On the math of tomorrow...

[kirby urner]

"""

As we train up our students on the humanities side,
we will be using math texts as objects of literary criticism.
Rather than be intimidated or made to feel inferior by
the cryptic notations therein, we will apply our tools of
the trade to rank them according to various criteria. We
will think more like publishers. Why did this work get
published and what interests did it serve? What was
the agenda of this curriculum? Why was this topic
left out, why was this one included?

We don't leave such discussion to math teachers.
On the contrary, the process of learning a math is
likewise the process of investigating its location in
whatever phase spaces.

"""

http://mathforum.org/kb/thread.jspa?threadID=2216602&tstart=0

"The math of tomorrow" sounds somewhat retro in flavor,

like some exhibit at a World's Fair, circa 1960s, 

Space Needle in the background.  Welcome to Seattle.

"Place based" curricula set the backdrop, as what 

UNESCO has been telling us is not to abduct children

into some foreign system run by aliens.  Bridging to

the indigenous cultures by a process of hybridization

is the way to go.  Not a new idea really.

Enter the idea of "memes", coined by Richard Dawkins,

and used all over the place to discuss "cultural 

genetics" i.e. the process of cross-pollinating many  

decry as "globalization" -- but then how could we escape

our destiny?  Who had the power to apply the brakes?

We've discovered our spherical campus, our "universe city".  

That's something to know about.  Geography matters.

Herbert Marshall McLuhan's "Global Village" is Bucky

Fuller's "Spaceship Earth" is our "Global U" of today, 

one spherical motherboard, solar powered.**

One aspect of "the math of tomorrow" I'm anticipating is

a more critical mindset.  We've learned that the best way

to counter the worst effects of TV is not to deny access

to TV, but to help cultivate "antibodies" and that means

taste, a sense of some internal guidance system.  We 

learn what feeds us, nurtures us, and what drains us

or saps our strength.  Learning mathematics likewise calls 

upon our "critical viewing" skills.  The best way to counter

the worst effects of TV is to make it oneself, to learn some

ropes.  As Maria says of mathematics:  make it your own.

Likewise we need to bring to mathematics a sense of 

the "opportunity costs" of learning and doing it one way,

instead of these others.  We're aware enough to know

what many have failed to realize:  that we have options.

Could you have learned computer programming while 

learning this?  Might robots have been involved?  How 

do others go about learning this material?  By rapping 

about it?  Do some students apply it in the field?  How?  

Crop circles?  Sailing?  Preparing and serving food?

Routing trucks?  Compiling statistics?  Monitoring 

sensors?  By means of music?  By building things?

Lets do some research and find out.  Don't wait for 

the math books to tell you what they think you should 

know.  Search for the applications as a part of your 

learning process.  Did you know quaternions are useful 

in game engines then?  What's a quaternion?  Who 

was Hamilton? Who was Grassmann?

Consider, for example, Milo's point that at some point 

a backlash against Teutonic influence in some sectors

of this world meant an across the board deprecation 

of number theory in place of a new kind of geometry 

teaching.  Cultures go through these evolutionary 

or devolutionary phases.  Great leaps forward, great 

leaps back.  Paying attention to time-lines heightens 

awareness of these patterns.  

Mathematics need not be unaware of its own context, 

its place in intellectual history.

So, for example, a continuing story today is the rise of 

so-called "chaos mathematics" from something considered

the primordial "opposite of order" to something more like 

"optimized problem solving strategies".  There's room for 

randomness and unpredictability, for butterfly effects.  Many

authors have written about this already, but then which 

mathematics classes bother to sketch in these backdrop

threads?  Does junior in algebra class get any kind of 

clue or heads up that these trends are happening?  Does

junior learn how to spot trends and follow them?

In art, music and fashion, there's always a sense of 

movements and time-lines, of seasons and change.  

Some may consider mathematics aloof, quite above

being fashionable.  It's eternal and therefore has the 

luxury of being as stodgy and boring as necessary, as 

there's no competition.

In contrast, in "the math of tomorrow" we go over textbooks

asking about what they exclude and include, looking for

clues about a culture.  We're anthropologist - detectives.

All math is ethno-math.

Why did just this set of topics make it to the top of the heap, 

and why were these others given short shrift?  What were 

the story problems like?  Did they share any lore?  How 

much of a road map were students given?  What level of 

visualization was assumed?  Were there animations?  

What were they like?  Did they use puppets or dolls for 

any reason?  How about string?  What models, what toys?

Were some children forbidden to learn.  One of my friends

just got back from India and in some zip codes a kid will

be beat up by others, including adults, of caught learning

to read.  Those would be kids of a certain caste or social

station, being groomed to live with without reading skills.

Their dramatic role has already been decided.  The idea 

of "social mobility" through skills acquisition is actively 

discouraged.  

But don't we find reflections of that in almost any culture?  

Look at barriers to learning everywhere, starting with the 

pricing structure.  Or what barriers are self imposed?  

Even with societal pressures removed, you'll find people 

self-flagellating because they "have no head for math".  

What's the memeplex?  Is there actual guilt involved?  To 

what degree do some feel inferior or even "made to feel" 

inferior?  There's no one right answer. We'd just like to 

know.  Anthropology is interesting.  Martians study 

Earthlings in some imaginary worlds.

So what was the teacher like, where this book got used?  

Go back to old records.  Was she or he like a religious 

leader?  Would mathematics have involved reading a 

compass and map?  How much geography might this 

math have included?  Did this culture even break it down 

into the subjects we're conversant with?  Was "mathematics" 

even a separable literature or activity?

The answers are not always obvious.  We project "mathematics" 

as an isolated subject as a matter of ethnic training, not 

because of any inherent logic or "law" of the universe (or do 

you wish to dispute my claim -- I welcome debate).

Remember Socrates and the slave boy.  Remember he was 

a "slave boy".  This was a teaching about social class, about 

transcending it through reason (Socrates leads him through

a proof, with comprehension).  Socrates was teaching about 

the potential for social mobility.  Slaves don't have to stay 

slaves. Remember what happened to Socrates.

Nor need women put up with any "2nd class" status.  In 

the "girl scout math" genre, the "boy version" is derivative.

Picture women-only submarines.  It's a diverse world out

there ain't it?

In sum, what "the math of tomorrow" is good at is helping 

"math" to disappear.  It becomes part of STEM (woven into 

the fiber), or a part of STEAM (STEM + Anthropology).  

We go back and read "math books" and do the exercises 

(some of them) but that doesn't constitute any tacit agreement 

to divide up the turf the way they did.  We're free to mix and 

match to form the "memeplexes" we prefer.  

Better to have "polymath" than "math" will be the decision in 

many cases, once they've tasted the difference.

Kirby

** http://groups.yahoo.com/group/synergeo/message/63780

(building a curriculum bridge, see Kabul Dome rant:

http://www.mathforum.org/kb/thread.jspa?forumID=206&threadID=2214399

)

[Joe Corneli]

> In sum, what "the math of tomorrow" is good at is helping
> "math" to disappear.  It becomes part of STEM (woven into
> the fiber), or a part of STEAM (STEM + Anthropology).

+1000

So that math punks become STEAMpunks. w00000t