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Ralph Abraham

scientific knowledge, and an understanding of complex whole systems. Complex systems theory has replaced chaos theory on the fashion pages of the science newspapers of our day. And I think the fascination of intellectuals with complex systems theory is not going to be a short-lived flash in the pan. This is somehow the real thing. Our challenge now is the reintegration of the sciences after their dissolution in the Renaissance into an understanding of whole systems, particularly planetary systems, that is to say the hydrosphere, the lithosphere, the atmosphere, the biosphere and the noosphere.

Within the lower spheres, a new direction called global modeling is already under way. Global modeling tries to put together reductionist models people have made for the oceans, for atmospheric phenomena, and for solar radiation. Individual models made by reductionist scientists of these different areas–the oceanographers, the atmospheric chemists, the solar physicist–are being synthesized into one global model. This global synthesis requires two things. First of all it needs models for the separate components or organs of the planetary system to be made in a common strategy so that they can relate to each other. Secondly, it requires a wiring diagram to put them together. In the field of global modeling a tremendous synthesis is now taking place, including conferences on the wiring diagram, which will provide a global model of the geosphere.

For the sociosphere, we must start from scratch. We don’t yet have many specialists producing mathematical models for society, although there are a few outstanding pioneering first steps. There are for example the archaeologists and anthropologists worrying about the demise of the Mayan civilization in Central America in the fifteenth and sixteenth centuries, because it was so complex and there are so many hypotheses, and it was such a controversial question, they tried to resolve it by building mathematical models. There are now a number of competing complex dynamical models for the Mayan society, taking into account the food chain, the weather, the population, and the distance between ceremonial centers.

All these factors are built into different competing models. Then they run them and try to see which one wins the best relationship to the archaeological data. And thus a model system can be created, because Mayan civilization was relatively small. This pioneering first step might lead to similar models for larger societies–for ancient Greece, for example, or for the downfall of Rome, where many more factors and more people were involved. Navigation, naval trade, the effect of inventions like better clocks for navigating: all these things might be included in the model.

So in the future then, as global planet models become more successful, global social modeling will begin. Then individual components have to be modeled, such as the political and economic systems of individual nations, their interactions, and so on. They have to be made into a common strategy, so they can be connected together. And then one has to extrapolate from the Mayan models and gain wiring diagrams for these different component parts, including psychological and medical factors. In the reductionist physical sciences, we wilt only have to connect existing components together, following a diagram, to get global models. For the social sciences we’ll have to start from scratch.

We’re going to have to make models for the organs, do experiments in simulation with various wiring diagrams, compare with data, improve the component models, the global models, the data, and so on. After many circuits of this hermeneutical circle we might create a global social model. Then the global planet model and the global social model have to be connected together. There’s also the mythological and the spiritual dimension and the understanding of the world of the unconscious. In other words, the whole thing has to take place once again in the noosphere, and then that has to be connected up. Eventually, we hope to get some kind of model for understanding what–if any–are the effects of choices we could make upon our long-range future. This may never happen, but if it did, mathematics would be of use to Gaia in creating the future, through the direct, conscious interaction with the evolutionary process. This seems to be our challenge.

DAVID: Could you tell us how your travels in India and the experiences you had in a cave there have influenced your outlook on life and mathematics?

RALPH: What I had done that was respected by mathematicians in the way of frontier research work was ancient history by the time I went to India and lived in a cave. So, to answer your question, I should first of all identify what I’ve done since then that could be regarded as mathematical. I would say that the computer revolution has presented enormous opportunities to mathematics, to the

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