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.

More Technoinvective

Fixed a typo, hyperlinks added.

Haim:

> Now, think of the math curriculum from arithmetic
> to the calculus as a closed system.

Now that's pretty clear. And I tend to agree with "closed" as in "not very open to sensory input" e.g. any proverbial "writing on the wall."

My own view of the curriculum, even K-12, is of a creature much more amoeboid and morphic, able to resequence and reshape far more radically than your theory'd permit.

I'd go with energy conservation though, as in: the average individual spends x calories over y hours towards developing her or his numeracy skills, whatever those may be in some culture. We don't easily squeeze more juice from the same finite time budget (and lets not forget sports practice, also very important).

"Capable of radical overhaul" is actually a good feature, because our world is fast changing, and freezing the numeracy content to a snapshot of what it once was, would make no sense at all. Also, it's a character trait of many USAers to welcome change. Oregon, home of the Trailblazers, is imbued with such a pioneering spirit.

However, within that context, of a liberal arts space, there are, I'd agree, these relatively rigid (calcified) "dead horse" shapes, of which I think the traditional late 1900s USA pre-calc-to-calc sequence is an excellent example.

Kirby

Wanderers 2008.3.4

Although I've resigned from any management responsibilities with Portland Wanderers, I still attend the neighborhood meetings at Linus Pauling House.

Tonight I showed up with my projector and flipped through a few items, including a preview of my Chicago Pycon talk.

Also, since Barry was telling Peace Corps stories from Brazil, focusing on Manaus and "rubber barons" enamored of opera, I couldn't resist seeking Fitzcarraldo links on Youtube and dredging up the Klaus Kinski vs. Jason Robards clip -- takes me back.

Bill has been writing a port scanner in assembler and had himself talking to a USB port at home. But on his Dell Inspiron, the same ports appear inert.

Aldona is a Lithuanian name. Her mom didn't learn English until later, as that Shenandoah mining community had its Lithuanian section, where one could get by in that language. Good seeing Steve again.

Bridging the Gap

Xrefs:
Reviewing some Theory... (Math Forum essay)
Pascal's Tetrahedron
Binomial Theorem
Focal Points
Boosting Bandwidth

Myth Busting

One popular myth people recite is "I do no programming" meaning of course that "writing in a computer language" is not a part of their job description and/or lifestyle, nevermind if they'd like it to be.

On the other hand, we Quakers speak of programmed versus unprogrammed Friends, referring to some differences going back some hundreds of years.

Likewise, when you walk into a theater, you may be handed something called a Programme (perhaps spelled in that funny way).

Apparently there's some meaning for "programming" that "writing computer language" doesn't quite cover.

This, then, is a mental exercise to try on for size: go around saying to yourself "I am a programmer" and see if you get that to mean something.

If you write software, OK, you're done. But maybe not so fast? Play with other meanings.

If you've never touched a computer, maybe you'll have a more interesting time of it.

Remember, in the television industy, programming refers not only to content, but to the sequence of that content, vis-a-vis the sequences used by other content providers (so-called "channels").

The Internet is not a mirror image of the early days of commercial television in the US, when three major network affiliations were prevalent: ABC, CBS, NBC. Don't be too facile with the analogies.

However, that being said, think of your ordinary day as a "scenario" and how you plan ahead of time, to some degree (yes, exceptions happen).

In that sense at least, you might be a "programmer" (no?) i.e. someone who imposes at least some degree of order on both the content and sequence of events. Welcome to the club in that case.

Quaker Geometry

[ quirky: making XYZ vs. Quadrays seem like a bone of contention among religious denominations, a different angle for sure! -- KTU ]

So most Anglicans, if pressed for how many directions in space, will think back to schooling and some chatter about three dimensional. "If by directions you mean dimensions, then space has three" the proud Anglo might say.

The graphic behind this is the six-sided die or hexahedron aka "qyoob."

Alternatively, take three BBQ skewers and intersect them in a mutually perpendicular arrangement, binding at mid-points with leather thong or whatever. Stabilizing the tips with fishing line might be good, in which case you'll get an octahedron of sorts.

In Quakerdom, some of us learn from Lakota about the four directions, typically designed for planar applications (the Lakota being a plains people), but with a corresponding four sided, four tipped arrowhead, or tetrahedron in Greek.

To morph the four-square into an arrowhead-tetrahedron, skew it and crease along the short diagonal, then fold the tips to within unit-edge distance (Richard Hawkins and I implemented this transformation in ClockTet awhile back).

You can see why the "4 directions of space" answer might be appealing: a minimal four vectors splay outward from a common origin, dividing space into four identical quadrants. The Anglican cubists introduce three more negative vectors starting with their positive three, creating an 8-fold partition for their so-called Cartesian coordinate system.

Using quadray coordinates, or Chakovians, as they're sometimes called, we address all the same points with only positives along each arm, starting from (0,0,0,0) at the origin, thereby saving the negatives for some inside-out dual or mirror space.

Of course nothing prevents us from inter-converting 3D XYZ coordinates with their 4D IVM counterparts, nor are Quakers raised without the usual XYZ savvy. These language games are not mutually exclusive obviously. Like, the calculus cookie doesn't now suddenly crumble, any more than it already did.

Anyway, we teach multiple meanings of 4D in some of our schools, gleaning from such excellent books as The Fourth Dimension and Non-Euclidean Geometry in Modern Art by Linda Dalrymple Henderson (ISBN 0691101426).

Like Coxeter's adding a fourth axis, turning a cube into a tesseract, was not the same move as Einstein's when adding a fourth "time dimension" (see Regular Polytopes page 119). Our Quaker 4D, inherited from American Transcendentalism and medicine wheel shamanism, is a move by yet different rules again. That's why Anglos call it "maths" (plural form), because of all this diversity lurking just beneath the surface.

Bleepography

Bleepography is that branch of ethnography in which we study one culture's ability to and/or criteria for censoring or otherwise denying self expression to another.

I'm not saying such dominance is always bad.

For example, older adults do tend to direct (control) youthful behavior, and there's often a protective, survival instinct at work, on behalf of the youth.

Protective parenting is not an "anything goes" standard in most ethnicities, at least not those in at-all challenging circumstances (which'd be most of 'em).

What's especially difficult is sudden translation, through immigration, to new sets of circumstances.

Such transplants may leave families way overprotective in some dimensions, insufficiently defensive in others, setting up intergenerational tensions as a next generation adapts in ways not always so available, or even comprehensible, to the one previous.

Anyway, just to take an example of an investigation in bleepography, I was recently watching some Katt Williams, a standup comic, in performances recorded to DVR.

Lo and behold, somewhere along the way, some dominant culture control freak had managed to go crazy with the bleeping. In some passages, almost every third word was occluded by this highly obnoxious audio blocking technique (the counterpart to "blacking out" in print media).

I was so grateful to not have to put up with this kind of dumbing down for long, thanks to easily rented copies not subject to the same rules of censorship.

If freedom means anything, it means the freedom to not have one's tastes dictated by some anonymous bleeper, some privileged adult in some other space and time, with the power to enforce whatever screwball ethnic standards.

Another story I heard recently: a teacher reprimanded by school authorities for assigning Ray Bradbury's Fahrenheit 451 in English class -- not an approved reading. Plus note many public schools are blocking YouTube, denying access even to teachers wishing to project during class.

Leaving home, going to school, represents a big downward step to a lower level of information access in so many cases, given the Internet. School becomes a sanitized playpen, a sandbox, prefiguring future corporate big brother cube farms (not all of which are equally illiberal, praise Allah).

In the old days, parents kept junior home for fear of exposing her or him to too many alien notions. These days, maybe it's because junior has done nothing to deserve prison, at so young and tender an age.

Curiosity deserves to be rewarded, not treated as a threat by insecure powers that be. Cultures that can't deal with curious humans are among those least likely to succeed over the long haul.

History is chock-o-block with anomalous cultures to which, happily, my family has never been overly subjected. I give the USA's secularism a lot of credit for this, as religions, left to their own devices, tend to lapse into bitter warfare, try to shut each other down willy nilly.

Secularism means keeping the public ways open to the public, not siding with any one faction in some effort to take over and put down, and not depending on enlightened ecumenists for what should be one of our government's built-in defensive functions, per founding designs.

Anyway, let's hope it stays this way -- InshaAllah as we say in Liberal Islamic (note CamelCase).

Wine & Cheese

:: destroyed heritage, courtesy of FHL ::

Buckaneers in the vicinity might be pleased to attend.

I've got a retreat scheduled that weekend or else might fire up the company jet and attend myself (just kidding, way too busy):

What: Heritage Lecture: Bucky's Life And Work: Lessons From A Loss
When: Thursday, February 28, 2008 at 6 PM
Where: The Old Governor's Mansion, 502 North Boulevard, Baton Rouge, LA
Who: Michael Desmond, Ph.D., architectural historian with the Louisiana State University (LSU) School of Architecture
Cost: Free to Foundation for Historical Louisiana (FHL) members and $10 for non-members

Michael Desmond will share his insights on R. Buckminster Fuller and the recently demolished Union Tank Car Dome in Baton Rouge. This one hour presentation, will be filled with the bright spots of Bucky's life and ideas, including an introduction to the specifics of geodesic geometry as it applies to the Baton Rouge dome. We will also look at other such structures in existence. As the now lost Union Tank Car dome was among the worlds largest and most elegant, the lecture will invite a lively discussion of this remarkable structure and the people that made it possible.

Enjoy wines and cheeses compliments of Calanadros Select Cellars at this event!

Call 387-2464 or go to www.fhl.org for more information on FHL preservation activities.

A Favorite Pillow

Wanderers in Eugene

I'm thinking Portland's version of Wanderers has evolved to a self-sustainable state, such that a copyable template might serve in other cities up and down the Willamette Valley, perhaps some of them to one day enjoy faster passenger rail service (still calling it Amtrak?).

What this might look like in practice, is a bunch of people sitting around a table (indoors or outdoors) at that McMenamins on High Street, another eGroup, website, snacks & beverages fund.

I've sent some ideas for branding, mug and T-shirt type stuff (clever slogans mostly).

I'll probably be specializing in these out-of-PDX operations, on the assumption that our top management here has it all handled.

Tacoma another focus.

Philosophy 101

Old timers among us may still remember when Nietzsche, a Prussian (then stateless) philosopher, was blamed for helping the Nazis fashion their idiotic Aryan superman idea (not at all what Nietzsche had in mind, that much we now know), a fantasy designed to whip up war hysteria and feed a sense of manifest destiny.

My Princeton education helped fill me in on what really happened. One of Nietzsche's best translators, Walter Kaufmann, my teacher at Princeton, made a career out of fighting the Nazis, plus check out this quote from Nietzsche's own Twilight of the Idols:

One pays heavily for coming to power: power makes stupid. The Germans -- once they were called the people of thinkers: do they think at all today? The Germans are now bored with the spirit, the Germans now mistrust the spirit; politics swallows up all serious concern for really spiritual matters. Deutschland, Deutschland uber alles -- I fear that was the end of German philosophy. [1]

Very prescient (we're talking like 1888). Lots of parallels to our own time.

Kaufmann was adamant that we ought not waste time reading Heidegger, given he'd sold out when it counted. You should judge a philosophy by the character of the philosopher, was his message.

Since WWII, from such histories as War Against the Weak, we've learned a lot about where Hitler did get much of his conceptual ammo: from North American eugenicists, many of them establishment types. [2]

The best we can say of 20th century philosophy is we're still here in the 21st, and becoming more viable. That's not really high praise though -- closer to "minimum acceptable." Academics are still pretty spineless, even today, especially those so-called philosophers (we've not had many of Kaufmann's caliber -- too much inbreeding I suppose (in a memetic sense, not talking genetics)).

Anyway, I'm glad we're overcoming at last (long overdue).

[1] Walter Kaufmann, The Portable Nietzsche, Penguin Books reprint, 1977, page 506.

[2] very lame to go after the Bush family on this however, as Kitty Kelly makes clear after checking into it more thoroughly

Wanderers 2008.2.13

Roger Paget took up some interesting themes this morning. His genealogical journey has taught him a lot, about this country, about the state of the art (many new tools, swift improvements).

So how shall we balance historians prying, wanting a complete picture, against the requirement for secrecy? In the case of ancestors, it's not that hard: the skeletons in the closet come out only long after the fact, and only with concerted digging -- they wait for the right historian.

But the security-minded often want access to stuff in the present, don't want to wait for some decent amount of time to fly by (the security-minded might not live that long either, eh?).

On the other hand, a lot of what marketing and medical researchers want is reliable anonymous data. They actually don't care to know who, don't need to know who, in order to do their jobs. Some police work is quite different obviously (not all of it though).

The technique of using pseudonyms to mask case histories, thereby providing doctors with true stories, yet fake identities, is an ethical one, and important to medicine.

The Golden Compass (movie review)

I liked the blend of Victorian aesthetics, ala Pirates of the Caribbean, with semi-believable high tech. We should be doing more with dirigibles. Neal Stephenson explores this meme complex as well, in Diamond Age, though with more emphasis on nanotech, ala Michael Chrichton's Prey.

All that concern about undermining dust and witches, separating kids from their animals, seemed like that old timers' religion to me, nasty and diabolical. I'm happy to keep ridiculing and/or demonizing the Inquisition for at least another century or two, why not, right up there with Nazis. Nicole plays a smooth villain, tries to pull a Darth Vader on Lyra (pretty name, Dakota).

I recognized the good guy cowboy (Sam Elliot) from Ghost Rider. He really gets around, that character. Plus I enjoyed seeing the new Bond (Daniel Craig) recruiting spy kids already (quick work for a new guy).

I found polar bear culture kinda dorky -- that "vying for the throne" meme gets tiresome, no matter how deep the voice (like, what a booby prize to fight over). But admirers of the book version tell me not to judge the book by the movie. Plus I maybe felt they were poking fun at Klingons, which gets me a little testy.

The pairings with animals (familiars) is fun, though Dakota reports the use of stuffed dead ones. Children have the more powerful counterparts, shape shifters, whereas adults have become set in their ways, settled into one character. Such sidekicks would help with diplomacy I'd think, as it'd be easier to "read the signs" as it were, figure out what's really going on, yet this civilization seems just as war torn and bumbling -- go figure.

Beer Note

I'll cop to sipping a beer yesterday, I believe my first since Vilnius, where I took some vows (which I didn't exactly break, but one could see a slippery slope here). Hey, the bottle had Frank Zappa on it, whose music I'll write some more about below.

Yes, I think Valley Girl is somewhat mean spirited, but then note he recruited a real pro VG speaker (his 14 year old, Moon), to give it some punch, which is what makes it art more than infantile dissing. He's part of a conspiracy to help kids keep from turning out empty-headed, always distressing when it happens, especially to one's self. In other words, one sister to another, read a few books (like Idiocracy in that way).

On the car trip to/from LA, Tara and I mostly didn't overlap on Zappa. We blared through the car speakers, using that Belkin gizmo, so mutual agreement was important, and turns out there was plenty we could both enjoy, like that Hate Me guy, and Sheryl Crow. She finds some of my Laurie Anderson stuff somewhat terrifying, but not unlistenable. I've got two from Britney she's OK with, if not my raving about (don't get me started).

Anyway, it was pretty good beer, I forget the brand, will maybe ask Stacy if she knows. Heading out for Lipton ice tea next, because "good for your karma" according to the beneficiary (and she's right). Then it's time to stalk the lonely Tinkerbell (I left her for fixin', but that was awhile back).

Mathematics in Nature

The Ivory Tower was in many ways designed as an escape from a harsh, cruel "real world" and "academic subjects" tend to be conducive to those wishing a life of quiet study, a purely monastic existence.

Of course marine biology, geology, other empirical sciences, tend to push our bell curve further away from such an indoors extremum, but the fact remains we're culturally inclined to insert a firewall between bookish types and athletic types, creating a nerds versus jocks kind of taxonomy (also a tyranny).

In contrast to these ethnic cliches, our integrative learning approach asks that we cut across these diabolical conventions. Finding mathematics in nature is not something to just read about. And especially now that we have fractals, it's easy enough to set a Cartesian-like canvas of XY cells in front of some scenery, and call that a complex plane, then iterate Mandelbrot style to achieve some coast of some island (like in Lost or wherever, maybe Uru).

The lab sciences have always been something of a bridge between the indoors and outdoors lifestyles. Heartening in this regard is this "math lab" meme, already out there, meaning we don't need to invent it from scratch (yay). Also under "maths" (in Britain a plural), come game-like simulations, which may be self-referential (cellular automata for example), but might just as well be about something (an ant colony say). Nowadays we run simulations as programmed executables, such that a well-equipped math lab includes workbenches (workstations) for programming.

Putting all this together, one can see why competence in driving one of our electric ATVs just goes with the territory. If you can't drive one of those, you'll have a harder time meeting the requirements of our math curriculum. And if you can't point to the current location of Saturn (might be under your feet?), then how can you claim to know your spherical coordinates properly? Sure, maybe those other math teachers let you get away with just being a nerd, but we don't think that way out here. We're extremely remote remember (but joining us is still a possibility, if you do your math homework).

Integrative Learning

svg graphic (converted), public domain

"Integrative learning" may be all the buzz, but what does it mean in practice?

Physics teachers may like an energy-based approach, which might involve draining rechargeable batteries, then using a money model "in the same breath" i.e. battery = bank account with pennies like electrons, flowing in circuits.

The velocity of money then relates directly to "power" i.e. the rate at which energy is spent (E/t). Food energy, exchanged for money, recharges the body's "batteries" and so on. That food in turn goes back to photosynthetic processes, driven by solar fusion. So here we have physics, economics, chemistry and astronomy all getting integrative treatment.

The goal is to find analogies that work, versus those that mislead.

XML is another integrative concept, in that we're given a Document Object Model (DOM) and ways to control it (model-view-controller).

Thanks to advances in browser technology, the SVG standard (an XML) has also come a long way (see picture above). So whereas language class used to just feature Roman numbered outlines, maybe a few network-like diagrams (so-called "concept maps"), today we have full-fledged XHTML, MathML and semantic webs to play with.

The tools have improved. The challenge is to encourage schools to take advantage of them, and to bring students up to speed on their use. Multi-track editors are but the tip of the iceberg.

The purpose of a backbone curriculum is to guide teachers in designing their own lesson plans, not necessarily to directly provide front-line materials. Good schools give teachers time to brainstorm, to research, to collaborate with their peers.

Teachers best know their own students, will adapt curriculum segments to meet local needs. If they're then willing to contribute these lesson plans back to a searchable repository (some database, or the Web itself) so much the better.

This process occurs globally already, so it's not really a matter of "making it happen" so much as managing and leveraging it, better optimizing teachers' time and effectiveness, per some Principle of Least Action.

Strong analogies promote integrative learning and good coverage, opening doors into many disciplines.

Students will then choose to specialize, following their natural inclinations, but not because they've been coerced into pigeon holes and/or ruthlessly "tracked" too early in their careers. Their ability to adapt, to switch tracks, will have been amplified, thanks to our integrative approach.

Nobody wants to be railroaded into a blind alley or dead end. Integrative learning decreases the likelihood of that happening, to teachers as well.

Story Problems

[ originally posted to math-teach @ Math Forum, two typos fixed, hyperlinks added ]

So the spectrum I'm addressing here is from meaningless to meaningful, with the former kind of story problem focusing on underlying abstractions, the latter having "real world" dimensions.

Wayne has championed the former, and indeed many of like mind ridicule anything deliberately reality based as "rain forest math" i.e. a transparent attempt to politicize, whereas aloof/removed abstraction is supposedly closer to apolitical vs. just head-in-sand Ivory Tower (i.e. "leave me alone, I just wanna do math problems, don't care what they're about").

The "physics first" movement, also "first person physics" represent a happier compromise, in that our story problems are "themed" around the concepts of energy and power. Given algorithms may be ranked for efficiency, all that's required is to understand that mathematics itself, the physical process of doing it, is energy-consuming. An inefficient algorithm is like an energy-hog SUV (oops, political -- no apology).

So in our computer math sequence, developing among various charters, other risk-taking academies not in the thraldom of some textbook (by definition out of date -- more on that some other time), we look at human productivity and algorithm efficiency "in the same breath" as it were, meaning we have that metrological component so despised by the "purists" (i.e. we actually care about empirical measures).

But rather than just wallow in joules and calories, we also have the concept of O-notation and the curves (graphs) those imply. Average 15 year olds understand what it means to "work inefficiently". That we might use mathematics to improve productivity, cut down on wastefulness, is a key point of this curriculum.

Apropos of that, we don't waste the opportunity to make our story problems meaningful, as the goal is to stay appropriately interdisciplinary and in sync with other subjects. This idea of "go it alone math" that doesn't care about physics or biology or history or whatever is in itself inefficient, typical of slower, more wasteful thought processes which we'd like not to perpetuate in our eager, thoughtful young.

To some extent, you can judge a math curriculum by its story problems. Steer clear of the willfully meaningless is my advice. Life's too short for such idleness.

First Day

Today was my first M4W in the newly remodeled "mother ship," followed by social hour.

Great seeing Eve Menger again (like me, a Quaker and a Wanderer), and Aimée, and to reconnect with members of the Brown family (our families go back to mom & dad's University of Washington days, well before I entered the picture).

I handed over a DVD of Quakers on YouTube for accessioning into the library, plus another for the archives.

Tara and I also shopped at Costco, the first time I'd been back since before Willamette Quarterly.

Victoria phoned from Canada, reconnecting, not retired yet. She hopes to check in with mom sometime next week.

We caught the thrilling conclusion of the SuperBowl. Go Giants.

Brainstorming Curriculum

Today I brainstormed curriculum ideas with Anna Roys, who dreams of a new charter school near Anchorage, Alaska. I'll be able to use much of the resulting six page document in my work with other schools as well.

I put a lot of emphasis on the transition from ASCII to Unicode, on the analogy of going from gray scale or "black and white" television to images with more color depth (pg. 5). Sums of successive rows of Pascal's triangle = successive doublings, i.e. 2**N, a tie-in to Unicode's permuting of bits for labeling/mapping purposes (pp. 2-3).

Should a core nonprofit or for-profit provide oversight services to multiple schools, each with a local executive team, plus parent, teacher and student councils (pg. 1)? We didn't reach an answer to this question in Anna's case (it's too early to know).

XRL in Switzerland

whitepod

Lunch in Old Town

Dave got me out of my Richmond / Sunnyside orbit to an older section of Portland.

We discussed the ramifications of my coming out as a "Quaker animist" in terms of my practices, of inviting dogs to Wanderers gatherings and/or being openly friendly with a reptile on my webcam.

Given Portland's cosmopolitan culture, these are hardly noticeable eccentricities (like, just read our Willamette Week), but hey, maybe I'm making waves in Peoria or someplace. Alabama? I doubt it.

Anyway, always good having a chat with another krew mate on these matters.

I took along my copy of Ghost in the Shell 2 in hopes of getting scene 10 (Festival) moved to my iPod for personal use.

Dave also yaks about kayaks, took one to Mexico recently.

:: happy birthday dave! ::

Hacker Ethics

To some, "hacker ethics" actually sounds oxymoronic, as they've been raised among bigots or, more likely, have met a lot of unethical types calling themselves "hackers" or, more likely still, have heard of such types, maybe seen them on TV, like on some cop show (and maybe they've tried to imitate what they've seen?).

As so often happens, the fictionalized version trumps reality by default. No wonder so many of our students suffer a crisis in confidence at some point, in trying to make the transition from some televised never-never land of dreams, to an actual career path in the real world. "What do you mean real doctors aren't like on House, M.D.?" -- and don't get me started on Numb3rs.

Why blame the screen writers though? Their job is to write engaging material, not set the bar on how much reality intrudes. Audiences have some collective responsibility for setting the standards. Liberal Vienna was known for its high quality piano parties because of how people could take in the music, not just for how they could pump it out.

Ivory Towerites often assist the entertainment industry in projecting lionized (Olympian) screen versions of themselves -- makes the profession look good (or foolish, as some peers will judge), plus maybe helps down the road with recruiting (or backfires, maybe by playing into the hands of spoof artists and yes men).

Cops do it, and private eyes, so why not mathematicians?And let's not forget lawyers. Everybody likes having "larger than life" more glamorous versions of themselves out there, even if only in pulp fiction.

Anyway, the dumber the audience, the less hard you have to work to get them to suspend their sense of disbelief, i.e. to turn off their reality checking facilities (mainly because they dont' have any worth mentioning). It's so easy to satisfy the gullible with cheap thrills, and yes, that is how some geeks have made I living, I don't deny it.

So if you really think hackers don't have ethics, ask yourself how you came to that conclusion, and especially whether fiction, including science fiction, might have had some role in shaping your views.

Where's the Beef?

Reposted from Synergeo...

Now, before I scare up this little essay, I need to get something off my chest: has anyone else checked out [the Yahoo! group] synergetics? Like there had to be one right? Only one post so far, although this one almost fits next to it (allusion to "on steroids"). Funny bumper sticker: "...like steroids on steroids" (reminds me of a long-ago joke on Dave Letterman about the sitting veep).

Some probably found it weird that Bucky did so much work to unify coinage (money) with head of livestock in Critical Path, as if that couldn't be good economics -- "some brand of myth-making ethnography" was the popular (correct) verdict.

I say "correct" because if you look into popular culture, that very identification is just below the surface, as in "bang for the buck" (what's a "buck"?) Bears versus Bulls (so much in the news these days -- Bears winning). Yes, other animals get into it too. Not saying it's always exclusively Minoan, Phoenician or whatever it was.

Did anyone else take Economics 101? "As people start to make more money, they substitute this good for that," we're told. "And [drum roll] they start to eat more beef " (more money = more beef, one of those axiomatic white man equations).

It was like a mantra. Kind of like Hollywood was to cigarettes (all the stars used 'em, including slim women) so were middle-o-the-road all-American economics teachers to fast food America. Wow, like we're livin' high now, woo hoo. Let's all go to the bowling alley and eat burgers (our "way of life").

In keeping with this Anglo bias (beefeaters ya know), we're starting to see more grossology of the flavor: how many pounds of hamburger does it take to fuel 300,000 long divisions? Like we count how many joules or calories it takes for some average 8th grader to divide 17 into 4558943, get a remainder, and multiply that by the number of 8th graders doing that and some similar problems in the course of a given school year.

That being calories, gets us talking transfats and proteins, other nutrients, plus makes a concrete link twixt "beef consumed" and "bang for the buck" (in terms of long divisions).

This may sound like busy work, but of course the analog to the busy kid in her chair, is some laptop computer (picture an XO), doing similar arithmetical problems. Now we're talking battery life, throughput, issues of chip design -- the kind of YouTubes they're watching, thinking ahead to a career in some hub, not necessarily this one (Portland one of several -- Singapore another).

I've run this by math-thinking-l and places. Many profs are on board with what we're doing. We're getting back to what Bucky termed "operational mathematics", which I write about in Synergetica Journal Vol 1, No 1, and republished on the web. Computerization of these key ideas, in the form of interlinked lesson plans, is by now a reality. Once you add in the old "energy slave" meme (a recasting of "horsepower"), you've got a decent bridge to many engineering namespaces, including robotics (a Python API is one thing, but if firing a given method takes thousands of energy-slave hours, you should know that ahead of time).

Curriculum Notes

My closer readers know I'm into a mix of Pythonic Algebra and Synergetics, in that my polyhedron modules tend to follow the proportions given them by Bucky in terms of a "concentric hierarchy" (of polyhedra: tetrahedron, cube, octahedron, icosahedron, rhombic triacontahedron and like that).

There's also a melding with movie industry jargon in that I make a big deal about "real time" versus "render time."

The former, used in game engines, supplies human speeds of interactivity, whereas render time is superhumanly slow, unless you beef up with amazingly powerful rendering farms, and even then, the pipeline is different.

A real time engine'll use quaternions to keep Alice oriented vis-a-vis her world and your viewpoint. Rendering involves POV-Ray type scene descriptions driving a ray tracer.

Both involve textures, plus rendering chips are pushing more realism to the screen every day, so I'm not saying the current skill mix and industry standards are set in stone or anything.

I just want my students to have a clue. This is ToonTown after all.

Koski on T-Modules

Dave Koski is doing some detailed chronology regarding his explorations of five-fold symmetric polyhedra, starting with his stumbling upon the golden mean, then the rhombic triacontahedron, its stellate and dimpled complements.

Dave writes (#37501, typo fixed):

The rhombic triacontahedron that is dimpled in at 8 locations can have 8 regular rh triac surround it by filling in at the dimples. The space left over can be filled in with more 8 dimpled rh triac. So the 8 dimpled rh triac and regular rh triac compliment each other in filling all space.

The rhombic triacontahedron that is dimpled in only four locations is an all space filler by itself because before there was an 8 dimple and a reg rh triac complementing each other. But with only four dimples, the 8 dimple concept is shared with reg rh triac so they all have four dimples and look the same. And that looks like closest packing to me, since they stack tetragonally. Too lazy to make image, sorry. I would love to give credit to whomever discovered this one. It was shown to me by man named David Noble (I think), out in LA, back in the eighties. I do not think I would have thought of it.

Dave's obsession with golden ratio geometry led him to study Fuller's Synergetics, which is where he and I started to overlap, in LA (me just passing through) and Santa Monica (his domicile at the time). We were both recipients of the Synergetics Explorer Award, presented by Fuller's grandson Jaime at BFI (this was before I became BFI's first web wrangler).

Back in the early 1990s, David, myself, Russ Chu, Robert Orenstein, and Bonnie Goldstein (later DeVarco) were trying to realize Hal Hildebrand's vision of a Smalltalk storage system for all of Bucky's many boxes of papers, collectively referred to as the Chronofile (plus he had a bound volume set by that name). Safe to say, with an 8 MB RAM motherboard (purchased by Russ), and no budget, we were ahead of our time.

Anyway, Koski dissected what Fuller named the T-module, 1/120th of a rhombic triacontahedron, into discrete numbers of smaller T-modules, edges scaled by 1/phi (some say tau or vice versa) i.e. 0.618... (volume scaled by a 3rd power of same) at each smaller size level -- except another shape tends to stand out in this project, what Dave termed a Remainder Tet, also recursively disassembling.

David is chronicling all this on Synergeo these days, complete with uploaded pictures made with vZome by Scott Vorthmann, a nifty free tool for Zome users.

T-mod, classic dissection
in vZome by D. Koski

Lunch on Hawthorne

I had a fine lunch with the Boltons today at Than Thao, followed by some show & tell at my residence -- they'd not met Naga before, are new to this whole YouTube business.

Chuck is a retired emeritus from a golden age at Portland State, his career as a sociologist a product of the post-WII GI Bill-sparked renaissance, North Carolina's Black Mountain a flagship of that era, from whence our own Catlin Gabel gained some of its founding faculty.

Mary is a WILPFaholic like mom (I say that affectionately, akin to Buckaneer) and during lunch was trying to remember where she'd sat next to Dennis Kucinich on Hawthorne that time.

Dawn and their eldest daughter were especially close, from solstice festivals and such.

On our subsequent tour of the Linus Pauling House, she thought maybe this was the place. Could've been. Certainly mom gave her talk here.

They recommended Kite Runner, the movie, which Chuck thought followed the book remarkably closely, unlike so many movies.

Our families go way back. When they first met dad in Portland, they already remembered him from University of Chicago days.

Mom and Mary were active in WILPF even then, protesting in the streets against strontium-90 in the milk etc. (I sometimes joined in my stroller).

Congratulations to Glenn Baker on winning a CINE Golden Eagle for Stand Up: Muslim American Comics Come of Age. Glenn and I were high school buddies in the Philippines, house mates for awhile in Jersey City, have stayed in touch.

Wanderers 2008.1.16

Today's discussion was one of those vital, free ranging, all topics fair game affairs.

We were all older Caucasoids (by the usual taxonomy) although at one point I came out as Asian with a rhetorical flourish.

Lots of talk about death, friends who'd passed on, near death, birth (one of us was a practicing midwife of sorts), and the fact that Australia leads the world in efficient flush toilet technology.

The tone was generally upbeat although much discouragement and frustration was expressed, with this or that feature of the world.

I was invited to pitch Python, which I did with some gusto. I was late, as usual on Wednesday mornings, so missed seeing Patrick, another busy bee (and new fan of our snake).

Speaking of vital topics, Tara did this beautiful analogy between a cell (the DNA kind) and an ant hill. She actually knows quite a bit about ants from previous research, so her analogy was as much about ants as about cells -- quite detailed in both directions.

I was impressed.

This cell analogy project is a longstanding part of 8th grade culture at Winterhaven. I'd say Tara has adapted to this culture very successfully.

Had to run off to test the new web cam, on a bad hair day (just got it cut (I'm sure it'll grow on me)). Getting back into Skype.

me on critter cam

Political Polling

I find it interesting that "the economy" and "the war" are considered two separate issues, such that voters might be polled on which matters more.

In point of fact, "the war" is what the economy is dying from, as a fixation on military solutions has meant delaying any real focus on the needs of civilians (including discharged veterans), languishing in their toxic trailers, substandard schools, overcrowded hospitals or whatever.

Inept bureaucracies won't be held accountable for the jobs they're not doing, so long as we're terrorized by nebulous terrorists (what they'd prefer remain our focus).

Moreover, many supranationals have colluded to not bid on lucrative development contracts in the Middle East, in order to punish this or that political elite -- a gamble.

Getting beyond "the war" is probably the only way to save the economy at this point.

Let's see if the politicians give us some straight talk about that.

Rich Data Structures

Another trend that emerges when you view the Internet as a primary source of raw curriculum materials, is a willingness to build lesson plans around big data sets, as opposed to little, deliberately ridiculous in many cases, sample data sets in hardcopy.

So, for example, a chemistry class might begin with 'import pt' (for Periodic Table), and for the rest of the class, students follow along interactively e.g. pt.au.neutrons would spit back the number of neutrons in gold (we'll get to isotopes later). Entering all this data the first time is tedious, but chances are, someone has done that for you or (and this is important) has provided an API to some back end updatable database.

The ridiculous little examples were sufficient for computer science majors because their topic was "parsing" and the data might as well be nonsense, so long as the challenges were realistic, i.e. there were delimiters, other regular expressions, that might serve as raw material for programmed algorithms. Today we're using XML a lot, or YAML.

However as we move more deeply into this cyberfrontier, professors of other subjects start wanting more topical richness. Their ability to import a Shakespeare play as a namespace, or some other (possibly holy) writ, in the form of a densely populated module of highly organized multimedia, is nothing to sneeze at.

Related thread on comp.lang.python.

Rights, Then and Now

Our first successful test of the new MMM projector in its home setting included showing a first segment of Eyes on the Prize, a PBS documentary about the post Civil War civil rights movement in the United States of America.

From watching this film, I learned that Rosa Parks and friends were able to boycott public transit for so long because the families that depended on them would chauffeur them by private car. Basic childcare, daycare, gardening, chaperoning, needed to occur, lest that famous Southern lifestyle fall apart for lack of a supporting cast of extras (this was pre Pixar).

Judging from the front page of today's Oregonian, something similar may be shaping up in Oregon, as Americans without club membership in the USA are soon to be denied their driving privileges.

For many Norte Americanos, this move is effectively shooting themselves in the economy (whatever body part), as those same non-members were the only backbone left, in terms of getting the basics accomplished (mostly construction, maintenance, remodeling in the cities, agriculture i.e. food supply in the rural areas).

So will we see the emergence of privately dispatched bus systems based around unmarked minivans, shuttling non-member former drivers to and fro? Hey, maybe the DMV could do it, or TriMet around Portland.

More chance to listen to headphones, watch podcasts that way.

Anyway, it's quite possible. On the other hand, people might not be that smart, fail to organize, and let the economy go more completely down the tubes.

As an observer of social trends, I'll get back to you on what happens.

Doing my part for the economy, I went over to Sears at Lloyd Center today and purchased a brand new Kenmore, complete with tax credt (ODOE CF-01 for premium efficiency) and service agreement. I also deposited some off-setting earnings through a partnership account.

Tara is back from DreamQuest.

Gender Studies (2 of 2)

In a model of competing role models, each recruiting for a subtype within the species, you have the cards you're dealt (nature) vs. the cards you gain during play (nurture) -- not that the fine line between these two is always crystal clear.

In terms of gender, I think the age axis must be conjoined to make sense of the scholarship. What age ranges are we talking? The subject is really "morphology" as children are eager to learn what kind of adult such and such portends, in terms of childhood personality. "What track am I on?" is a perennial question. Gender studies potentially has some answers, if it deigns to fully embrace the time dimension.

However, even with a time dimension, the topography is way incomplete. If the "multiple genders" really are culturally ingrained to a large extent, as many contend, then in the next breath we need to admit of many divergent cultures. So don't be too confidant, just eyeballing someone on the bus next to you, that you have any insight into the role, or even the ethnicity.

To be cosmopolitan means to not be overconfident in such matters. Which doesn't mean you have to find out, either, i.e. don't be boorishly inquisitive just because you're in a shared public space. That might be Jodie Foster you're dealing with (smile).

PinBall in PDX

I bounced around a lot today, between telecommutes, although Razz only had a couple of errands.

Fun intersecting with Brian the other day.

Fired up Camtasia Studio really for the first time since swapping the Santa Cruz sound card from KTU2 (basement) to KTU3 (office).

I did some like Viiv type actions to compile YouTube fragments for inhouse perusal, by NPYM Quakers, of Quakers on YouTube.

AFSC is in Facebook in various guises.

Now I'm off again, Tara in tow.

Good to see the midwest sex ed segment on CBS News as it dovetails with my own message about YouTubes™ and/or Podcasts™ being relevant when it comes to shaping religious sects.

Hey, wanna work on a railroad in Oregon?

Gender Studies (1 of 2)

In terms of nomenclature, I sometimes prefer "girl / boy" over "woman / man" because the latter makes a statement about an added / missing "wo" whereas the former simply says "genetic distance" (less spin in some dimensions).

In my writings, you'll sometimes see me saying my XX-friend or my XY-friend, instead of girlfriend / boyfriend. That's in part an homage to those beautiful Sigourney Weaver films and that idea of a special planet for "double Y" guys. Cracks me up every time (no offense to my XYY-friends, whom I can't tell from XYs).

In any case, I'm sympathetic to the "multiple genders" school, don't really care how many. Having worked as a school teacher in a Catholic academy for girls of high repute, I can attest that girls, like boys, differentiate into subtypes, which I don't need to rank in order to name.

But then as a theater / TV /movie type thinker in some ways, I tend to more or less abandon "gender" in favor of "role" and get more into stereotypes / archetypes at that point.

In terms of namespaces, in other words, I don't really sound like any kind of gender therapist or whatever, neither do I talk about "chakras" that much (I keep getting the colors mixed up), although I have male / female friends who do talk this way, and I'm able to follow to some degree.

School Tools

Schools have a lot of resources at their fingertips, if they know where to look.

It's not every math teacher who knows about the Cortona or Flux Player plug-ins, that'll bring virtual worlds to life -- I'm talking VRML and/or X3D here, great tools for studying geometry.

Then there's Peda's stuff, and ZomeTool.

VIP Koski likes vZome for the virtual versions. Build the 59 stellations of the icosahedron or whatever it is.

The Portland Knowledge Lab still has a StrangeAttractors kit in its collection, worth a fortune given its rarity.

One Whale of a Wanderer

The story of Keiko has been told many times.

In this version, lots of kids saw Free Willy (a movie) and realized that amidst the Hollywood style gimmickry there had to be a real whale in there somewhere, a Lassie, a Flipper.

Sure enough, our celebrity lived in captivity and so kids of the world, insistent that adults walk their talk, campaigned to have him moved to a state of the art facility in Newport, Oregon, with an ultimate goal of truly freeing Willy (not his real name).

As it turned out, that last chapter was maybe not so successful, in that a cetacean raised in aquariums since childhood isn't going to adapt all that easily to the cold, cruel world outside. On the other hand, it was maybe worth a try.

I like to think of Keiko is an honorary Wanderer, the protagonist of a long, strange trip under the auspices of many adoring fans, many of whom got to see him up close and personal (me included).

Related reading: #1944 wwwanderers eGroup.