Any way, it's a long time ago for me too! Andye^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:
AndyIt 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 saythat Einstein was avoiding metaphysics. That was the interpretation the logical positivists made, arguing that Einstein had exposed the factNewtonian physics had hidden metaphysical assumptions, but that, with hisoperational definitions (Bridgman's term, but his ilustrations were fromEinstein), Einstein had finally showed that science was a purely logical (or if you prefer practical) activity, free from metaphysics. What a mess thathas 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 scientificpractice, each with their metaphysical assumptions. (The metaphysics ofEinsteinian 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* asmetaphysics 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
-- ------------------------------------------------------------------------ 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