Leibniz on the Logic of Computation
Binary Logic is considered to the foundational paradigm in computation using electronic circuits. It is interesting to see that we can find references to binary logic even in the early writings of the famous mathematician Leibniz. Leibniz first mentioned binary logic in a letter to the German mathematician Detlev Cliver in 1680. It is described in detail in the recently published book by MIT Press, Leibniz and the Logic of Binary.
Leibniz clearly understood that binary representation can help us to implement arithmetic operations. However when it comes to the representation of mathematical computation, he understood there are finer nuances in the binary logic. He had worked extensively on the periodicity and power relations in binary numbers. He had presented the idea of binary progression as a construct to symbolise the harmony between quantities. He expressed the periodity of number sequences in binary arithemtic.
It is further more interesting to note that Leibniz shared this idea with a wider network of mathematicians and royalities. He came across interesting hexagrams invented by ancient Chinese mathematicians. He realized that computation techniques existed even in the prehistoric times. The Egyptian method of multiplication illustrated in the Rhind Papyrus computes a product by repeatedly doubling and then adding up certain of resulting values until the value reaches the target number.
The idea of connecting an arithmetic progression with a computational apparatus is quite striking as it helps us to understand the modern representations such as Turing machines. An arithemtic progression is a mathematic construct that represents the computational capacity of numbers. The periodicity and power of binary arithmetic is another interesting aspect observed by Leibniz. It helps us to model computation into modular units in a periodic manner harnessing the power of harmonies. It also helps us to reperesent a progressive machinery that can calcuate and propogate the state changes in an efficieint manner. Thus we can understand that Leibniz left his marks in the historic annals of computation as one of the founding fathers of binary logic.
