Mathematics, as a science, owes its appearance to the Ancient East. There are no exact dates of its origin, but it is reliably known that almost every individual eastern state had its own system of calculus and calculation methods. In this article we will discuss the phenomenon of Babylonian numbers, consider archaeological artifacts that confirm their existence, and evaluate their impact on the further development of science.
Introduction
The Babylonian kingdom began to exist in the II millennium, and fell in 539 BC. During this period, this eastern region has taken a major step forward in many areas of life, with particular attention to architecture and astronomy. But in order for buildings to be stable and durable, so that observations of celestial bodies can be recorded and analyzed, mathematics was required. Therefore, at the dawn of the birth of a new civilization, new Babylonian numbers appeared in Mesopotamia.
Since the state was built on the wreckage of the once existing Sumer and Akkad, also very powerful powers, the inventions and scientific achievements of their predecessors helped the Babylonians become a developed and progressive race.
Number system of the Babylonian kingdom
At the first glance at the Babylonian numbers, an association immediately arises with the Roman ones, since the principle of their writing is almost identical, and at the same time much simpler. The system uses only two signs: a straight blade, representing units, and a lying blade, which is estimated at ten.
To record numbers from 1 to 9, only the first character is used, and for all subsequent indicators, one or another combination of two wedges is used. It is important to note that the number system was six-decimal and was divided into corresponding digits, and this is no coincidence. Babylon owes the sixfold division to the Sumerians, and the presence of a dozen to Akkadians. Subsequently, the Babylonian numbers are duplicated in Arabic, Roman and Greek and became the basis of time calculus. Since then we have divided the hour by 60 minutes, and every minute by 60 seconds.
Difficulties in Babylonian Mathematics
As we see on the table, the number series in Ancient Babylon ended at 59, since the system was six-decimal. But after all, such a developed civilization could not be limited only to such a volume of numbers? That's right. The Babylonian numbering implied huge indicators, which today we call three-, four- and five-digit.
As an example, we take a segment from 60 to 120. For the number 60, the same blade was used as for the unit, only larger. A large gap was left after it, and then the rest of the number was recorded. Over time, this began to create confusion, which even the ancient users themselves sometimes could not figure out. One can only guess how experts who decrypted such artifacts racked their brains. In addition, the Babylonians did not have a zero, and this would greatly simplify the recording of complex numbers.
From confusion to order
To recognize the Babylonian numbers in a number of other calculus systems, it is enough to remember two signs. To correctly read them and determine the value, you need to familiarize yourself with the principle of positioning. This is not difficult for us, since in the modern world there is a single positional system. Its essence is that the place of a particular figure affects the significance of the number. Agree, if we swap 1 and 7 in the number 17, then the result becomes completely different. But for the ancient peoples, this was not so obvious, since earlier the position of the number in the number did not matter. The Babylonians were the first in the history of mankind to realize that there is no need to create many signs, writing them randomly. It will be enough two, the value of which will depend on the position.
Babylonian "notebooks"
In the states between the Tigris and the Euphrates, not only rulers, but also ordinary people were very educated, but for complete harmony they lacked one element - paper. In Egypt, they used papyrus instead, on which ancient hieroglyphs and icons were painted, and the Babylonian record of numbers and letters-pictures was carried out on clay tablets.
This technique is called cuneiform writing, and its essence is that while the clay is soft, the necessary symbols are displayed on it with a sharpened wooden blade, which subsequently harden. The tablets were of varying size, thickness and quality. Depending on these indicators, laws and decrees, scientific papers, or the stories of ordinary people, their observations and incidents were recorded on them.
History and science
Today, there is a clear division of professions into technical professions, which imply knowledge of mathematics, physics, and other exact sciences, and humanities, where languages, literature, history, and philosophy play the main role. When ancient civilizations existed and developed, all these industries were not only closely intertwined, but also formed a single whole, which allowed people to gain new knowledge. Above, we have already touched on such a topic as the history of mathematics, and we would like to reveal a couple more points.
Precisely because the Eastern Ancient World had the honor of being the cradle of world civilization, he was forced to calculate literally everything. Early enough, an economy appeared there, which was built on such elements as the number series and operations with numbers. Grain and cereal were counted, the area of the fields was measured, the masses and parameters of the buildings were calculated. Astronomy was also actively developing. To further advance work in this area, the first formulas were developed that calculated the distances to visible stars and planets. Scientists still use some of them in an unchanged format.
Today we say that mathematics is the basis of physics, chemistry and astronomy, but in fact it arose on the foundation of the data of existing sciences, as it was a necessity.