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Re: [xmca] Where is thinking
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.
>>>> _______________________________________________
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>>>
>>> --
>>> ------------------------------------------------------------------------
>>> 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/>.
>>>
>>> _______________________________________________
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>>>
>>>
>>
>>
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