Why Did Leibniz Invent Binary?

Strickland, Lloyd ORCID: https://orcid.org/0000-0003-2560-6909 (2023) Why Did Leibniz Invent Binary? In: Le present est plein de l’avenir, et chargé du passé: 11th International Leibniz Congress, 31 July 2023 - 04 August 2023, Leibniz University Hannover, Germany.

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Abstract

Many scholars have wondered what led Leibniz to his independent invention of binary arithmetic in the late 1670s. Oddly, in every case, the question that scholars ask is: “who influenced Leibniz?”,1 as though Leibniz had to have taken or adapted the idea for binary from someone else.2 Some scholars have thought that John Napier was Leibniz’s influence, some have claimed that Erhard Weigel was, but neither of these suggestions stands up to scrutiny.3 What I am going to suggest right at the outset is that we be open to the idea that “who influenced Leibniz?” might be the wrong question to ask. Perhaps a better question would be: “why did Leibniz invent binary?” There are two ways to answer this question: by looking at Leibniz’s own answer to it, and by looking at his earliest manuscripts on binary. In this short paper, I shall do both, suggesting that binary was developed as an aid to a variety of mathematical problems Leibniz was dealing with in the late 1670s. But let’s start with Leibniz’s own account.