On Wed, Oct 17, 2012 at 6:57 AM, Joe Niederberger <niederberger@comcast.net> wrote:
> Kirby says:
>>Lots of interesting musings and speculations, but I see nothing there to dissuade us from sharing more widely and effectively what 21st century math notations include
>
> Functional or "to one" relationships are pretty well understood today, no need to imbue them with mystical powers of action, or connotations of "belonging to" or "contained within". By the way, which is it? "Belong to"? or "contained in", or yet more? Is "dot" a superverb?
>
> Joe N

The skill we want to encourage in students is the ability to look out over a vista, be it physical and/or conceptual, and break it down into "objects".

People will see "break it down" is "reductionism" and I can't fight the etymological links between "break down" and "reduce" so I guess they're right.

A classic "object" would be an atom.  We can unify with chemistry by going:

Br.s  Ba.s

to refer to the s orbitals of Bromine and Barium respectively.

Lets change frequencies and look at a more macro world instead:  tractors plow, plant and help harvest (by pulling other devices) and food flows to market and overflow in city centers.  Problem:  revectoring overflow to serving centers via quality control, storage, prepping and cooking, serving.

That's a story problem I've proposed on the Math 2.0 listserv (Google group) a few times, in different ways.

Lets start with the Tractor, a blueprint / template (open source) of which many instances plow the fields.  So each tractor has gps coordinates, lat / log, and a timeline (snap shots of lat/longs passed), and a fuel level.

thistractor = Tractor()
thistractor.fuel = 10   # filled on Oct 13

thistractor.moveto("FieldA start")  #   a lookup table provides lat/log
thistractor.plow()                           #   a routine kicks in, already programmed w/r to a field (see API)

and so on.  William Kent ways warehouse inventory is a game that modeling languages might indeed play accurately and with gusto.  It's when you zoom out and include more players that you get into trouble.  Keep your language games simple and discrete.  Divide responsibility.  We agree.  That doesn't destroy the big picture because you, the architect of this system, need to keep all the agents in view (your like some "overseer" of your "energy slaves" **).

On the city side, you have these cargo bike trailers, some hand made.  The bike is a lot like the tractor in the field in having lat/long.  It's human powered, so the "fuel level" has to do with said human spending calories.  Fortunately, said human has access to "servings" (a "tank up" station in tractor terms) so will be "renewable" in our model.

Are we outside what a Kent model could handle?  I don't know yet.  Maybe not.  In any case, in the real world we have:

cycle12.moveto("SDW")     # a church, a real one, you can check my data (St. David of Wales, 28th and Harrison, use Google Earth)
cycle12.trailer.unload(satmart)     # so like a verb, where satmart is it's own object:  that which was retrieved from Saturday markets

You're probably thinking "turtle graphics" i.e. our cycle and tractor objects seem a lot like Seymour Papert style turtles.  No question about it.  Very much so.

Note that cycle12 is pulling a trailer, an object in itself.  SkyBlue is one of ours, parked at my seFnb.bluehouse i.e. my household belongs in the Southeast Portland Food Not Bombs chapter.  This is true.  Bishop & Milgrim are free to look.  I'm the math teacher.   This is math.   Washington High School.  OPDX.  It's all transparent.

Anyway, that's how dot notation really works in the real world.  We have machines that know it, virtual machines.  They control YouTube, work at Google, have all the best jobs in the universe (not talking about humans, talking about languages).  If you want to work in that kind of infrastructure, where Java, C++ and Python are used (that's today, always changing), then of course you need to know dot notation, no question.  All of the above are dot notation languages.  Objective C is proudly in another camp, and that's fine.  I'm not saying dot notation is god or the be all end all.  I'm saying here's another notation that STEM math introduces, but that 1900s math does not.  Vote with your feet.  I predict zero jobs for the 1900s illiterate.  But that's just me (here today, gone tomorrow).

Kirby