Calculus, Newton and Columbus

So I guess what I'm trying to say is that the solution to the problem isn't that you abandon rationality but that you expand the nature of rationality so that it's capable of coming up with a solution."

"I guess I don't know what you mean," Gennie says.

"Well, it's quite a bootstrap operation. It's analogous to the kind of hang-up Sir Isaac Newton had when he wanted to solve problems of instantaneous rates of change. It was unreasonable in his time to think of anything changing within a zero amount of time. Yet it's almost necessary mathematically to work with other zero quantities, such as points in space and time that no one thought were unreasonable at all, although there was no real difference. So what Newton did was say, in effect, `We're going to presume there's such a thing as instantaneous change, and see if we can find ways of determining what it is in various applications.' The result of this presumption is the branch of mathematics known as the calculus, which every engineer uses today. Newton invented a new form of reason. He expanded reason to handle infinitesimal changes and I think what is needed now is a similar expansion of reason to handle technological ugliness. The trouble is that the expansion has to be made at the roots, not at the branches, and that's what makes it hard to see.

"We're living in topsy-turvy times, and I think that what causes the topsy-turvy feeling is inadequacy of old forms of thought to deal with new experiences. I've heard it said that the only real learning results from hang-ups, where instead of expanding the branches of what you already know, you have to stop and drift laterally for a while until you come across something that allows you to expand the roots of what you already know. Everyone's familiar with that. I think the same thing occurs with whole civilizations when expansion's needed at the roots.

"You look back at the last three thousand years and with hindsight you think you see neat patterns and chains of cause and effect that have made things the way they are. But if you go back to original sources, the literature of any particular era, you find that these causes were never apparent at the time they were supposed to be operating. During periods of root expansion things have always looked as confused and topsy-turvy and purposeless as they do now. The whole Renaissance is supposed to have resulted from the topsy-turvy feeling caused by Columbus' discovery of a new world. It just shook people up. The topsy-turviness of that time is recorded everywhere. There was nothing in the flat-earth views of the Old and New Testaments that predicted it. Yet people couldn't deny it. The only way they could assimilate it was to abandon the entire medieval outlook and enter into a new expansion of reason.

"Columbus has become such a schoolbook stereotype it's almost impossible to imagine him as a living human being anymore. But if you really try to hold back your present knowledge about the consequences of his trip and project yourself into his situation, then sometimes you can begin to see that our present moon exploration must be like a tea party compared to what he went through. Moon exploration doesn't involve real root expansions of thought. We've no reason to doubt that existing forms of thought are adequate to handle it. It's really just a branch extension of what Columbus did. A really new exploration, one that would look to us today the way the world looked to Columbus, would have to be in an entirely new direction."