Plotting with VPython

(click for close up)

I haven't seen a lot of curriculum writing making use of VPython's nifty 2D plotting capabilities. Sure, other packages have more bells and whistles, plus 3D plotting of various kinds, but then VPython has all these other advantages, including a rather streamlined API.

I'm looking forward to the new release. Currently, installing VPython on Linux and/or Mac is not trivial. Better installers would go a long ways towards making this a more usable add-on for Python.

Free cone day at Ben & Jerry's, just got a text message. Gotta run.

Hackerdom

from {Kusasa / Analytical Education }

Youthful protagonists now test their metal against the challenges, temptations and frustrations of cyberspace.

These skills, very much needed by real world development teams, are partially reinforced by the genre itself; the comics and cartoons include some technical content, not just cues about ethics and values.

Speaking of ethics and values, the free software movement, started by Richard Stallman and friends, is briefing new generations on the importance of collaborating within the guild.

Keeping our tools freely sharable makes positive synergies so much more likely and lasting. By mutual agreement, we don't criminalize collaboration amongst ourselves, a hallmark of liberal cultures.

from Hackerteen, O'Reilly Books

Philosophy Posting

To some Yahoo! eGroup:

Followup re Russell, Linguistic Turn etc.

So in the interim since my last post I've traveled around quite a bit, find that I'm not alone in sharing this vision of a curriculum newly revamped by the open source assets aka collateral we've been building up over the last decade or so.

How Wittgenstein fits in is when explaining to career math teachers how this is not the same as New Math, although yes it seems similar, because in the Russell-Whitehead-Wittgenstein era it looked like everything was boiling down to Sets as integral to some grand unification thing happening in Logic (ball gets rolling with Frege especially).

With the benefit of hindsight, I'd say a lot of talent developed in that era got siphoned off by the AI movement, which predicted some kind of new mechanized intelligence, which we got actually, in that now an entry level home computer comes with maybe 3 gig RAM, a terabyte hard drive, and who knows what else -- lots of futurism came true in these devices. But no AI to speak of, with programming being a very human activity, interface design an art as much as a science and so on. The "ape class" mammal proves once again that we're versatile, adaptive, so here for the long haul, actually looking forward to peaceful coexistence with our iPods, not some immanent takeover ala Terminator or whatever.

I'd say a lot of philosophers got hoodwinked by the AI dream and ended up wasting a lot of our time. On the other hand, Alonzo Church and the lambda set, authors of LISP, Scheme and so on, took off from that Bertrand Russell type stuff and moved us in many promising new directions. The dream of mechanized languages, ala Leibniz and later Ada, is alive and well. Wittgenstein's concepts ala the PI are helping us think about "namespaces" and so on -- a way to protect against "name collisions" of the kind that have always plagued any philosophy insufficiently aware of its responsibility to sustain its own context (many just use the prevailing cultural backdrop, and so may not transmit well downstream, whereas the PI is clearly a book for the ages).

Rave Review

"Obviously we're frustrated by the ratings. We don't believe that the broadcast or Katie are getting the credit they deserve," CBS News senior vp Paul Friedman said. "It's a first-rate broadcast. Most people who watch it carefully inside and outside the broadcast will tell you that. She's doing a great job." [story]

Yeah, we don't get it about the low ratings out here either, except to say some Americans like to be pandered to, like to see key players bend to mob rule, get in line with the program, whatever that means.

The CBS News team has the best access and best stories, we'd be completely at sea without 'em (in some perfect storm if Fox had its way, very good for ratings -- if you still have electricity).

Sitting around Pauling House table today, speaking freely about whatever. Lunch with the Boltons again. Good seeing Barbara, Jim Buxton. More sparring with Wayne on Math Forum, did some DemocracyLab stuff, other puttering.

More from Synergeo

Note: I've always classified Synergetics as not-Euclidean and I think Bucky did too, insofar as one requires a taxonomy.

I go back to dimension theorist Karl Menger's "geometry of lumps" essay, as another way to do axioms that'd break the Euclidean mold -- the very path Bucky chose, in making spatiality a primitive starting place, and four-directional in the sense of the tetrahedron being its primitive topology (if it has shape, this'll be simplest, in terms of dividing space into two volumes of complementary aspect, concave and convex).

But then of course it's so obvious: no infinite planes, and when you zoom back on anything locally flat or straight, it's seen to curve -- definitely a strong sense of horizon in this one, whereas Euclideanism permits these infinite parallelisms (inspiring of XYZ more than IVM, which is only special-case tunable, not really "there" in any physical sense (same as XYZ, but they still want to claim infinity on their side, I say let 'em, no skin off our noses)).

Mostly geometry is used to get stuff done, and it's still as useful as always in that regard. Whether one "believes" in infinite planes or "dimensionless points" is sort of beside the point.

These "infinite" attributes may be regarded as "don't need to specify" settings e.g. we need to talk about a flat surface, as thin as you care to make it, as expansive as you care to make it ("don't care, say infinity"), and now here's a point (call it A), no limit on how small you want it to be (again, "don't care, wouldn't matter").

Axioms and definitions were a good way to "get on with the show" but then scholastics tend to come along and cruft up the discussion with questions of allegiance and belief e.g. will you pledge to support the Euclidean Chair or whatever in some university -- means you need to recite certain mantras. By this time, we're a long way from just getting stuff done, have entered the fantasy life of a cult, like the Pythagoreans, with their degrees of insider, innermost circle, all that claptrap.

How to turn geometry from being a fun useful tool, into a dreary "belief system": that's a lot of the western civ story right there. Synergetics is Bucky's attempt to power wash some of the cruft off this very workable machinery, dispel some cobwebs. Not easy to do, but refreshing anyway, to see some shiny metal still under there, not rusted away.

Earmarks

Although it's wise journalism to remain safely cynical in public, when it comes to following the money through Byzantium, I can see why some of these congress folk are so proud of their earmarks. To say they have the ability to dispense funds by some inscrutable process, is just another way of saying they wield power. What was the USA government apparatus supposed to provide, if not powerful positions, let's be honest about it.

So let's take the example of congressman X who gets a lot of money allocated to some grateful campus, which then names a building after the guy. Happens all the time in the private sector, where we call it philanthropy. What it comes down to is partly how we feel about taxes, and do we respect the judgment of the people we elect to high office. I'm thinking the system could work, but has become distorted in some ways we need to fight back against.

Sometimes it's convenient to say "Hollywood" as if that means something monolithic. Other times, we remember that individual stars may be as far apart as the universe itself in some dimension, i.e. just because books all look similar, sit next to one another in the library, doesn't mean each shares the same world view. All of which is a long way of saying that "Washington D.C." is not a mono-culture, never has been, and politicians are not all cut from the same cloth.

Part of the political life of our nation is to provide good role models. The power to earmark doesn't in and of itself erode our ability in this regard, much as we may opt to play with the rule book. I'm betting tomorrow's high office holders, no matter how ethical, will have what amounts to the same thing: an ability to get work done behind the scenes that leaves many wondering how it all really works i.e. we'll have "Washington insiders" so long as we have politicians in Washington.

Homework

I'm the hunkered-down recluse these days, gearing up for new classes, catching up on hospital work.

Thinking ahead to my next DemocracyLab meeting, I'm pleased and intrigued by this Google TechTalk entitled "Don't Make Me Click" by design scientist Aza Raskin. He lectures about how to design less annoying interfaces by avoiding "the seduction of interaction" (9:00).

I'd call it Tufte School in some ways.

Guido asks a question at the end, about needing a pattern language or working toolkit for implementing these simple, minimalist or "zen" (I'd add "quaker") front ends. We need a Julia Child of interfaces to come forward, with some fairly bulletproof recipes, so web designers aren't always making the same silly mistakes.

Also, Adrian Rossiter continues to produce some fine mathcasts. I recently transcribed his Jitterbug Torus to a YouTube-compatible format, with permission:

Another Portland BarCamp is coming soon, will probably swing by, maybe catch an exotic language session (and/or lead one on J?).

Wanderers 2008.4.15

Our conversation seemed quite disjointed, like broken pottery shards, focusing a lot on currency exchange rates, airlines, and proposed solutions to various "big problems" like "illegal immigration."

As a Fuller Schooler, my bias is to accept that each individual gets the same generic freedoms of movement vis-a-vis our in-common planetary ecosystem. Of course any given community (Catalina comes to mind) may post no vacancy signs. We still encounter barriers, gatekeepers, locked doors and so on.

As a futurist, I tend to use a global university metaphor, bordering on hospital (so call it a teaching hospital), then seek solutions in those terms. And don't call the Earthian economy a "closed system" as our main energy source is a star.

I distributed one copy of Pythonic Quaker, my new DVD.

Resident Evil (movie review)

A not-so-great wannabe I'd file under The Matrix and horror, complete with stylized (choreographed) violence, basically dance numbers with a video game sound track -- basic / transparent outreach to a teen audience, by the book Hollywood.

On the brighter side, it highlights favorite clichés, gives new insight on the "what makes it tick" level. For example, as soon as our adorable Lost chic makes some reference to wanting sex (after all she's been through, she deserves gobs of it), she's fair game for the blender. Very formula.

Our advice in the vid store was to skip the 2nd and go straight to the 3rd. We'll see. Life is short.

Spring Puttering

I've contracted with my fellow Americans to do some yard work for me, as I'm lacking many middle class accouterments, such as an edger or blower, not even a weed whacker I'm pretty sure.

Way cool to have a pickup haul stuff away, although we contract for curbside lawn debris pickup as well, along with regular garbage and recycling.

This particular contract terminates end of June, as I let stuff go dry in the summer, not wanting to pay for cosmetics, although I do keep those washers going (both dishes and clothes), believe in hygienics, pay attention to pull dates and like that.

While I believe in doing my part for property values in these parts, I'm so glad we're not in some Over the Hedge scenario, with knocks on the door because the shrubs aren't regulation, or whatever the hell.

Corporate Structure

I'm saying "corporate" more in the Quaker sense, versus discorporate, or "out of body" which is what some other religions report as closer to their standard m.o.

So like DWA is not a C or S Corporation, nor an LLC or LLP, but an old fashioned partnership of the 1065 variety, formed in the days of Wild West ranches, gold mines, and multiple stake holders. There's a pass-through of gross revenue, minus incurred business expenses, charitable deductions and so on.

Of course in Oregon's ephemeralized Pacific Rim economy (health care, advertising, digital sciences, design and some fab, NGOs, sports shoes and recreation, tourism, casinos), that's more metaphoric, but you'll see how Wall Street uses a lot of the same metaphors (livestock and so on).

The partnership, to the world a hired gun of some kind (Wild West talk again), accrues revenue for its partners, which receive receipts as stakeholders, which show up later in IRS computers, to be reconciled as income on the 1040, the standard way individuals report earnings in this country.

Note that nothing precludes an individual from netting K1 income via multiple partnerships, nor must an individual forswear moonlighting or whatever, i.e. partners need not have bossy relationships, though complementary skills are nice.

In our neck of the woods, medical doctors, other brands of therapist, often gravitate to the partnership model, simply because it's an easy and forgiving template for what are essentially affiliated freelancers or professional practitioners (dentists, lawyers and so on).

:: example expense (check image online) ::

:: example donation ::

Banking Mix Up

Checks for deposit to my business need to be made out to the business, or to my late wife, for whom the business is named (it was hers).

Sometimes I get sloppy and try transferring from a personal account with a check made out to me, for deposit in DWA. Doesn't work, bank algorithms block that.

Really OK, as I just rewrite it to DWA instead, which is easy.

I did that recently, netting a $30 penalty from OnPoint, which saw both checks (including the one UBank rejected).

Upon clearing up what happened, I was credited back the penalty.

Lesson: I need to not be so stupid.

Unicode Experiments

Glenn Stockton knows a lot about the I Ching and gave me a lesson today. I'd studied The Book of Changes before, but never as deeply as Glenn has.

Now I have a new reason to revisit this ancient text: to experiment with unicode in Python.

On the Road

:: tools of the trade ::

I'm often asked what my life as a gnu math teacher is like. In some ways I'm like a journalist, with name tags like press passes, color coded to denote my rank and/or privileges, plus with these blogs in which to journal.

For example, the red tag on the right let me get up in front of the cameras in Chicago. The hand-written Portland BarCamp tag (cleverly reusable) merely announces to peer geeks that I'm interested in Python, Toons, Math e.g. my 4dstudios does mathcasting around Python quite a bit.

I don't actually encourage stuffing two CubeIts! in your carry-on, as the 24 MITEs apiece are highly magnetized, might mess with your other media.

:: close up ::

And speaking of "on the road," my uncle Bill Lightfoot was by today, sans the red Aztek, which he'd exchanged for a newer white one.

Happy Birthday Matt, great being included in your family, since age five or six as the neighborhood newbie. Wonderful seeing all those brothers and sisters again, plus spouses and offspring.

Gnu Math Chatter

Per my Chicago Pycon talk, an early bridge twixt lexical math type expressions and graphical sphere packing ala the IVM (CCP, FCC) are the figurate and polyhedral number sequences, developed minus any foreground coordinate system apparatus, although you need something under the hood in support of the ray tracer (a mechanical device).

This focus on geometric growth (gnomon studies) is prominent in late 20th century geometry: The Book of Numbers by Conway and Guy, Encyclopedia of Integer Sequences by Sloane et al (AT&T), Gnomon by Midhat Gazale, and of course Cuisenaire bricks ala Caleb Gattegno (more about linear color coded distances and the various time serialized entrainings thereof).

Coxeter was leading this charge in many dimensions with polyhedral numbers -- made sense Bucky would see the connection twixt his own deliberately remote vocab and this soon to be mainstream stuff.

Pascal's Triangle and Tetrahedron form a Grand Central here, where these many threads converge / diverge. Python insinuates some generators at this point, syntax that has already spread to the latest JavaScript, along with list comprehensions, in turn credited to Haskell no? The languages all swap DNA with wild abandon -- actually in tightly controlled fashion, but still not predictably.

Pascal's Triangle and Fibonacci Numbers are part of what go out preloaded on XOs, those "little green monsters" (Shrek colored) showing up in places like Peru, Uruguay... Alabama, any number of privileged homes in North America. The application is called Pippy and provides early exposure to Python.

Math Objects

As I was explaining to Gordon recently, we like to treat our classroom modules (a growing library of py files) like aquariums, small ecosystems. Then we feed their top-level denizens directly, their various functions and class constructors.

Or call it "feeding the fish" maybe, drawing attention to how "top-level" really means "freely floating" in some cases, with no top-to-bottom flow of execution implied. It's a namespace, a toolbox, not a sequential story. Consider Python's math module a paradigm.

A Python module may be cast as a dynamic scratch pad, lesson plan and self-testing suite all in one, with an end user very likely another Pythonista or Pythoneer (both brands of snake charmer) and therefore having both access to, and fluency in, the module's source. There's really no need to prompt ourselves with "raw_input" as there's no "dumb user" in this picture, walled off from the code.

So like in the above figure: partial source for a number type M that adds, subtracts, self-negates, multiplies, divides, powers, reciprocates, always modulo some modulus, superimposed on a fragment of interactive dialog, wherein m-number objects, instances of this M class, get a workout.

A math student would typically have both windows open, switching back and forth, thereby gaining an appreciation for both the objects' encodings and their dynamic behaviors "in the field" as it were. Vectors look one way under the hood (their machinery), and another way out there in their native habitat, in action, more like spikes on a sea urchin.

We teach rational numbers, matrices, polynomials, and polyhedra the same way, as more "math objects" embedded in an extensible type system, a model that makes sense even in the context of pre-computer philosophy of mathematics discussions.

The notion of "types of object" is very ingrained in our native grammar, part of why Python "fits your brain" as they say.

Crossing Paths

We took in Bodies today, now at the Carnegie Science Center in Pittsburgh, PA.

I'm getting to know this traveling exhibition quite well, having first encountered it in London, traveling solo, then again in Seattle with Tara and Dawn.

Alexia, Pat and Lil had not seen it before.

Body Worlds 3, which came through Portland, is a separate production.

This morning I posted more of my usual to math-teach @ Math Forum, from Indiana, PA.

I'm glad we included a Garmin StreetPilot with the Alamo rental car. She -- female voice, we nicknamed her Bessie -- got us all the way from Chicago, no other maps needed.

Fractions R Us

:: congrats to anna ::

[first posted to Math Forum, earlier today (typos fixed for this version, code colorized)]

I'm noticing with our novel approach to teaching fractions, that we're discounting the importance of the LCM in connection with adding them. The reason for that is our use of Euclid's Algorithm for the GCD upon instantiation, meaning when we create a fraction object, we automatically convert to the canonical delegate in each equivalence class, namely that for which the numerator and denominator are relatively prime.

The background context is "building fractions" (yes, this is constructionism) from the ground up, in some computer language facilitating operator overloading. That's right, we're doing some programming as a part of our standard mathematics curriculum, what of it? TIs have been programmable for years, and we've heard no one fussing ("more features!" has always been the battle cry, no?).

As I've posted about numerous times here (math-teach), irrespective of whether programming's involved, it's interesting to see if a curriculum dodges Euclid's Method for finding the GCD, escaping into "factor trees" (which I have nothing against -- very important for teaching the meaning of the Fundamental Theorem of Arithmetic).

I'd call that a kind of litmus test, to see if your proposal meets minimum standards -- let's apply it to the states first and foremost, see which state legislatures are being lobbied intelligently, vs. getting fed a lot of mumbo jumbo. Good project for a PhD candidate.

So how do we add fractions then? Of course the old fashioned way: a/b + c/d == (a/b)(d/d) + (c/d)(b/b) == (ad + cb)/bd as justified by using multiplicative identity, other axioms (I'm sure Paul could help out here).

Then you get gcd((ad + cb), bd)), call it thegcd (could be 1), so your new (reduced) numerator, denominator (p,q) become p/thegcd, q/thegcd (multiplying by x/x is to multiply by 1, the multiplicative identity -- this came up earlier, in justifying (a/b)==(a/b)(d/d).

How does this look in actual Python? Here's a fraction class (rational number class) developed to the point of enabling its instances (p/q) to multiply and add (p,q integers, q <> 0). Click for larger views.



Kirby

PPUG 2008.3.11

Our core presentation was on Mocker, a code testing tool.

I stayed late seeking to help a guy with some confusing code.

In the background, I empathized with a Python teacher told to keep certain core concepts off limits in the name of keeping the course introductory.

And yet it's harder to master Python if you have to bleep over the part about its being an object oriented language. What does that even mean? My advice: start early with objects.

My hope is our brand of college prep math, laced with computer programming, will result in much stronger computing skills among new recruits.

Mortgage Mess

Omitted from most journalistic accounts of the mortgage meltdown, is the fact that some well off North Americans no longer dream of McMansions, but have their hearts set on something from the pages of Ecotrust, a very high tech fishing village, complete with broadband and real fishing.

So yes, post Depression Era bulwarks against conflicts of interest, enormous temptations to cheat, were gradually eroded away, like dikes in New Orleans, leaving USAers with few protections against predators (Congress was in on the deal). That's certainly part of it, and we've had no shortage of accounts taking this line.

But since the 1930s and before, this culture has nursed utopian visions in which we get off the grid, or at least have more freedom. Mobile home and RV subcultures, plus the usual yachting crowd, have prototyped the lifestyle. What's missing is much investment by aerospace companies, the ongoing status quo so long as cruise missiles appear the safer bet, Airstream an exception.

So another part of the story is simply not wanting to admit failure. The Vietnam generation wasted helicopters on military instead of civilian enterprising, and now we're all paying, with squalid living standards, stuck with housing designs from the dark ages.