TED演讲:估算大数目的妙诀(2)

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　　That is the perfect application for a power-of-10 estimation, as we don't need an exact answer, an estimation will work. 这是运用10的次方数极好的例子，因为我们并不需要知道确切的数字——只要估算即可。

　　We can start by determining how many people live in the city of Chicago. 我们可以从估算芝加哥的人口开始。

　　We know that it is a large city, but we may be unsure about exactly how many people live in the city. 我们都知道芝加哥是一个很大的城市，但并不知道确切的人口数。

　　Are the one million people? Five million people? 一百万人吗？还是五百万人？

　　This is the point in the problem where many people become frustrated¹ with the uncertainty², 问题的重点在于很多人对这种不确定性感到棘手，

　　but we can easily get through this by using the power of 10. 而我们可以通过运用10的次方数轻易做到。

　　We can estimate the magnitude of the population of Chicago as 10 to the power of six. 我们估计芝加哥城人口大约是10的6次方。

　　While this doesn't tell us exactly how many people live there, 即使我们不知道确切的人数，

　　it serves an accurate estimation for the actual population of just under three million people. 但还是能了解其实际人数应该不会超过三百万。

　　So if there are approximately 10 to the sixth people in Chicago, how many pianos are there? 如果芝加哥人口约有10的6次方，那会有多少钢琴呢？

　　If we want to continue dealing³ with orders of magnitude, 要是我们还想用数量级来处理，

　　we can either say that one out of 10 or one out of one hundred people own a piano. 就可以估测，每10人或每100人就有一人拥有钢琴。

　　Given that our estimate of the population includes children and adults,  先前的人口估算包括大人和小孩，现在我们只算小孩的部分。

　　we'll go with the latter estimate, which estimates that there are approximately 10 to the fourth, or 10,000 pianos, in Chicago. 那么芝加哥的钢琴数约有10的4次方，差不多相当于1万。

　　With this many pianos, how many piano tuners are there? 有这么多架钢琴，那调音师到底有几位呢？

　　We could begin the process of thinking about how often the pianos are tuned⁵, how many pianos are tuned in one day, 可以从一架钢琴多久调一次音，一天调几架钢琴，

　　or how many days a piano tuner works, but that's not the point of rapid estimation. 调音师工作几天等等开始着手，但这不是快速预估的重点。

　　We instead think in orders of magnitude, and say that a piano tuner tunes⁶ roughly 10 to the second pianos in a given year, 我们在这里用数量级估算，一位调音师一年中，大约要为10的2次方架钢琴调音，

　　which is approximately a few hundred pianos. 也就是差不多几百架钢琴。

　　Given our previous estimate of 10 to the fourth pianos in Chicago,  先前估计出芝加哥的钢琴约有10的4次方架，

　　and the estimate that each piano tuner can tune⁴ 10 to the second pianos each year, 又估算了每位调音师一年可以替10的2次方架钢琴调音，

　　we can say that there are approximately 10 to the second piano tuners in Chicago. 现在我们就可以说，芝加哥的调音师人数约有10的2次方这么多。

　　Now, I know what you must be thinking: How can all of these estimates produce a reasonable answer? 现在你一定在想：为什么这些预估都能算出合理的数字？

　　Well, it's rather simple. 答案再简单不过。

　　In any Fermi problem, it is assumed that the overestimates⁷ and underestimates balance each other out, 每个费米问题都会假设高估和低估会彼此平衡，

　　and produce an estimation that is usually within one order of magnitude of the actual answer. 而其估计误差通常只与其实际数值相差一个数量级。

　　In our case we can confirm this by looking in the phone book for the number of piano tuners listed in Chicago. 我们也可以用黄页来确认这个例子中芝加哥到底有几位调音师，

　　What do we find? 81. 有几位呢？答案：81。

　　Pretty incredible, given our order-of-magnitude estimation. 数量级的估算方法很不可思议吧。

　　But, hey, that's the power of 10. 看，这就是10的力量。

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