New York Times on the Web Forums
Resource
Area for Forum Hosts and Moderators
Technology has always found its greatest consumer in a
nation's war and defense efforts. Since the last attempts at a
"Star Wars" defense system, has technology changed
considerably enough to make the latest Missile Defense
initiatives more successful? Can such an application of
science be successful? Is a militarized space inevitable,
necessary or impossible?
Read Debates, a new
Web-only feature culled from Readers' Opinions, published
every Thursday.
(4822 previous messages)
rshow55
- 09:32am Oct 12, 2002 EST (#
4823 of 17697) Can we do a better job of finding
truth? YES. Click "rshow55" for some things Lchic and I have
done and worked for on this thread.
Technical problems (handled by real people, in real
socio-technical systems) have human limitations, too. I've now
taken steps where one can argue that I ought to be jailed
(though I think Casey would argue otherwise)
Psychwarfare #330-338 http://talk.guardian.co.uk/WebX?14@@.ee7a163/352
- - and those steps seem to have been noticed. It feels to me
like a good time to set out reasons - intellectual reasons -
why I had a hard time meeting Casey's "try-this-first" set of
instructions - that I should make a purely technical case in
the academic community - and communicate other matters
standing from there.
I couldn't make that case, in part, because of
inflexibilities built into my system, and weaknesses of my
own. But in large part, the problem was one of paradigm
conflict and many of the problems involved there have been
clarified - with help from the TIMES - and especially Dawn
Riley.
The statement of a technical point here -- 1566 rshow55
4/20/02 4:07pm - - is much sharper than anything Steve
Kline and I had - because we hadn't had contact with Dawn
Riley's distinguished mind.
Some of the reasons for the paradigm conflict on the
connection between the concrete world and abstract math have
been basic ones. Here is part of a draft that I was preparing
for my thesis advisor - before an unbelievably disastrous trip
to Washington DC in September 2000 derailed a great deal.
rshow55
- 09:34am Oct 12, 2002 EST (#
4824 of 17697) Can we do a better job of finding
truth? YES. Click "rshow55" for some things Lchic and I have
done and worked for on this thread.
"I'm more clear now than Steve and I were in 1997 on the
nonaxiomatic nature of the world of measurement that S-K fits
into. Our work does not pertain to pure math, based on the
conventional axioms alone, but requires some additional
assumptions, which some might call axiomatic, and some might
call acts of faith. Here are the formal “acts of faith” on
which our derivation logically rests:
. I assume that parts of the physical
world are representable by mathematics.
. I assume that there are arithmetical
and dimensional rules that correctly represent these
physical things.
. I assume that the parts of the physical
world that can be described by correctly stated rules are
self consistent, so that values that should be identical
according to different computational sequences are
identical.
. I assume that a valid system of
physical description can represent any combined effects that
occur by a permitted construction within the system.
"These assumptions may or may not seem self-evident. I
personally feel that they are self-evident. Self evident or
not, these assumptions are external to pure math as it is now
practiced in the academy. Steve and I assumed these things
implicitly, and I believe that some classical mathematical
physicists, notably J.C. Maxwell, assumed something like these
things.
"We also assumed that the world, rightly understood, was
a consistent place - that the right derivations, based on the
right assumptions, would in fact fit the evidence of correctly
conducted and relevant experiments. This assumption is widely
held, though logically baseless, and many feel it is plausible
on Bayesian grounds. Scientists often act as if they believe
this assumption.
"We also chose to give priority to our basic
assumptions, even if the logic of our assumptions required us
to discard or modify notations or conventions. . We assumed
that that long established notations in mathematical and
mathematical physics practice, including very old ones, could
include hidden errors or oversimplifications. We assumed that
when notations and procedures did not fit the requirements of
our “acts of faith” above, we could question those notations
and procedures. We also assumed that, after consideration, we
could change them.
"Whether such changes are right or wrong in positive
terms, they are socially awkward, and we knew it. To question
standard notations, especially longstanding ones, is to
question reflexes that are organic parts of the people who use
these notations.
"Lipman Bers expressed some core facts about math, that
make the social and conceptual difficulty of challenging
notation clear:
" “What is the strength of mathematics?
What makes mathematics possible? It is symbolic reasoning.
It is like “canned thought.” You have understood something
once. You encode it, and then go on using it without each
time having to think about it.”
"What if the “something” that is “understood” is wrongly
or incompletely encoded? What if that canned encoding was done
hudreds of years ago, so that no one alive can easily think
about the “something” that was encoded, apart from the
symbolic encoding itself? Problems with such canned encodings
ought not to be inconceivable, and should be discussable and
testable. For some purposes, the discussions and testing may
be best done with people involved who are not committed to the
canned encoding under discussion.
"Encodings and usages that are sanctified by the passage
of time may not have been carefully done in the first place.
Cajori quotes Augustus de Morgan as follows:
“ Mathematical notation, like language,
has grown up without much looking to, at the dictates of
convenience and with the sanction of the majority.”
(12873 following messages)
New York Times on the Web Forums
Resource
Area for Forum Hosts and Moderators Missile Defense
|