[Wittrs] Re: Debating with Functional Programmers
- From: "kirby_urner" <kirby.urner@xxxxxxxxx>
- To: wittrsamr@xxxxxxxxxxxxx
- Date: Sun, 21 Feb 2010 20:51:10 -0000
--- In WittrsAMR@xxxxxxxxxxxxxxx, "iro3isdx" <wittrsamr@...> wrote:
>
>
> --- 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.
>
I also associate Bourbaki with a strong bias against visualizations
as too informal. Not much with the polyhedra. The idea of a "visual
proof": an anathema to them. Benoit Mandelbrot sees himself at the
other end of the spectrum, investigating a space one wouldn't find if
that steeped in the Bourbaki approach. He has some harsh words for
Bourbakians.
Thinking back to the New Math, I'd agree that it was not all that
visually stimulating, but I'm not sure why. Caleb Gattegno was
championing those algebra bricks (Cuisenaire rods) but by they time
the showed up in the New Math context, I'm thinking they were pretty
much bereft of his surrounding curriculum (he was the founder of the
UK version of the USA's NCTM).
Many more archeological documentary shorts could be done on these
topics. Those of us who lived through this period could especially
relate, but it'd also give our younger generation more of an
opportunity to see what a long strange trip it's been.
'Duck and Cover' (ala Atomic Cafe) + New Math (ala Tom Lehrer) --
pretty kooky. Then came Vietnam and Nixon: all out full throttle
psychosis, still under-reported on (proper name Nixon is a theme in
these threads, per Kripke et al).
>
> > 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.
>
You sound more like a latter day Wittgensteinian then...
>
> > 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.
>
I'm not doing battle for New Math per se, as it died long ago. I've
punned on the moniker, calling what I'm into Gnu Math. I think
Richard Stallman, into clever word play, would find this clever
enough. I've also gone with Martian Math in marketing niches.
In between New Math and what gets ridiculed as New New Math was the
rise and fall of intervening schools of thought. Constructivism,
constructionism... you know the ones. The Math Wars plays out daily,
in mostly ritualistic fashion, the positions well known. It's like
karaoke out there. Put up something they don't know and the room
falls silent, people leave in frustration. Original music is hard
to come by in the Great Masquerade Ballroom.
>
> > 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.
>
I'm not inclined to see any difference between "mapping" and "set of
ordered pairs" right off the bat. The set of pairs is simply another
way of encoding the same information the map does: domain elements
get paired with (mapped to) co-domain elements, according to rules
(or even randomly). Some rules break the "function" definition,
whereas others typify the type of function (injective, bijective...).
Regarding your earlier post, yes, the FP vs OO (functional versus
object oriented) battle seems to have been simmering for a long
time, another semi-inchoate soup of visceral emotion and bitterness,
seems to be.
What irks me is how little we do to converge any of these long
simmering debates, bring them to a boil. Everyone seems content to
imagine infinitely parallel lines, not ever converging.
If I were advising the USA president, I'd say getting students really
good at debate is of the essence, as USAers are mostly incoherent
these days, about why they fight (per movie 'Why We Fight'), about
what they're really up to in the world.
Sitcoms and sports have apparently trashed the neocortex and all
that's left is limbic system punditry, a lot of knee-jerking spasms,
semi-paralysis.
We would like the next generation to not take after their parents in
this regard. But will there even be a next generation? The fast
fooders wanna prep 'em for heart disease at 30, have 'em on a fast
track through childhood diabetes. H.G. Wells anticipated Eloi. You'd
think we'd have defenses, but they've been cynically deployed out of
sight out of mind, while the USA is raped and pillaged by those guys
in The Matrix (machine world reps, misanthropic to the core).
Philosophers should be like cooks, help bring things to a head in a
safe manner that provides solutions going forward, now that the
positions have been clearly articulated and disambiguated.
Lots of work that needs doing, a kind of institution-level therapy
(like what Wittgenstein showed us). Not fair to let any silly
pro wrestling twixt OO and FP slow down the overall progress of the
Freedom Train.
>
> > 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.
>
On the other hand, this is not a static picture. The late 70s was
a very different era, when it comes to what software is available.
>
> > (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.
>
We have many views in common it seems to me.
>
> > 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
Usenet is mirrored in Google groups a lot... anyway, ditto sci.math.
I used to spar with a guy named Chapman, also spelled out my quirky
use of "nominalism" (like I've done here), which owes a lot to
the Henry LeRoy Finch book on the later Wittgenstein. I think I
mentioned he was invited to come speak with us at 1879 Hall.
Kirby
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