Leibniz on Binary: The Invention of Computer Arithmetic

This book is interesting, not only from the standpoint of the development of the binary arithmetic system, and thus, as the title indicates, Leibniz’ “invention of computer arithmetic,” but also for showing how Leibniz considered the binary principle to have philosophical and theological significance. For example, the 1 and 0 reflect the first principles of being and nothing, of God and nothing, and thus of the principle of privation in creatures, i.e., their creation from nothing by what is fully positive. It shows Leibniz’ interest in connecting this principle to the figures of the ancient Chinese Emperor, Fuxi. It includes Leibniz’s reflections on a demonstration of God’s existence, put forward by his mathematics professor Erhard Weigel, based on divine conservation and continual creation. Point is, the book is not simply for number nerds. But the main task of the authors, Strickland and Lewis, is to set the record straight on the history and development of binary, including the revelation, based on texts unpublished until now, of Leibniz’s invention of the hexadecimal system (base 16 notation) widely used in computing today. Throughout, the authors provide excellent translations and clean presentations of Leibniz’s work, employing the highest standards of scholarly editorial practice, and lots of pictures and diagrams. The extensive introduction is very helpful, as are the introductions, commentaries, and footnotes on the individual manuscripts. Well-worth pouring through for added insight into Leibniz’s philosophy and more particularly into one of his more obscure but, as it turned out, more consequential preoccupations.

Thanks for putting this together. I hope more of Leibniz's papers on binary are translated. A remarkable insight by Leibniz.

In 1959-60 my high school math class had a guest speaker visit to talk about computers. He told us we'd all have to learn binary arithmetic. My classmates and I talked about this afterward and concluded, "Nah." More than a decade later, I was just starting out as a computer scientist. I did need to learn some binary arithmetic then, and along with that, hexadecimal.I had no idea that Leibniz had developed both centuries before. Talk about prescience! Anyway, a fascinating story well told in this book.On a related note, I've tried to explain to non-computer-science colleagues that once language development got away from pictographic versions - hieroglyphics, cuneiform, et al. - and developed a finite alphabet instead, the road to computer science was clear. In hindsight, it's easy to go from a finite alphabet to a binary alphabet. Am in awe of Leibniz for figuring this out when he did. Early computer hardware types were still focused on decimal machines into the late 1940s, an engineering dead end. Don't know if anyone had read Leibniz.My thanks to the authors for getting the details of this story into a book.

Nur etwas für "Mathematik-Archäologen". Einfach langweilig.

You can rarely go wrong with Leibniz, in my opinion, and this book is no exception. It's fascinating from the get go, with Strickland and Lewis providing a deep dive into Leibniz's work on binary, correcting various misconceptions along the way. The texts themselves (I've read half so far) are beautifully presented and there is so much illuminating information about how and why each one was written, as well as detailed explanations to help the reader to understand what Leibniz was thinking and doing as he devised and slowly fleshed out binary arithmetic and --- and this I wasn't expecting --- what we now call hexadecimal or base 16. Almost every page shows a genius mind at work. And to add even more flavor, lots of manuscript pages are reproduced throughout the book, showing the human side of an invention that sits at the heart of the computer age. Absorbing.

Great book for my research.