Folha: "Leibniz and the mathematics of the 'I Ching'"

Reproduction of Marcelo Viana's column in Folha de S. Paulo. He wrote about topics such as music, philology, games, history, law, politics, ethics, theology, and philosophy. He made important contributions to physics , technology, and library science. He introduced several fundamental concepts in computer science , linguistics, psychology, geology, medicine, biology, and probability theory. Mathematician, philosopher, scientist, inventor, and diplomat, the German Gottfried Wilhelm von Leibniz (1646–1716) has been called "the last universal genius." Leibniz occupies a prominent place both in the history of philosophy, where he led the rationalist and idealist currents, and in the history of mathematics, where he is known, above all, as the co-discoverer of infinitesimal calculus, along with Isaac Newton (1643–1727). But the development of the binary number system, explained in his work "Explanation of Binary Arithmetic," published in 1703, also earned him the title of "first computer scientist." In the binary system (or base 2), every number is represented using only two digits, 0 and 1. And the multiplication table couldn't be simpler: 0x0=0x1=1×0=0 and 1×1=1. Therefore, all electronic computers use the binary system. A lesser-known fact is that Leibniz was also one of the first European intellectuals to be interested in the cultures of other continents, especially the remarkable civilization of China . He discovered it through correspondence with Jesuit missionaries such as Joachim Bouvet (1656–1730), a mathematician and member of the French Academy of Sciences, who gave him access to various Chinese manuscripts. Read more: One month left until registration closes for IMPA Tech IMPA launches 4th edition of José Plínio de Oliveira's book Marcelo Viana receives the Planeta Rio 2024 Award Some of these dealt with philosophical systems developed in China, such as Taoism and Confucianism. Leibniz was one of the first readers of "Confucius, Philosopher of the Chinese," published in 1687 by the Jesuit Philippe Couplet (1623–1693), and sought to reconcile Confucianism with European philosophy. It was also in these manuscripts that he encountered the "I Ching" ("Book of Changes"), the fascinating divination manual that dates back to the 10th century BC and is certainly the most famous of all Chinese books. In the "I Ching," certain fundamental concepts are represented by figures formed by three lines (trigrams), each of which can be broken ("yin") or continuous ("yang"). There are trigrams, which correspond to the concepts of heaven, earth, thunder, water, mountain, wind, fire, and lake. By combining any two of them, we can form the 64 hexagrams, figures composed of six lines, broken or continuous, which represent even more concepts: for example, hexagram 35 represents progress. Leibniz perceived the analogy with the binary system, with yin and yang in place of the digits 0 and 1, which he considered conclusive proof of the advancement of Chinese thought. He also saw in the binary system a representation of Creation, with 1 as a symbol of divinity and 0 representing the void. He transmitted these ideas to the Emperor of China, hoping to convince him to convert to Christianity, but he was unsuccessful. To read the full article, visit the newspaper's website. Also read: Henrique Bursztyn is awarded the 2026 TWAS Prize. From the Navy to mathematics, Hallison Paz completes his doctorate.