The Beginning of Infinity: Explanations That Transform the World

And the intuitive fact to which he was appealing was that although such hardness is always a negative factor when choosing among means to pursue an objective, when choosing the objective itself it can be a positive one, because we want to engage with projects that will involve creating new knowledge.

I specified robot space vehicles because all technological knowledge can eventually be implemented in automated devices. This is another reason that ‘one per cent inspiration and ninety-nine per cent perspiration’ is a misleading description of how progress happens: the ‘perspiration’ phase can be automated – just as the task of recognizing galaxie

That made us fairly unusual, but still not obviously creative: several other species have memes. But what they do not have is the means of improving them other than through random trial and error.

The other kind of problem, the pure kind, which has no analogue in biology, is that of creating beauty for its own sake – which includes creating improved criteria for beauty: new artistic standards or styles. This is the analogue of pure scientific research.

what made the difference was not the matter, but the knowledge that it encoded. In response to that knowledge, the substance of the moon reorganized itself in a new, increasingly extensive and complex way, and started to create an indefinitely long stream of ever-improving explanations. A beginning of infinity.

This suggests that he, and ancient Greek culture in general, may not have had the concept of an abstract number at all, so that, for them, numerals could refer only to objects

But in a static society that beginning of infinity never happens.

All knowledge growth is by incremental improvement, but in many fields there comes a point when one of the incremental improvements in a system of knowledge or technology causes a sudden increase in reach, making it a universal system in the relevant domain.

An optimistic civilization is open and not afraid to innovate, and is based on traditions of criticism. Its institutions keep improving, and the most important knowledge that they embody is knowledge of how to detect and eliminate errors.