The original problem that puzzled me was why innovations seemed to occur so slowly (and seemingly linearly) in the early few thousands of years of man (approximately 50,000 years ago), but have been accelerating ever since. Steve Weinberg has pointed out to me we mustn't underestimate the rate of innovation among pre-industrial cultures. I'll grant that early man (and his predecessors) was in fact probably a great deal more innovative than we normally give him credit for and that a visit to a good museum is a salutary experience. Nevertheless, I would still maintain that the pace was indeed extremely slow compared with today. If we get into arguments about this then we would have to start comparing the creativity of entirely different innovations from different cultures throughout history, and I think this would be an impossible, and essentially meaningless, task.
So the above must remain an assumption which satisfies me. There is one more basic assumption which I make. This is that it takes two to tango. It's all very well for one person to have a brilliant idea, but it doesn't get very far unless there's at least one other person to appreciate it. And this second person, I'd maintain, has to be as brilliant, or almost as brilliant, as the original innovator.
The first strand of my solution was given by Jane Jacobs in her various books, such as "Cities and the Wealth of Nations". She showed that, in historical times, all great surges of economic growth start in very small geographical areas, particularly cities. The reason for this, Jane Jacobs says, is that cities are a way of concentrating highly-talented people in one locality so that they synergise one another and and thus able to produce cascades of new ideas and innovations (in short, they "bisociate", although she didn't use that term).
However, what happened before cities? It is my view that during the days of early man, great innovations must have been invented (and re-invented) thousands and thousands of times all over the world in thousands and thousands of tribes, but they fell on stoney ground because there was no-one else in the tribe at the time who could appreciate it.
Let me do some simplistic arithmetic now with several more secondary assumptions. Let's assume that hunter-gatherer tribes never contained more than, say, 100 individuals at the most. Let's also assume that creative geniuses occur once every 1,000 people, and that people of almost that degree of creativity (sufficient to appreciate an innovation) also occur every 1,000 people. So, for an innovation to be thought-up AND adopted within a tribe, then the minimal chances against that happening randomly are 1,000 x 1,000 divided by 100 = 10,000 to 1. If we further assume that the "creative lifetime" of an individual is, say 20 years, then the chances of an innovation being discovered and adopted within a tribe at any one time are probably of the order of 500 to 1. Or, in other words, one innovation per 500 tribes per year.
If we are more realistic and say that an innovative-genius would need at least two other supporters in his tribe in order to pull it off politically as well as conceptually (if necessary taking over the leadership of the tribe and making sure of consolidating it for all time), then the rate of innovation works out at one per 500,000 tribes per year. We could further assume 100,000 tribes existing in Cro-Magnon times, thus giving one innovation every five years over the whole earth--or about 8,000 innovations in the whole history of man up to the establishment of the first cities.
Of course, these figures don't mean anything in absolute terms. Using different definitions, the number of significant innovations of early man could be as low as 800 or even as high as 80,000. But, intuitively, these relatively small finite numbers of innovations seems to agree with what actually happened (especially when compared to the number of innovations of even just the last 100 years).
However, once tribes started coalescing, or simply growing numerically, as they did when the first cities were established (at around 8,000 BC), then the odds in favour of innovation occurring would rise steeply. The larger the city (within reason--we're talking here of density of social intercourse, rather than just size), the more innovative it was likely to be. Also, as some cities gained reputations for being particularly innovative in one respect or other, then they would preferentially attract yet more people of genius or near-genius level from outlying areas or other more backward cities, thus multiplying the social intercourse of these individuals. The phenomenon of extensive travel by brilliant people (musicians, scientists, philosophers, etc) from city to city is very much a part of the history of the Middle Ages and the foundation of universities.
Thus, the above is the solution to my puzzle in simple terms. (In strictly bisociation terms, it was the conjunction of Jane Jacobs' thesis about cities and the size of pre-city tribes, that clinched the argument in my mind.)
In the next part, I will describe Koestler's Bisociation Theory of creativity, together with a practical methodology for carrying it out.