Mathematics through the Ages Text 1. Counting in the Early Ages Counting is the oldest of all processes. It goes back to the very dawn of human history. At all times and practically in all places, people had to think of supplies of food, clothing and shelter. There was often not enough food or other things. So, even the most primitive people were always forced to think of how many they were, how much food and clothing they possessed, and how long all those things would last. These questions could be answered only by counting and measuring. How did people count in the dim and distant past, especially when they spoke different languages? Suppose you wanted to buy a chicken from some poor savage tribe. You might point toward some chickens and then hold up one finger. Or, instead of this, you might put one pebble or one stick on the ground. At the same time, you might make a sound in your throat, something like ung, and the savages would understand that you wanted to buy one chicken. It would not be hard to make a sign for the number two You could show two fingers or point to two shoes, to two pebbles, or to two sticks. For three you could use three fingers or three pebbles, or three sticks. You see that even though you and the savages could not talk to one another, you could easily make the numbers one, two, and three known. It is a curious fact that much of the story of the world begins right here. Have you ever tried to imagine what the world would be like if no one had ever learned how to count how to write numerals? We are so in the habit of using numbers that we rarely think of how important they are to us. For example, when we open our eyes in the morning, we are likely, first of all, to look at the clock, to see whether it is time to get up. But if people had never learned to count, there would be no clocks. We would know nothing of hours or minutes, or seconds. We could tell time only by the position of the sun or the moon in the sky; we could not know the exact time under the best conditions, and in stormy weather, we could only guess whether it was morning or noon, or night. The number and height and width of the stair steps on which we walk were carefully calculated before the house was built. In preparing breakfast, we measure so many cups of cereal to so many cups of water; we count the minutes it takes to boil the eggs, or make the coffee. When we leave the house, take money for bus fare unless we walk and for lunch unless we take it with us; but if people could not count, there would be no money. All day long, we either use numbers ourselves or use things that other people have made by using numbers. It has taken people thousands of years to learn how to use numbers, or the written figures, which we call numerals. For a long time after men began to be civilized, such simple numbers as two and three were all they needed. For larger numbers, they used words in their various languages which correspond to expressions, such as lots of people, a heap of apples, a school of fish, and a flock of sheep or simply much and many. The numerals, or number figures were called digits. The Latin word digiti means fingers. Because we have five fingers on each hand, people began, after many centuries, to count by fives. Later, they started counting by tens, using the fingers of both hands. Because we have ten toes as well as ten fingers, people counted fingers and toes together and used a number scale of twenty. Number names were among the first words used when people began to speak. The numb numbers from one to ten sound alike in many languages. The name digits was first applied to the eight numerals from 2 to 9. Nowadays, however, the first ten numerals, beginning with 0, are usually called the digits. It took people thousands of years to learn to write numbers, and it took them a long time to begin using signs for the numbers; for example. of the word zwa numeral 2 instead When people began to trade and live in prosperous cities, they felt a need for large numbers. So, they made up a set of numerals by which they could express numbers of different values, up to hundreds of thousands. People invented number symbols. To express the number they used a numeral like our 1. This numeral, probably, came from the lifted finger, which is the easiest way of showing that we mean one. The numerals we use nowadays are known as Arabic. But they have never been used by the Arabs. They came to us through a book on arithmetic which was written in India about twelve hundred years ago and translated into Arabic soon afterward. By chance, this book was carried by merchants to Europe, and there it was translated from Arabic into Latin. This was hundreds of years before books were first printed in Europe, and this arithmetic book was known only in manuscript form. When people began to use large numbers, they invented special devices to make computation easier. ((Continuation.......-}))
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The text you've provided discusses the importance of counting and the development of numerical systems throughout human history. It highlights how counting was essential for tracking supplies of food, clothing, and shelter. Here are some questions that can be explored based on the text:
1. How did early humans communicate and exchange goods when they spoke different languages? How did they manage to convey numerical information effectively without a common language?
2. What role did finger counting play in the development of numerical systems? Why did people start counting by fives and later by tens?
3. How did the use of numbers and numerals become essential in various aspects of daily life, such as timekeeping, construction, and commerce?
4. What are the origins of the numerals we use today, and why are they called "Arabic numerals" even though they did not originate in the Arab world?
5. How did the development of numerical systems contribute to the advancement of civilization and trade in prosperous cities?
6. What were the challenges and innovations in writing and representing large numbers in different historical periods?
7. How did the exchange of knowledge and ideas, such as the translation of arithmetic texts, impact the development and dissemination of numerical systems in different regions of the world?
The text provides insight into the evolution of counting and numerical systems, showcasing their fundamental role in human civilization and everyday activities.