TED演讲:估算大数目的妙诀(1)

 　　Whether you like it or not, we use numbers every day. 不管你喜不喜欢，我们每天都会用到数字。

　　Some numbers, such as the speed of sound, are small and easy to work with. 有些数字比如音速，数值不大，容易计算。
　　Other numbers, such as the speed of light, are much larger and cumbersome 1 to work with. 另一些数字，比如光速，就要大得多，不方便计算。
　　We can use scientific notation 2 to express these large numbers in a much more manageable format 3. 我们能用科学计数法来表示它们，这样的格式更容易进行操作。
　　So we can write 299,792,458 meters per second as 3.0 times 10 to the eighth meters per second. 那么我们可以把每秒299,792,458米，写成每秒3.0乘10的8次方米。
　　Correct scientific notation requires that the first term range in value so that it is greater than one but less than 10,  把第一项数值按照科学计数法改写后，应该比1大但是比10小，
　　and the second term represents the power of 10 or order of magnitude by which we multiply the first term. 而用来与第一项相乘的第二项的数值应该为10的次方数，或者叫数量级。
　　We can use the power of 10 as a tool in making quick estimations when we do not need or care for the exact value of a number. 运用10的次方就能迅速估算出我们只需了解其大约数值的数字。
　　For example, the diameter of an atom is approximately 10 to the power of negative 12 meters. 举例来说，原子的直径大约是10的负12次方米。
　　The height of a tree is approximately 10 to the power of one meter. 树的高度大约是10的1次方米。
　　The diameter of the Earth is approximately 10 to the power of seven meters. 而地球的直径大约是10的7次方米。
　　The ability to use the power of 10 as an estimation tool can come in handy every now and again,  把10的次方数当作估算工具有时能方便我们进行估算，
　　like when you're trying to guess the number of M&M's in a jar, 例如，猜广口罐里有几颗M&M豆，
　　but is also an essential skill in math and science, especially when dealing 4 with what are known as Fermi problems. 而这也是解决数学和科学问题的必要技巧，尤其是在处理所谓的“费米问题”的时候。
　　Fermi problems are named after the physicist 5 Enrico Fermi, “费米问题”是以物理学家恩里科·费米的名字命名，
　　who's famous for making rapid order-of-magnitude estimations,or rapid estimations, with seemingly little available data. 他因为能利用一些看似极少的数据，迅速估算数量级和数字而闻名于世。
　　Fermi worked on the Manhattan Project in developing the atomic bomb, and when it was tested at the Trinity site in 1945, 费米在曼哈顿计划中指导制造原子弹，1954年，进行三位一体试验时，
　　Fermi dropped a few pieces of paper during the blast 费米在核爆途中扔下一些纸张，
　　and used the distance they traveled backwards 6 as they fell to estimate the strength of the explosion as 10 kilotons of TNT, 利用纸张往后落下的距离估算爆炸的威力，结论是相当于一万吨的TNT，
　　which is on the same order of magnitude as the actual value of 20 kilotons. 跟实际值的两万吨在同一个数量级。
　　One example of the classic Fermi estimation problems is to determine how many piano tuners there are in the city of Chicago, Illinois. 举一个关于费米问题的经典例子：估算在伊利诺伊州的芝加哥有多少钢琴调音师。