A year or two ago I bought a book at the Strand called Investigations. (The author is Stuart Kauffman, who works with Lee Smolin, Roger Penrose, and Fotini Markopoulou-Kalamara on Loop Quantum Gravity.) I often don't know whether a book is good or not while I am reading it. The way you can tell if a book is good is if it comes into your mind for months or years later. This was one of those good ones.
The main idea that struck me from it was: in creative or inventive thought, and in evolutionary development, the space of possibilities can't be defined beforehand.
Evolutionary biologists talk about the "fitness landscape." The idea is that there is some high-dimensional space of possibilities (leg length, tooth sharpness, number of toes, are three of the axes, perhaps) with some regions marked as high fitness and others as low fitness. The organism that is evolving can be pictured as moving through this space blindly, but responding to its local conditions like a ball rolling downhill, so that it ends up in areas of high fitness.
But when you try to actually create such a space (for a computer simulation, for example) you find that you can only label axes that already exist in nature. But nature doesn't just recombine old forms to create new species; instead, entirely new features appear. What seemed a minor, irrelevent detail in any previous species is the critical key to a new ability or structure.
This is exactly like Hofstadter's point about Metafont: you can't capture the space of all possible typefaces with a predefined set of parameters. Instead people invent new parameters with each new font.
(Those who studied math in college are likely to object that technically you could define a space large enough to contain all the possibilities-- for example, the space of 100 x 100 pixel squares contains essentially all fonts. But this kind of characterization isn't useful due to the sheer number of possibilities and the fact that so few of them actually are typefaces.)
This also applies to the space of useful inventions. There's no way it can be precharacterized. It can only be represented as a growing, branching tree.