johnreed Posted June 30, 2012 Posted June 30, 2012 Plain English Physics 101-1 Excerpts from Published under new title Modified Monday, May 21, 2012 johnlawrencereed jr Excerpt on Ptolemy: Where Wigner noted the "uncanny" usefulness of mathematics, I noted that the usefulness remains, regardless of the veracity of our a priori assumptions. As an example, first consider the Ptolemaic, Earth centered model of the solar system. The sole quantitative connection to the real universe in this "still useful" model is the efficient, least action, time-space property, attendant to each of the otherwise contrived, circular, cyclic and epi-cyclic orbits. A circle is an efficient enclosure of area. Equal arc lengths will radially enclose equal areas of the circle. This is an efficient area enclosing property of the circle itself. It is consistent with Kepler's law of areas which law would be redundant in the case of perfectly circular uniform orbits. With the circle it is the circumference arc and its radially enclosed area. With the orbit it is the time interval of the orbit trajectory and its radially enclosed area. The law of areas is a function involving time and space. It is a least action function. So Ptolemy constructed several imaginary mathematical least action consistent circles[*] upon circles to match the time space function of the real orbits. The least action consistent aspect of the mathematics in describing the least action consistent aspects of stable universe systems, assured his success. Imagine it otherwise. The Ptolemaic model shows that accurate mathematical predictions serve us to a limited operational extent, but provide no absolute basis for an accurate conceptual view. Viewed through the clearer lens of hindsight here, we can see that our conceptual questions must be framed correctly, prior to accepting a physical reality for the mathematical model. Must we frame our conceptual questions any less correctly today? johnreed
John Cuthber Posted July 2, 2012 Posted July 2, 2012 Weird. I wonder what he thinks of First consider the Earth-centered model of the solar system, which Ptolemy suggested, as an example,
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