4.3 Asia — Parallel Paths

Parallel Paths: How Asia Discovered the Same Truths as the West — and Was ForgottenGreat discoveries never occur just once. They emerge simultaneously, in places that know nothing of each other.In Japan's closed Edo period, Seki Takakazu discovered infinitesimal calculus independently of Newton. He presented the concept of the determinant ten years before Leibniz. His disciple Takebe Katahiro obtained the expansion of the arc sine fifteen years before Euler. They were nicknamed "Japanese Newtons" — as if Newton were the reference and they the imitation, when in fact they were walking on parallel paths toward the same summits.In 1868, the Meiji Restoration opened Japan. Reformers looked at wasan — two and a half centuries of mathematical tradition — and saw only a backward system. Within decades, this treasure was swept away in favor of Western mathematics.Akira Nakashima formulated switching circuit theory between 1934 and 1936. Shannon published the same discovery in 1938, cited him — and became a legend. Nakashima remained unknown.In colonial India, Srinivasa Ramanujan, largely self-taught, proved more than three thousand theorems that Western mathematicians took decades to understand. Prasanta Chandra Mahalanobis invented in 1930 the distance that bears his name — still used every day in machine learning.Asia teaches us that intelligence has never had only one form. That paths to truth are multiple. That we have lost other routes, other ways of arriving at the same results.Parallel paths still exist. We need only look for them.