Download PDF by Miller G. A.: Felix Klein and the History of Modern Mathematics

By Miller G. A.

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Example text

And just so long as we retain one trace of ethical discrimination, the use of great powers for base purposes will constitute the full moral equivalent of Sorcery and Simony. As long as automata can be made, whether in [ 53 ] the metal or merely in principle, the study of their making and their theory is a legitimate phase of human curiosity, and human intelligence is stultified when man sets fixed bounds to his curiosity. Yet there are aspects of the motives to automatization that go beyond a legitimate curiosity and are sinful in themselves.

The product of their outputs, [43] averaged over the entire shot-effect distribution of their common input, will be the coefficients of the white box i n the development of the black box as a sum of all the white boxes with appropriate coefficients. To obtain this is seemingly impossible, as it would appear to involve the study of the system Eor the entire statistical range of shot-effect inputs. However, there is an important accident that enables us to circumvent this difficulty. There is a theorem i n mathematical physics which enables us in certain cases to replace averages over distributions with time averages, not in every single case, but in a set of cases with the probability 1.

I n this process, the feedback goes through us, and we can turn back before it is too late. I f the feedback is built into a machine that cannot be inspected until the final goal is attained, the possibilities for catastrophe are greatly increased. I should very much hate to ride on the first trial of an automobile regulated by photoelectric feedback devices, unless there were somewhere a handle by which I could take over control if I found myself driving smack into a tree.

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Felix Klein and the History of Modern Mathematics by Miller G. A.

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