The history of numbers and the number system are closely interconnected, because the number system is a way of writing such an abstract concept as number. This topic does not apply purely 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. Systems as a whole are divided into positional, non-positional and mixed. From their alternation the whole history of numbers and number systems consists. Positional systems are those in which the value denoted by a number in a number entry depends on its position. In non-positional systems, accordingly, there is no such dependence. Mankind has created mixed systems.
Studying number systems in school
Today the lesson "History of numbers and number systems" is held in grade 9 as part of a course in computer science. Its main 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 today's multidisciplinary approach. In the framework of the general course of history, in principle, not only the history of economic development, socio-political movements, boards and wars could be studied, but also, to a small extent, the history of numbers and number systems. Grade 9 in a computer science course in this case could, in terms of translating numbers from one system to another, provide a significantly larger number of examples from previously passed material. 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 sure when, and most importantly, how a language arose). It is only known that all ancient civilizations already had their own account systems, which means that the history of numbers and the number system were born in pre-civilization time. Stones and bones are not able to tell us what was happening in the human mind, but they did not yet create written sources. Perhaps the account was needed for a person during the division of production or much later, already during the Neolithic revolution, that is, during the transition to agriculture, to divide the plots of the field. Any theories on this subject will be equally groundless. But some assumptions can still be made by studying the history of various languages.
Traces of the ancient number system
The most logical initial system of counting is the juxtaposition of the concepts of “one” - “many”. It is logical for us because in modern Russian there is only a singular and plural. But in many ancient languages there was also a dual number for two objects. It 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, in the most ancient civilizations known to us, more detailed number systems were developed.
Mesopotamian notation of numbers
We are used to the notation that the number system is decimal. This is understandable: 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 six-decimal. Therefore, it is still 60 minutes in an hour, and 60 seconds in a minute. Therefore, the year is divided by the number of months that is a multiple of 60, and the day is divided by the same number of hours. Initially, it was a sundial, that is, each of them was 1/12 of a day (in the territory of modern Iraq, its duration did not vary much). Only much later did the hour begin to be determined not by the sun and 12 night hours were also added.
It is interesting that the signs of this hexadecimal system were written as if it were decimal - there were only two signs (to indicate one and ten, not six and not sixty, namely ten), the numbers were obtained by combining these signs. It’s scary to even imagine how difficult it was to write any large number in this way.
Ancient Egyptian number system
And the history of numbers in the decimal system, and the use of numerous icons to indicate numbers began with the ancient Egyptians. They combined hieroglyphs, which denoted one, one hundred, one thousand, ten thousand, one hundred thousand, one million and ten million, thus indicating the desired number. Such a system was much more convenient than the Mesopotamian one, which used only two signs. But at the same time, it had an obvious 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 records
The history of European philosophy, science, political thought, and much more begins in many ways in Ancient Hellas ("Hellas" is a self-name, it is preferable to that invented by the Romans "Greece"). Developed in this civilization were mathematical knowledge. Hellenic numbers were written in letters. Separate 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 the unit, but with a different sign next to the letter. The system allowed even large numbers to indicate relatively short inscriptions.
Slavic number system as the heiress of 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, because the Slavic system of recording numbers was also based on the Hellenic. Here, also, 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 the Hellenic texts at that time and the Slavic ones were written from left to right from the very beginning, Slavic numbers were written from right to left, that is, the letters denoting dozens put to the right of the letters denoting units, letters , denoting hundreds to the right of letters denoting dozens, etc.
Attic Simplification
Hellenic scientists have reached tremendous heights. The Roman conquest did not interrupt their research. 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, Hellenic scientists were helped by their number recording system.
But for ordinary people, for example, traders, the system often turned out to be too complicated: to use it, it was necessary to remember the numerical values of 27 letters (instead of the numerical values of 10 characters that modern schoolchildren teach). Therefore, a simplified system appeared, called Attic (Attica is the region of Hellas, at one time leading in the region as a whole and especially in the maritime trade of the region, since the famous Athens was the capital of Attica). In this system, only the numbers one, five, ten, one hundred, one thousand and ten thousand began to be designated in separate letters. It turns out only six characters - they are much easier to remember, and traders did not make too complicated calculations anyway.
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 Hellenic history. The Attic system was taken as a basis, simply the Hellenic letters were replaced by Latin ones and a separate designation of fifty and five hundred was added. At the same time, scientists continued to make complex calculations in their treatises by the Hellenic system of writing 27 letters (and they usually wrote the treatises themselves in Hellenic).
The Roman system of notation of numbers can not be called particularly perfect. In particular, it is much more primitive than Old Russian. But historically, it still remains on a par with the Arabic (so-called) numbers. And forget this alternative system, stop using it is not worth it. In particular, today, Arabic numerals often denote quantitative numerals, and Roman numerals .
The great ancient Indian invention
The numbers that we use today appeared originally in India. It is not known exactly when the history of numbers and the number system made this momentous turn, but most likely no later than the fifth 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 Indians allowed us to fully include it in mathematical records, and hence in calculations.
The spread of the Indian number system on Earth
Presumably in the 9th century, Indian numbers were borrowed by Arabs. While the Europeans neglected the ancient heritage, and in some regions at one time even intentionally destroyed it as a 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 treatises of Arab scholars, medieval Europeans regained the heritage of ancient thinkers. Along with these treatises came Indian numbers, which in Europe began to be called Arabic. They were not immediately accepted, because for most people they were less understood than the Roman ones. But gradually the convenience of mathematical calculations with the help of these signs defeated ignorance. The leadership of European industrialized countries has led to the fact that the so-called Arabic numbers have spread throughout the world and today are used almost everywhere.
Binary number system of modern computers
With the advent of computers, many areas of knowledge gradually made a significant turn. The history of numbers and number systems was no exception. The photo of the first computer resembles little 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 remains surprising that using a combination of only two characters (actually a signal or its absence), you can perform the most complex calculations and automatically (if you have the appropriate program) translate numbers in the decimal system of calculation into numbers in binary, hexadecimal, and hexadecimal and any other system. And with the help of such binary code, this article is depicted on the monitor, which reflects the history of numbers and the number system of different civilizations in history.