sábado, junho 20, 2015

Matemática, esparguete à carbonara e tu

Mathematics, spaghetti alla carbonara and you

Jim Henle, Smith College
I’ve come to believe that mathematics, as an investigative science, as a practical discipline and as a creative art, shares many characteristics with cookery. It’s not just spaghetti alla carbonara, it’s the whole business of inventing dishes and preparing them. It’s an analogy with many parts, and it has consequences.
To introduce myself: I’m 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’ve found that:
  1. I do mathematics for much the same reasons that I cook.
  2. I use the same problem-solving methods in math and cooking.
  3. I judge dishes and math papers with many of the same criteria.
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.

My reasons

I am motivated in both fields by curiosity and by thrills. I grew up reading Martin Gardner’s Mathematical Games column in Scientific American. It’s hard to describe how exciting these were. I read about logical paradoxes, about hexaflexagons, about rep-tiles, Sprouts, and Dr Matrix. I folded flexagons, I analyzed Sprouts, I teased classmates with paradoxes. It was thrilling.
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.
I also play with food and mess with math to satisfy an insistent curiosity.

Where will I bounce? Jim Henle, CC BY

What happens if I combine Chartreuse and avocado?
Where will I end up if I start in one corner of this figure and start bouncing off the sides?
What vegetables can I caramelize?
How much of the infinite plane can I cover with different-sized squares?

Squares and squares and squares on an infinite plane. Jim Henle, CC BY


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:
Make mistakes.
Make mistakes and learn from them. It’s the go-to method in both fields.
It’s hard teaching this to students. They believe that mathematicians figure things out first and then act. But mathematicians don’t. We jump in and mess up. It’s the best way to see what’s going on.
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
3 x n = n + 12
and solve for n. But let’s say you don’t know algebra. So you jump in. You guess 10. Does that work? Tripling 10 gets you 30, but adding 12 gets you 22.
3 x 10 = 30 10 + 12 = 22
30 doesn’t equal 22. Let’s try again. Guess 12 (after all, that’s a number in the problem). But tripling 12 gets you 36 and adding 12 gets you 24.
3 x 12 = 36 12 + 12 = 24
So 12 is worse! Let’s move in the other direction. Guess 8. Tripling 8 gets you 24. Adding 12 gets you 20.
3 x 8 = 24 8 + 12 = 20
Closer! Maybe your next guess is 6. And if it is, you solved the problem.
3 x 6 = 18 6 + 12 = 18

Knead that dough. TIA, CC BY-NC-ND

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’re doing before you start putting ingredients in a bowl. But that belief can prevent you from ever baking your first loaf.
I don’t claim, by the way, that making mistakes is easy. It takes guts (sometimes). It also takes perseverance and hard work. But it doesn’t take a “math brain.”

You can judge a dish or a math problem on its aesthetics. Chris Baird, CC BY


Simple lines work in a food and in math. Jim Henle, CC BY

Some dishes are wonderful for their simplicity, for their simple, clean taste. Cheesecake, for example.
In the same way, a mathematical object can be attractive because it has a clean, simple structure.

Fiery flavors? Wes Peck, CC BY-ND

On the other hand, some foods are celebrated for the complexity of their taste. Wine, for example.
In the same way, a mathematical structure can be alluring for its mystery and depth.
“Simplicity” and “complexity” are just two aesthetics that math and gastronomy share. Some others are “elegance,” “playfulness” and “novelty.”

Complexity has appeal in cooking and math. Jim Henle, CC BY

You can do it

You have the analogy now: a moderately strong similarity between mathematics and cooking. What does that similarity suggest?
Well first of all, I’ve 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.
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’s what we do. I love logic and geometry. Don’t ask me about statistics.
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’t like you.

Send it back to the kitchen if it doesn’t suit you. US Army Africa, CC BY

But if you don’t like the food a restaurant serves you, you go somewhere else, right?
Now students today do go somewhere else. But many do it because they feel they have no choice; math doesn’t like them. Forget that! Math doesn’t play favorites. If you dump math, it should be because in your judgment, math is not attractive.
The third consequence follows from the first two, and it’s 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’t stick with it.
The most important goal of any mathematics course is not that the students learn – that’s secondary. The real goal is simple: help the students love mathematics.
The Conversation
Jim Henle is Professor of Mathematics and Statistics at Smith College.
This article was originally published on The Conversation. Read the original article.

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