Babylonians: The Sexagesimal System And Astronomy

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Babylonians: the sexagesimal system and astronomy

The numbering system of the ancient Babylonian civilization was a numbering system based on number 60 currently known as the sexagesimal system, one of the first positional notation systems in which the numerals on the left side of the notation are greater than those ofThe right, as in the current decimal system that is based 10, of which we know the units, tens, hundreds, etc.

The best known vestiges of Mesopotamian mathematics are the tables of cuneiform writings where the Sumerians and Babylonians wrote their business transactions records, tables that facilitate obtaining this knowledge today.

According to ing. Eladio Sáenz Quiroga, in his Compendium of Notes for the Mathematics History Course of the Faculty of Physicomathematics Sciences of the Autonomous University of Nuevo León. The most accepted hypotheses establish that mathematics arose from the practical needs of development of primitive societies, the organization of agriculture, planting control and rivers, irrigation systems, constructions and commerce. Other hypotheses attribute the origin of mathematics through mystical revelations and religious ritual , etc.

The ancient Babylonians maintained a detailed record of the exits and stars, the movement of the planets, the solar and lunar eclipses; all of which require familiarity with angular distances measured on the celestial sphere. They also used a form of analysis to calculate ephemeris, which was subsequently discovered in the fifties by Otto Neugebauer. From the rediscovery of the Babylonian civilization, it has become clear that the mathematicians and astronomers of ancient Greece and the Hellenistic period took a lot of the Babylonians. 

The Babylonians expressed all periods in synodic months, possibly because they used a luni-solar calendar. Various relationships with annual events determined different values for the duration of the year. Similarly, various relationships between the planet periods were known. All this knowledge was transferred to the Greeks probably shortly after the conquests of Alexander the Great (331 to. C.). According to the classic simplium philosopher, Alejandro ordered the translation of the historical astronomical archives under the supervision of the historian Calistenes of Olinto (nephew and disciple of Aristotle, who sent them to them). The use of number 60 as a basis for the measurement of angles, coordinates and time measures is linked to old astronomy and trigonometry. It was common to measure the elevation angle of a star and trigonometry uses rectangles.

In ancient times, what we now call positive numbers excluded zero were the only bona fide numbers. The current rational numbers were considered reasons between whole numbers, since the prevailing philosophy resorted to the proportion and a fraction, in short, it was a proportional comparison between two segments of whole values. All this linked to what we call minimum common multiple. All rectangles triangles of whole sides have the property that the product of their three sides is always a multiple of 60. If one of the legs is cousin, the other is at least multiple of twelve and is a multiple of sixty if the hypotenuse is also a cousin. If there is no cateto cousin, one cateto is divisible by three and the other by four;Any of the three sides is five.

There are vestiges of the sexagesimal system in time measurement. There are 24 hours in a day, 60 minutes in an hour and 60 seconds in a minute. The smaller units that a second are measured with the decimal system. This method of calculating units is also used in typography, where the basic units Cicero or Pica are divided into twelve points, which in turn are divided into tenths of point. In addition to the historical reasons that may be at the origin of this way of calculating the size of the type of printing and other typographic composition elements such as columns, chorondels or streets, the reason for its permanence is due to comfort with thethat divisions in media, rooms and thirds with entire typographic points can be made mentally without resorting to decimals.

During the Umayya Caliphate, the sexagesimal system was used by the Arabs both to count the time and for the geometry and trigonometry that had evolved from the Babylonian ancestors, through old Egypt and many other cultures. It was precisely the Arabs who settled the use of the sexagesimal system in modern culture, since for almost 500 years they held all scientific potential without discussion. As at the time the Babylonians drawn the first lines for the Arabs to use their system years later, they cemented the use of the sexagesimal system as we know it today. And however curious it is still working perfectly.

In Babylon the circumference was divided into equal arches. Each of those parts received the name of degree and each of them was assigned a god. In the zodiac, twelve reappears, because that amount of signs or "houses" has the system, covering an arc of 30 degrees and a set of the same number of gods.

The religious system was very strict and dogmatic and demanded that the angles be built by meansIt was not possible to use it to transport segments or measures. This geometric construction system was considered of divine origin and use;According to these beliefs, the universe had been created with that geometric construction method.

Every 315 years the sun and the moon are again in the same place in the sky, with an error of 7 or 8 minutes of arc. This constitutes a little more than double the minimum separation that the human eye can detect without increases in increase. The little error should have a religious meaning ignored by our civilization, since the degree was occupied by a God and was divided into 60 minutes. But both the sun and the moon fell into the same "divine" domain. Four periods cover 1260 years, equivalent to 3 + ½ times 360 years. Taking the whole to its minimum entire expression we have the 2520 -year -old astronomical period, which is part of a right triangle with a cateto and the hypotenuse cousins: (71, 2520, 2521). These numbers, 1260 and 2520, are multiples of 12, 40 and 60 and can occupy any cateto and the hypotenuse of rectangles similar to the Egyptian sacred triangle (3, 4, 5) and, in general, of any right triangle of whole sides, especially those with a cateto cousin.

In conclusion we can take that the importance of the sexagesimal system in todayThe minutes and hours of the day, the days of the week and weeksSimple full moon count, and, much of this information is thanks to the record that the Babylonians retained, the sexagesimal system was the previous one, was the birth of mathematics and the possibility of reaching where we have done it, it is asuccessful and present legacy in just some of the ancient civilizations.

References

  1. Boyer, c. B.: A History of Mathematics. New York: Wiley, 2.ª edition reviewed by Uta C. Merzbach, 1989.
  2. O’Connor, j. J., and e. F. Robertson: "An Overview of Babylonian Mathematics", (http: // www-history.MCS.Standrews.AC.uk/historics/babylonian_mathematics.html) in Macuctor History of Mathematics, December 2000.
  3.  Robson, Eleanor: Mathematics in ancient Iraq: a social history. Princeton University Press, 2008.
  4. Toomer, g. J.: Hipparkus and Babylonian Astronomy, 1981.
  5. Ecured.Cu. (2019). Sexagesimal – Ecured. [Online] https: // www.Ecured.CU/SYSTEM_SEXAGESIMAL 

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