Manuscripts on Dyadica

Medallion, from the correspondence between Rudolf August Herzog von Braunschweig-Wolfenbüttel and Gottfried Wilhelm Leibniz.

This section contains Leibniz’s unpublished manuscripts concerning his studies on the binary numeral system or dyadics, as he called it. While Leibniz is rightfully considered the discoverer of the binary numeral system, or at least of its importance in a computational context and is thus the father of today’s computer science, of the over 170 manuscript sheets concerning dyadics less than 10% of them have been transcribed at the time of writing, oftentimes without a proper critical edition. Leibniz started working on dyadics in around 1679, as is believed from one of the earliest manuscripts, De Progressione Dyadica, dated 15 March 1679. Even though Leibniz’ production on dyadics spans his life, he never really showed publicly his most complex results on this topic, probably because he thought they were too far from what was usually debated during those times in mathematical circles. Despite this reluctance, he was, on a more general level, a keen advocate of the importance of the new numeral system, as it is shown for example by his discussions with the Bernoulli brothers (A III, 8, N. 233) or his correspondence with Joachim Bouvet on the connection between dyadics and the Chinese I Ching (A I, 19, N. 202, A I, 20, N. 318-319), which culminated with the publication of the Explication de l’arithmétique binaire for the Académie royale des sciences in 1703 (LBr. 68, 21r). As the way in which Leibniz develops dyadics is a unique case of a direct relationship between metaphysics and mathematics, he often discusses the topic from a philosophical standpoint: the correspondence between Leibniz, Rudolf Augustus, Duke of Braunschweig-Wolfenbüttel, and Müller on the possibility of producing a coin representing the connection between 1 and 0 and unity and nothingness is the most famous example of this relationship (LBr. F 15). The collection presents manuscripts relating mostly to Leibniz’s mathematical achievements: the foundation and development of binary arithmetic, studies on the binary expression of numbers and on the binary expansion of their squares.

[LH 35 III B 2 Bl. 1-4] De Progressione Dyadica : Overview | Translation | Transcription | See Original

[LH 35 XII 1 Bl. 190-191] Periodus numerorum : Overview | Translation | Transcription | See Original