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Ralph Abraham

destroying it through the inculcation of false concepts and through the production of avoidance mechanisms connected with certain mathematical ideas.

It’s a very serious problem. One possible response would be to revise mathematical education so that, within the same system, one would try to provide teachers who are more highly trained. That could only make matters worse, you see, since the teachers are already highly mistrained. Many have already been taught to hate mathematics and so they can only teach hatred for mathematics. They don’t really have any idea what mathematics is. For them, it’s a knee-jerk response of this dark emotion, so retraining them more wouldn’t help. Rather than revision of the schools–which are full of false ideas and bad habits built into the field on a deep level–the most efficacious, practical solution would be the construction of a new educational system outside the usual channels of the school system. This is not too radical, as we have all been brought up to think of our real education as going on outside the school system. In school, for example we do have music classes, yet if parents want their children really to know music, they provide a separate teacher outside the school. We also have religious instruction and dance instruction outside the school–anything that you really want to learn is studied outside of the school. And so also it may be with mathematics.

I think that one practical solution to this challenge to create a school outside of school would be a new breed of learning machines based on computers, educational software, and digital video. Even programs like Hypercard on the Macintosh, for example, could provide alternative education that could be approached by individuals without teachers. So far, however, the creation of educational software has proved to be a very unrewarding activity for authors. And in spite of all different kinds of alternative funding agencies, nobody has seen this as a very important problem although the National Science Foundation, the American Mathematical Society and like organizations have convened conferences to discuss possible solutions of the crisis in mathematical education. The most promising alternative solution at this time has not been funded. And so there are very few existing alternatives for children now. Maybe after another generation or two there will be.

RMN: The principles of chaos theory and other mathematical ideas appear to echo in the myths and philosophies of some ancient cultures; the Greeks had a Goddess of Chaos, for example, and the I Ching is full of references to such ideas. What level of understanding do you think earlier civilizations had of these concepts and how was this expressed?

RALPH: Well, the repression of chaos began with the patriarchal takeover six thousand years ago. So to look at an example of a high culture accepting chaos as part of their mythological pantheon and in their arts and behavior, one has to go back before that takeover. And the most common example of such a culture is Minoan Crete. This culture was excavated by Sir Arthur Evans, and his reconstruction of the temples and religion, etc., have since been seriously questioned by archeologists. In short, there was a controversy as to what were their arts, their social patterns and so on.

A lot of things are known through mythology that are traced back to Crete. One thing that’s known from paintings is the dance with bulls. There were the Bacchic mysteries, derived from the Orphic, the Dionysian and so on. Following this backwards, like tracing roots or Ariadne’s thread, you come to a certain mythic kernel which would be associated with Minoan Crete. I wouldn’t say these are expressions of chaos. They might be, but there are so many differences between our culture and the Cretan culture. We know something about Dionysian ritual: the importance of music in ritual, the dichotomy of religious ritual into two types, outdoors on the open plain and indoors in a cave. The mystic revelation that came with Gaia sees the planet as an organism, and the plain as its surface. Gaia is very chaotic, so if you reject chaos, you reject Gaia. It goes together: the orphic trinity of Chaos, Gaia, and Eros.

That’s what I suggest to you to think about: Gaia as the Earth, the love of the planet, the integrity of life-forms; Chaos as the essence of life: more chaos is healthier; Eros as human behavior in resonance with Chaos and Gaia. It’s rumored that the Minoans had a very high degree of bisexual activity, licentious behavior and wild parties. This may be the quality of the genders in a partnership society as described by Riane Eisler.

RMN: Why do you think it was that later Western Culture tended to view chaos as an undesirable quality in nature?

RALPH: Well, that’s a very big question, and speculation can’t be taken too seriously, but I think that this has to do primarily with the

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