Problem Solving Made Easier

2021年1月29日发(作者：相交线)

On a Monday morning in July 1945, the world's first atom bomb exploded in the New Mexico desert.

Forty

seconds

later,

the

blast's

shock

wave

reached

the

base

camp

where

scientists

stood

in

stunned contemplation.

First to stir was the Italian-American physicist Enrico Fermi.

194 5

年

7

月的一个星期一早晨，世界上第 一颗原子弹在新墨西哥沙漠爆炸了。

40

秒后，爆

炸的冲击波到达了大本营，

科学家们站在那里目瞪口呆地沉思着。

< p>
第一个引起轰动的是美籍

意大利物理学家恩里科·费米。

< br>

Before the detonation, Fermi had torn a sheet of notebook paper into bits.

As he felt the first

quiver

of

the

shock

wave, he released

the

shreds

above

his

head.

They

fluttered

down

and

landed about two and a half yards behind him.

After a mental calculation, Fermi announced

that the bomb's energy had equaled 10,000 tons of TNT.

Sophisticated instruments, which took

weeks to analyze the wave's velocity and pressure, confirmed Fermi's instant estimate.

在爆炸之前，

费米已经把一张笔记本纸撕成碎片。

当他感觉到冲击波的第一次颤动时，

他把

碎纸片从头顶撒下。

它们飘落下来，

落在他身后大约两码半的地方。经过心理计算，费米宣

布核弹的能量相当于< /p>

1

万吨

TNT

炸 药。

复杂的仪器花费了数周时间来分析波的速度和压力，

证实了 费米的即时估计。

The bomb team was impressed, but not surprised.

Fermi's genius was known throughout the

scientific world.

In 1938 he had won a Nobel Prize; four years later he produced the first self-

sustaining nuclear chain reaction, ushering in the nuclear age.

Since Fermi's death in 1954, no

physicist has been at once a master experimentalist and a leading theoretician.

炸弹小组对此印象深刻，但并不惊 讶。费米的天才在科学界闻名遐迩。

1938

年，他获得了

诺贝尔奖

;

四年后，他制造了第一个自我维 持的核链式反应，宣告了核子时代。自从

1954

年

< p>
费米去世以来，还没有哪位物理学家能像他一样既是实验高手又是理论大师。

Like

all

virtuosos,

Fermi

had

a

distinctive

style.

He

preferred

the

most

direct,

rather

than

intellectually elegant, route to an answer.

And he excelled at dividing difficult problems into

small,manageable bites—a talent we all can use in our daily lives.

像所有的艺术大师一样，

费米有自己独特的风格。

他更喜欢用 最直接的方式来回答问题，

而

不是用优雅的思维方式。

他擅长将困难的问题分解易于处理的单位——这是我们在日常生活

中都可 以使用的一种才能。

To develop this talent in his students, Fermi would pose a type of question now known as a Fermi

problem.

Upon fist hearing one of these, you haven't the remotest notion of the answer, and

you feel certain that too little information has been given to solve it.

Yet when the problem is

broken into sub-problems, each answerable without the help of experts or books, you can come

remarkably close to the exact solution.

为了培养他的学生的这种 天赋，

费米提出了一种现在被称为费米问题的问题。

当你第一次 听

到其中一个问题时，

你对它的答案毫无概念，

你肯定会觉得所提供的信息太少，

无法解决它。

然而，

当问题被分解成子问题，

每个子问题都可以在没有专家或书籍的 帮助下回答时，

你就

可以非常接近精确的解决方案。

Suppose you want to determine Earth's circumference without looking it up.

Everyone knows

that New York and Los Angeles are about 3,000 miles apart and that the time difference between

them is three hours.

Three hours is one-eighth of a day, and a day is the time it takes the planet

to complete one rotation, so its circumference must be eight times 3,000,or 24,000 miles.

This

answer differs from the true value, 24,902.45 miles, by less than four percent.

假设你想确定地球的周长而不查阅它。每个人都知道纽约和洛 杉矶相距约

3000

英里，它们

之间的 时差是

3

个小时。

三小时是一天的八分 之一，

而一天是这颗行星完成一次自转所需的

时间，所以它的周 长必须是

3000

的

8

倍，即

24000

英里。这个答案与真实值

< p>
24902.45

英里

相差不到

< br>4%

。

How many piano tuners are there in Chicago?

Fermi posed this whimsical question to his classes

at the University of Chicago.

One way to get an answer: If Chicago's population is three million,

an

average

family

consists

of

four

people,

and

one-third

of

all

families

own

pianos,

there

are

250,000 pianos in the city.

If each piano is tuned every five years, there are 50,000 tunings a

year.

If each tuner can service four pianos a day, 250 days a year, for a total of 1,000 tunings a

year, there must be about 50 tuners in the city.

The answer is not exact; it could be as low as 25

or as high as 100.

But, as the Yellow Pages attest, it is definitely in the ballpark.

芝加哥有多少钢琴调音师

?

费米在芝加哥大学向他的学生提出了这个古怪的问题。有一种方

< p>
法可以回答这个问题

:

如果芝加哥的人口是

300

万，平均每户四人，三分之一的家庭拥有钢

琴，那么芝加哥就有

25

万架钢琴。如果每架钢琴每五年调 一次音，那么一年就要调

5

万次

音。如 果每个调音师能一年

250

天每天为

4

架钢琴调音，一年总共调音

1000

次 ，那么这个

城市就必须有大约

50

名调 音师。答案并不确切

;

可能低至

25< /p>

，也可能高至

100

。但是，正如

黄页所证明的那样，这绝对在大致的正确的范围内。

Fermi's intent was to show that we can make assumptions and still arrive at fairly close estimates.

The

reason

is

that,

in

any

string

of

calculations,

errors

tend

to

cancel

out

one

another.

If

someone assumes, for instance, that every sixth family, rather than every third, owns a piano, he

is

just

as

likely

to

assume

that

pianos

are

tuned

every

two

and

a

half

years,

not

every

five.

Because bad guesses tend to compensate for one another, the results will converge toward the

right number.

费米的目的是要证明我们可以做出假设，< /p>

并且仍然能得到相当接近的估计。

原因是，

在任何

一串计算中，

错误往往会相互抵消。

< br>例如，

如果有人假设每六个家庭而不是每三分之一拥有

一 架钢琴，

那么他很可能会假设钢琴每两年半调一次音，

而不是每 五年调一次音。

因为错误

的猜测往往会相互补偿，所以结果会会 聚到正确的数字。

Questions about atom bombs and piano tuners have little in common.

But the manner in which

they are answered is the same and can be applied to more practical questions.

Whether the

problem concerns cooking, automobile repair or personal relationships, the fainthearted usually