{"id":118924,"date":"2023-12-12T11:20:00","date_gmt":"2023-12-12T15:20:00","guid":{"rendered":"https:\/\/www.shortform.com\/blog\/?p=118924"},"modified":"2023-12-14T11:47:02","modified_gmt":"2023-12-14T15:47:02","slug":"definition-of-mathematical-model","status":"publish","type":"post","link":"https:\/\/www.shortform.com\/blog\/definition-of-mathematical-model\/","title":{"rendered":"The Definition of a Mathematical Model (Cathy O&#8217;Neil)"},"content":{"rendered":"\n<p>What&#8217;s the definition of mathematical models? Are math models biased toward a specific group of people?<\/p>\n\n\n\n<p>In <em>Weapons of Math Destruction<\/em>, data scientist Cathy O\u2019Neil details the insidious ways mathematical models are being used to determine everything from interest rates to prison sentences. She contends that, while mathematical models can efficiently sort through vast amounts of information, they can produce dangerous results.<\/p>\n\n\n\n<p>Let&#8217;s take a look at O&#8217;Neil&#8217;s definition of a mathematical model.<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-explaining-mathematical-models\"><strong>Explaining Mathematical Models<\/strong><\/h2>\n\n\n\n<p>According to O\u2019Neil, this is the <strong>definition of mathematical models: mathematical simulations of a real-world event<\/strong>. Organizations use mathematical models to make predictions and decisions more efficiently than they would otherwise be able to when handling large amounts of data.&nbsp;<\/p>\n\n\n\n<p>For example, suppose you recently adopted 100 cats, which you allow to freely roam your 100-acre property. To figure out where and when to leave food for the cats, you equip 20 of them with GPS collars to track their movements throughout the day. Based on the data from the collars, you estimate where the best places to leave food are\u2014you\u2019ve used data to create a simple mathematical model that simulates the movement of your cats without having to track all 100 cats.<\/p>\n\n\n\n<p>(Shortform note: Mathematical models fall within the field of <a href=\"https:\/\/www.ibm.com\/topics\/data-science\" target=\"_blank\" rel=\"noreferrer noopener\">data science<\/a>, which involves analyzing data, identifying patterns, and making predictions. Organizations increasingly rely on mathematical models with the explosive growth of <a href=\"https:\/\/www.investopedia.com\/terms\/b\/big-data.asp\" target=\"_blank\" rel=\"noreferrer noopener\"><em>big data<\/em><\/a>\u2014vast amounts of information that organizations collect from sources like social networks, electronic check-ins, and internet searches. Companies use this information to determine things like your spending habits and consumer preferences, which they then use in various ways such as targeting you with relevant ads.)<\/p>\n\n\n\n<p>O\u2019Neil argues that<strong> mathematical models are inherently reductive<\/strong>. Real-world events and people are immensely complex, and it\u2019s impossible to input every factor that influences them into an equation. Lacking all the information necessary to simulate an event flawlessly, mathematical models inevitably produce a few mistakes. Organizations that use mathematical models are aware of these limitations, but they nonetheless use mathematical models because they\u2019re willing to accept the trade-off between accuracy and efficiency.<\/p>\n\n\n\n<p>To return to our example, your mathematical model of cat movements will occasionally return inaccurate results. As any cat owner can tell you, cats do what they want, when they want, coming and going in ways that aren\u2019t entirely predictable. However, you decide that it\u2019s still worth it to feed the cats based on the information your model spits out, as it\u2019s much more efficient than tracking down and feeding each cat each day\u2014and as long as all the cats are getting enough food, there\u2019s no harm done.<\/p>\n\n\n\n<p>(Shortform note: Though, as O\u2019Neil argues, mathematical models are reductive, the trade-off is often worth it because models can solve highly complicated problems, offer many benefits in various industries, and even save lives. For example, mathematical models <a href=\"https:\/\/theconversation.com\/mathematical-modelling-a-language-that-explains-the-real-world-131476\" target=\"_blank\" rel=\"noreferrer noopener\">help keep miners safe<\/a> by predicting roof collapses, help governments prepare for and <a href=\"https:\/\/research.unimelb.edu.au\/strengths\/updates\/impact\/preparing-for-and-managing-pandemics-using-mathematical-modelling\" target=\"_blank\" rel=\"noreferrer noopener\">respond to threats of infectious diseases<\/a> such as Covid-19, and may be used to <a href=\"https:\/\/newn.cam.ac.uk\/wp-content\/uploads\/2022\/07\/Maths1-Dabke_Oorvi.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">address climate change<\/a>.)<\/p>\n\n\n\n<p>O\u2019Neil cautions that in addition to their limited accuracy, mathematical models also have ethical limitations. <strong>Mathematical models reflect the biases and incorrect assumptions of the people who make them.<\/strong> Additionally, unlike humans, mathematical models are unable to factor in moral and ethical concepts like equality.<\/p>\n\n\n\n<p>For example, a cat feeding model designed by someone who incorrectly assumed that cats spend most of their lives in trees would probably place food sources up high. Based on this model, you\u2019d end up distributing food unfairly, placing it where only the most nimble and adventurous cats would have access to it, while their terrestrial siblings would be left to fend for themselves.<\/p>\n\n\n\n<p>(Shortform note: What kind of biases might someone unknowingly include in a mathematical model? In <a href=\"https:\/\/www.shortform.com\/app\/book\/decisive\/1-page-summary\" target=\"_blank\" rel=\"noreferrer noopener\"><em>Decisive<\/em><\/a>, Dan and Chip Heath cite <a href=\"https:\/\/www.shortform.com\/app\/book\/decisive\/1-page-summary#why-we-need-a-better-decision-making-process\" target=\"_blank\" rel=\"noreferrer noopener\">four unconscious biases that compromise people\u2019s decision-making<\/a>: 1) binary thinking, which is our tendency to consider only two options, 2) <a href=\"https:\/\/www.shortform.com\/blog\/confirmation-bias-definition-2\/\">confirmation bias<\/a>, which is our tendency to search for information that supports our beliefs, 3) <a href=\"https:\/\/www.shortform.com\/blog\/status-quo-bias\/\">status quo bias<\/a>, which makes us averse to change, and 4) hubris, which makes us overly confident in our predictions.)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What&#8217;s the definition of mathematical models? Are math models biased toward a specific group of people? In Weapons of Math Destruction, data scientist Cathy O\u2019Neil details the insidious ways mathematical models are being used to determine everything from interest rates to prison sentences. She contends that, while mathematical models can efficiently sort through vast amounts of information, they can produce dangerous results. Let&#8217;s take a look at O&#8217;Neil&#8217;s definition of a mathematical model.<\/p>\n","protected":false},"author":14,"featured_media":119177,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[160,25],"tags":[1343],"class_list":["post-118924","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-science","category-statistics","tag-weapons-of-math-destruction","","tg-column-two"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.3 (Yoast SEO v24.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The Definition of a Mathematical Model (Cathy O&#039;Neil) - Shortform Books<\/title>\n<meta name=\"description\" content=\"Mathematical models are used every day by scientists, mathematicians, and even you. Learn the definition of mathematical models here.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.shortform.com\/blog\/definition-of-mathematical-model\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Definition of a Mathematical Model (Cathy O&#039;Neil)\" \/>\n<meta property=\"og:description\" content=\"Mathematical models are used every day by scientists, mathematicians, and even you. 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