part 17

160 Air travel would have seemed very strange two or three thousand years ago, to men keeping their sheep on the mountainsides. All these changes are the outcome of the great step taken in the invention of numbers. Before men could count, how did anyone know which were his sheep and which were another man's? He put his mark on his sheep. He was their owner. They were his own sheep. He owned them. Sometimes he gave his sheep names, and then he would go through all the names—with his sheep—to see if they were all there.

两三千年前，对于在山腰上放羊的人来说，航空旅行是非常奇怪的。 所有这些变化都是数字发明这一伟大步骤的结果。 在人类会数数之前，怎么知道哪些是自己的羊，哪些是别人的呢？ 他在羊身上做了记号。 他是它们的主人。它们是他自己的羊。 他拥有它们。有时他给他的羊取名字，然后他会和他的羊一起检查所有的名字，看看它们是否都在那里。

161 Before the invention of writing how did people keep records? They made pictures on soft earth or sand. But rain and wind and waves quickly washed away such records. Smooth stone or wood was better, and best of all, the smooth stone walls of caves whose roofs kept the rain and wind away. It may be that the drawings copied on page 142, or others like them, were records made by early humans. (Someone recording animals on a cave wall may have taken pleasure in the drawing for itself and become the first artist.)

在发明文字之前，人们是如何记录的？ 他们在软土或沙子上作画。 但风雨和海浪很快就把这些记录冲走了。 光滑的石头或木头更好，最好的是洞穴光滑的石墙，它的屋顶可以挡风挡雨。 有可能在第142页上复制的图画，或其他类似的图画，是早期人类所做的记录。 （有人在洞穴墙壁上记录动物，可能是为了自己享受绘画的乐趣，成为第一个艺术家。）

162 How did a man know how many sheep he owned? Sometimes he used small stones or sticks, putting one of them into a bag or pocket for each sheep he had. When he came to the end of his sheep, the number of stones in the bag was the same as the number of his sheep. The stones and the sheep were equal in number. The stones gave him a record of how many sheep he owned. When a sheep died he could take a stone out of the bag. And when lambs were born he could put in another stone for each lamb.

一个人怎么知道他有多少只羊？ 有时他用小石头或小棍子，每养一只羊，就往袋子或口袋里放一根。 当他的羊数完的时候，袋子里的石头的数目和羊的数目是一样的。 石头和羊的数量相等。 这些石头记录了他拥有多少只羊。 当一只羊死了，他可以从袋子里拿出一块石头。 当羊羔出生时，他可以为每只羊羔放另一块石头。

163 Sometimes a record was made by taking a sharp, hard stone and making cuts on a stick. The number of cuts in the stick equaled the number of things to be recorded. Then the stick was cut in half down the middle so that each half had half of every cut on it. The two half sticks were tallies. If they were put side by side, the halves of the cuts came together. They tallied. One man took one tally and another the other, and both then had the record.

有时唱片是用一块又尖又硬的石头在一根木棍上刻出来的。 棍子上的伤口数量等于要记录的东西数量。 然后把棍子从中间切成两半，这样每一半上都有每个切口的一半。 两根半棍是记分牌。 如果把它们放在一起，两半的削减就会合在一起。 他们清点。一个人做了一个记录，另一个人做了另一个记录，然后两人都保持了记录。

164 Tallies are some of the earliest and simplest records of the numbers of things. They tell how many things have been counted. Even today in a bank a person who takes money in and gives it out is sometimes named a teller. The shelf or table where the teller works is a counter. On it the teller does the counting of the money coming in and going out, and keeps a record of all this in an account book. A person who makes a statement tells something. Most banks make a statement every month to each person banking with them to tell them what their account is. The statements tell them how much money they have in the bank at that date. Then both they and the bank have the record straight. To get these statements ready, the banker has to take the amount of money given out (for any one person) from the amount of money put in.

164计数是最早和最简单的数字记录。 它们告诉我们数了多少东西。 即使在今天，在银行里，收钱和出纳的人有时也被称为出纳员。 柜员工作的架子或桌子是柜台。 出纳员在这张支票上清点进出的钱，并把所有这些记录在帐簿上。 一个人发表声明说明了一些事情。 大多数银行每个月都会给每个在他们那里开户的人发一份对账单，告诉他们他们的账户是什么。 对账单告诉他们那天他们在银行里有多少钱。 这样一来，他们和银行都有了正确的记录。 为了准备好这些对账单，银行必须从存入的金额中取出（对任何一个人来说）流出的金额。

165 Bank tellers must keep a complete record of the money they take in and give out. This is their way of making certain that their accounts are in order. Banking is a very important sort of business. A bank must keep all its accounts in good order and the statements which the bank makes must be true statements.

银行出纳员必须完整地记录他们的收入和支出。 这是他们确保账目正常的方式。 银行业务是一种非常重要的业务。 银行必须妥善保管其所有帐目，银行所作的报表必须是真实的。