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.

為了理解時間單位，我們需要研究一下古代文化的數(shù)字系統(tǒng)。蘇美爾人怎樣用一只手?jǐn)?shù)到12，用兩只手?jǐn)?shù)到60？巴比倫人取得了哪些進(jìn)展，他們怎樣利用這一數(shù)字系統(tǒng)來計算？�；�人在時間測量方面做了哪些改，才留給了我們至今仍在使用的方法。

蘇美爾人計數(shù)法

十進(jìn)位（以10為基數(shù)）數(shù)字系統(tǒng)很容易理解。我們的手有10根手指可以用來數(shù)數(shù)，因此10進(jìn)位系統(tǒng)自然產(chǎn)生了。再加上我們的雙腳的腳趾，二十進(jìn)位（以20為基數(shù)）數(shù)字體系也是合情合理的。但理解蘇美爾人使用的六十進(jìn)位（以60為基數(shù)）數(shù)字系統(tǒng)，還要費點兒腦筋。

迅速看一眼我們的一只手，可發(fā)現(xiàn)有4根手指和1根大拇指可以用來計數(shù)。但人類的手是一架包括27塊骨頭的復(fù)雜機器，如下圖：

有一些特征是外表明顯的，特別是在手指上。以大拇指為指針，并劃分出每根手指的末端、中端和底端指骨，我們可以在一只手上一直數(shù)到12，如下圖所示。

更進(jìn)一步，用另一只手表示12的5倍，我們可以把計數(shù)擴充到60，32 (= 2 x 12 + 8)可以表示如下。

巴比倫人的數(shù)學(xué)

蘇美爾人的數(shù)字系統(tǒng)被傳給了巴比倫人。六十進(jìn)制是一個有用的系統(tǒng)，加為60有很多因數(shù)。每一堆60件的東西都可以分成2, 3, 4, 5, 6, 10, 12, 15, 20 或 30件一組的整數(shù)組。

巴比倫人只用2個符號作為他們的數(shù)學(xué)符號。用 代表1，用  代表10。通過這些符號的聯(lián)合，可以記錄從1到59的數(shù)。例如35可表示成 。

早期符號的一個顯著進(jìn)展是巴比倫人對位置的使用。在我們的十進(jìn)位計數(shù)法中，我們把10表示成包含1和它后面包含0的兩位數(shù)。巴比倫人用同樣的方式把超過59的數(shù)表示成多位數(shù)。例如64是 1 x 60 + 4 ，或者是 ，盡管沒有符號表示0，卻用兩位之間的一個較大的間距表示了出來。

度量和時間

數(shù)字60和它的因數(shù)被用來度量很多東西，有幾種至今仍在使用。在長度測量中，12英寸為1英尺。在角度測量中，一個圓是6 x 60 = 360度。在英國采用十進(jìn)制貨幣之前，12便士為1先令。

但還是讓我們把注意力轉(zhuǎn)回到時間和一天的劃分上吧。巴比倫人將一天的每一小時劃分成60分鐘。每一分鐘劃分成60秒。然而，這些并不是我們今天認(rèn)可的分和秒。

每天被分為晝夜兩部分。于是每一部分就被分成了12小時。由于全年的晝夜長度是變化的，所以巴比倫人的時、分和秒的長度也是不同的。

�；�人的改進(jìn)

�；�人改進(jìn)了時間的度量，消除了這些變化。他們忽略了晝夜小時的差異，但保留了全部的24個小時。這樣，全天就被分成了相同間隔的24小時，我們至今仍在使用。

盡管不時有我們應(yīng)該采用十進(jìn)制時間的建議，這一古老的度量體系已經(jīng)存在了幾千年了。因此，1小時有60分鐘的原因要歸結(jié)于蘇美爾人的數(shù)學(xué)，巴比倫人、�；�人和人類手的結(jié)構(gòu)。