CONCEPT
Leibniz’s Binary Arithmetic
The notation of zeros and ones that
Leibniz devised in 1679 for metaphysical reasons—and that became the literal alphabet of every digital computer, every neural network weight, and every word generated by a large language model.
Around 1679, decades before any machine could exploit it,
Gottfried Leibniz worked out a way of writing all numbers using only two symbols: zero and one. He published it in 1703 in a paper for the French Royal Academy of Sciences, the
Explication de l’Arithmétique Binaire, explaining that every quantity can be built from the combination of being and nothing—one and zero—the way, he believed, God had built every created thing from existence and its absence. He was enchanted by the system for metaphysical reasons and proposed a commemorative medal be struck to celebrate it. What he could not have known was that he had given the entire digital age its alphabet. Every transistor state, every bit of memory, every floating-point weight in a neural network, every token generated by a
large language model—all of it is, at the lowest level, Leibniz’s notation. The machines that now write and argue and unsettle us are built from his