[Wittrs] Re: Debating with Functional Programmers
- From: "kirby_urner" <kirby.urner@xxxxxxxxx>
- To: wittrsamr@xxxxxxxxxxxxx
- Date: Sun, 21 Feb 2010 12:03:00 -0000
--- In WittrsAMR@xxxxxxxxxxxxxxx, "iro3isdx" <wittrsamr@...> wrote:
<< SNIP >>
> I'm also not sure what it is about America, but it seems that we are
> far more prone to fads than most other places in the world.
>
> I am old enough to have gone through school before the "new math" fad
> pretty much destroyed the teaching of mathematics in the schools. But
> even there we see how it has done far more damage in USA than in most
> other parts of the world. Now don't get me wrong. I really do love
> the Bourbaki style of doing mathematics. There's a sort of beauty and
> elegance about it. But it seems to me that this is a beauty that can
> only reveal itself to those who are already mathematicians. So we
> should teach mathematics, not mathematical elegance, in the schools,
> and allow those graduates who become mathematicians to enjoy the beauty
> of the Bourbaki style for themselves and without us force-feeding them.
>
I've not often heard New Math identified with the Bourbaki initiative,
but I see several authors making that connection in my quick check
through Google.
New Math inherited from the Bertrand Russell school quite a bit.
I've always considered it more English than French, but perhaps my
version of the story could use some spit and polish at this point.
Remember the motivation: Russia had launched Sputnik and Americans
were newly paranoid that they were falling behind. New Math
represented a somewhat furious attempt to get early math
education "up to date".
The level of future shock was difficult for teachers to handle and
many of the reforms fell by the wayside.
On the other hand, scholars will point to lasting improvements in
some areas of math teaching, now accepted as ordinary and mundane,
no longer a part of anything "new".
Compare post 1960s treatments of the concept of "function" for
example. You'll find nothing as formal or thought out pre 1950s
at the high school level, is what I'm thinking.
Here's a good little postmortem from a The Tuscaloosa News in
December 1977. Ain't Google wonderful? You get to look at the
actual newsprint, with the ads and everything. Just like
microfiche, yet with no need to scrounge through an impossibly
well stocked library.
http://tinyurl.com/y8kql27
<< SNIP >>
> Addendum: It seems to me that Kirby Urner has been trying to push his
> own faddish way of doing mathematics. I seem to recall arguing with
> him about his ideas on the sci.math usenet group (several years ago).
> Fortunately, Kirby's fad doesn't seem to be taking hold in the way that
> Chomsky's took hold in linguistics.
>
Kirby's fad mostly revolves around two initiatives:
(a) lets move beyond just using scientific calculators in math
class and have at least some high school level courses where
programming, of one kind or another, is used to help explicate
math concepts.
(b) lets do more to share our geometrical heritage from the 1900s,
including excursions into "tetrahedral (vs. cubic) mensuration"
as pioneered in various published sources (relates to that "geodesic
dome fad" you might remember).
I've summarized these two initiatives somewhat recently on math-teach:
http://mathforum.org/kb/thread.jspa?threadID=2041688&tstart=0
Neither reform is depending upon myself as its solo champion. I got
behind both causes because I considered them worthy, important and
not completely hopeless.
These two reforms (colliding math and computer science, streamlining
spatial geometry) also beget some powerful synergies when merged.
In retrospect, analysts will likely ascribe a high degree of
inevitability to these changes, explain how they were actually
foredoomed.
> Addendum 2: Isn't philosophy itself largely a system of fads? I guess
> part of what I like about the later Wittgenstein, is that he seemed to
> be breaking away from the fads that had obsessed him in his earlier
> years.
>
> Regards,
> Neil
>
In relation to Thomas Kuhn's 'Structure of Scientific Revolutions'
Rorty suggested that philosophy, unlike the sciences, doesn't settle
down into these longish periods of settled paradigms.
Sciences only get get shaken to their core now and then. Philosophy
seems to be characterized by being perpetually in tumult.
These were remarks from some lecture to undergrads, don't have a
citation to a published essay handy.
The word "fad" is one of those meaning-as-use cases. In geological
terms, perhaps human beings are a fad. Dinosaurs certainly had a
longer tenure, so far.
Did we really argue on sci.math a couple years ago? I've had my
debates in that forum (including about Wittgenstein's philo and its
implications) but have mostly steered clear for more years
than that.
sci.math is really frenetic and scattered, hard to get any work done
there in my experience YMMV.
Kirby
=========================================
Need Something? Check here: http://ludwig.squarespace.com/wittrslinks/
Other related posts:
