I recently listened to a radiolab podcast (from this past November!) that featured two authors: Steven Johnson (author of Where Good Ideas Come From) and Kevin Kelly (author of What Technology Wants). The thrust of the argument, that both authors defended, was that the things we make (from tools to gadgets to computers) are an extension of the evolutionary processes that make us. There is a lot to be gained from this perspective. However, the proposal that there is an individual-like willfulness in the technology, may go a bit too far. I say this not because the technology is seen as living (which I think it is) but because we understand so little about the source and nature of our own willfulness. Yet I found myself willing to allow it. Perhaps because an extreme like this is necessary to nudge the common perspective (which I think is wrong) away from the idea that individuals are discreet entities, fully aware of themselves, what they want, and what they are doing. The biological relatedness of ourselves and our equipment is very interesting and very plausible but we need to understand ‘the will’ better before we begin extending it to our equipment.
I’m more interested, however, in the fundamental idea that brings Steven Johnson to the table, and is very nicely rendered by him. His talk at a TED conference summarizes his perspective. There he says the following:
…an idea is a network on the most elemental level. I mean, this is what is happening inside your brain. A new idea is a new network of neurons firing in sync with each other inside your brain. It’s a new configuration that has never formed before. And the question is: how do you get your brain into environments where these new networks are going to be more likely to form? And it turns out that, in fact, the kind of network patterns of the outside world mimic a lot of the network patterns of the internal world of the human brain.
This sense that interior worlds and exterior ones mirror each other will inevitably provoke some useful new philosophical thoughts. And there are two other metaphors Johnson uses that I like very much because they match up with my own sense about things, including mathematics. They are: the slow hunch and the liquid network. In his book he refers to the concept of flow, that was coined by psychologist Mihaly Csikszentmihalyi, to describe the internal state of a productive mind. He says:
It’s a lovely metaphor precisely because it suggests the essential fluidity that good ideas often need……it is not the miraculous illumination of a sudden brainstorm. Rather, it is more the feeling of drifting along a stream, being carried in a clear direction, but still tossed in surprising ways by the eddies and whirls of moving water.
I particularly like this because it is about water, encouraging one to see ‘the thought’ in ‘the flesh’ again. It can also be used, quite easily, to characterize the development of ideas in mathematics’ history.
The slow hunch lines up with two things I like to think about. One, is the centuries of introspective labor that move mathematics forward. But the other is illustrated in the story he tells about Darwin. Johnson retells Darwin’s own account of how the basic algorithm of natural selection “kind of pops into his head.” But, Howard Gruber, who went back and looked at Darwin’s notebooks from the time, found that Darwin had the full theory, with apparent textbook clarity, for months and months before “his alleged epiphany.” What Johnson proposes is that Darwin had the idea but in some way was unable to fully think it. This not only illustrates the nature of “the slow hunch” but it demonstrates the spottiness of our awareness, the way our own thoughts can produce something that we don’t actually comprehend yet. This is a way that I have thought about mathematics when I’ve looked at its many conceptually extended notions – like the various extensions of our original number concept till they lead to the real number continuum (or the value of the complex number for that matter). I continue to think that the earlier notions are not built up into these extensions, but are instead already part of the larger ones when we first glimpse them. It may not be easy to defend this view, but trends in cognitive science, neuroscience, culture studies, even evolutionary psychology usually help me support it.
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