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To understand the units of time we need to investigate the number systems of ancient civilizations. How did the Sumerians count to 12 on one hand and to 60 on two? What advances did the Babylonians make and how did they use this number system for measurement? And what refinements did the Egyptians make to time measurement to give us the system we still use today?
Sumerian Counting
It is easy to see the origins of a decimal (base 10) number system. Our hands have 10 digits to count on, so a decimal system follows naturally. With the addition of the toes on our feet a vigesimal (base 20) number system, like that of the Maya, also makes sense. But understanding a sexagesimal (base 60) number system, as used by the Sumerians, takes a little more thought.
A quick glance at a hand shows us four fingers and a thumb that can be used for counting. But the human hand is a complex machine consisting of 27 bones, as shown in the diagram below.
Some of these features are evident externally, especially in the fingers. By using the thumb as a pointer, and marking off the distal phalanx, middle phalanx and proximal phalanx of each finger, we can count up to 12 on one hand, as shown below.
Furthermore, by using the other hand to mark five multiples of 12 we can extend the count up to 60. For instance, 32 (= 2 x 12 + 8) would appear as follows.
Babylonian Mathematics
The Sumerian number system was passed on to the Babylonians. Sexagesimal was a useful system as 60 has a large number of factors. Each collection of 60 objects could be divided into whole groups of 2, 3, 4, 5, 6, 10, 12, 15, 20 or 30.
The Babylonians used just two symbols for their mathematical notation. There was a for 1 and a for 10. All the numbers from 1 to 59 were written as combinations of these marks. For instance, 32 appeared as
A significant advance from earlier notation was the use by the Babylonians of a positional system. In our decimal notation we represent 10 as a column containing a 1 followed by a column containing a 0. In a similar way the Babylonians represented numbers over 59 in multiple columns. For instance, 64 was 1 x 60 + 4 or
Although there was no symbol for a zero it was shown as a larger gap between the columns.
Measurement and Time
The number 60 and its factors were used in the measurement of many things, several of which are still in use today. In length there are 12 inches to a foot. In angular measurement there are 6 x 60 = 360 degrees in a circle. In pre-decimalised currency in the UK there were 12 pence in a shilling.
But let us bring our attention back to time and the division of a day. The Babylonians divided each hour of the day into 60 minutes. Each minute they divided into 60 seconds. These are not, however, the minutes and seconds we would recognise today.
Each day was divided into a daylight portion and a night portion. These portions were then divided into 12 hours each. As the length of day and night varied throughout the year, so the length of the Babylonian hours, minutes and seconds varied too.
Egyptian Refinements
The Egyptians refined the measurement of time to remove these variations. They ignored the distinction between daylight hours and night hours but kept the total of 24. The whole day was then divided into 24 equal periods creating the hour that we still use today.
Despite occasional suggestions that we should adopt decimal time, this ancient system of measurement has survived for thousands of years. And so, the reason there are 60 minutes in an hour is due to the mathematics of the Sumerians, Babylonians and Egyptians and the structure of the human hand.
为了理解时间单位，我们需要研究一下古代文化的数字系统。苏美尔人怎样用一只手数到12，用两只手数到60？巴比伦人取得了哪些进展，他们怎样利用这一数字系统来计算？�；嗽谑奔洳饬糠矫孀隽四男└�，才留给了我们至今仍在使用的方法。
苏美尔人计数法
十进位（以10为基数）数字系统很容易理解。我们的手有10根手指可以用来数数，因此10进位系统自然产生了。再加上我们的双脚的脚趾，二十进位（以20为基数）数字体系也是合情合理的。但理解苏美尔人使用的六十进位（以60为基数）数字系统，还要费点儿脑筋。
迅速看一眼我们的一只手，可发现有4根手指和1根大拇指可以用来计数。但人类的手是一架包括27块骨头的复杂机器，如下图：
有一些特征是外表明显的，特别是在手指上。以大拇指为指针，并划分出每根手指的末端、中端和底端指骨，我们可以在一只手上一直数到12，如下图所示。
更进一步，用另一只手表示12的5倍，我们可以把计数扩充到60，32 (= 2 x 12 + 8)可以表示如下。
巴比伦人的数学
苏美尔人的数字系统被传给了巴比伦人。六十进制是一个有用的系统，加为60有很多因数。每一堆60件的东西都可以分成2, 3, 4, 5, 6, 10, 12, 15, 20 或 30件一组的整数组。
巴比伦人只用2个符号作为他们的数学符号。用 代表1，用 代表10。通过这些符号的联合，可以记录从1到59的数。例如35可表示成 。
早期符号的一个显著进展是巴比伦人对位置的使用。在我们的十进位计数法中，我们把10表示成包含1和它后面包含0的两位数。巴比伦人用同样的方式把超过59的数表示成多位数。例如64是 1 x 60 + 4 ，或者是 ，尽管没有符号表示0，却用两位之间的一个较大的间距表示了出来。
度量和时间
数字60和它的因数被用来度量很多东西，有几种至今仍在使用。在长度测量中，12英寸为1英尺。在角度测量中，一个圆是6 x 60 = 360度。在英国采用十进制货币之前，12便士为1先令。
但还是让我们把注意力转回到时间和一天的划分上吧。巴比伦人将一天的每一小时划分成60分钟。每一分钟划分成60秒。然而，这些并不是我们今天认可的分和秒。
每天被分为昼夜两部分。于是每一部分就被分成了12小时。由于全年的昼夜长度是变化的，所以巴比伦人的时、分和秒的长度也是不同的。
�；说母慕�
埃圾人改进了时间的度量，消除了这些变化。他们忽略了昼夜小时的差异，但保留了全部的24个小时。这样，全天就被分成了相同间隔的24小时，我们至今仍在使用。
尽管不时有我们应该采用十进制时间的建议，这一古老的度量体系已经存在了几千年了。因此，1小时有60分钟的原因要归结于苏美尔人的数学，巴比伦人、�；撕腿死嗍值慕峁�。
