Greek Numbers
摘要
The ancient Greeks inherited many of their numerical concepts and methods from the Babylonians and Egyptians. They also had their own peculiar notions about numbers. They thought that numbers were somehow real, the Platonic realism that many mathematicians continue to accept today. They also didn’t think that one, two, or zero were numbers, for reasons having to do with metaphysical philosophy: one was the unity, two was the dyad, and zero represented nonbeing, notions that wouldn’t change until fairly recent times. The ancient Greek philosophers were also terrified by numbers that failed to fulfill their assigned metaphysical role; in the first millennium BCE, the mathematician Hippasus is said to have drowned himself over the irrationality of numbers like pi and the square root of two. The Greeks used several systems of numerical notations, including one comparable to the Roman numerals. They also thought numbers differed according to what they counted, so the ten used to count horses differed from the ten used to count dogs. This notion is similar to the idea that numbers are either concrete, connected to the things they count, or abstract, related only to other numbers.