Re: Sectionals questions

acfraud <*no_reply_at_yahoogroups.com*> · Fri, 14 Feb 2003 18:58:04 -0000

It's about time the vaunted mathematical acumen of Kelly McKenzie were
unleashed upon the unsuspecting quizbowl world. While I do question to
some extent the ubiquity of the use of Zorn's lemma, it does have
notable algebraic importance (mmm, Noetherian rings). I further
question that there is any 'troublesome issue faced in modern
mathematics' associated with such undecidable propositions. Sure, some
constructivists may question the axiom of choice and work happily in
their little constructive world, but most people with any sense quite
happily accept the axiom of choice and move on with their lives. In my
experience, it's only in the social sciences that people have some
funny notion that undecidability has shaken the world of mathematics.
It's not as rampant as, say, the misinterpretation of "Heisenberg
uncertainty" in physics. But it's bad.

Of course, there are instances in which mathematicians remain unaware
of the deep philosophical and social influence of their work. Why not
more questions on Lacan's criticism of mathematics? It's clearly
brilliant:

"This diagram [the Möbius strip] can be considered the basis of a sort
of essential inscription at the origin, in the knot which constitutes
the subject. This goes much further than you may think at first,
because you can search for the sort of surface able to receive such
inscriptions. You can perhaps see that the sphere, that old symbol for
totality, is unsuitable. A torus, a Klein bottle, a cross-cut surface,
are able to receive such a cut. And this diversity is very important
as it explains many things about the structure of mental disease. If
one can symbolize the subject by this fundamental cut, in the same way
one can show that a cut on a torus corresponds to the neurotic
subject, and on a cross-cut surface to another sort of mental disease."

  -- Lacan, Jacques. 1970. Of structure as an inmixing of an otherness
prerequisite to any subject whatever. 

In fact, I'll get started on that six-part bonus, "Match the mental
disease to the 2-manifold with boundary", right now. I think its time
has come.

--- In quizbowl_at_yahoogroups.com, mac4731 <no_reply_at_y...> wrote:
> I hesitate to post too much about technical mathematics theorems 
> here, so feel free to ignore the rest of this, but a few things have 
> been mentioned that I think are worth addressing since they've 
> already been brought up. First of all, in my experience, the axiom of 
> choice has come up as an answer far more often than Zorn's lemma. In 
> fact, the only times I've heard Zorn come up is as a (overused) lead-
> in to the axiom of choice; I can't remember Zorn ever being an answer 
> in its own right (though maybe things have changed recently, and I 
> just haven't played on the right question sets to see this). There's 
> probably nothing wrong with this, since the axiom of choice version 
> is likely the one most easily understood by the non-math crowd. 
> However, as someone who is currently doing algebra research, I can 
> tell you that Zorn's lemma is the version of the axoim of choice idea 
> that is used almost ubiquitously in modern mathematics; I can't 
> recall ever using the axiom of choice version, but I have used Zorn's 
> lemma multiple times in the last week alone. I think both have their 
> place in quizbowl, being a major example of an undecidable 
> proposition (the same reason the continuum hypothesis comes up) and 
> one of the most troublesome issues faced in modern mathematics.
> 
> Kelly