[Wittrs] Re: Debating with Functional Programmers
- From: "iro3isdx" <xznwrjnk-evca@xxxxxxxxx>
- To: wittrsamr@xxxxxxxxxxxxx
- Date: Sun, 21 Feb 2010 15:41:00 -0000
--- In Wittrs@xxxxxxxxxxxxxxx, "kirby_urner" <wittrsamr@...> wrote:
> 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.
Interesting. I was not actually suggesting that the Bourbaki
collaborators were themselves involved in the new math initiatives. It
was more that both looked at mathematics from a similar viewpoint. The
Bourbaki approach emphasized elegance, a kind of minimalism, and a
strict underlying formal structure.
> New Math inherited from the Bertrand Russell school quite a bit.
I have never been a particular fan of Russell (on mathematics, that
is). But, yes, I guess he had a lot to do with "foundations of
mathematics", and that kind of foundationalism was part of the new math
movement. For myself, I like to sometimes point out that mathematics
existed, and was doing well for several thousand years before
foundations of mathematics even existed. So it seems clear to me that
whatever "foundations of mathematics" is about, it isn't about the
foundation of mathematics.
> Remember the motivation: Russia had launched Sputnik and Americans
> were newly paranoid that they were falling behind.
And so they introduced the new math, to make damned sure that we would
fall behind. (Okay, I'm a cynic). I saw the effort as well intended,
but poorly conceived.
> 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.
I seem to have survived the 1950s. A function used to be a mapping,
and then it became a set of ordered pairs. Sorry, but a function
always was a mapping, and always will be a mapping. Defining a
function as a set of ordered pairs is forced, unnatural, and contrary
to the intuitions that a mathematician needs. Sure, it is elegant,
minimalist, and comes directly from foundations of mathematics. But it
still fails to adequately feed mathematical intuition.
> 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.
In the late 70s, I taught a class - I think we called it "Calculus with
computing" - where we introduced students to using the computer along
with teaching calculus. And I did use loops in a computer program to
illustrate the sigma notation in math. That part worked, but my
overall assessment was that combining math and computing was a misfit.
> (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).
Yes, I remember geodesic domes. IDOT (Illinois Department of
Transportation) still builds them for regional headquarters.
One of my biggest criticisms of the new math, is that it destroyed the
teaching of geometry in the school math class. I would hear
mathematicians saying that geometry was all about teaching proof, and
that we could better teach proof with formal logic. They seemed to miss
the fact that the intuition driven proofs in Euclidean geometry were
very different from the formalistic proofs that the new math preferred.
I see geometry as the heart and soul of mathematics, and as far more
important that foundations.
> 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.
Perhaps that is because it lacks any real subject matter. (There's
that cynicism again).
> 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.
I think so, though it was longer ago than a couple of years, and my
record of past posts does not go back far enough for me to check. In
any case, I no longer follow sci.math. Usenet was dwindling in
importance anyway, and when my ISP cut of its support last year, I
decided it was time to quit.
Regards,
Neil
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