John Brockman's book **The Greatest Inventions of the Past 2,000 Years** is an interesting hodge-podge, often silly and occasionally thought-provoking. Dozens of semi-celebrity scientists and techno-pundits write a few paragraphs each on their nominations. Some play one-upmanship games. Some show off their knowledge of obscurities. Some are myopic in their focus on recent novelties. Among the better suggestions that are actual "inventions" (mostly):

- the printing press
- the plow
- the electric light
- flying machines
- computers
- guns
- contraceptives
- the Internet
- plumbing
- paper
- hay
- batteries
- atomic bombs

... or in a more philosophical direction:

- science
- the university
- social structures that enable inventions
- Indo-Arabic numbers
- the bit
- democracy and social justice
- cosmology
- evolution by natural selection
- calculus

... and perhaps tongue-in-cheek (or perhaps not?):

- the eraser
- classical music
- reading glasses
- board games
- nothing

Best of all, in my humble opinion: Lee Smolin's proposal * Mathematical Representation*, which I would simplify and call

The most important invention, I believe, was a mathematical idea: the notion of

representation—that one system of relationships, whether mathematical or physical, can be captured faithfully by another.The first full use of the idea of a representation was the analytic geometry of Descartes, which is based on the discovery of a precise relationship between two different kinds of mathematical objects—in this case, numbers and geometry. This correspondence made it possible to formulate general questions about geometrical figures in terms of numbers and functions; and when people had learned to answer these questions, they had invented the calculus. Now we come to understand that it is nothing other than the existence of such relationships between systems of relations that gives mathematics its real power. Many of the most important mathematical developments of the twentieth century—such as algebraic topology, differential geometry, representation theory, and algebraic geometry—and the most profound developments in theoretical physics—are based on the notion of a representation, which is the general term we use for a way to code one set of mathematical relationships in terms of another. There is even a branch of mathematics, called category theory, whose subject is the study of correspondences between different mathematical systems. According to some of its developers, mathematics is at its root

nothing butthe study of such relationships, and for many working mathematicians, category theory has replaced set theory as the language in which all mathematics is expressed....

Smolin goes on to discuss physics, computer science, information theory, and the possibility that mind itself can be understood, or at least studied, in terms of representations. Deep waters indeed ...

*(cf. online version of parts of the book, BuildingBookWeb, PublicDomain, ...)* - * ^z* - 2011-06-09