The Prehistory of Computing, Part II
4 days ago
- #Mechanical Calculators
- #Computing History
- #Approximation Theory
- Pascal invented the Pascaline in 1642, the first mechanical calculator capable of addition and subtraction, featuring the world's first successful mechanical carry mechanism.
- Leibniz built the first 4-operation calculator, the stepped reckoner, using a stepped drum (Leibniz wheel) for multiplication and division, though it never saw practical adoption in his lifetime.
- Leibniz's theoretical contributions include the concept of a universal formal language (Characteristica universalis), influencing Boolean algebra, set theory, and formal logic.
- Chebyshev's approximation theory showed that polynomials can uniformly approximate continuous functions, leading to practical algorithms like Remez's for polynomial approximation in computing.
- Babbage's Difference Engine automated polynomial evaluation using finite differences, enabling efficient table generation for polynomial functions.
- Despite mechanical computing's limitations, pioneers like Leibniz and Babbage laid the groundwork for modern computing, which eventually transitioned to digital with transistors and CMOS technology.