Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Replies: 1   Last Post: Dec 6, 2011 8:17 PM

 Messages: [ Previous | Next ]
 kirby urner Posts: 2,578 Registered: 11/29/05
Posted: Dec 6, 2011 6:09 PM

On Tue, Dec 6, 2011 at 1:13 PM, Joe Niederberger
<niederberger@comcast.net> wrote:
> Kirby,
>
> I've been enjoying the paper off and on -- haven't really read the whole thing. I did read his take on teachnig functions.
>
> I don't think I ever conveyed successfully what my main point was concerning "math function" and "computing function". I just state it outright once more: The modern concept of "function" in math is an abstract set or mapping, that has been separated from "how" once might compute said function, if its computable at all.
>

Yes, and my response to that was to translate to a picture of a "key :
value store" where you don't necessarily have any algorithm or rule
for deriving the value (range) from the key (domain), but you do
follow the rule of a key pointing uniquely to one determinate outcome
(whether "computed" or no), this in contrast to "a relation". I'd
call this the Dolciani presentation, as promulgated to the rank and
file starting in the 1960s or so, bringing new formalism to the hodge
podge that had mostly been arithmetic.

By using this image of an SQL or noSQL engine pulling up a mapping
(however not-computed), I show how, without leaving the realm of
machinery and technology (STEM-sounding stuff), we might contrast
abstract mathematical ideas of "rule following" -- with some functions
suggesting a rule -- versus functions that are ruleless or maybe have
rules about which we are clueless.

> So, does this concept have any cousins in the world of everyday computing? I think it does - its in the abstract notion of "interface" & "information hiding" (ala D.L. Parnas). Its the "rough consensus" part of the IETF moto.
>

Forgetting about higher brain function in the math department
(imagined as a neocortex), way down in the limbic system of everyday
high school we have that yakkity yak about "functions" day in and day
out in the teenage years.

A few hundred yards away from that math classroom, or (perhaps more
likely) back at the family home, the same student is trying to figure
out what all the buzz is about, regarding Python (for example [1]),
and encounters the following lines:

>>> def f(x): return x * x

>>> def g(x): return x + 2

And then there's

>>> g(f(4))
18

and

>>> f(g(4))
36

- -- "looks a lot like composition of functions we were doing in math
class that day" thinks the wondering student...

So the Python concept of "function" may be bent, really not that
dramatically, to just seamlessly take the place of the TI calculator
that has been dominating for decades.

Or not. Chances are not, in most North American zip codes so far.
Pythons are dangerous snakes and on computers you get people called
hackers. Just not appropriate for schools. That's the administration
talking. That's why the USA is among the most backward among nations,
whatever the scores are telling you.

True, writing "functions" that open a CD drive bay, or cause the
lights to flicker, might seem a little more event-related than
functions in math books, which are mostly too insensitive to mouse
clicks to be worth much.

We want to talk about event loops and changes in machine/system state,
but our approved math texts keep us on a short leash, won't let us go
astray into such topics (they're heavy-handed and patronizing).

The way I see it, those math book authors just didn't have the
perspective we need today, not saying they could have known.

Getting on one's knees before any textbook series, paying dues as a
bleating follower, is the mark of the meek for sure. If you'd prefer
to be a geek, best to snap out of it then, maybe find some less

In any case future shock has been such that committing it all to
paper, binding it up, and then shipping palettes of textbooks by truck
to the states (TX, CA... NY), for replacement every 15 years or so, is
just too laughably stupid (too slow, too unable to keep up) to be
taken seriously at a subconscious level, though consciously some
manage to keep a straight face about it all (adults seem especially
immune to environmental cues -- have you noticed?).

> (I'm old enough to have met and remember Parnas first time around, now I see he's being 'rediscovered' - here's a nice paper): http://www.google.com/url?

I checked the link. That idea each object should manage its own
secret, privately / independently manipulable, is still a powerful
influence I'd say, in some schools of thought (object oriented).
Others distrust that vocabulary (the more functional schools, which
claim to avoid both variables and state).

Kirby

[1] http://xkcd.com/353/

[2] http://controlroom.blogspot.com/2011/12/afsc-banter.html

"""
There's a computer lab elsewhere
in the building, but the math side and the computer side are separated
by a mental fence. This fence has cost the USA its priority on many
levels, if we're thinking in nation-state terms. I'm not saying only
the USA suffers from this rift / schism / wound. It's a question of
how fast might we heal.
"""

http://mathforum.org/kb/message.jspa?messageID=7622029&tstart=0

>
>
> Joe N

Message was edited by: kirby urner

Date Subject Author
12/6/11 Joe Niederberger
12/6/11 kirby urner