The history of numbers and the number system are closely related, because the number system is a way of writing such an abstract concept as a number. This topic does not belong exclusively to the field of mathematics, because all this is an important part of the culture of the people as a whole. Therefore, when the history of numbers and number systems is analyzed, many other aspects of the history of the civilizations that created them are briefly touched upon. Systems as a whole are divided into positional, non-positional and mixed. The whole history of numbers and number systems consists of their alternation. Positional systems are those in which the value denoted by a digit in the notation of a number depends on its position. In non-positional systems, accordingly, there is no such dependence. Humanity has also created mixed systems.
Studying number systems at school
Today the lesson "History of numbers and number systems" is held in the 9th grade as part of the course in computer science. The main thingits practical significance is to teach how to translate numbers from one number system to another (primarily from decimal to binary). However, the history of numbers and number systems is an organic part of history as a whole and could well complement this subject of the school curriculum as well. It could also improve the interdisciplinary approach that is being promoted today. Within the framework of a general history course, in principle, not only the history of economic development, socio-political movements, governments and wars could be studied, but also, to a small extent, the history of numbers and number systems. Grade 9 in the course of computer science in this case could be provided with a much larger number of examples from previously covered material in terms of translating numbers from one system to another. And these examples are not without fascination, which will be shown below.
The emergence of number systems
It is difficult to say when, and most importantly, how a person learned to count (just as it is impossible to find out for certain when, and most importantly, how a language arose). It is only known that all ancient civilizations already had their own counting systems, which means that the history of numbers and the number system originated in pre-civilizational times. Stones and bones are not able to tell us what was happening in the human mind, and written sources were not created then. Perhaps a person needed an account when dividing the booty or much later, already during the Neolithic revolution, that is, during the transition to agriculture, for dividing the fields. Any theories about this would be equally baseless. However, some assumptions can still be made by studyinghistory of various languages.
Traces of the ancient number system
The most logical initial counting system is the opposition of the concepts "one" - "many". It is logical for us because in modern Russian there is only singular and plural. But in many ancient languages there was also a dual number for two things. It also existed in the first Indo-European languages, including Old Russian. Thus, the history of numbers and the number system began with the separation of the concepts of "one", "two", "many". However, already in the most ancient civilizations known to us, more detailed number systems were developed.
Mesopotamian notation of numbers
We are used to the fact that the number system is decimal. This is understandable: there are 10 fingers on the hands. Nevertheless, the history of the emergence of numbers and number systems has gone through more complex phases. The Mesopotamian number system is sexagesimal. Therefore, there are still 60 minutes in an hour, and 60 seconds in a minute. Therefore, the year is divisible by the number of months, a multiple of 60, and the day is divisible by the same number of hours. Initially, it was a sundial, that is, each of them was 1/12 of a light day (in the territory of modern Iraq, its duration did not vary much). Only much later, the duration of the hour began to be determined not by the sun, and 12 hours of night were also added.
It is interesting that the signs of this sexagesimal system were written as if it were decimal - there were only two signs (to designate one and ten, not six and notsixty, namely ten), the numbers were obtained by combining these signs. It's scary to even imagine how difficult it was to write down any large number in this way.
Ancient Egyptian number system
Both the history of numbers in the decimal number system and the use of numerous signs to represent numbers began with the ancient Egyptians. They combined the hieroglyphs that stood for one, one hundred, one thousand, ten thousand, one hundred thousand, one million, and ten million, thus denoting the desired number. Such a system was much more convenient than the Mesopotamian, which used only two signs. But at the same time, it had a clear limitation: it was difficult to write down a number much larger than ten million. True, the ancient Egyptian civilization, like most civilizations of the Ancient World, did not encounter such numbers.
Hellenic letters in mathematical notation
The history of European philosophy, science, political thought and much more begins in Ancient Hellas (“Hellas” is a self-name, it is preferable to “Greece” coined by the Romans). Mathematical knowledge was also developed in this civilization. The Hellenes wrote the numbers in letters. Individual letters denoted each number from 1 to 9, each ten from 10 to 90, and each hundred from 100 to 900. Only a thousand was denoted by the same letter as one, but with a different sign next to the letter. The system allowed even large numbers to be indicated by relatively short inscriptions.
Slavic number system as the successor to Hellenic
The history of numbers and number systems would not be complete without a few words about our ancestors. Cyrillic, as you know, is based on the Hellenic alphabet, and therefore the Slavic system of writing numbers was also based on the Hellenic one. Here, too, each number from 1 to 9, each ten from 10 to 90, and each hundred from 100 to 900 were designated by separate letters. Only not Hellenic letters were used, but Cyrillic, or Glagolitic. There was also an interesting feature: despite the fact that both the Hellenic texts at that time and the Slavic ones from the very beginning of their history were written from left to right, the Slavic numbers were written as if from right to left, that is, the letters denoting tens were placed to the right of the letters denoting units, the letters, denoting hundreds to the right of letters denoting tens, etc.
Attic Simplification
Hellenic scientists have reached great heights. The Roman conquest did not interrupt their explorations. For example, judging by indirect evidence, Aristarchus of Samos, 18 centuries before Copernicus, developed the Heliocentric system of the world. In all these complex calculations, the Hellenic scientists were helped by their system of writing numbers.
But for ordinary people, such as merchants, the system often turned out to be too complicated: to use it, it was necessary to memorize the numerical values of 27 letters (instead of the numerical values of 10 characters that modern schoolchildren learn). Therefore, a simplified system appeared, called the Attic (Attica is the region of Hellas, at one timeleading in the region as a whole and especially in the maritime trade of the region, since the capital of Attica was the famous Athens). In this system, only the numbers one, five, ten, one hundred, one thousand and ten thousand began to be designated by separate letters. It turns out only six characters - they are much easier to remember, and traders still did not make too complicated calculations.
Roman numerals
And the number system, and the history of the numbers of the ancient Romans, and in principle the history of their science is a continuation of the Hellenic history. The Attic system was taken as the basis, the Hellenic letters were simply replaced with Latin ones and a separate designation for fifty and five hundred was added. At the same time, scientists continued to make complex calculations in their treatises using the Hellenic recording system of 27 letters (and they usually wrote the treatises themselves in Hellenic).
The Roman system of writing numbers cannot be called particularly perfect. In particular, it is much more primitive than Old Russian. But historically it turned out that it is still preserved on a par with Arabic (so-called) numerals. And you should not forget this alternative system, stop using it. In particular, today Arabic numerals often denote cardinal numbers, and Roman numerals denote ordinal numbers.
Great ancient Indian invention
The numbers we use today originated in India. It is not known exactly when the history of numbers and the number system made thisa significant turn, but, most likely, not later than the 5th century from the birth of Christ. It is often emphasized that it was the Indians who developed the concept of zero. Such a concept was known to mathematicians and other civilizations, but really only the system of the Indians made it possible to fully include it in mathematical notation, and therefore in calculations.
Distribution of the Indian number system on Earth
Presumably in the 9th century, Indian numbers were borrowed by the Arabs. While the Europeans disdained the ancient heritage, and in some regions at one time even deliberately destroyed it as pagan, the Arabs carefully preserved the achievements of the ancient Greeks and Romans. From the very beginning of their conquests, translations of ancient authors into Arabic became a hot commodity. Mostly through the treatises of Arab scholars, medieval Europeans regained the legacy of ancient thinkers. Together with these treatises, Indian numbers also came, which in Europe began to be called Arabic. They were not immediately accepted, because for most people they turned out to be less understandable than the Roman ones. But gradually the convenience of mathematical calculations with the help of these signs won over ignorance. The leadership of the European industrialized countries has led to the fact that the so-called Arabic numerals have spread throughout the world and are now used almost everywhere.
Binary number system of modern computers
With the advent of computers, many areas of knowledge have gradually made a significant turn. Didn't becomeexcept for the history of numbers and number systems. The photo of the first computer bears little resemblance to the modern device on the monitor of which you are reading this article, but the work of both of them is based on the binary number system, a code consisting only of zeros and ones. For everyday consciousness, it still remains surprising that with the help of a combination of only two characters (in fact, a signal or its absence), you can perform the most complex calculations and automatically (if you have the appropriate program) convert numbers in the decimal system to numbers in binary, hexadecimal, sixty-six and any other system. And with the help of such a binary code, this article is displayed on the monitor, which reflects the history of numbers and the number system of different civilizations in history.
