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Topic: Re: Making time spent on math less painful and more productive
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Kirby Urner

Posts: 4,713
Registered: 12/6/04
Re: Making time spent on math less painful and more productive
Posted: Jul 7, 2009 3:34 PM
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PT3 wrote:

> I'd concentrate on the definitions and theorems
> (proved propositions), where algorithms are forms of
> theorems. (If an algorithm has not proved or is not
> at least provable, then how could one trust that the
> algorithm will always deliver as advertised?)


We definitely remind 'em to read what's on the bottle,
e.g. the Jython algorithm (pulled into Python from the
JFC) promises only probable primes, with the degree of
probability very high, but not 100%. The fact that RSA
depends on these numbers is considered non-critical to
security, although I'm too lazy to cite references in this
context.

At the Pycon workshop for DM track teachers, we used an
already cracked RSA number, giving some of the lore behind
it (German security service earned itself $20K for all
its hard labor). This was good advertising for the
company, as you could just add a few more bits and it'd
take a powerhouse greater than all Germany to crack her.
Wow. Good to show how the mathematical properties of
things actually feed advertising, give substance to claims
(even if only a glimmering).

The "geometry of lumps" we use in some DM segments is in
no way anti-theorem, even if the assumptions (definitions)
are non-Euclidean by design. We want our students to have
a sophisticated grasp of these "math pyramids" (axioms
a foundation, theorems ascending to an apex -- not always
the case, but a good image on which to build).

Wittgenstein used to quip that Bertrand Russell type Logic
underpins a painted castle (higher order arithmetic) much
as a painted foundation would (paraphrase) i.e. it *looks
like* we're "proving arithmetic" (that's what "adding a
foundation" means in that neck of the woods) even though
most of these dons hadn't read 'On Certainty' yet (came
out in notes first) and so didn't have those 'form of
life' associations we take for granted today (in some
circles, not saying every town is like Vienna or one of
those).

I've updated the edu-sig group about some of our business
here, hoping to keep our threads moving. There's nothing
wrong with nostalgia for Turtle Graphics or Turtle Art.
As a genre, these aren't going away. Python's newest
turtle module (Standard Library) is being managed from
Vienna at this point (might've mentioned) and is being
used in elite academic trainings (for teachers as well?).
Also, note use of Python in this investigation of Ulam's
Spiral. These are skills-building experiences. If you're
just listening to a teacher drone, I suggest you tune out
and get with the program! Use an iPod maybe? We're
podcasting some of our stuff.

http://mail.python.org/pipermail/edu-sig/2009-July/009423.html
(updates for teachers)

http://www.dcs.gla.ac.uk/~jhw/spirals/index.html
(for constructivist play periods)

Kirby



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