Connectionist Statistical Inference

The yin and yang of science are synthesis and analysis, which ebb and flow in harmony with the intellectual currents of the ages. In the twentieth century, we have witnessed the power and glory of analysis: matter has been subdivided into molecules, molecules into atoms, atoms into electrons and nuclei, nuclei into hadrons, hadrons into quarks and gluons,.... The onward march to the ultimately small, requiring probes with energies approaching those unleashed in the creation of the universe, has reached a stage where further progress cannot be made without the pooled resources of many nations. In this pragmatic post-postmodern era, the remoteness of the submicroscopic world and its apparent irrelevance to the problems of the “real” world make it doubtful that the vigorous thrust of analysis that has dominated 20th century physics can be maintained. It is to be expected, then, that the tide will turn as the millennium draws to a close and that the 21st century will see a new and sophisticated phase of synthesis. We, as physicists, have broken the world apart into its elemental components, and now we must learn how to put these parts back together into a functioning whole: we must learn how to rebuild the world. This is the theme of the new science of complex systems. The story of this science will be the story of many-body physicspar excellence:of how miraculous phenomena — life, thought, society — can arise out of the relationships and interactions of simple (or simplified) units or agents. We already see hints of the grandeur and excitement of this quest in the remarkable recent advances of dynamical systems theory (fractals, chaos,…) and of statistical physics (spin glasses, theories of learning,…). Quite obviously, it will be necessary to adopt a probabilistic view of nature in much of this work, and much can be gained by applying powerful techniques that already exist in mathematical statistics (but are little appreciated by physicists).

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