莱布尼茨二进制算数与二进制机械计算器——再论二进制发明权之争

Leibniz's Binary System and Binary Mechanical Calculator: Response to the Argument of the Right of Priority of Binary System

莱布尼茨在1679年系统发明了二进制,并设计了一款二进制机械计算器。莱氏二进制,本质上是一种组合数,反映了用一种元素组合成整个世界的哲学思想。从发明组合数,到创立二进制,再到提出单子论,在莱氏那里具有逻辑必然性。在1666年发明组合数的时候,莱氏就已经发现了2的幂运算与组合度的密切关系,为发明二进制奠定了理论基础;魏格尔四进制的发明,以及自身的机械论哲学转向,构成了莱氏发明二进制的条件。莱氏二进制计算器的设计理念,直观地反映出了二进制作为组合数的本质,以及二进制与单子论的关系。因此,从"内史"的角度来看,二进制是莱氏的系统性发明,是其思想的必然延续和有机组成部分,不能简单理解为一种计数方式。

On May 15,1679,in a three pages manuscript,Leibniz invented the Binary System and a kind of Binary Calculator.Actually,in Leibniz’s view,the Binary System is a kind of Combinatorial Number,which was invented by Leibniz in 1666.For Leibniz,there is a logical necessity from inventing the Combinatorial Number,to inventing the Binary System,and to proposing the Monads Theory.In 1666,Leibniz had found that there was a mysterious relationship between Complexions and the Exponentiation of Number 2,but at that time,Leibniz didn’t understand this kind of relationship.After entirely changed his philosophy into Mechanical Philosophy,and inspired by Weigel’s Tetractyn,Leibniz invented the Binary System.The design concept of Leibniz’s Binary Mechanical Calculator,which has been rebuilt by modern engineers,directly shows the nature of Binary System as Combinatorial Number,and the relationship between Binary System and Monads Theory.Therefore,in the inner-view,Binary System is the logical development and the organic part of Leibniz’s thoughts.