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John von Neumann's "The Mathematician" and Control Theory

已有 3870 次阅读 2009-7-24 13:42 |个人分类:Engineering Cybernetics|系统分类:观点评述| Theory, John, von, Neumann

Control theory nowadays can be well considered as a mathematical discipline.

The last two paragraphs of John von Neumann's The Mathematician is as follows [John von Neumann wrote The Mathematician which was published in Works of the Mind Vol. I no. 1 (University of Chicago Press, Chicago, 1947), 180-196. It has also been published in von Neumann's Collected Works.]:


"As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from "reality" it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely I'art pour I'art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical; when it shows signs of becoming baroque, then the danger signal is up. It would be easy to give examples, to trace specific evolutions into the baroque and the very high baroque, but this, again, would be too technical.


In any event, whenever this stage is reached, the only remedy seems to me to be the rejuvenating return to the source: the re-injection of more or less directly empirical ideas. I am convinced that this was a necessary condition to conserve the freshness and the vitality of the subject and that this will remain equally true in the future."

Control theory is not just a mathematical discipline, and it will not "show signs of becoming baroque". But it is already "at a great distance from its empirical source".

The remedy for mathematical discipline suggested by John von Neumann is "the re-injection of more or less directly empirical ideas". When it comes to control theory, I think the remedy would be "the rejuvenating return to the source", to control engineering.



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