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Ralph Abraham

historical accident, and for six thousand years people repressed chaos to the unconscious. So there has been a totally unnecessary gap where there should have been chaos theory. And the filling of this gap is really a big thing only because the gap was there. But after it’s filled, it is perfectly normal to have chaos models, and wheel models, and static models. It was very bizarre that among all these models there was such a huge gap. But now it’s filled, now we’re back to: “No big deal, aha, fine, so it’s chaotic.”

But dynamics is offering more. It’s offering bifurcation diagrams, catastrophe models. It’s offering fantastically good models for processes. And few of these models would actually be there on the shelf for our use in trying to understand the world around us if we denied the existence of chaos–because chaos is ubiquitous in process. You can’t model process very well if you’re in denial about the existence of chaos. You’re certainly not able to model any process which is full of chaos, and that’s practically all of them, most especially those involved with life, love and creativity. So we do have something important in dynamics, and chaos has an important role in a sort of double-negative sense. That’s what’s going on with dynamics.

As far as my work in it is concerned, I think it doesn’t matter very much. Some people think I shouldn’t waste my time at a computer terminal doing research on specific problems because my role is to go around saying what I just said.

DAVID: What are some of the problems that you see with the present state of American mathematical education and how do you think improvements could be made?

RALPH: Well, I would say a good thing to do with mathematical education in the United States or in the world today would be just to cancel it and start over again from scratch, two or three generations later. The whole thing is in a really dangerous plight. And I’ve been saying this for years and so have other people, but only recently has the problem risen to a scale of national prominence where even the president and the governor and everybody’s saying, “Well hey! our Gross national product might be threatened, because our people are no good at mathematics.”

So we have a serious situation. First of all, mathematics is akin to walking as a human experience; it’s just really easy. I mean it shouldn’t be easy, how can you tell somebody how to walk, you know? But people do find it easy and they naturally learn how to do it. They just watch, and by imitation they can do it. It’s the same with mathematics! It’s part of our heritage, all of us, to be genius at mathematics. It is a completely human activity. It involves the resonance between prototypical objects in the morphogenetic field and specific examples of similar forms in the field of nature, as they’re experienced by human beings through the doors of perception. And as life forms a resonant channel between these two fields, it’s just as natural as understanding anything, including walking, playing tennis, and so on. Mathematical knowledge is part of our human heritage.

Furthermore it’s essential to evolution. Where there’s no mathematical knowledge there can be no evolution, because evolution to a stable life form requires a kind of mathematical, sacred guidance. This can be understood in many different images, the least controversial one being that there would be a harmonious resonance between all of the components, parts, sub-systems and so on involved in the life process. Where there is an disharmonious resonance, or dissonance, there would be some kind of illness whether the organism is a snail, a human, a society, or the all and everything that we know by the name history. So for the harmonious resonance to be maintained during the process of our own growth, or social evolution, evolution requires mathematical understanding. You see the dissonance of the lack of mathematical understanding through the gross national product, or the number of wars, or the spread of AIDS, for example.

Another importance of chaos theory is in correcting a problem in mathematical education that has consisted, in part, of denial. People have been taught the non-existence of some of the essential mathematical forms, namely, chaotic forms. This kind of denial produces an educated adult somewhat less capable than an uneducated adult. So that education which functions in this way is not the same as no education. It’s worse, because it destroys intelligence, it destroys functionality, it destroys harmony with the resonance of the all and everything which is necessary for health. Our educational system, in short, is producing sickness and contributing to the global ecological problems on the planet by destroying the native intelligence that children have, the capability they have to understand the world around them in its complexity, in its chaos, in its resonance and harmony and love,

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