Poincaré, Intuition and Chance

Henri Poincaré was an exacting mathematician, one of the first to successfully challenge Newtonian physics. He is the father of modern quantum mechanics.
We are not so much interested in his scientific contributions as in the philosophical stance of such a careful, logical thinker.

First, Poincaré was careful not to accept logical, formal proofs as truth or a working model of reality. He viewed logic as an organizing structure which could grow without feedback from the real world and lead to erroneous conclusions. This (idea) not only confronts some areas of mathematics, but also questions the very earliest philosophical basis for Western thinking. Everything, including that construct which we call 'logic', is questionable. Today's logic may be tomorrow's superstition.

I admire Poincaré for his lack of complacency and his ability to accept conflicting facts as a means to a larger truth. He does not seek to create a neat and orderly model of the universe, but a dynamic one which has room for inconsistencies and growth. A perfectly organized, logical system of thought must be a closed system which does not allow contact with the chaotic, ultimately unpredictable real world, so a logical system then is an inherently flawed and limited model of reality.

Second, Poincaré recognized that to rely entirely on logic was to accept restrictions not only in the accuracy of the model, but also to accept a limited number of solutions to a problem. The range of acceptable possibilities is always larger than the set produced by deductive reasoning.

These ideas are familiar to Zen and Eastern mystical thinking, but they seem rather peculiar in the writing of a Western mathematician. Dogmatic, deterministic thinking is the basis of Western religions, governments, and institutions. In order to protect his credibility, the pastor, the politician and the teacher often become the purveyors of absolute, and thus inaccurate, truths. Deterministic, linear thinking is the hallmark of the status quo and power brokers; chaos and free thinking are the purview of revolutionaries.

What does this have to do with design? Each design contains an inherent political statement about not only the designer, but also his expectations of his audience. Design can reflect the control of man over nature or it can reflect man in the context of an unpredictable universe. Design addresses not only aesthetic and utilitarian issues, but also issues of morality and world view. The progress of design theory, like the progress of scientific theories has profound political and philosophical implications. When the Nazis invaded northern Italy and Austria among the first of the intelligentsia to be eliminated were the printers and typographers.

Finally, Poincaré believed in the power of intuition. Intuition is seen as an unconscious or even mystical phenomena. This is a philosophical issue which one either accepts or does not accept. It is an issue separate and apart from the limitations of logic. Chance processes should not be confused with intuitive processes. They have different, though not necessarily conflicting, philosophical assumptions. The use of chance process assumes that the logical mind is not powerful enough to encompass all possibilities. The use of intuitive process assumes that the mind has certain abilities which cannot be defined by logical constructs.

I am willing to accept both of these assumptions in the context of this thesis. I think, however, it is important to distinguish between chance and intuition. If one does not want intuition to interfere in a chance process, then one must construct morphological systems which minimize human choice. If one wishes to express intuition, then mechanisms may be built into a morphological system which allow choice and preference.

The computer as a non-determinate system

The computer possesses some characteristics which make it uniquely suited for carrying out chance procedures. It can be precise in its ability to measure without accumulating errors as measures are based on one another (a draftsman must periodically cross-check his work and average the differences). Unlike a camera, it can replicate an image indefinitely, making changes between duplicates, with no degradation of resolution or color. It is also possible to replicate, modify and measure in an unstructured mode, and to allow random changes within very precise parameters.

A computer also allows us to trace our steps and go back to previous compositions, to look for solutions in branching patterns rather than linear process. The drawback to this is that it is still easy to rely on one successful solution and modify it almost indefinitely. This tendency has resulted in a lot of flashy computer graphics which look disturbingly similar to one another. The desire to go in new directions is not enough, intelligence and insight are not enough, one must eventually look for those new directions in some place other than our own limited intellects or the mass culture. We have compared three basic systems for creative problem-solving: logic, intuition, and chance. A proper problem-solving process should have room for all three components to function and a means for controlling those functions.


copyright 2006, M. Blair Ligon, all rights reserved worldwide.