Early Mechanical Reasoning and the Dream of Universal Calculation
Thirteenth century theologian Raymond Llull wrote forty treatises on a novel approach to discovering universal truths, collected in his Ars magna1. The work serves as a user’s manual for a device containing concentric rotating wheels inscribed with letters meant to represent what he believed were the fundamental axioms of truth: God, justice, goodness, eternity, and so on. By turning the wheels, one could explore combinations of these principles and arrive at new metaphysical insights. Llull’s Ars magna stands as one of the earliest documented attempts to apply formal and mechanical reasoning to problems that had previously belonged to philosophy, theology, and human judgment.
Gottfried Wilhelm Leibniz, co-inventor of the calculus and early champion of symbolic logic, encountered Llull’s ideas as a teenager and renamed the method ars combinatoria2. He expanded Llull’s rotating diagrams into his own interlocking gear mechanisms, which eventually inspired the first mechanical calculator capable of addition, subtraction, multiplication, and division: the calculus ratiocinator. Leibniz imagined a far more ambitious future. He dreamed of a characteristica universalis3, a symbolic language that could resolve intellectual disputes through calculation alone. In 1666 he wrote:
If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, to sit at their slates, and say to each other (with a friend to witness, if they liked): Let us calculate.
Leibniz believed abstraction and formal symbol manipulation could remove subjective interpretation and lead to universally agreed truths. This vision foreshadows modern computing’s tendency to offload decision making onto mechanical procedures and automated systems. Today we routinely compute outcomes for people at massive scale in the form of mortgage approvals, bail recommendations, algorithmic rankings, and content curation. In a sense Leibniz’s dream has begun to come true, although it invites a difficult question: what do we trade away when we let calculation decide?