{"id":1205,"date":"2022-10-04T12:09:35","date_gmt":"2022-10-04T16:09:35","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=1205"},"modified":"2022-10-04T12:09:35","modified_gmt":"2022-10-04T16:09:35","slug":"math-digests-september-2022","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-september-2022\/","title":{"rendered":"Math Digests September 2022"},"content":{"rendered":"<h3><a id=\"1\" href=\"https:\/\/www.scientificamerican.com\/article\/quantum-physics-titans-win-breakthrough-prize\/\"><span style=\"font-weight: 400\">Quantum Physics Titans Win Breakthrough Prize<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">Scientific American<\/span><\/i><span style=\"font-weight: 400\">, September 22, 2022<\/span><\/p>\n<p><span style=\"font-weight: 400\">When you shop online with a credit card or send an email to a friend, your information is packaged, encrypted, and sent through systems that were designed using math and physics\u2014but not quantum physics. A fundamentally different kind of computer, called a quantum computer, could use properties of quantum mechanics to efficiently solve problems that are impractical for ordinary computers. Quantum computers, which exist today but are small and not yet powerful, could completely change how information is communicated and protected. In an article for <\/span><i><span style=\"font-weight: 400\">Scientific American<\/span><\/i><span style=\"font-weight: 400\">, Daniel Garisto reports on the latest <\/span><a href=\"https:\/\/breakthroughprize.org\/News\/73\"><span style=\"font-weight: 400\">Breakthrough Prize in Fundamental Physics<\/span><\/a><span style=\"font-weight: 400\">, awarded to Charles H. Bennett, Gilles Brassard, David Deutsch, and Peter Shor for \u201cfoundational work in quantum information.\u201d The prize was for trailblazing research on the ideas behind the machines: they developed much of the conceptual framework for quantum computing and quantum cryptography.<\/span><\/p>\n<p><b>Classroom activities<\/b><span style=\"font-weight: 400\">: <\/span><i><span style=\"font-weight: 400\">quantum computing, quantum physics<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) Play the <\/span><a href=\"https:\/\/aps.org\/programs\/outreach\/physicsquest\/upload\/Quantum-Circuits-cards.pdf\"><span style=\"font-weight: 400\">Quantum Circuits<\/span><\/a><span style=\"font-weight: 400\"> card game from the American Physical Society <\/span><a href=\"https:\/\/aps.org\/programs\/outreach\/physicsquest\/pq21.cfm\"><span style=\"font-weight: 400\">PhysicsQuest 2021 kit<\/span><\/a><span style=\"font-weight: 400\">, following the game\u2019s <\/span><a href=\"https:\/\/aps.org\/programs\/outreach\/physicsquest\/upload\/Pictorial-rules.pdf\"><span style=\"font-weight: 400\">pictorial rules<\/span><\/a><span style=\"font-weight: 400\"> for quantum gates. (There is also a teacher\u2019s guide <\/span><a href=\"https:\/\/aps.org\/programs\/outreach\/physicsquest\/quantum-curcuit.cfm\"><span style=\"font-weight: 400\">here<\/span><\/a><span style=\"font-weight: 400\">.) Note that this game has cards that need to be printed out in advance!<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) Play through the puzzles in the <\/span><a href=\"https:\/\/iqim.caltech.edu\/quantum-puzzles\/#game\"><span style=\"font-weight: 400\">Quantum Chess<\/span><\/a><span style=\"font-weight: 400\"> game.\u00a0<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(High level) Come up with your own example of a chess puzzle using superposition and measurement or entanglement.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(High level) Read this article about <\/span><a href=\"https:\/\/scienceexchange.caltech.edu\/topics\/quantum-science-explained\/quantum-superposition\"><span style=\"font-weight: 400\">quantum superposition<\/span><\/a><span style=\"font-weight: 400\">. Compare this to the way that superposition is represented in the chess game.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><i><span style=\"font-weight: 400\">\u2014Tamar Lichter Blanks<\/span><\/i><\/p>\n<hr \/>\n<h3><a id=\"2\" href=\"https:\/\/www.netflix.com\/title\/81273453\"><span style=\"font-weight: 400\">A Trip to Infinity<\/span><\/a><\/h3>\n<p><span style=\"font-weight: 400\">Netflix, September 26, 2022<\/span><\/p>\n<h3><a href=\"https:\/\/iai.tv\/articles\/how-infinity-threatens-cosmology-peter-cameron-auid-2246\"><span style=\"font-weight: 400\">Infinity: the question cosmology can&#8217;t answer<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">IAI News, <\/span><\/i><span style=\"font-weight: 400\">September 23, 2022<\/span><\/p>\n<p><span style=\"font-weight: 400\">No matter what level you\u2019re at, infinity is indispensable to how we do mathematics today. Even elementary school students implicitly rely on it when they add and subtract using integer numbers\u2014a fact duly acknowledged by any child who, in a contest to name the biggest number, has triumphantly yelled \u201cinfinity plus one!\u201d But does infinity ever enter into the physical world? Both Peter Cameron\u2019s article and this 80-minute Netflix documentary discuss the mathematics of infinity as well as its role in physics.<\/span><\/p>\n<p><b>Classroom activity: <\/b><i><span style=\"font-weight: 400\">infinity, integers, real numbers<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) If students are not already familiar with the concept of rational and irrational numbers, use <\/span><a href=\"https:\/\/flexbooks.ck12.org\/tecbook\/ck-12-interactive-middle-school-math-8-for-ccss-teachers-guide\/section\/10.4\/primary\/lesson\/introduction-to-irrational-numbers-math-8-ccss-msm8-ccss-te\/\"><span style=\"font-weight: 400\">this online lesson<\/span><\/a><span style=\"font-weight: 400\"> before doing the other activities.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Middle school and up) Use this lesson plan, <\/span><a href=\"https:\/\/archive.nytimes.com\/learning.blogs.nytimes.com\/2013\/01\/30\/teaching-the-mathematics-of-infinity\/\"><span style=\"font-weight: 400\">&#8220;Teaching the Mathematics of Infinity&#8221;<\/span><\/a><span style=\"font-weight: 400\">, to study different kinds of infinity in class.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(High level) Watch <\/span><a href=\"https:\/\/www.youtube.com\/watch?v=elvOZm0d4H0&amp;ab_channel=Numberphile\"><span style=\"font-weight: 400\">this video<\/span><\/a><span style=\"font-weight: 400\"> from Numberphile explaining countability and Cantor\u2019s diagonal argument.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Ask students if they think the following sets are countable: The points on an <\/span><i><span style=\"font-weight: 400\">xy<\/span><\/i><span style=\"font-weight: 400\">-plane, the set of prime numbers, the set of odd numbers, the set of line segments of any length.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><i><span style=\"font-weight: 400\">\u2014Leila Sloman<\/span><\/i><\/p>\n<hr \/>\n<h3><a id=\"3\" href=\"https:\/\/ec.europa.eu\/research-and-innovation\/en\/horizon-magazine\/beautiful-game-theory-using-mathematics-resolve-human-conflicts\"><span style=\"font-weight: 400\">The Beautiful Game Theory &#8211; using mathematics to resolve human conflicts<\/span><\/a><span style=\"font-weight: 400\">\u00a0<\/span><\/h3>\n<p><i><span style=\"font-weight: 400\">Horizon Magazine<\/span><\/i><span style=\"font-weight: 400\">, September 1, 2022<\/span><\/p>\n<p><span style=\"font-weight: 400\">Conflicts between humans are a lot like games. You can win, or you can lose. You can draw, or compromise to win some battles and accept defeat in others. If two people win the lottery, they simply split the winnings 50\/50. But what\u2019s the best compromise for conflicts that involve concepts more abstract than money? In math, \u201cgame theory\u201d deals with finding the optimal strategies to resolve competing interests. Game theory can help win a game of poker, and it\u2019s also used to understand global conflicts. Researchers recently created tools based on game theory to facilitate discussions about land use conflicts around the world, such as a conflict between farmers and geese conservation efforts in Scotland. In an article for <\/span><i><span style=\"font-weight: 400\">Horizon,<\/span><\/i><span style=\"font-weight: 400\"> Gareth Willmer writes about this research and describes the role of math in messy human situations.<\/span><\/p>\n<p><b>Classroom activities:<\/b> <i><span style=\"font-weight: 400\">game theory<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Low level) Can you guess how your classmates will behave? Given a range of integers between 0 and 100, guess the whole number that is closest to <\/span><b>two-thirds of the average<\/b><span style=\"font-weight: 400\"> of all numbers guessed by your classmates. Collect all the individual guesses, calculate the average, then two-thirds of the average. Discuss how you did.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">After playing, watch this TED Ed video about <\/span><a href=\"https:\/\/www.youtube.com\/watch?v=MknV3t5QbUc\"><span style=\"font-weight: 400\">predicting human behavior with game theory<\/span><\/a><span style=\"font-weight: 400\">, which explains the math behind this game.<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Play <\/span><a href=\"http:\/\/178.62.196.186:5000\/crops_vs_creatures\/3\/game\/\"><span style=\"font-weight: 400\">crops versus creatures<\/span><\/a><span style=\"font-weight: 400\">, a game designed by the researchers to illustrate the math of settling complex conflicts. Note: Game play will be recorded and used in a study by researchers at the University of Stirling. Students must be 16 or older to fill out the consent form.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Algebra II) For more information on game theory and helpful games and examples, use this NSF-sponsored <\/span><a href=\"http:\/\/pi.math.cornell.edu\/~mec\/2008-2009\/Anema\/games.html\"><span style=\"font-weight: 400\">teaching tool <\/span><\/a><span style=\"font-weight: 400\">by Cornell University.<\/span><\/li>\n<\/ul>\n<p style=\"text-align: right\"><span style=\"font-weight: 400\">\u2014<\/span><i><span style=\"font-weight: 400\">Max Levy<\/span><\/i><\/p>\n<hr \/>\n<h3><a id=\"4\" href=\"https:\/\/www.popularmechanics.com\/science\/math\/a40971517\/p-value-statistics-fragility-index\/\"><span style=\"font-weight: 400\">How Scientists Massage Results With \u2018P-Hacking\u2019<\/span><\/a><span style=\"font-weight: 400\">\u00a0<\/span><\/h3>\n<p><i><span style=\"font-weight: 400\">Popular Mechanics<\/span><\/i><span style=\"font-weight: 400\">, August 23 2022<\/span><\/p>\n<p><span style=\"font-weight: 400\">Good science is not a story of what happened one time in one lab\u2014it is repeatable and significant. Scientists strive to draw broad conclusions based on experiments that let them study the effects of an \u201cexperimental variable\u201d on a sample. For instance, clinical trials let scientists conclude that vaccines protected people from Covid-19 better than a placebo did. To measure the <\/span><i><span style=\"font-weight: 400\">statistical significance <\/span><\/i><span style=\"font-weight: 400\">of these effects, scientists calculate a \u201cp-value.\u201d A p-value represents the likelihood that observed effects can be explained by chance, rather than the variable. (Lower p-values mean a result is less likely to be due to chance.) The p-value is standard across science, but it\u2019s not foolproof: Researchers can cleverly analyze data to get better p-values, thereby overstating weak results. Though sometimes harmless, writes Sarah Wells, \u201cwhen this practice is used in medical trials, it can have much deadlier results.\u201d In this article, Wells explains how some scientists are exploring ways to close those loopholes.<\/span><\/p>\n<p><b>Classroom activities: <\/b><i><span style=\"font-weight: 400\">probability, statistics, p-hacking, fragility index<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) Watch this brief TED-Ed video that explains <\/span><a href=\"https:\/\/youtu.be\/i60wwZDA1CI\"><span style=\"font-weight: 400\">how p-hacking works<\/span><\/a><span style=\"font-weight: 400\"> in more detail.\u00a0<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Statistics) Now watch this Khan Academy <\/span><a href=\"https:\/\/www.khanacademy.org\/math\/ap-statistics\/xfb5d8e68:inference-categorical-proportions\/idea-significance-tests\/v\/p-values-and-significance-tests\"><span style=\"font-weight: 400\">video about calculating p-values<\/span><\/a><span style=\"font-weight: 400\"> and answer the <\/span><a href=\"https:\/\/www.khanacademy.org\/math\/ap-statistics\/xfb5d8e68:inference-categorical-proportions\/idea-significance-tests\/a\/p-value-conclusions\"><span style=\"font-weight: 400\">quiz questions here<\/span><\/a><span style=\"font-weight: 400\">.<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) According to the article, scientists hope to weed out significant yet weak results with a new measure called the fragility index. An experiment\u2019s <\/span><i><span style=\"font-weight: 400\">fragility <\/span><\/i><span style=\"font-weight: 400\">corresponds to how sensitive it is to small perturbations. For example, if a drug\u2019s clinical trial data turns from significant (p &lt; 0.05) to insignificant (p &gt; 0.05) if one single participant would have had a weaker outcome, then it would be considered fragile. Discuss why you think it\u2019s important to make such a distinction.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(Mid level) Suppose you are testing whether an antibiotic works better than a placebo to treat an infection. Your clinical trial has 200 total participants, who are all infected at the start of the experiment. Half receive the placebo. Half receive the drug. By the end of the study, 10 placebo recipients and 90 drug-recipients are infection-free.<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Calculate an experiment\u2019s fragility index using <\/span><a href=\"https:\/\/clincalc.com\/Stats\/FragilityIndex.aspx\"><span style=\"font-weight: 400\">this online calculator<\/span><\/a><span style=\"font-weight: 400\">.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Repeat this calculation assuming instead that 30 placebo recipients and 45 drug-recipients are infection-free.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Discuss what each result means in terms of whether the antibiotic should be recommended as a treatment.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><i><span style=\"font-weight: 400\">\u2014Max Levy<\/span><\/i><\/p>\n<hr \/>\n<h3><a id=\"5\" href=\"https:\/\/www.snexplores.org\/article\/lets-learn-about-dealing-with-math-anxiety\"><span style=\"font-weight: 400\">Let\u2019s learn about dealing with math anxiety<\/span><\/a><\/h3>\n<p><i><span style=\"font-weight: 400\">Science News Explores, <\/span><\/i><span style=\"font-weight: 400\">September 6, 2022<\/span><\/p>\n<p><span style=\"font-weight: 400\">As a mathematician, I can\u2019t count the number of people who have told me they hated math as a kid. It\u2019s hard not to wonder how many of those people would feel differently if they\u2019d been able to engage with math without timed tests or the <\/span><a href=\"https:\/\/www.snexplores.org\/article\/dont-let-math-stress-you-out\"><span style=\"font-weight: 400\">&#8220;genius myth&#8221;<\/span><\/a><span style=\"font-weight: 400\"> hanging over their heads. Maria Temming\u2019s article for <\/span><i><span style=\"font-weight: 400\">Science News Explores <\/span><\/i><span style=\"font-weight: 400\">looks at ways to deal with math anxiety, sharing articles and resources to help students practice math in a stress-free way.<\/span><\/p>\n<p><b>Classroom Activities: <\/b><i><span style=\"font-weight: 400\">math anxiety, algebra, geometry, arithmetic<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) Ask students to read some of the suggested articles under \u201cWant to know more?\u201d. After reading, ask students to reflect on the following discussion questions:<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Do math assignments or tests make you more or less anxious than assignments in other subjects? Do you think you experience math anxiety? Why or why not?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Do you know anyone who you think experiences math anxiety? Write what you notice about this person\u2019s relationship with math.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">In this 2017 <\/span><a href=\"https:\/\/www.snexplores.org\/article\/dont-let-math-stress-you-out\"><span style=\"font-weight: 400\">article<\/span><\/a><span style=\"font-weight: 400\">, Evelyn Lamb writes about how a \u201cfixed mindset\u201d and the \u201cgenius myth\u201d may contribute to math anxiety. Do you agree or disagree that these concepts make math anxiety worse? Why?<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">(All levels) Mathematical skills come up in many areas of our lives, sometimes when we\u2019re not even aware of it. As a class, brainstorm some games and activities that use logical thinking or numbers. For homework, ask students to spend 20 minutes on an activity they enjoy that involves some mathematical skills, and answer the following questions:<\/span>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Did you feel more or less anxious during the activity than you normally are while doing math?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">How was the experience different or similar to your usual experience of math?<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Did you use skills that might help you in math class? If so, what?<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><span style=\"font-weight: 400\">\u2014<\/span><i><span style=\"font-weight: 400\">Leila Sloman<\/span><\/i><\/p>\n<hr \/>\n<h3>Some more of this month&#8217;s math headlines:<\/h3>\n<ul>\n<li><a href=\"https:\/\/www.newscientist.com\/article\/2336176-the-number-that-is-too-big-for-the-universe\/\">The number that is too big for the universe<\/a><br \/>\n<em>New Scientist, <\/em>September 9, 2022<\/li>\n<li><a href=\"https:\/\/www.register-herald.com\/news\/life\/w-va-week-in-history---katherine-johnson\/article_cd5a20f0-1dab-11ed-a13d-93e1cc06b7ae.html\">W.Va. Week in History \u2013 Katherine Johnson<\/a><br \/>\n<em>The Register-Herald, <\/em>August 27, 2022<\/li>\n<li><a href=\"https:\/\/nautil.us\/are-all-brains-good-at-math-238539\/\">Are All Brains Good at Math?<\/a><br \/>\n<em>Nautilus<\/em>, August 31, 2022<\/li>\n<li><a href=\"https:\/\/dailyprogress.com\/entertainment\/arts-and-theatre\/play-puts-mathematician-emmy-noether-in-the-spotlight\/article_4cc8cb62-2ed6-11ed-9dcc-5f7f2d16e72f.html\">Play puts mathematician Emmy Noether in the spotlight<\/a><br \/>\n<em>The Daily Progress<\/em>, September 7, 2022<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Quantum Physics Titans Win Breakthrough Prize Scientific American, September 22, 2022 When you shop online with a credit card or send an email to a friend, your information is packaged, encrypted, and sent through systems that were designed using math and physics\u2014but not quantum physics. A fundamentally different kind of<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-september-2022\/\">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":[6,155,153,151,35,110,149,154,152,73,107,148,150,84],"class_list":["entry","author-leilasloman","post-1205","post","type-post","status-publish","format-standard","category-math-in-the-media-digests","tag-algebra","tag-arithmetic","tag-fragility-index","tag-game-theory","tag-geometry","tag-infinity","tag-integers","tag-math-anxiety","tag-p-hacking","tag-probability","tag-quantum-computing","tag-quantum-physics","tag-real-numbers","tag-statistics"],"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\/1205","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=1205"}],"version-history":[{"count":9,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/1205\/revisions"}],"predecessor-version":[{"id":1214,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/1205\/revisions\/1214"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=1205"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=1205"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=1205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}