【翻译】Why Do We Learn Math? 作者: a5_reed 时间: 2024-08-09 18:46 分类: 默认分类 正如维特根斯坦所言，*“我语言的界限就是我世界的界限。”* 原文:[BetterExplained](https://betterexplained.com/articles/why-do-we-learn-math/ "BetterExplained") <!--more--> --- ### Why Do We Learn Math? ### 我们为什么要学数学? I cringe when hearing "Math teaches you to think". "数学教会你思考"这样的说法让我尴尬。 It's a well-meaning but ineffective appeal that only satisfies existing fans (see: "Reading takes you anywhere!"). What activity, from crossword puzzles to memorizing song lyrics, doesn't help you think? 这种号召听起来很好，但是没什么用，它只会使已经喜欢数学的人满意。(比如:阅读可以带你去你想去的任何地方！)难道纵横字谜和记歌词就不能教会你思考了吗? Math seems different, and here's why: it's a specific, powerful vocabulary for ideas. 数学看起来不一样，原因在于:它使用了特定的，有力的词汇来描述想法。 Imagine a cook who only knows the terms "yummy" and "yucky". He makes a bad meal. What's wrong? Hrm. There's no way to describe it! Too mild? Salty? Sweet? Sour? Cold? These specific critiques become hazy variations of the "yucky" bucket. He probably wouldn't think "Needs more umami". 设想一个厨师只知道"好吃"和"难吃"两个词。他做了顿难吃的饭。哪里有问题呢?额，没法描述。味道淡了?咸了?甜了?酸了?凉了?这些具体的问题变成了模糊的"难吃"。也许厨师根本不会想到"再加点味精。" Words are handholds that latch onto thoughts. You (yes, you!) think with extreme mathematical sophistication. Your common-sense understanding of quantity includes concepts refined over millennia: base-10 notation, zero, decimals, negatives. 词语是用来抓住思想的把手。你(对，就是你！)去用高度复杂的数学思想想象:过去几千年以来，人们对数量的定义被一次又一次重新改写:十进制，0，小数，负数。 What we call "Math" are just the ideas we haven't yet internalized. 被我们称之为"数学"的东西其实是还没有被我们内化的事物。 Let's explore our idea of quantity. It's a funny notion, and some languages only have words for one, two and many. They never thought to subdivide "many", and you never thought to refer to your East and West hands. 让我们探索一下数量的概念。这个概念比较奇特，有些语言只有表示1、2和许多的词汇。他们从来没有想过细分"许多"这个概念。你也没有想过称你的右手和左手为"东手""西手"。 Here's how we've refined quantity over the years: 数量的概念是这样被改写的: > We have "number words" for each type of quantity ("one, two, three... five hundred seventy nine") 各种各样的数(1，2，3…579) > The "number words" can be written with symbols, not regular letters, like lines in the sand. The unary (tally) system has a line for each object. 数词可以用符号来表示，就像沙滩上划出的线。"正"字每一笔画都代表着一份。 > Shortcuts exist for large counts (Roman numerals: V = five, X = ten, C = hundred) 大的数字有缩写(罗马数字5，10，100) > We even have a shortcut to represent emptiness: 0 甚至"什么都没有"也有缩写:0。 > The position of a symbol is a shortcut for other numbers. 123 means 100 + 20 + 3. 符号的位置也可以表示缩写:123=100+20+3。 > 123=100+20+3Numbers can have incredibly small, fractional differences: 1.1, 1.01, 1.001... 数字可以非常小，只有极细微的区别:1.1，1.01，1.001… > Numbers can be negative, less than nothing (Wha?). This represents "opposite" or "reverse", e.g., negative height is underground, negative savings is debt. 数字甚至可以是负的，比"什么都没有"还小。(啥?)它表示"相反的"或者"颠倒的"。比如，负的高度是在地下，而负的存款是负债。 > Numbers can be 2-dimensional (or more). This isn't yet commonplace, so it's called "Math" (scary M). 数字可以是二维或以上的。但它还不够常见，所以尚且被称作"数学"(真可怕) > Numbers can be undetectably small, yet still not zero. This is also called "Math". 数字可以无穷小，但并不是零。这也是"数学"。 Our concept of numbers shapes our world. Why do ancient years go from BC to AD? We needed separate labels for "before" and "after", which weren't on a single scale. 我们对数字的理解塑造了我们的世界。为什么古代是从bc到ad?我们需要给公元前和公元后分别贴上标签，因为它们并不是同一个时间尺度上的。 Why did the stock market set prices in increments of 1/8 until 2000 AD? We were based on centuries-old systems. Ask a modern trader if they'd rather go back. 为什么股市在公元2000年以前都是以增量的八分之一设置价格?因为它基于一个古老的系统。去问问现在的交易员愿不愿意回到过去吧。 Why is the decimal system useful for categorization? You can always find room for a decimal between two other ones, and progressively classify an item (1, 1.3, 1.38, 1.386). 为什么小数对分类有用呢?因为你总可以在两个数字间找到更小的数字，并据此分类(1，1.3，1.38，1.386) Why do we accept the idea of a vacuum, empty space? Because you understand the notion of zero. (Maybe true vacuums don't exist, but you get the theory.) 我们为什么能理解"什么都没有"的概念?因为你理解了零。也许真空并不存在，但不妨碍你理解它。 Why is anti-matter or anti-gravity palatable? Because you accept that positives could have negatives that act in opposite ways. 为什么反物质和反重力可以被我们理解?因为你理解了负数就是正数相对的那一面。 How could the universe come from nothing? Well, how can 0 be split into 1 and -1? 为什么宇宙可以从什么都没有发展到今天这样?呃，我们能把0分成1和-1吗? Our math vocabulary shapes what we're capable of thinking about. Multiplication and division, which eluded geniuses a few thousand years ago, are now homework for grade schoolers. All because we have better ways to think about numbers. 我们的数学用词决定了我们能理解什么。乘和除曾困扰了几千年前的天才们，现在却只是小学生的家庭作业。这全都是因为我们有了能更好理解数字的方法。 We have decent knowledge of one noun: quantity. Imagine improving our vocabulary for structure, shape, change, and chance. (Oh, I mean, the important-sounding Algebra, Geometry, Calculus and Statistics.) 我们很清楚一个词:数量。再设想——我们理解了结构，形状，改变和偶然性的词……(用听上去很正式的话来说就是代数，几何，微积分和统计学。) Caveman Chef Og doesn't think he needs more than yummy/yucky. But you know it'd blow his mind, and his cooking, to understand sweet/sour/salty/spicy/tangy. 原始人厨师当然不会觉得他需要比好吃和难吃更具体的词。但是如果他理解了甜、酸、咸、辣、浓的意思，他的思想和厨艺都会爆炸式进步。 We're still cavemen when thinking about new ideas, and that's why we study math. 在思考新的概念时，我们仍是原始人。这就是我们学数学的原因。 -END- --- "What we call 'Math' are just the ideas we haven't yet internalized."让我大为震撼。而结尾"We're still cavemen when thinking about new ideas, and that's why we study math."则是一个很好的诠释。这句话仿佛是说我们学数学学的是怎么探究数学的界限在哪里，或者更应该说抛弃错误的成见去学数学，毕竟学习实际上是把正确的东西转化成直觉的过程。困扰着千年前的数学天才们的负数的概念如今只是小学生的家庭作业，因为负数这一概念已经被我们完全接纳了。：) 标签: 翻译文章, 数学