A couple typos fixed, embedded hyperlinks activated.
Link to Math Summit account

Date: Thu, 29 Jan 1998 10:56:33 -0800
To: synergetics-l@teleport.com
From: Kirby Urner <pdx4d@teleport.com>
Subject: Syn-l: Math Centers (was: irrelevant observation)

>After correction, I can confidently say (check me on this) that:
>cos(central) = -1/3
>cos(dihedral) = 1/3
>and they add to zero.
>David Chako

This is primo stuff Dave -- how to make friends and gain 
influence among classroom teachers is by providing these little 
'tips and tricks' that segue 21st century geometry into the 
existing curriculum without so much as a hiccup.  Here we have 
this "yucky" angle of 109.471 degrees in need of PR, and right 
away we see it's simply the acos of (-1/3).  Easily memorable, 
quickly absorbed.

Right now, huge numbers of kids are sitting in rows and 
columns, calculators on their desks, unit circle on the 
chalkboard, teacher struggling to impart the sin and cos 
concepts, relate that to wavilinear stretchout xyz 
"radio-waves" and so on.  

In a math center, kids would be sitting at NASA-style consoles 
-- calculators handy maybe, but a computer screen, recessed and 
augmented with controls, would be more the focus.  The central 
server would be stocked with lesson plan software, and if the 
day's unit were on trig-based oscilloscope functions, kids 
would net-access Java (or whatever) applications with native 
ties to twist-knobs or push buttons for changing amplitude, 
frequency, whatever other parameters.

I realize it's perfectly feasible to provide whatever controls 
on screen and have just a mouse to twiddle the cartoon knobs, 
click buttons and so on, but I think it would be fun and useful 
to have these standard math center consoles come pre-equipped 
with generic bells and whistles that programmers could tie to 
applications (the kids themselves being programmers in many 
situations), and also with sockets for receiving input from 
compatible devices.  This is important because we're not just 
training kids for bizapp cubicles here, but for workbench 
engineering, wherein a lot of the instrumentation controls are 
not just screen based, and wherein computers are very much used 
for realtime data aggregation via sensors of various 

The big screen up front shows the teacher's screen, or might be 
guest-slaved to any console in the room, say if junior is doing 
show and tell about some project and has slides to share 
(perhaps pre-screened with an advisor to keep the presentation 
tightly focussed).  The big and small screens all have the 
capability to show documentaries and history is a big part of 
what goes on in math centers -- you need to see how hard the 
adults have worked to get us where we are, what dedication, 
even if the technologies no longer exist except in museums.  

What gets kids inspired is a sense of being a part of a long 
haul critical path project aimed at local problem solving in 
Universe, and not with an end goal in mind of wiping out humans 
in other math centers around the world (videogames OK, 
simulations OK, but making the point of the curriculum be mass 
death scenario planning is by its very nature demoralizing and 
tends to implicitly invalidate all the hard work of those long 
dead adults on screen, who worked their butts off for a more 
serious purpose than seeing it all go up in smoke).

So we show documentaries about the origins of radio and TV (not 
forgetting Baird in any way), maybe in snippets, and then turn 
to our Java applet oscilloscopes, then a live interview with 
some guru in a real lab someplace (teacher moderating, kids 
asking questions via high bandwidth webcam), back to the 
applet, more puzzles.

Then at some point the teacher can segue back to acos(-1/3) and 
zoom in on the central angle of an A-modularized tetrahedron, a 
well-known "home base" in math centers investing at all in 4D 
geometry (i.e. any with real brains behind them).  The A-mod 
exploded view of the regular tet, the unfolding and 
inside-outing of the A (from left to right and back), the 
volumetric equivalence to the B -- this is all old hat to your 
average 6th grader.

And now that we're doing trig, it all synchs.  But we don't 
have lines to infinity so much as chords and arcs on giant 
spheres, which may seem locally flat.  For example, out here at 
Hanford, we have some very long concrete casement used to 
detect gravity waves, so-called, but because it's supposed to 
be perfectly straight, it starts to slant into the earth, as a 
chord.  That's something kids will appreciate.

At first, math centers will be more the exception than the 
rule, and may need to be assembled, circus-fashion, at some 
point outside of town, versus trashing ancient factory-style 
school buildings to fit aerospace accoutrements into these 
ill-suited geometries.  Kids will have to be bussed, and won't 
get more than a few hours of hands-on instruction per week or 
per month.  Corporate logos will no doubt be a part of the 
veneer, proving to parents that the high tech sector is serious 
about getting kids conceptually outfitted for real work in the 
real world ala Project Renaissance -- something the current 
curriculum is simply not about any more, having fallen way out 
of synch on so many fronts (and I don't blame the front liners 
for losing this war for hearts and minds -- their generals 
failed them).

The bizmos are more like those Army recruiting vans, which 
currently fan out across the country blaring "Be All You Can 
Be" to sleepy neighborhoods, show John Wayne movies or whatever 
it is.  The NASA versions would be more like the Navy's 
(storyboard here):  fully equipped with zoomable Fuller 
Projections complete with omnitriangulated GIS/GPS database 
access, and simulations about keeping terrorists from using 
this data for goo-goo brained short-circuitings of motherboard 
earth.  We'll tell kids the military is about militating 
against spazzing out when a trully disciplined response is 
what's called for -- kind of like what the stereotypical 
martial arts teacher shares as playground etiquette:  if 
you're really good, you won't find yourself in any physical 
combat situations at all, and not because you did anything out 
of cowardice or laziness that gave your opposition an advantage 
(nor were you a teacher's pet or tattle tail).

I expect many teachers will line up to receive certification as 
math center trainers, and many kids will be at first wide-eyed 
with respect for this job as well, but may in time be recruited 
into other walks of life, or come back to these trainer 
positions after long and distinguished careers as CEOs or 
whatever.  There will be no automatic seniority or social 
promotion of personnel from federally subsidized institutions 
-- all will compete on an even footing.  Except the government 
itself may choose to fund some math centers of its own, in 
competition with the private sector, because it has a mandate 
to serve and to train in ways commensurate with its own 
mission-critical enterprise ideals and global responsibilities.  
In the USA, these may mean NASA itself gets into the act, 
in which case the staffing may well be preferentially tilted 
towards individuals with a NASA-style background (including 
cosmonauts of course -- Russians make some of the best math 
trainers, I know from experience).

Of course other services already have math center like 
situation rooms, where videogame simulations of tank battles 
and so on take place.  One would hope that the war colleges are 
likewise serious about 4D geometry, so that strategies aimed at 
providing real and lasting security at the global level aren't 
sidetracked by a lot of irrelevancies stemming from Victorian 
Era factory-based curricula.  The last thing we need are more 
major generals of the Gilbert and Sullivan variety, who know 
many cheerful facts about the "square" of the hypotenuse, 
but know nothing whatever about their 20th century American 
heritage and the 4D geometry it supplies. If you don't know 
quite a bit of synergetics by this time, then you're simply 
out of the loop -- forget about your command and control 
responsibilities for now and go back to school and we'll get 
you retrained for active duty ASAP.

Curriculum writer
4D Solutions


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