Re: Patriarchy: Re: What Matriarchy?

Eric Brunner (brunner@mandrake.think.com)
20 Aug 1996 12:47:53 GMT

William Edward Woody (woody@alumni.caltech.edu) wrote:
: brunner@mandrake.think.com (Eric Brunner) wrote:
: > Stephen Barnard (steve@megafauna.com) wrote:
: > : Godel's famous Incompleteness Theorem proves that any formal deductive
: > : system of sufficient power (at least the power of Peano arithmetic,
: > : which isn't that powerful) will be incomplete. That is, it will be
: > : possible to state theorems in that system that cannot be proven true or
: > : false. This is very closely related to Turing's Halting Problem, but I
: > : won't go into that.
: >
: > Pity. I'm sure that if anyone noticed that a fundamental theorem in
: > theoretical computer science was very closely related to a fundamental
: > theorem in foundations that there would be at least one paper in the
: > literature.
: >
: > A single cite please, refereed, in SIAM, or AMS, or the equivalents.

: Sorry, Eric, but here I have to step in and defend Stephen Banard.
: In my Theory of Computation class, we used Godel's theorem to prove
: the halting problem, and showed them equivalent. It was the only
: interesting part of the class (a class which pretty much reduced
: itself to writing state graphs for Turing machines by the end of the
: first trimester).

I hardly mind a useful pointer, as foundations is something I've only
the slightest passing familiarity with. My office was at one poin on
the 7th floor of Evans Hall (Berkeley) "logic land", but my interests
were non-constructionist and measure theoretic. I first mentioned Godel
as I find the common faith in the concreteness of mathematics akin to
any other faith, despite its central position in modernist empiricism.

Where the pseudo-mathematical content of this thread began was in the
all too common invocation of "Chaos Theory" as a mechanism to evade
causal mechanisms.

I do sympathize with your having to spend weeks writing TM state graphs.
I occasionally have to write FSM for the work I do, but I can't say that
it is mathematcially interesting, but interests do vary.

: [Or at least, my fuzzy little head *remembers* doing this. It's been
: a few years...but Godel certainly did show up. It was right about the
: same time I read the book "Godel, Echer, Bach," and hurt my poor brain.]

An odd work. Clearly the author had no familiarity with the self-symmetric
images of several groups outside of Europe. For the reader interested in
visual expressions of reflective symmetry, I recommend the pottery styles
of nearly any South Western group prior to contact, or the basketry styles
of quite a few groups in the Americas, from Eastern Algonquins to California
Pomos.

: > : Godel's theorem has very little to do with physical science, however,
: > : because physical science is based on inductive reasoning.
: >
: > Now that is an interesting statement. Here I thought that mathematics is
: > a representational system, a vocabulary, a construct of mind. Oh well, I
: > suppose that inductive reason must work for all of the (anumerate) exams
: > of (data) evidence, the interior logic of hypothetical frameworks, their
: > methods of test, not to mention all of the points at Schools Debates...

: Now here is where I stop.

: Somehow he's decided that 'induction' and 'deduction' aren't even
: kissing cousins. And as science uses 'induction' instead of 'deduction'
: to arrive at the original conclusions, Godel's theorem doesn't apply.

: A crock, to be sure.

: But an amusing crock. Though dancing naked around the fire invoking
: the Gods to come down from heaven and bless the dancers is certainly
: a lot more entertaining.

: - Bill

I'm sure he'll have an answer for this as well. Isn't it neat? All us
Injuns getting all Oxonian and everything? Well, I'm going to leave the
ain't-Injun-bait'n poster from NASA to his own devices, along with the
rest of the sci.anth virulently-above-boarders, my spouse and I are now
needing to center on something a bit more productive than educating the
Napikwans.

: --
: William Edward Woody | e-mail: woody@alumni.cco.caltech.edu
: In Phase Consulting | WWW: http://www.alumni.caltech.edu/~woody
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--

Kitakitamatsinohpowaw,

Eric Brunner