The Binary System is the simplest numeration of all positional number systems. The basic of this system is discovered by Gottfried Leibniz, who was also the co-creator of Calculus, in his work Explication de l'arithmétique binaire in 1679. In this work, he was trying to translate verbal statements into mathematical ones.
Yi Jing, which was said to be created by the so-called Third millennium father of Chinese writing Fu Xi, depicts yin and yang. It was represented in binary, with yin as 0 and yang as 1, involving eight trigrams and sixty-four hexagrams. Leibniz’s works were ignored at first, but when he found out about this, he even thought that he was able to find the missing past of ancient China’s mathematical science. It backs up his theory about the translation of life into simplified mathematical propositions. In the 11th century, Shao Yang used this in “proto-scientific” fashion and regarded in “metaphysical views” which is the same with Leibniz’s work. Similarly, he also developed a method for arranging the hexagrams which corresponds to the sequence 0 to 63. His works were corresponded to this discovery, later on.
Furthermore, even before Leibniz came across this theory, there were others who have been meddling on the same thought, at the same time. During the sixteen hundreds Thomas Hariot, a philosopher, left hundreds of unpublished manuscripts which shows different techniques of tabulating data. There was also Francis Bacon, who in his De augmentis scientarium included his bi-lateral code for the letters of the alphabet. This is called today as the 5-bit code and instead of 0 and 1; it uses the letters A and B for coding. It supported Leibniz’s indication of translating verbal statements into equations. He proposed a sequence of the binary digits that can represent each letter of the alphabet. In the same way, Bishop Juan Caramuel y Lobkowitz wrote Meditatio where he discussed binary arithmetic. His works follows the bases of 3, 4, 5, 6, 7, 8, 9, 10, 12, and 60 which had been touched in Pascal’s work. It was him who was revered the first publisher who talked about binary arithmetic, since Hariot’s works weren’t published yet and Bacon’s were all subject to interpretation. Take note that all of these are happening simultaneously, thus, can be concluded that there were separate areas of development in the binary system at the time. It is also difficult to pinpoint the exact moment of the binary system’s discovery as it was gradually and constantly rising in the field of philosophy and mathematics.
Although attempts were made to explain the system, it was Leibniz’s works that is accounted for the development of the binary system. In his creation of the Imago Creationis, a medallion that is offered to the Duke of Brunswick, the diagram of binary digits was embedded. He also included in a letter, which comes together with it, that the alternation between the numbers one and zero if continued cyclically will create a “harmonious order and beauty” even if seen as completely random in small scale. His theology of binary numbers was grounded to the “Christian idea of creating out of nothing”.
After Leibniz’s introduction of the binary, there were philosophers and mathematicians who continued from his works. There were exchange of letters between Leibniz and Johann Jean Bernoulli where they talked about the binary system. The former offered more explanation of what he had mentioned in his letter for the Duke. According to Anton Glaser, perhaps there could be more development over what Leibniz was able to present to the Duke. Yet the only thing that went beyond that letter was that Bernoulli acknowledged that the binary representation were in bases of two given the example 1701 = 210 + 29 + 27 + 25 + 22 + 1 = 11010100101. In his letter to the Duke, he even stated in the letter that this discovery is for figuring the secrets of numbers and is not intended for everyday use.
In the early nineteen hundreds, The Mathematical analysis of logic was published. George Boole, its proprietor, described here the use of logic in the algebraic system. The system involved the use of the binary system together with the operations and, or, and not. This system became known as the Boolean algebra and was Claude Shannon’s thesis in 1937 relating the algebraic system to electric circuits. This started the practical use of binary codes.
Even though the use of binary numbers did not develop, it did not disappear entirely. In the late twentieth century, something put it in to work in the recreational mathematics area. The base of binary or radix is 2, which means that only two digits 0 and 1 can appear in a binary representation of numbers. It became a useful tool to the Nim games such as Plainim, Turning Turtles, NorthCott’s Game, and Scoring. Nim Games are mathematical games where players take turns in removing objects on a certain stack.
The bit string is the most commonly used of all the forms of binary code. The others include the Braille which is widely used by blind people in order to be able to read and write; the Bagua are diagrams that are used in Feng shui which is actually the hexagrams that are being pointed out by Shao Yang; the Ifá divination is the ancient system used by Nigerians for communicating their spiritual divinity; and the Morse Code which is a method used by the early telegraphs and was the foundation of electronic communication.
In the computer science field, binaries are used to put up a set of instructions or task for a specific program. Since the representations are 0 as on and 1 as off, binary number can be used in currents. Computers follow the same principle as it can only follow this on and off charge. Binary uses two as its base, such that when you write 2 in binary, it will be 10, 3 as 11, 4 as 100, 5 as 101, 6 as 110, and so on.
Because any number can be represented by the binary system, it is easier to lay a set of instructions for programs. This is called the Binary Integer Programming. There is also the American standard code information interchange or ASCII which uses the 7-bit binary coding. It translates computer logic into symbols that can be distinguished by the human mind, so that when one looks into a computer long set of numbers have been translated to letters that can be understood by humans. Since computers are made basically designed for binaries, it is the only system that can distinguish between two definite sets.
However, computer programs are long sets of codes. These codes are composed of billions of binary numbers which is almost impossible for typing manually and writing a program. Programs that we use as of today for computers have become too complex to be written just in binaries. Programming languages now comes into place. Programming languages uses a set of instructions or syntax rules to format a program that the human mind can easily put up with, such as words. Programs that translate these words into binary come within programming languages so that it will not be as tedious as the old times.
The use of binary system has come a long way for it was originally set as Shao Yang’s and Leibniz’s beliefs for the formation of the cosmos. Yang believed that the scientific use of the binary was “perniciously dualist and spiritually detrimental”. But in the age of the scientific revolution and age of modernization, it has become more important than just as a basis of counting the stars. It became the groundwork for almost everything that we work on, especially the computer.
Bibliography
Coudert, Allison, Popkin, Richard, and Weiner, Gordon. Leibniz, Mysticism and Religion. Netherlands: Kluwer Academic Publishers, 1998. Print.
Chinneck, John. Practical Optimization: a Gentle Introduction. sce.carleton.ca, 2004. 30 Nov 2014.
Glaser, Anton. History of Binary and Other Nondecimal Numeration. USA: Tomash Publishers, 1971. Print.
Ryan, James. Philosophy East and West. University of Hawaii Press, 1966. Print.
