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Evolution of Abacus
Abacus? . . . . . .What is Abacus?
A very simple tool then why it is so difficult to understand it?
Abacus is present in our culture since ancient times and has its reference nearly in every ancient culture. I found references of Abacus in the ancient history of Mesopotamian Abacus, Egyptian Abacus, Persian Abacus, Greek Abacus, Roman Abacus, Chinese Abacus, Indian Abacus, Japanese Abacus, Korean Abacus, American Abacus etc.
Abacus had been a tool for calculations in the ancient times by various cultures but limited to the knowledge of time for numbers, number system and method of calculations.
Each of this Abacus is called with different names, like in Hindi it is called it called Gintara (Couting Guitara), Chinese it is called Suan Pan (Couting Tray) , In Russian, it is called Sckoty, in Japanese it is called Soroban (Counting Tray), in Korean it is called jupan. Meaning resulting into the one and only one idea of recording the numbers in the form of beads on a structurally arranged on either string in a frame or plate with grooves as per best-known number system of time in which it is being used.
Logically understanding the evolution of Abacus from simple calculation tool to advance calculation tool is directly connected to our understanding of numbers and number system and further evolving 'THE CALCULATION TOOL' up to the latest known understandings. The Abacus we see and use today has been evolved with a time of our understanding on the same and the recently updated tool with 1/4 bead arrangement meets the purpose accordingly.
Modern Abacus with 1/4 bead arrangement we are using today uses the decimal place value system introduced by the world accepted numbers system of Hindu-Arabic Number System.
Abacus and Hindu–Arabic numerals
Gerbert learned of Hindu–Arabic digits and applied this knowledge to the abacus, but according to Charles Seife without the numeral of zero. According to William of Malmesbury (c. 1080–c. 1143), Gerbert got the idea of the computing device of the abacus from a Spanish Arab. The abacus that Gerbert reintroduced into Europe had its length divided into 27 parts with 9 number symbols (this would exclude zero, which was represented by an empty column) and 1,000 characters in all, crafted out of animal horn by a shield maker of Rheims. According to his pupil Richer, Gerbert could perform speedy calculations with his abacus that were extremely difficult for people in his day to think through in using only Roman numerals. Due to Gerbert's reintroduction, the abacus became widely used in Europe once again during the 11th century.
"The Japanese Soroban's Brief History"
The soroban's physical resemblance to the Chinese suanpan clearly indicates its origin. The number of beads, however, is similar to the Roman abacus, which had four beads below and one at the top.
Most historians on the soroban agree that it has its roots on the suanpan's importation to Japan via the Korean peninsula in the 15th century. When the suanpan first became native to Japan as the soroban (with its beads modified for ease of use), it had two heavenly beads and five earth beads. But the soroban was not widely used until the 17th century, although it was in use by Japanese merchants since its introduction. Once the soroban became popularly known, several Japanese mathematicians, including Seki Kowa, studied it extensively. These studies became evident on the improvements on the soroban itself and the operations used on it.
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In Chinese numerals, a circle (O) is used to write zero in Suzhou numerals. Many historians think it was imported from Indian numerals by Gautama Siddha in 718, but some think it was created from the Chinese text space filler "◊".
In the construction of the soroban itself, the number of beads had begun to decrease, especially at a time when the basis for Japanese currency was shifted from hexadecimal to decimal. In around 1850, one heavenly bead was removed from the suanpan configuration of two heavenly beads and five earth beads. This new Japanese configuration existed concurrently with the suanpan until the start of the Meiji era, after which the suanpan fell completely out of use. In 1891, Irie Gary further removed one earth bead, forming the modern configuration of one heavenly bead and four earth beads. This configuration was later reintroduced in 1930 and became popular in the 1940s.
Chinese and Japanese finally adopted the Hindu–Arabic numerals in the 19th century, abandoning counting rods.
Also, when the suanpan was imported to Japan, it came along with its division table. The method of using the table was called kyukiho ("nine returning method") in Japanese, while the table itself was called the Hassan ( "eight calculation"). The division table used along with the suanpan was more popular because of the original hexadecimal configuration of the Japanese currency. But because using the division table was complicated and it should be remembered along with the multiplication table, it soon fell out in 1935 (soon after the soroban's present form was reintroduced in 1930), with a so-called standard method replacing the use of the division table. This standard method of division, recommended today by the Japan Abacus Committee, was, in fact, an old method which used counting rods, first suggested by mathematician Momokawa Chubei in 1645, and therefore had to compete with the division table during the latter's heydey.
Now it is more important to note the following:
"A Brief About - History of Hindu-Arabic Number System"
A decimal place system has been traced back to ca. 500 in India. Before that epoch, the Brahmi numeral system was in use; that system did not encompass the concept of the place value of numbers. Instead, Brahmi numerals included additional symbols for the tens, as well as separate symbols for hundred and thousand.
The Indian place-system numerals spread to neighbouring Persia, where they were picked up by the conquering Arabs. In 662, a Nestorian bishop living in what is now called Iraq said:
I will omit all discussion of the science of the Indians ... of their subtle discoveries in astronomy — discoveries that are more ingenious than those of the Greeks and the Babylonians - and of their valuable methods of calculation which surpass description. I wish only to say that this computation is done by means of nine signs. If those who believe that because they speak Greek they have arrived at the limits of science would read the Indian texts they would be convinced even if a little late in the day that there are others who know something of value.
The addition of zero as a tenth positional digit is documented from the 7th century by Brahmagupta, though the earlier Bakhshali Manuscript, written sometime before the 5th century, also included zero. But it is in Khmer numerals of modern Cambodia where the first extant material evidence of zero as a numerical figure, dating its use back to the seventh century, is found.
This Evolution Of Abacus Part - III is a unique piece. As it was from the Arabs that the Europeans learned this system, the Europeans called them Arabic numerals; the Arabs refer to their numerals as Indian numerals. In academic circles, they are called the Hindu-Arabic or Indo-Arabic numerals.
The significance of the development of the positional number system is probably best described by the French mathematician Pierre Simon Laplace (1749–1827) who wrote:
It is India that gave us the ingenious method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity.
Tobias Dantzig, the father of George Dantzig had this to say in Number:
This long period of nearly five thousand years saw the rise and fall of many civilisations, each leaving behind a heritage of literature, art, philosophy, and religion. But what was the net achievement in the field of reckoning, the earliest art practised by man? An inflexible enumeration so crude as to make progress well nigh impossible, and a calculating device so limited in scope that even elementary calculations called for the services of an expert [...] Man used these devices for thousands of years without contributing a single important idea to the system [...] Even when compared with the slow growth of ideas during the dark ages, the history of reckoning presents a peculiar picture of desolate stagnation. When viewed in this light, the achievements of the unknown Hindu, who sometime in the first centuries of our era discovered the principle of position, assumes the importance of a world event.
Adoption in East Asia
In China, Gautama Siddha introduced Indian numerals with zero in 718, but Chinese mathematicians did not find them useful, as they had already had the decimal positional counting rods.
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