Date: Dec 28, 2012 12:15 PM Author: kirby urner Subject: Re: A Point on Understanding 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)