binarius

Binarius in Latin means 'consisting of two,' from bini (two by two, a pair), from bis (twice), from PIE *dwi- (two). The word described anything arranged in pairs. The mathematical application — a number system using only 0 and 1 — was explored by several people before it became standard, but Leibniz's 1703 paper 'Explication de l'Arithmetique Binaire' is the landmark text.

Leibniz saw the binary system as more than mathematics. He corresponded with Joachim Bouvet, a Jesuit missionary in China, who showed him the I Ching hexagrams — six-line figures composed of solid (yang) and broken (yin) lines. Leibniz recognized these as a binary system and was thrilled by the convergence. He also saw theological meaning: 1 is God, 0 is nothing, and all of creation is built from these two. The binary system, for Leibniz, was evidence of divine order.

George Boole formalized binary logic in The Laws of Thought (1854). True/false, yes/no, on/off — Boolean algebra operates in two states. Claude Shannon's 1937 master's thesis at MIT showed that Boole's logic could be implemented with electrical switches. A switch is either on or off. A wire carries current or does not. The physical world offered a perfect substrate for binary logic. The digital computer was born from this insight.

Every digital device — every phone, every computer, every router — operates in binary. All photographs, all music, all text messages, all software are encoded as sequences of 0s and 1s. Leibniz's mystical number system, Boole's abstract logic, and Shannon's electrical switches converged into the foundation of the information age. The Latin word for 'two by two' now describes the substrate of modern civilization.