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Re: A Point on Understanding
Posted:
Dec 28, 2012 12:15 PM
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On Fri, Dec 28, 2012 at 7:30 AM, Paul Tanner <upprho@gmail.com> wrote:
<< SNIP >>
> If p is actually a proved statement, a theorem, then person B is
> simply showing himself or herself to be a fact-denier - and if he or
> she persists in such fact-denial, to be a crackpot.
>
That's quite an illuminating statement in light of your earlier claims
to have "proved" this and that about the sloppy world of voting and
health care. In your model, the statements you put forth are "as
theorems" (truths of the same caliber) and those who oppose you in
argument are in fact fact-denying crackpots and/or slobs.
This attitude might well work to your advantage in debate, if you're
able to communicate your utter disregard for the opponent's view in a
way that makes you seem professorial. Keep to the tone of the "expert
witness" but don't let the jury think you arrogant, as if the trial's
outcome were more up to you than them (or maybe it's no jury and all
judges -- in NFL debate we lean towards tribunals in the higher
"courts" with even more judges at the championship level).
> The problem is, if a person does not first do the careful work needed
> to prove that a mathematical result is actually incorrect, then that
> person's claim that that result is incorrect - along with his or her
> sloppy argument - shows himself or herself to be mathematically inept
> and ignorant and a sloppy thinker.
>
You're aware from literature classes and/or from life experience that
some kind of tension builds suspense and serves as a plot driver. We
want to see how things turn out. A "gripping page turner" (as the New
York Times might describe some book) is one that keeps us motivated to
move through its plot twists, its state changes and transformations.
In setting up this debate between two views, one that the limit is
zero, and the other that the limit is an iotum (so long as there's
curvature), I provide a motive (like a motor) to break through the ice
of:
(a) Descartes' Deficit (rarely if ever taught in US elementary
schools, probably taught in all the better Swedish ones **)
(b) an algorithm for generating high frequency icosa-spheres (like at
EPCOT -- though that's triacontahedron based)
(c) vocabulary words like "icosa-sphere" and "frequency" (important in
architecture, geometry)
(d) lots of standard notation used for talking about limits (a boost
if you're delving into calculus, one of the maths many islands /
locales / namespaces).
Student listeners to this debate are likely to pick up quite a bit of
shop talk, all the better if they see peers using such, and not just
those already steeped in this material.
In the better classrooms (e.g. in Sweden), a teacher will have
students stand in front and conduct parts of the lesson.
Naturally this requires a classroom in which there's respect and
decorum. It's still controversial to place classroom surveillance
cameras. &&
"To contradict" is to speak in opposition to. In making this an
humanities event that uses math content, we're having this not be your
turf. You're not here to serve the state on the punch clock. You
wandered in as a member of the audience. The mathematical meaning of
"contradiction" is not front row. p & ~p is close enough to what A
and B are doing. The judges need the audience to remain politely
silent, or you may rap on the chair with your knuckle to indicate you
think a point was made well.
> Again: Students need to be taught that in mathematics, they ought not
> throw the term "contradiction" around casually - it's just plain
> sloppy. To prove a contradiction one does not merely negate a given
> statement with a sloppy argument.
They need to become masters of their mother tongue, including the
sloppy uses of terms, such as "voting" and "health care", which have
no existence in strongly logical mathematics (except in science
fiction and fantasy).
To have debaters mine mathematics for a resolution is commendable and
both the Aff and the Neg did a good job.
The Aff argued persuasively that there's no limit on how close epsilon
might get to 0, where epsilon is size of the "tax" a vertex must pay
for the privilege of being a local apex, at the tip of a radial, on a
hill with a view.
Give me a large enough frequency, and we continue our asymptotic
approach to where we might say "each vertex on a perfect "at infinity"
sphere is instantaneously flat i.e. is surrounded by 360 degrees".
The Neg pointed out that there's a discrete iotum of "tax" that comes
from just being in a sphere-like polyhedron, inheriting Descartes
Deficit (a tetrahedron of degrees) as a builtin characteristic of the
ecosystem.
No matter what the frequency, there's a constant 720 "ownership fee"
(might be a better term for "tax" in capitalist thinking) that must be
contributed by all who have purchase on this globe. Taxpayers may
indulge themselves in the illusion that Zero is a reachable ideal, but
of course it never is. Inside that epsilon is a grain of sand, a
positive amount, ad infinitum, and there's no getting rid of it, or
rather, the tetrahedron has been subtracted and is not coming back.
My approach is not all that different from taking 1 == 0.99999... and
saying there's dramatic tension here, and using that to motivate
exposure to additional concepts. Will that magical "..." be strong
enough to give us 9s forever, or will it peter out and leave us
asserting a falsehood. Everything hinges on the ability of "..." to
really deliver. One needs to cultivate utter confidence to that
effect, and to say things like "we're not talking about a *physical*
possibility" (in contrast to what?).
That's a known pedagogical technique (andragogical too), to use
tension and suspense ("who will win?") as a motivation to pick up more
of the relevant terminology. I don't think it's a stupid technique
myself, though I understand if you choose to avoid it in your own
dramatic role as teacher in a mathematics classroom setting (a very
special case condition which 99.9% of us do not experience with much
frequency if at all -- and yet we might teach math and logic and
rhetoric and PR, including for money).
Kirby
Notes:
** those knowing a wee bit of history will remember that Descartes
became a controversial member of the Swedish court, as beloved
personal tutor to the queen, not unlike the role of John Dee, mentor
of Sir Francis Bacon. Descartes was nominally Catholic though he
feared the Inquisition enough to encrypt major findings, while Sweden
was a Protestant country such that his influence aroused deep
suspicion, making his presence there something of a trial
http://www.cathnews.com/article.aspx?aeid=19371 (Catholics were
suspicious of him too, given ties to Rosicrucianism, which the
Wikipedia article doesn't talk about).
&& sometimes prisons have been transformed into centers of study as
well, in which case the surveillance cameras just fit right in. One
of the famous warden-scholars, of San Quentin, led prisoners through a
multi-year course in General Semantics and other topics.
http://www.youtube.com/watch?v=ww8sYTfYJlA This may have been when
poet Gene Fowler ('Waking the Poet') encountered a bigger world of
ideas (reminiscent of the Malcolm X story -- prison is sometimes
educational, if enough agreement builds)
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