Telluride Aug. 1995

I'm listening to the radio in the car. Rush Limbaugh was talking about a baseball player and a record. In this context, he explained the difference between a conservative and a liberal. The conservative, he said, operates on the individual principal. The liberal operates on a cooperative principal. The neuronets of computer science are conservative. They operate like the post office. Messages are sent from one node to another over a connection. Neuronets are liberal. Peramecium can't swim without cooperation of the flagella. We can't walk without coordination of the limbs. We can't communicate without waving our hands. The cooperation, the liberal function, is the basic mechanism of morphogenesis. Another M. Mushroom. Music. Mind. Mathematics. Morphogenesis. What must happen in neurometama brain, or a mycelial mat is to have an idea, a sequence of ideas, and an idea involves cooperation of all the neurons and all the links in a space-time pattern which itself is the idea. 

In the studies of smell, Walter Friedman discovered that smell, as experienced by the olafactory bulb, by a large neural net, had a space-time pattern. Different space-time patterns represent different smells. And the mapping from smells to space-time patterns is not a universal law of nature. Each individual mind creates its own map and modifies the map as necessary. 

How to learn this cooperation? How to recognize our space-time patterns? Certainly this is where music comes in. Music is our highest teaching of skillful coordination and complicated cooperation of many different elements operating on different levels. The musical metaphor applies particularly to the sonic field, to space-time patterns, vibrations, sound waves, vibrations in an elastic medium. The brain is a neural net embedded in an elastic medium and certainly sound waves play a role in the coordination of the space-time pattern which is in an idea in our mind. 

Other possible fields useful for coordination, especially across larger distances, are electromagnetic fields, gravitational fields, all of the physical fields, and other fields unknown to science perhaps. Mental fields, immaterial fields, morphogenetic fields of Rupert Sheldrake, fields of infinite intelligence of the Sanskrit classics. These are models for a cognitive strategy to understand thought, understand morphogenesis, the emergence of form in a space-time pattern, the main subject of mathematics. 

We've tried to learn about space-time patterns in nature since the advent of chaos theory. Space-time patterns studied before chaos theory are new space-time patterns and we don't see them very much in nature. If you drop a pebble in a swimming pool you see smooth patterns, classical vibrational patterns understood by Greek science and by Pythagorus. By nature we see chaotic patterns and it turns out that chaotic patterns have resonant behavior. That means that one chaotic space-time pattern can speak to another one across space and time through an elastic medium or the electromagnetic field. These are the patterns which are seen to be fundamental throughout nature, in the galaxies, in the ecosystems, in the human brain, and, I'm sure, in the mycelial mat. 

We've tried to study these new patterns, space-time patterns of smooth cooperation of chaotic agents, by using super computers and large workstations to visualize through computer graphics the actual space-time patterns generated by these chaotic computer models while we vary the strength of the connection between the nodes in a way that would imitate, for example, the learning process ** described in the human brain. These are the space-time patterns of the messages--a letter is sent from one place to another, and similar letters are sent from many stations to many recipients, according to a certain space-time pattern. When we see these computer generated space-time patterns of chaotic cooperation on the computer screen, we recognize them. We've seen them in our dreams. We've seen them in our telescopes. We have seen them in our microscopes. The universal language of space-time pattern is the subject matter of the mathematics of tomorrow.