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As an undergraduate I was in a class in which we solved Shrodinger's wave equation for a hydrogen atom (the simplest case, and I think the only salvable one) using tensor notation. I can confirm that it is beautiful mathematics, and it almost prevented me from becoming a psychologist. Martin On 4/23/09 10:32 PM, "Andy Blunden" <ablunden@mira.net> wrote: > :) Yes, Ed, I found tensor calculus a genuine thing of > beauty. After learning about e^ip=-1 a couple of years > earlier only ijGlm=0 could top it (excuse lack of sub- and > superscripts and Greek letters). But it is not so much the > mathematics that is at issue I think, when someone says > "relativity is simple" but just how the mathematics is > related to experience. Einstein himself wrote an > introduction to the Special Theory which does the whole > thing up to the variation of length with relative speed, > without using mathematics. But tensors are a mathematics > whose object is not physical relations, but differential > equations. That's tricky! > > Any way, it's a long time ago for me too! > > Andy > > > > e^ip means the base of natural logatrithms raised to the > power of the square root of minus one times the ratio of the > diameter to the circumference of a circle, and it = -1 > Beautiful. > In ijGlm , G is a tensor of space-time, ij are subscripts > and lm are superscripts. But I may have that wrong! > > Ed Wall wrote: >> Andy >> >> It has been quite awhile since I have taught a course in >> special/general relativity (about 20 years); however, the tensor >> calculus is, I thought then, a nice way to go about it and brings some >> things to light that are important on the way to general relativity. >> Tensor algebra is actually somewhat straightforward by the way, but that >> is a matter of opinion. However, all of this has now become perhaps a >> bit off topic (smile) and you are correct that special relativity does >> not, at a certain level of understanding, require manipulation of tensors. >> >> Ed >> >> On Apr 22, 2009, at 10:40 PM, Andy Blunden wrote: >> >>> Yes and No. I was using the word "metaphysics" in the way Pragmatists >>> use it. Strictly speaking, of course, *all* thinking contains >>> metaphysical assumptions. So in that you and Kuhn are right and I was >>> wrong. >>> >>> Perhaps I could stop using the word Metaphysics to mean the >>> reification of thought forms into independently existing substances, >>> and others stop using the word Ontology to refer to personal identity >>> formation? :) >>> >>> But I disagree with you about your Kantian conclusion that "science is >>> a purely logical". It was this Kantian belief (along with Euclid) that >>> was overthrown by Einstein. The Logical positivists were wrong of >>> course, because they interpreted the subject in Kantian terms, as an >>> individual person and their private psyche having direct access to >>> eternal reason. >>> >>> Interstingly Einstein disagreed with Bridgman. Einstein said that >>> within the context of a consistent theory, not every entity in the >>> theory has to be subject to an operational definition. Einstein right, >>> Bridgman wrong. But I think Bridgman got the right idea nonetheless. >>> >>> Where Hegel and you are wrong, I believe, is the presumption that we >>> are at the end of history (neither of you claim that of course, but it >>> is a valid implication in both cases.) If the nature of time and space >>> can be deduced completely from a critique of the cultural practices at >>> any given time, e.g. in 1807 before the Michaelson-Morley experiment >>> was possible, then obviously the practices whose critique will allow >>> the Special Theory of Relativity to be deduced "by logic" i.e., >>> critique of practice, are impossible. If "science is a purely logical" >>> then that presumes that no further significant developments in social >>> practices (such as the Michelson-Morlet experiment) can be made. >>> >>> BTW Ed, I think we have to treat the Special Theory and the General >>> Theory differently. There is absolutely nothing simple about the >>> general theory and its tensor calculus! >>> >>> Andy >>> >>> Martin Packer wrote: >>>> Oh Andy, I'm going to have to disagree with you once again! >>>> At least, I'm going to disagree if by your statement here you mean to >>>> say >>>> that Einstein was avoiding metaphysics. That was the interpretation the >>>> logical positivists made, arguing that Einstein had exposed the fact >>>> Newtonian physics had hidden metaphysical assumptions, but that, with >>>> his >>>> operational definitions (Bridgman's term, but his ilustrations were from >>>> Einstein), Einstein had finally showed that science was a purely >>>> logical (or >>>> if you prefer practical) activity, free from metaphysics. What a mess >>>> that >>>> has led us into! >>>> I'm on Kuhn's side on this issue: every scientific paradigm has >>>> metaphysical >>>> assumptions embedded in its practices. So we don't have metaphysics >>>> on the >>>> one hand and practice on the other. We have alternative kinds of >>>> scientific >>>> practice, each with their metaphysical assumptions. (The metaphysics of >>>> Einsteinian physics include the assumption that space is something >>>> that can >>>> be curved by a mass, for example.) The merits of each of the >>>> alternatives is >>>> what scientists spend their careers hotly debating. Even what >>>> *counts* as >>>> metaphysics is different from one paradigm to another. >>>> But that's probably what you meant! :) >>>> Martin >>>> On 4/22/09 8:17 PM, "Andy Blunden" <ablunden@mira.net> wrote: >>>>> All Einstein did was, instead of regarding time and space as >>>>> metaphysical entities existing independently of human >>>>> practice, he closely examined the practice of measuring time >>>>> and distance. That's all. >>>> _______________________________________________ >>>> xmca mailing list >>>> xmca@weber.ucsd.edu >>>> http://dss.ucsd.edu/mailman/listinfo/xmca >>> >>> -- >>> ------------------------------------------------------------------------ >>> Andy Blunden http://home.mira.net/~andy/ >>> Hegel's Logic with a Foreword by Andy Blunden: >>> From Erythrós Press and Media <http://www.erythrospress.com/>. >>> >>> _______________________________________________ >>> xmca mailing list >>> xmca@weber.ucsd.edu >>> http://dss.ucsd.edu/mailman/listinfo/xmca >>> >>> >> >> _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca