Think beyond
the obvious.

Several years ago, interviewing candidates for a job, I grew tired of asking, “What experience do you have?” So I decided on a one-question quiz to find out how resourceful a thinker the new hire might be. Here it is:

几年前，在面试求职者时，我已经厌倦了反复问：“你有什么经验？”于是我决定只出一道题，看看新员工可能有多善于随机应变、独立思考。题目是这样的：

You are on a yacht sailing the Pacific Ocean. Your navigator announces you are over the deepest point, the Mariana Trench. Just then, a clumsy guest accidentally drops a twelve-pound cannonball over the side. How long will it take for the cannonball to reach the bottom of the ocean?

你正乘坐一艘游艇航行在太平洋上。领航员告诉你，船正位于海洋最深处——马里亚纳海沟的上方。就在这时，一位笨手笨脚的客人不小心把一枚十二磅重的炮弹掉到了船外。这枚炮弹需要多长时间才能到达海底？

Before reading on, please try to solve this yourself—paying special attention to how you might solve it.

在继续读下去之前，请先自己试着解决这个问题——尤其留意你会怎样解决它。

Did you make a completely wild guess because “there wasn’t enough information”? Did you get too bogged down in the details trying to come up with the “exactly right” answer? Or did you zero in on the two most important problems—how deep is the Mariana Trench and how fast might a cannonball fall through the water—then hazard a guesstimate?

你是否因为“信息不够”就完全凭空猜了一个答案？你是否为了找出“绝对正确”的答案而陷在细节里无法前进？还是你抓住了两个最重要的问题——马里亚纳海沟有多深，以及炮弹在水中下沉得多快——然后大胆作出一个大致估算？

Most of my candidates simply made a wild guess, thinking that they couldn’t be one hundred percent right. Rarely was someone willing to risk an approximation.

我的大多数应聘者只是随意猜了一个答案，因为他们认为自己不可能百分之百正确。很少有人愿意冒险给出一个近似答案。

What does this have to do with business or creativity? A great deal. In the real world, we frequently need to make decisions when the full information does not exist. From what foods we eat to how to raise our kids, creative people must think for themselves. There may not be the time or the money to make sure of all your decisions. Your best guess will often be the best you can do.

这和商业或创造力有什么关系？关系大着呢。在现实世界中，我们经常必须在信息并不完整时作出决定。从吃什么食物到怎样养育孩子，有创造力的人都必须独立思考。我们可能没有足够的时间或金钱来确保每一个决定都万无一失。你所能作出的最佳估计，往往就是你能做到的最好结果。

Suppose, for example, you’ve been asked to write a marketing plan for a new telephone device that will send your name, company, address, and telephone number to a visual display or printer on another person’s phone. In addition to conventional outlets like mass merchandisers and electronics stores, you’d like to know the number of “phone stores” in the United States. Unfortunately, this figure is not available, either from the market-research houses or from the United States government. What do you do?

例如，假设有人请你为一种新型电话设备制定营销方案；这种设备可以把你的姓名、公司、地址和电话号码传送到对方电话上的显示屏或打印机。除了大型零售商和电子产品商店等传统销售渠道之外，你还想知道美国有多少家“电话商店”。遗憾的是，无论市场研究机构还是美国政府都没有这一数据。你会怎么办？

One solution would be to go to your local library, pull out a few phone directories from around the country, turn to the Yellow Pages, and start counting. You could then guesstimate how many stores there are per one hundred thousand people in each of the cities you counted. This, by the way, is exactly what a marketing consultant I know did for a large telecommunications client.

一种办法是去当地的图书馆，找出几本美国不同地区的电话簿，翻到黄页，然后开始统计。接着，你可以估算所统计的各个城市中，每十万人大约有多少家商店。顺便说一句，我认识的一位营销顾问正是这样为一家大型电信客户做的。

The question about phone stores was an example of what scientists call a Fermi problem, named after Nobel Prize-winning scientist Enrico Fermi, who used problems such as this to teach his students how to think for themselves. A Fermi problem does not contain all the information you need to solve it precisely.

关于电话商店的问题，就是科学家所说的“费米问题”的一个例子；这个名称来自诺贝尔奖得主恩里科·费米，他曾用这类问题教学生独立思考。费米问题不会提供精确求解所需要的全部信息。

Fermi is said to have once asked his university students how many piano tuners there were in Chicago. To answer the question, he recommended breaking it down into smaller, more manageable questions, and then having the courage to make some guesses and assumptions. How many people live in Chicago? Three million would be a reasonable estimate. How many people per family? Assume an average of four. How many families own pianos? Say one out of three. Then there were about two hundred fifty thousand pianos in Chicago. How often would each be tuned? Maybe once every five years. That makes fifty thousand tunings a year. How many pianos can one tuner tune in a day? Four? And how many in a year? Assuming two hundred fifty working days, one tuner can handle one thousand pianos a year.

据说，费米曾问大学生：芝加哥有多少名钢琴调音师？为了解答这个问题，他建议把它拆成更小、更容易处理的问题，然后勇敢地作出一些猜测和假设。芝加哥有多少人口？三百万人是一个合理的估计。每个家庭平均有多少人？假设平均为四人。有多少家庭拥有钢琴？就算三分之一。那么，芝加哥大约有二十五万架钢琴。每架钢琴多久调一次音？也许五年一次。这样每年就需要调音五万次。一名调音师一天能为多少架钢琴调音？四架？那么一年能调多少架？假设一年工作二百五十天，一名调音师一年可以处理一千架钢琴。

So there’s work for approximately fifty piano tuners in Chicago—which, as it turns out, is reasonably close to the actual number in the Yellow Pages.

因此，芝加哥大约有五十名钢琴调音师的工作量——事实证明，这与黄页上的实际人数相当接近。

Why was guesswork so accurate? The law of averages is partly responsible. At any point, your assumptions may be too high or too low. But because of the law of averages, your mistakes will frequently balance out.

为什么这样的估算会如此准确？平均律在一定程度上起了作用。在任何一个环节，你的假设都可能偏高或偏低。但由于平均律的作用，你的误差常常会相互抵消。

Here’s another puzzle. You probably already know that black absorbs the most heat, while white reflects the most. But what about the other colors in between? How could you find the answer? Hint: it’s wintertime, but not too cold.

再来看一个谜题。你大概已经知道，黑色吸收的热量最多，而白色反射的热量最多。那么介于二者之间的其他颜色呢？你怎样才能找出答案？提示：当时是冬天，但天气不算太冷。

Ben Franklin’s solution was elegant. He simply laid broadcloth samples of various colors on the snow on a sunny morning. “In a few hours,” he reported, “the black, being warmed most by the sun, was sunk so low as to be below the stroke of the sun’s rays; the dark blue, almost as low; the lighter blue not quite so much as the dark; the other colors, less as they were lighter, and the quite white remained on the surface of the snow, not having entered it at all.”

本杰明·富兰克林的解决办法十分巧妙。在一个阳光明媚的早晨，他只是把各种颜色的粗呢布样品铺在雪地上。他写道：“几小时后，黑布因被太阳晒得最热，已经陷得很深，低到了阳光照不到的位置；深蓝色几乎同样深；浅蓝色没有深蓝色陷得那么深；其他颜色越浅，陷得就越少；纯白色仍留在雪面上，完全没有陷进去。”

One of my favorite “guesstimators” is west Connecticut inventor Stan Mason, who developed microwave cookware specially designed to position food in the best spot for cooking.

我最喜欢的“估算高手”之一，是康涅狄格州西部的发明家斯坦·梅森；他研制了一种微波炉炊具，专门让食物处在最佳受热位置。

To do this, Mason needed to know where the microwave’s “hot spots” were—the places where the rays hit the food with the highest intensity. To find out, he put shelves of unpopped popcorn kernels in the microwave and watched to see which kernels popped first. He discovered a pattern in the oven’s hottest rays. They weren’t in the corners or at the center, but in the shape of a mushroom cloud.

为此，梅森需要知道微波炉的“热点”在哪里——也就是射线最强烈地照射食物的位置。为了找出这些位置，他把几层尚未爆开的爆米花玉米粒放进微波炉，观察哪些玉米粒最先爆开。他由此发现了炉内最强射线的分布规律。这些热点既不在角落，也不在中心，而是呈蘑菇云状。随后，他按照这一分布形状设计了烹饪容器。

Then he designed cooking dishes to fit the pattern. He had come up with a resourceful way to approximate the answer rather than using scientifically sophisticated testing equipment.

他找到了一种机智的近似求解方法，而没有使用复杂精密的科学测试设备。

Fermi would have approved.

费米一定会赞同这种做法。

By the way, the Mariana Trench is about six nautical miles deep, and a cannonball drops at a rate of ten feet per second. So it took the cannonball about an hour to reach the bottom of the trench.

顺便说一下，马里亚纳海沟大约深六海里，炮弹下沉的速度约为每秒十英尺。所以，炮弹到达海沟底部大约需要一小时。

Could this be guessed? If you know that Earth’s highest point, Mount Qomolangma, is twenty-nine thousand feet, you might reasonably conclude that its lowest point would be close to the same distance. Then you might imagine that a heavy object would take one second to fall through the water of a ten-foot-deep swimming pool. These estimates would bring you close enough to the correct answer.

这个答案可以估算出来吗？如果你知道地球最高点珠穆朗玛峰高二万九千英尺，就可以合理推断地球最低点的深度可能也差不多。然后你可以设想，一个重物穿过十英尺深的游泳池，大约需要一秒钟。这些估算足以让你相当接近正确答案。