\/p>\n<p>Frederick\u2019s bat and ball problem offers an obvious decoy for the fast-thinking system to grab, while also having a correct answer that can be worked out using simple algebra or even trial and error. Most people consider the decoy answer of 10 cents even if they eventually produce the correct answer. The decoy answer is more popular when people are distracted or rushed and the correct answer takes longer to produce. (Have you got it yet?)<\/p>\n<p>Frederick\u2019s poser is not merely a curiosity: research by the Cornell psychologist Gordon Pennycook and others has found that people who score well on problems such as the bat and ball do a better job of distinguishing truth from partisan fake news.<\/p>\n<blockquote class=\"n-content-pullquote n-content-pullquote--no-image\" aria-hidden=\"true\">\n<div class=\"n-content-pullquote__content\">\n<p>If you think about the way we think, it\u2019s obvious that our intuitions are varied and complicated<\/p>\n<\/div>\n<\/blockquote>\n<p>The problem also raises some intriguing questions about the dual-system model of the mind. For example, when people get the answer wrong, what intuitive shortcut is leading them astray? And are they really wrong because they are careless? Or is it because the puzzle is beyond their capabilities?<\/p>\n<p>In a fascinating new article in the journal Cognition, Andrew Meyer and Shane Frederick unleash a barrage of new studies, many of them subtle tweaks of the bat and ball problem. These tweaks enable Frederick and Meyer to distinguish between people who err because they subtly misread the question and those who thoughtlessly subtract the smaller number from the larger one.<\/p>\n<p>The truth is murkier than the fast- and slow-thinking model: there are different intuitions and different ways to be wrong.<\/p>\n<p>I suppose that shouldn\u2019t be a surprise. Pennycook reminds me that \u201cthe bat and ball question is just a single problem and if you think about the way we think in the real world, it\u2019s obvious that our intuitions are varied and complicated\u201d.<\/p>\n<p>What blew my mind about Meyer and Frederick\u2019s article was the way they painstakingly undermined the idea that made the bat and ball question famous \u2014 which is that many people can figure out the right answer if only they slow down for long enough to avoid the decoy.<\/p>\n<p>Meyer and Frederick suggest that this is not the case. They try variants on the question: in one case people are told, \u201cHINT: 10 cents is not the answer\u201d; in another they are offered the bold prompt, \u201cBefore responding, consider whether the answer could be five cents\u201d. Both prompts help people find the right answer \u2014 which is, yes, five cents \u2014 but in many cases, people still don\u2019t figure it out.<\/p>\n<p>Some experimental subjects were given the question, followed by the bold and explicit statement: \u201cThe answer is five cents. Please enter the number five in the blank below: ___ cents.\u201d More than 20 per cent of people did not give the correct answer despite being told exactly what they should write.<\/p>\n<p>Are they just not paying attention at all? Surely not. \u201cThey definitely ARE paying attention,\u201d Frederick tells me in an email. More likely, he says, they are stubbornly clinging to their intuitive first guess and are fearful of being tricked by a malevolent experimenter.<\/p>\n<p>Pennycook agrees. \u201cThere\u2019s always 20 per cent,\u201d he offers, somewhat tongue in cheek. \u201cTwenty per cent of people have crazy beliefs, 20 per cent of people are highly authoritarian.\u201d And 20 per cent of people will not write down the right answer to a maths problem even when it\u2019s handed to them on a plate, because they trust their gut more than they trust some tricksy experimenter.<\/p>\n<p>Meyer and Frederick propose that we could sort the responses to the bat and ball question into three buckets: the reflective (taking the time to get it right the first time), the careless (who succeed only when given a prompt to think harder) and the hopeless (who cannot solve the problem even with heavy hints).<\/p>\n<p>If this was just about funny logic puzzles, it would all be good clean fun. But the stakes are higher: remember Pennycook drew a clear connection between the ability to solve such puzzles and the ability to spot fake news.<\/p>\n<p>I argued in my book <em>How to Make the World Add Up<\/em> that a few simple mental tools would help everyone think more clearly about the numbers that swirl around us. If we calmed down, slowed down, looked for helpful comparisons and asked a couple of basic questions, we\u2019d get to the truth.<\/p>\n<p>I didn\u2019t have the vocabulary at the time, but implicitly I was arguing that we were careless, not hopeless. I hope I was right. After some reflection, I am not so sure. <\/p>\n<p><em>Tim Harford\u2019s new book for children, \u201cThe Truth Detective\u201d (Wren &amp; Rook), is now available<\/em><\/p>\n<p><em>Follow <\/em><a rel=\"nofollow\" href=\"https:\/\/twitter.com\/FTMag\" data-trackable=\"link\"><em>@FTMag<\/em><\/a><em> to find out about our latest stories first<\/em><\/p>\n<div class=\"n-content-video n-content-video--internal\">\n<div class=\"n-content-video__placeholder\" data-o-component=\"o-video\" data-o-video-id=\"83635452-ccfd-4280-ae52-00079d648574\"><span>Video: Why the UK has a problem with maths | FT Film<\/span><\/div>\n<\/div>\n<\/div>\n<p><script async src=\"\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script><br \/>\n<br \/>Read the full article <a href=\"https:\/\/www.ft.com\/content\/222fed3d-b2c1-4e27-81ae-3600bc4d4647\" target=\"_blank\" rel=\"noopener\">here<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Unlock the Editor\u2019s Digest for free Roula Khalaf, Editor of the FT, selects her favourite stories in this weekly newsletter. For certain&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[],"class_list":{"0":"post-9740","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-business"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The simple maths puzzle that shows us how to separate fact from fiction | ZoomInFinancial<\/title>\n<meta name=\"description\" content=\"Unlock the Editor\u2019s Digest for freeRoula Khalaf, Editor of the FT, selects her favourite stories in this weekly newsletter.For certain kinds of questions,\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/zoominfinancial.com\/?p=9740\" \/>\n<meta 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