{"id":3362,"date":"2025-03-19T10:00:56","date_gmt":"2025-03-19T14:00:56","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=3362"},"modified":"2025-03-18T15:27:48","modified_gmt":"2025-03-18T19:27:48","slug":"math-digests-february-2025","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-february-2025\/","title":{"rendered":"Math Digests February 2025"},"content":{"rendered":"<h3><a href=\"https:\/\/theconversation.com\/the-butterfly-effect-this-obscure-mathematical-concept-has-become-an-everyday-idea-but-do-we-have-it-all-wrong-246577\">The butterfly effect: this obscure mathematical concept has become an everyday idea, but do we have it all wrong?<\/a><\/h3>\n<p><em>The Conversation<\/em>, February 5, 2025<\/p>\n<p>In the 2004 movie <a href=\"https:\/\/www.imdb.com\/title\/tt0289879\/\"><em>The Butterfly Effect<\/em><\/a>, protagonist Evan Treborn alters the entire course of his life by going back in time and changing minute decisions. The film\u2019s title is an homage to a term coined by meteorologist Edward Lorenz, who famously asked: &#8220;Does the flap of a butterfly\u2019s wings in Brazil set off a tornado in Texas?&#8221; The term &#8216;butterfly effect&#8217; now refers to the potential for small changes to generate large effects. But according to Milad Haghani of the University of Melbourne, this overstates Lorenz\u2019s original intent. \u201cIn reality, not all systems are chaotic, and for systems that aren\u2019t, small changes usually result in small effects,\u201d Haghani writes for <em>The Conversation<\/em>. In this article, Haghani describes what motivated Lorenz, and what this well-worn phrase really means.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>chaos, randomness, prediction<\/em><\/p>\n<ul>\n<li>(Mid level) Read the article and answer the following questions:\n<ul>\n<li>Why did Lorenz\u2019s computer simulation of the weather give a different answer the second time he ran it?<\/li>\n<li>Explain in your own words the meaning of the words <strong>random, deterministic, chaos, <\/strong>and the <strong>butterfly effect<\/strong>. Which of these words applies to the following systems? Justify your answer.\n<ul>\n<li>Flipping a coin<\/li>\n<li>A presidential election<\/li>\n<li>The daily temperature in your city<\/li>\n<li>A ball tossed in the air<\/li>\n<\/ul>\n<\/li>\n<li>Haghani writes that there have been \u201coversimplifications and misconceptions\u201d about the meaning of the butterfly effect. What oversimplifications and misconceptions might he be referring to?<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Compare how easy it is to predict a random system versus a chaotic system.\n<ul>\n<li>Write down the daily high temperature predictions for your town for the next 10 days. As the days progress, write down the true temperature.<\/li>\n<li>On Day 10, predict a random system. In pairs, assign one partner to be a random walker, and the other to be the predictor. The random walker will take 10 steps, each randomly chosen to be either to the left or the right. Before the walk begins, the predictor will try to predict the walker\u2019s path. Then switch roles and repeat.<\/li>\n<li>Calculate the prediction errors for both systems. Compare and contrast what\u2019s involved in predicting the daily temperature versus a random walk.<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Check out our <a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-october-2021\/\">October 2021<\/a> and <a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-july-2023\/#5\">July 2023<\/a> digests for more activities on chaos theory.<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3><a href=\"https:\/\/www.nature.com\/articles\/d41586-025-00381-z\">Kids\u2019 real-world arithmetic skills don\u2019t transfer to the classroom<\/a> (<em>timestamp 00:45<\/em>)<\/h3>\n<p><em>Nature<\/em>, February 5, 2025<\/p>\n<p>It\u2019s often hard to apply what you learn in school to the real world. With math class it\u2019s no different. This podcast from <em>Nature<\/em> describes children in India who excel at arithmetic related to the markets where they work but struggle with traditional math problems taught in school. \u201cI had been to markets and could see there were kids there, 8-year-olds, who could do the mathematics involved in selling,\u201d an economics researcher told <em>Nature<\/em>. \u201cWhen we gave them the nation-wide test, it was very clear that they were worse.\u201d <a href=\"https:\/\/www.nature.com\/articles\/s41586-024-08502-w\">According to that researcher\u2019s recent study<\/a>, the opposite tended to be true as well: When students learned arithmetic with problems from school, they weren\u2019t as proficient with market-related problems. &#8220;These findings highlight the importance of educational curricula that bridge the gap between intuitive and formal maths,&#8221; the researchers wrote in their abstract.<\/p>\n<p><strong>Classroom Activities:<\/strong><em> arithmetic, mental math<\/em><\/p>\n<ul>\n<li>(All levels) With a partner, review this guide to <a href=\"https:\/\/www.thoughtco.com\/mental-math-tricks-games-4177029\">mental math tricks<\/a> and test each other.<\/li>\n<li>(All levels) Play the online mental math game <a href=\"https:\/\/mathheads.net\/\">Math Heads<\/a> (free, but registration required).<\/li>\n<li>(Mid levels) Practice your ability to switch between real-world and school-style math with these examples.\n<ul>\n<li>You start an after-school job that earns \\$20\/hour working the 4-hour long dinner shift at a local restaurant. How many shifts do you need to work to save \\$900?<\/li>\n<li>Suppose you now have \\$900 in your bank account, and you want to save a greater amount, $y$. Write an equation to calculate how many more hours you need to work ($x$) in order to save a total of $y$ dollars.<\/li>\n<li>How does this equation change if you are now taxed at 20% on every dollar you earn?<\/li>\n<li>Plot the equation with and without taxes.<\/li>\n<li>How much tax revenue ($) do you generate for every 100 hours that you work?<\/li>\n<li>How much would someone who earns $300\/hour be taxed for 100 hours of work, if they find a loophole that allows them to pay just 1% in taxes?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a href=\"https:\/\/grist.org\/cities\/rat-population-cities-heat-climate-research\/\">Oh, great: Rat populations are surging as cities heat up<\/a><\/h3>\n<p><em>Grist<\/em>, January 31, 2025<\/p>\n<p>As temperatures increase due to climate change, rat populations are up as well. Scientists recently analyzed the relationship between rat populations and the environment in American cities. \u201cFemales will reach sexual maturity faster. They\u2019re able to breed more, and typically their litters are larger at warmer temperatures in the lab,\u201d one researcher told <em>Grist <\/em>reporter Matt Simon. This article analyzes the new data.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>\u00a0data analysis, correlations, algebra<\/em><\/p>\n<ul>\n<li>(High level) Use <a href=\"https:\/\/www.science.org\/doi\/10.1126\/sciadv.ads6782\">the original scientific article<\/a> to answer the following questions:\n<ul>\n<li>How many cities did the scientists include in their analysis? List all of them in <strong>ascending<\/strong> order of climate change driven increase.<\/li>\n<li>Figure 3 shows \u201cPositive association between warming temperatures and rat numbers.\u201d What does \u201cpositive association\u201d mean, and what do the scientists conclude? (Hint: read the figure caption and any references to \u201cFig. 3\u201d in the text)<\/li>\n<li>Figure 4 shows \u201cNegative association between vegetation cover and rat numbers.\u201d What does \u201cnegative association\u201d mean, and what do the scientists conclude? (Hint: read the figure caption and any references to \u201cFig. 4\u201d in the text)<\/li>\n<li>Explain the following conclusion in your own words: \u201cIn a relative weights analysis, <strong>7% of the variation in trend strength<\/strong> was linked to the <strong>mean temperature increase a city had experienced relative to long-term temperature averages<\/strong>.\u201d (Hint: refer to Figure 2.)<\/li>\n<\/ul>\n<\/li>\n<li>(Mid level) Suppose that you can model Big City\u2019s future average temperature with the following equation: $$T_{2024+t} = 60 + 0.25t$$\n<ul>\n<li>Based on the description of the equation, how would you define the variables $T$ and $t$?<\/li>\n<li>What will be Big City\u2019s average temperature for 2025?<\/li>\n<li>Which units does this equation most likely use? And by how much does temperature increase every 10 years?<\/li>\n<li>If Big City\u2019s rat population increases by 18% for every 1 degree of temperature increase, by what percent will the population increase after 20 years?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a href=\"https:\/\/www.newsweek.com\/plane-crash-statistics-american-airlines-2023691\">How Common Are Plane Crashes? What Statistics Show<\/a><\/h3>\n<p><em>Newsweek<\/em>, January 30, 2025<\/p>\n<p>This year, the country has already witnessed several high-profile plane crashes. One recent collision near Washington D.C. between an American Airlines flight and a military helicopter killed every person involved. &#8220;Commercial aviation in the U.S. hasn&#8217;t had a major accident since 2009,\u201d an aviation lawyer told <em>Newsweek,<\/em> asserting that flying remains safe. Still, it\u2019s normal to worry when seeing news and tragedy. This <em>Newsweek <\/em>article shares statistics to analyze flight safety over the years.<\/p>\n<p><strong>Classroom Activities:<\/strong> <em>data analysis, statistics<\/em><\/p>\n<ul>\n<li>(Mid level) Answer the following questions based on the article\n<ul>\n<li>How many total fatal and nonfatal crashes occurred in 2023, according to the National Transportation Safety Board (NTSB)?<\/li>\n<li>How many fatal and nonfatal crashes occurred in 2023 <em>per million flight hours<\/em>?<\/li>\n<li>How many fatal and nonfatal crashes occurred in 2008 per million flight hours?<\/li>\n<li>By what percent did the rates of fatal and non-fatal crashes change between 2008 and 2023?<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Create a spreadsheet table using the data from 1982 through 2025 from <a href=\"https:\/\/www.ntsb.gov\/safety\/data\/Pages\/monthly-dashboard.aspx\">this NTSB data of yearly and monthly totals of <\/a><a href=\"https:\/\/www.ntsb.gov\/safety\/data\/Pages\/monthly-dashboard.aspx\"><strong>fatal <\/strong><\/a><a href=\"https:\/\/www.ntsb.gov\/safety\/data\/Pages\/monthly-dashboard.aspx\">accidents<\/a>.\n<ul>\n<li>Which <strong>month of the year<\/strong> has the highest average over this period?<\/li>\n<li>Which <strong>year <\/strong>has the highest average over this period?<\/li>\n<li>What are the limitations of comparing data from the 1980s to data from the 2020s?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a href=\"https:\/\/www.kpcw.org\/show\/local-news-hour\/2025-02-21\/mathematics-professor-explains-ranked-choice-voting\">Mathematics professor explains ranked choice voting<\/a><\/h3>\n<p><em>KPCW Local News Hour<\/em>, February 21, 2025<\/p>\n<p>In this segment on <em>KPCW<\/em>, a public radio station in Utah, mathematician Alan Parry gives the rundown on instant runoff voting\u2014how it works, some of its mathematical quirks, and how it stacks up against traditional plurality voting.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>voting, monotonicity<\/em><\/p>\n<ul>\n<li>(Mid level) Listen to the segment.\n<ul>\n<li>What is the connection between the monotonicity property in voting, and the <a href=\"https:\/\/mathworld.wolfram.com\/MonotonicFunction.html\">monotone functions<\/a> you might have studied in math class?<\/li>\n<\/ul>\n<\/li>\n<li>(High level) In <a href=\"https:\/\/www.votingmatters.org.uk\/ISSUE6\/P4.HTM\">a 1996 paper<\/a>, mathematician Douglas Woodall studied a hypothetical election in which 11 voters rank Candidate A first and Candidate B second; 7 voters vote only for Candidate B; and 12 voters vote only for Candidate C. He used this example to show that no voting method can simultaneously satisfy all three of the following properties:\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li><strong>Plurality: <\/strong>Suppose Cynthia receives $m$ votes in all (in some votes, she\u2019s ranked first-choice votes and in others, she\u2019s second- or third-choice), and Jane receives $n$ first-preference votes. If $n &gt; m$, Jane should have a better chance of winning than Cynthia.<\/li>\n<li><strong>Condorcet:<\/strong> If Jane would beat each of her opponents in a head-to-head race, Jane should win the election.<\/li>\n<li><strong>Monotonicity:<\/strong> If Jane is set to win the election, and new voters arrive at the last minute with ballots that rank Jane first, Jane should still win the election when votes are recounted.<\/li>\n<\/ul>\n<\/li>\n<li>Who do you think should win Woodall&#8217;s hypothetical election? Why?<\/li>\n<li>What if two voters are added who rank B first and A second?<\/li>\n<li>What if five voters are added who rank C first and B second?<\/li>\n<li>To see Woodall\u2019s conclusions, navigate to <a href=\"https:\/\/www.votingmatters.org.uk\/ISSUE6\/P4.HTM\">Section 4<\/a> of the paper. Does this exercise change your thinking about fair voting methods?<\/li>\n<\/ul>\n<\/li>\n<li>Read more about <a href=\"https:\/\/electionlab.mit.edu\/research\/instant-runoff-voting\">instant runoff voting<\/a> in this article by MIT\u2019s Election Lab.<\/li>\n<li>(All levels) In our <a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-november-2022\/#3\">November 2022 digests<\/a>, students can analyze more hypothetical elections that do not respect monotonicity.<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3>More of this month\u2019s math headlines<\/h3>\n<ul>\n<li><a href=\"https:\/\/theconversation.com\/whats-the-shape-of-the-universe-mathematicians-use-topology-to-study-the-shape-of-the-world-and-everything-in-it-235635\">What\u2019s the shape of the universe? Mathematicians use topology to study the shape of the world and everything in it<\/a><br \/>\n<em>The Conversation<\/em>, February 26, 2025<\/li>\n<li><a href=\"https:\/\/gizmodo.com\/a-maze-the-size-of-earth-new-ai-tackles-math-problems-that-take-millions-of-steps-2000564057\">\u2018A Maze the Size of Earth\u2019: New AI Tackles Math Problems That Take Millions of Steps<\/a><br \/>\n<em>Gizmodo<\/em>, February 15, 2025<\/li>\n<li><a href=\"https:\/\/www.nytimes.com\/2025\/02\/14\/science\/mathematics-figalli-optimal-transport.html\">A Mathematician Who Makes the Best of Things<\/a><br \/>\n<em>The New York Times<\/em>, February 14, 2025<\/li>\n<li><a href=\"https:\/\/www.economist.com\/science-and-technology\/2025\/02\/12\/ai-is-being-used-to-model-football-matches\">AI is being used to model football matches<\/a><br \/>\n<em>The Economist<\/em>, February 12, 2025<\/li>\n<li><a href=\"https:\/\/www.scientificamerican.com\/article\/mathematical-symbols-wild-history-explained\/\">The Wild and Contentious History of Mathematical Symbols<\/a><br \/>\n<em>Scientific American<\/em>, February 7, 2025<\/li>\n<li><a href=\"https:\/\/www.newscientist.com\/article\/2466657-the-100-year-old-symmetry-theorem-that-is-still-changing-physics-today\/\">The 100-year-old symmetry theorem that is still changing physics today<\/a><br \/>\n<em>New Scientist<\/em>, February 4, 2025<\/li>\n<li><a href=\"https:\/\/www.quantamagazine.org\/new-proofs-probe-the-limits-of-mathematical-truth-20250203\/\">New Proofs Probe the Limits of Mathematical Truth<\/a><br \/>\n<em>Quanta Magazine<\/em>, February 3, 2025<\/li>\n<li><a href=\"https:\/\/www.nytimes.com\/2025\/02\/01\/obituaries\/annie-easley-overlooked.html\">Overlooked No More: Annie Easley, Who Helped Take Spaceflight to New Heights<\/a><br \/>\n<em>The New York Times<\/em>, February 1, 2025<\/li>\n<\/ul>\n<p><em>\u00a0<\/em><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The butterfly effect: this obscure mathematical concept has become an everyday idea, but do we have it all wrong? The Conversation, February 5, 2025 In the 2004 movie The Butterfly Effect, protagonist Evan Treborn alters the entire course of his life by going back in time and changing minute decisions.<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-february-2025\/\">Read More &rarr;<\/a><\/span><\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[2],"tags":[6,155,11,435,19,434,436,433,432,84,170],"class_list":["entry","author-leilasloman","post-3362","post","type-post","status-publish","format-standard","category-math-in-the-media-digests","tag-algebra","tag-arithmetic","tag-chaos","tag-correlations","tag-data-analysis","tag-mental-math","tag-monotonicity","tag-prediction","tag-randomness","tag-statistics","tag-voting"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/3362","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/comments?post=3362"}],"version-history":[{"count":16,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/3362\/revisions"}],"predecessor-version":[{"id":3378,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/3362\/revisions\/3378"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=3362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=3362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=3362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}