[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

*To*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Subject*: Re: [xmca] Where is thinking*From*: Andy Blunden <ablunden@mira.net>*Date*: Sat, 25 Apr 2009 11:24:32 +1000*Delivered-to*: xmca@weber.ucsd.edu*Domainkey-signature*: a=rsa-sha1; s=2007001; d=ucsd.edu; c=simple; q=dns; b=BjlYPTqufPFjd4Af1vWgMNjFm3NQhtHlg8lidm+uTYTuIbo1D5uU1m8CQaYOUoxWx wAA98x4WYMR4ZB/a53MUg==*In-reply-to*: <545862A6-9A98-43DC-9180-E09CE262AFA4@umich.edu>*List-archive*: <http://dss.ucsd.edu/mailman/private/xmca>*List-help*: <mailto:xmca-request@weber.ucsd.edu?subject=help>*List-id*: "eXtended Mind, Culture, Activity" <xmca.weber.ucsd.edu>*List-post*: <mailto:xmca@weber.ucsd.edu>*List-subscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=subscribe>*List-unsubscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=unsubscribe>*References*: <C6179756.1F6AE%packer@duq.edu> <545862A6-9A98-43DC-9180-E09CE262AFA4@umich.edu>*Reply-to*: ablunden@mira.net, "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Sender*: xmca-bounces@weber.ucsd.edu*User-agent*: Thunderbird 2.0.0.14 (Windows/20080421)

Andy Ed Wall wrote:

Martin and AndyThis is interesting (and an experience I had also with Shrodinger'swave equation for a hydrogen atom although I was lured away byeducation) as I am trying with some of my students (who, so theybelieve, have neither strong interests or abilities in mathematics -elementary school teachers presently or on the way) to develop a senseof beauty within mathematics. Part of this is because their students dohave sort of a sense and part of this is because I have been wonderingif I can crank it up a notch (not all the way to tensor algebra - smile)and also, partially negate, their, these teachers, abominablemathematical experiences.I have begun to have a little success as without coaching (and anhour or so thinking, talking, and working) they seem to be able todistinguish on their own between two or so acceptable proofs - onesthey, for the most part, understand and generate - as to the one thatsomehow is elegant (whatever that means although I happen to agree withtheir choice). Assuming that taste is cultural (although there are waysin which mathematics, one might say, isn't. I don't mean by thisPlatonic), I've been sort of bemused by the response. Anyway, it seemsthat Vygotsky would have been interested in 'intellectual' taste.Ed On Apr 24, 2009, at 5:20 PM, Martin Packer wrote: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, butthatis a matter of opinion. However, all of this has now become perhaps a bit off topic (smile) and you are correct that special relativity doesnot, at a certain level of understanding, require manipulation oftensors.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 theinterpretation thelogical positivists made, arguing that Einstein had exposed the fact Newtonian physics had hidden metaphysical assumptions, but that, with hisoperational definitions (Bridgman's term, but his ilustrationswere fromEinstein), 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 scientificpractice, each with their metaphysical assumptions. (Themetaphysics 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* 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_______________________________________________ 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

**Follow-Ups**:**RE: [xmca] Where is thinking***From:*"David H Kirshner" <dkirsh@lsu.edu>

**Re: [xmca] Where is thinking***From:*Ed Wall <ewall@umich.edu>

**References**:**Re: [xmca] Where is thinking***From:*Martin Packer <packer@duq.edu>

**Re: [xmca] Where is thinking***From:*Ed Wall <ewall@umich.edu>

- Prev by Date:
**Re: [xmca] Where is thinking** - Next by Date:
**RE: [xmca] Where is thinking** - Previous by thread:
**Re: [xmca] Where is thinking** - Next by thread:
**RE: [xmca] Where is thinking** - Index(es):