{"id":3847,"date":"2015-06-20T21:43:05","date_gmt":"2015-06-20T21:43:05","guid":{"rendered":"http:\/\/www.lifeandnews.com\/articles\/?p=3847"},"modified":"2016-08-13T21:56:27","modified_gmt":"2016-08-13T21:56:27","slug":"mathematics-spaghetti-alla-carbonara-and-you","status":"publish","type":"post","link":"https:\/\/www.lifeandnews.com\/articles\/mathematics-spaghetti-alla-carbonara-and-you\/","title":{"rendered":"Mathematics, spaghetti alla carbonara and you"},"content":{"rendered":"

Jim Henle<\/a>, Smith College<\/a><\/em><\/p>\n

I\u2019ve come to believe that mathematics, as an investigative science, as a practical discipline and as a creative art, shares many characteristics with cookery. It\u2019s not just spaghetti alla carbonara, it\u2019s the whole business of inventing dishes and preparing them. It\u2019s an analogy with many parts, and it has consequences.<\/p>\n

To introduce myself: I\u2019m a professional mathematician, an amateur cook and an enthusiastic eater. The ideas in this essay are distilled from years of formal reasoning, mad culinary experiments and adventurous meals. In short, I\u2019ve found that:<\/p>\n

    \n
  1. I do mathematics for much the same reasons that I cook.<\/li>\n
  2. I use the same problem-solving methods in math and cooking.<\/li>\n
  3. I judge dishes and math papers with many of the same criteria.<\/li>\n<\/ol>\n

    Together these observations suggest a picture of mathematics (or a picture of cooking) quite different from the popular view. The analogy is fun and the payoff is liberating.<\/p>\n

    My reasons<\/h2>\n

    I am motivated in both fields by curiosity and by thrills. I grew up reading Martin Gardner<\/a>\u2019s Mathematical Games<\/a> column in Scientific American. It\u2019s hard to describe how exciting these were. I read about logical paradoxes, about hexaflexagons<\/a>, about rep-tiles<\/a>, Sprouts<\/a>, and Dr Matrix<\/a>. I folded flexagons, I analyzed Sprouts, I teased classmates with paradoxes. It was thrilling.<\/p>\n

    At the same time I experienced thrills of a different sort. I remember keenly the first time my mother made apple pie. I remember the time my father grilled tuna steak. I remember the first time I tasted a whiskey sour. In all, these experiences made me what I am today: a seeker of thrills, a mathematical and gustatory glutton.<\/p>\n

    I also play with food and mess with math to satisfy an insistent curiosity.<\/p>\n

    \"\"<\/a>
    Where will I bounce?<\/span>
    \nJim Henle<\/span>,     CC BY<\/a><\/span><\/figcaption><\/figure>\n

    What happens if I combine Chartreuse and avocado?<\/p>\n

    Where will I end up if I start in one corner of this figure and start bouncing off the sides?<\/p>\n

    What vegetables can I caramelize?<\/p>\n

    How much of the infinite plane can I cover with different-sized squares?<\/p>\n

    \"\"<\/a>
    Squares and squares and squares on an infinite plane.<\/span>
    \nJim Henle<\/span>,     CC BY<\/a><\/span><\/figcaption><\/figure>\n

    Problem-solving<\/h2>\n

    Many books have been written about mathematical problem-solving. And many, many books have been written about cooking. But there is one single principle that is fundamental to both disciplines. It may be the only essential principle of problem-solving:<\/p>\n

    Make mistakes.<\/p><\/blockquote>\n

    Make mistakes and learn from them. It\u2019s the go-to method in both fields.<\/p>\n

    It\u2019s hard teaching this to students. They believe that mathematicians figure things out first and then act. But mathematicians don\u2019t. We jump in and mess up. It\u2019s the best way to see what\u2019s going on.<\/p>\n

    Suppose you are asked to find a number such that tripling the number is the same as adding 12. If you know algebra, you write<\/p>\n

    3 x n = n + 12<\/p>\n

    and solve for n. But let\u2019s say you don\u2019t know algebra. So you jump in. You guess 10. Does that work? Tripling 10 gets you 30, but adding 12 gets you 22.<\/p>\n

    3 x 10 = 30 10 + 12 = 22<\/p>\n

    30 doesn\u2019t equal 22. Let\u2019s try again. Guess 12 (after all, that\u2019s a number in the problem). But tripling 12 gets you 36 and adding 12 gets you 24.<\/p>\n

    3 x 12 = 36 12 + 12 = 24<\/p>\n

    So 12 is worse! Let\u2019s move in the other direction. Guess 8. Tripling 8 gets you 24. Adding 12 gets you 20.<\/p>\n

    3 x 8 = 24 8 + 12 = 20<\/p>\n

    Closer! Maybe your next guess is 6. And if it is, you solved the problem.<\/p>\n

    3 x 6 = 18 6 + 12 = 18<\/p>\n

    \"\"<\/a>
    Knead that dough.<\/span>
    \n    TIA<\/a>, CC BY-NC-ND<\/a><\/span><\/figcaption><\/figure>\n

    Leaping into the unknown is also the best way to learn to cook. Home cooks are often reluctant to try baking bread. They believe you have to know what you\u2019re doing before you start putting ingredients in a bowl. But that belief can prevent you from ever baking your first loaf.<\/p>\n

    I don\u2019t claim, by the way, that making mistakes is easy. It takes guts (sometimes). It also takes perseverance and hard work. But it doesn\u2019t take a \u201cmath brain.\u201d<\/p>\n

    \"\"<\/a>
    You can judge a dish or a math problem on its aesthetics.<\/span>
    \n    Chris Baird<\/a>, CC BY<\/a><\/span><\/figcaption><\/figure>\n

    Aesthetics<\/h2>\n
    \"\"<\/a>
    Simple lines work in a food and in math.<\/span>
    \nJim Henle<\/span>,     CC BY<\/a><\/span><\/figcaption><\/figure>\n

    Some dishes are wonderful for their simplicity, for their simple, clean taste. Cheesecake, for example.<\/p>\n

    In the same way, a mathematical object can be attractive because it has a clean, simple structure.<\/p>\n

    \"\"<\/a>
    Fiery flavors?<\/span>
    \n    Wes Peck<\/a>, CC BY-ND<\/a><\/span><\/figcaption><\/figure>\n

    On the other hand, some foods are celebrated for the complexity of their taste. Wine, for example.<\/p>\n

    In the same way, a mathematical structure can be alluring for its mystery and depth.<\/p>\n

    \u201cSimplicity\u201d and \u201ccomplexity\u201d are just two aesthetics that math and gastronomy share. Some others are \u201celegance,\u201d \u201cplayfulness\u201d and \u201cnovelty.\u201d<\/p>\n

    \"\"<\/a>
    Complexity has appeal in cooking and math.<\/span>
    \nJim Henle<\/span>,     CC BY<\/a><\/span><\/figcaption><\/figure>\n

    You can do it<\/h2>\n

    You have the analogy now: a moderately strong similarity between mathematics and cooking. What does that similarity suggest?<\/p>\n

    Well first of all, I\u2019ve argued that the key to success in math is to make mistakes. Accepting this principle pushes you to accept a really powerful idea. If making mistakes is the key, then everyone can cook. And everyone can do mathematics.<\/p>\n

    Second, the similarity points out that mathematics has aesthetics. Mathematicians believe this. You should too. You can pick winners (I like that math) and losers (that stuff bores me). That\u2019s what we do. I love logic and geometry. Don\u2019t ask me about statistics.<\/p>\n

    Most students intuitively get this about history, about literature, about science. But mathematics appears different to them. Math, they fear, is the judge. Math, they think, either likes you or it doesn\u2019t like you.<\/p>\n

    \"\"<\/a>
    Send it back to the kitchen if it doesn\u2019t suit you.<\/span>
    \n    US Army Africa<\/a>, CC BY<\/a><\/span><\/figcaption><\/figure>\n

    But if you don\u2019t like the food a restaurant serves you, you go somewhere else, right?<\/p>\n

    Now students today do go somewhere else. But many do it because they feel they have no choice; math doesn\u2019t like them. Forget that! Math doesn\u2019t play favorites. If you dump math, it should be because in your judgment, math is not attractive.<\/p>\n

    The third consequence follows from the first two, and it\u2019s the best of all. If students work hard, if they make mistakes, if they persevere, they will succeed in mathematics. But if students find mathematics unlovable, they won\u2019t stick with it.<\/p>\n

    The most important goal of any mathematics course is not that the students learn \u2013 that\u2019s secondary. The real goal is simple: help the students love mathematics.<\/p>\n

    \"The<\/p>\n

    Jim Henle<\/a> is Professor of Mathematics and Statistics at Smith College<\/a>.<\/p>\n

    This article was originally published on The Conversation<\/a>.
    \nRead the     original article<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Jim Henle, Smith College I\u2019ve come to believe that mathematics, as an investigative science, as a practical discipline and as a creative art, shares many characteristics with cookery. It\u2019s not just spaghetti alla carbonara, it\u2019s the whole business of inventing dishes and preparing them. It\u2019s an analogy with many parts, and it has consequences. To […]<\/p>\n","protected":false},"author":40,"featured_media":5935,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/posts\/3847"}],"collection":[{"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/users\/40"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/comments?post=3847"}],"version-history":[{"count":2,"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/posts\/3847\/revisions"}],"predecessor-version":[{"id":5936,"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/posts\/3847\/revisions\/5936"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/media\/5935"}],"wp:attachment":[{"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/media?parent=3847"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/categories?post=3847"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lifeandnews.com\/articles\/wp-json\/wp\/v2\/tags?post=3847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}