Ramble, Part 39: The Complexity of Numbers
Dec. 9th, 2007 02:53 pmLet me recap some things I discussed in the very first Ramble posts. The concept of "number" has two distinct and not entirely compatible origins: counting, which gives rise to the positive whole numbers, and measuring, from which are derived the positive real numbers. The two constructions have been melded together since time immemorial, though, with consequences which I've talked about at some length.
As time passed, various lines of mathematical study made it clear that the notion needed to be extended. First in India, then in the Muslim world and finally in Europe1, the notion of negative numbers arose; somewhere along the line, complex numbers put in an appearance. These extensions, though, were haphazard, tentative, and mistrusted. Around the turn of the nineteenth century, though, European mathematicians finally confronted these ideas, in a variety of ways, and the next two or three Rambles will discuss this.
( A Plane and Simple Idea )
1. I omit China from consideration; I don't know enough about Chinese mathematics, and in any case it followed a largely separate line of development from the rest of Eurasia.
Ramble Contents
As time passed, various lines of mathematical study made it clear that the notion needed to be extended. First in India, then in the Muslim world and finally in Europe1, the notion of negative numbers arose; somewhere along the line, complex numbers put in an appearance. These extensions, though, were haphazard, tentative, and mistrusted. Around the turn of the nineteenth century, though, European mathematicians finally confronted these ideas, in a variety of ways, and the next two or three Rambles will discuss this.
( A Plane and Simple Idea )
1. I omit China from consideration; I don't know enough about Chinese mathematics, and in any case it followed a largely separate line of development from the rest of Eurasia.
Ramble Contents