Marxism-Thaxis] Van Heijenoort's critique of Engels Hans G. Ehrbar ehrbar at lists.econ.utah.edu Thu Mar 3 12:21:52 MST 2005
Previous message: [Marxism-Thaxis] Van Heijenoort's critique of Engels Next message: [Marxism-Thaxis] Van Heijenoort's critique of Engels Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] -------------------------------------------------------------------------------- Abraham Robinson's nonstandard analysis adds more numbers, infinite numbers and infinitesimal numbers, to the numbers line. Just as Margaret Thatcher says that society does not exist, modern mainstream mathematics is based on the dogma that infinitesimals do not exist. Robinson showed, by contrast, that one can use infinitesimals without getting into mathematical contradictions. He demonstrated that mathematics becomes much more intuitive this way, not only its elementary proofs, but especially the deeper results. I understand that the so-called "renormalization problem" in physics, according to which certain physically relevant integrals become infinite and somehow have to be made finite again, has a much more satisfactory solution in nonstandard analysis than in standard analysis. The well-know logician Kurt Goedel said about Robinson's work: ``I think, in coming years it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.'' When I looked at Robinson I had the impression that he shares the following error with the ``standard'' mathematicians whom he criticizes: they consider numbers only in a static way, without allowing them to move. It would be beneficial to expand on the intuition of the inventors of differential calculus, who talked about ``fluxions,'' i.e., quantities in flux, in motion. Modern mathematicians even use arrows in their symbol for limits, but they are not calculating with moving quantities, only with static quantities. Robinson does not explicitly use moving quantities, he uses more static quantities, and many mathematicians criticize nonstandard mathematics because it simply has too many numbers. The Chinese manuscript you just sent to the list seems to have a much more dialectical view of nonstandard analysis than Robinson himself, and in addition it makes a bridge between Marx's Mathematical Manuscripts and nonstandard Analysis. This is very exciting News to me. Can we find out more about this? Hans. -- Hans G. Ehrbar http://www.econ.utah.edu/ehrbar ehrbar at economics.utah.edu Economics Department, University of Utah (801) 581 7797 (my office) 1645 Campus Center Dr., Rm 308 (801) 581 7481 (econ office) Salt Lake City UT 84112-9300 (801) 585 5649 (FAX) This message has been scanned for malware by SurfControl plc. www.surfcontrol.com _______________________________________________ Marxism-Thaxis mailing list Marxism-Thaxis@lists.econ.utah.edu To change your options or unsubscribe go to: http://lists.econ.utah.edu/mailman/listinfo/marxism-thaxis
