Read e-book online A century of mathematics in America. PDF

By Peter Duren

ISBN-10: 0821801309

ISBN-13: 9780821801307

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Then the particles get close to one another and interact. Finally, after a sufficient time there is again a group of free particles. But in the newly constructed theory the positing of such free particles is thought of as representing only the probabilities of correlations between appropriate particle detections. Now there is no longer any attempt to represent the processes intermediate between initial and final detections in terms of some quantum fields whose past and future limits in time are the fields corresponding to free particles.

These generalizations are not to be identified with the formal laws of our fundamental theories. Those formal laws are taken not to be genuinely descriptive of the real stuff of the world, for the reasons we have just noted. " Scientists use the laws as necessary, always in the context of their implicit, unformulated, and unformalizable practice determined by the open rules for correct application of these now instrumentalistically understood laws. I can make only a very few brief remarks about this account of science here.

And in each case the basic error of the standard theory has been alleged to be, in part, its illegitimate assumption that certain systems could be properly conceptualized as being isolated systems. (i) In standard versions of Newtonian mechanics we deal with the dynamics of the usual systems (tops, buckets of water, solar systems) by thinking of these systems as isolated from the remaining material systems of the universe. We treat these systems by applying the fundamental dynamical laws and invoking a range of forces.

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A century of mathematics in America. by Peter Duren


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