Tuesday, July 13, 2021

Go By Train

P1300623
Bill Lightfoot at Papa Haydn in NW Portland, June 2021

My intrepid Uncle Bill Lightfoot, last of my grandma Esther's sister's kids, made it to Union Station (PDX) from King Street Station (SEA) this morning.  

He left Seattle around 7:30 AM and was here by a little after 11:00 AM.  My expectation is he'd return, as usual (this has been his routine), on the Coast Starlight at 4:00 PM.

Bill likes these day trips.  He usually only has a couple hours in town.  We typically squeeze in a visit to a brewpub, Ringlers maybe.  This was all before covid.  Since the pandemic, he's been down one time, in late June.

Anyway, contrary to my expectations, the Coast Starlight has been canceled perhaps until September 1st. Fires in the Mt. Shasta region (Dry Canyon Bridge) have damaged the tracks.  

Apparently there's no way to break the route in two and have a bus intertie.  That's likely because rail travel is somewhat redundant to air travel in the region, and the passenger rail system doesn't get to treat itself as especially critical.  It's more of a luxury, a form of entertainment.  

Freight rail, on the other hand, still sees itself as essential and has some way to reroute.

Bill favors Papa Haydn, the dessert place, when we can fit it in.  We did that last time, visiting their northwest location.  This time, we would in theory have time to get to the Milwaukie / Sellwood location, however both establishments are closed Mondays and Tuesdays.  Today is a Tuesday.

Yesterday we had another gathering in my backyard.  Derek ("Deke") supplied much of the food from the back of his roving pickup truck, a logistical link in the city's feeding program, decentralized and cybernetic.

A lot of people still believe the world is run by "bosses".  I agree we have many breeds of crime boss, managing their criminal networks (religions, cults, banks, corporations, gangs, schools, governments).  

However nature presents us with a more optimized type of efficiency, pre-human, pre-money, pre-conscious.  Some philosophers acknowledge these deeper layers of the economy.  Others are apparently oblivious.

Sunday, July 11, 2021

Recruiting Drive

Whereas my curriculum writing might be interesting and suggestive, it doesn't tackle all the issues regarding workflow.  

How do the students encounter the material?  How do they demonstrate growing competence?

At this point, when I look for competence on my own terms, I look for teachers willing to tackle the main topic in my slide show, namely the concept of "dimension" in Synergetics.  

A willingness to take that on, shows a willingness to acknowledge the importance of semantics in this post Linguistic Turn world (namespace).

In addition, I'm putting my documents in a Github repo for a reason:  I'm encouraging forking, if not pull requests.  

My inclination is to keep my repos under my exclusive control while encouraging other teachers to use them as raw material for their own original works.

So yes, I'm at the beginning of my own recruiting drive, even though I've been recruiting for decades.  

I'm still looking for teachers willing to actually tackle a topic as exotic and esoteric as Quadrays.  

I think calling them "syntactic sugar", another "API" to the XYZ coordinate system, removes any sense that they're a significant threat.  

Sure, Caltrop Coordinates comprise a door into the Synergetics meaning of "4D" but that's a topic more in art and architecture than in Establishment Mathematics (EM). 

Unless you're into investigating the philosophical foundations of mathematics, Quadrays might remain an idle curiosity, a trinket, or a harmless gimmick.


Wednesday, July 07, 2021

Curriculum Writing

The workflow of being a professor and adopting a write-as-you-go approach to teaching, means getting a pipeline of textbooks flowing, with a captive focus group (to put it cynically -- in actuality they signed up voluntarily, for a front row seat). Anyway, it's a well known design pattern on which many capitalize, not only the teacher-author.

In the world of "free and open" the wheel spins even faster, as authors publish their updates through notebooks hosted on Github or one of those.  The world of wikis and repos now permeates academia, with librarians staffing a front door or gateway, in terms of providing training.

My latest project recapitulates old themes:  lets preview high school math through the lense of learning a computer language.  The executable scripting notation helps explicate the ancient Greek letter typography, involving capital Sigma to signify a looping construct, with a subscript.  

We write our own Sigma function in Python, passing in "any callable" (function or lambda expression) for driving a specific sequence.  Sigma provides the framework, of a start and stop index, and whatever index-driven expression, for producing the successive terms to be added.  Summation is the overall theme, ditto for the calculus Riemann Sum symbol, Sigma's analog.

Seeing the scaffolding in Python helps students bootstrap their appreciation for the original notation.

The process of using LaTeX in the context of a Jupyter Notebook teaches "school of tomorrow" level skills.  We can use it in Blogger as well, provided the MathJax Javascript library, invoked per this blog posts, comes through.

$$ \sum\limits_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6} $$

You know how when your children learn to drive, and the professional driving school teachers invite the parents i.e. you?  

Perhaps you have no experience with that, but in any case my point is how driving gets taught, evolves over time, and parents deserve the updates, if only to appreciate how their children are being trained.  

Side mirrors splayed further apart.  Headlights always on.  Etc.

Imagine going through something like high school, revisiting of the basics, as a fully grown adult, every ten to fifteen years or so, because of how quickly things change.  You might be adding a career change on top of that, reinventing yourself yet again.

Since I went to high school in the Philippines, in the 1970s, they've proved the AKS Primality Test, meaning when we get to Pascal's Triangle, we really should take advantage and show off how prime row numbers evenly divide the other numbers on that same row, whereas composite row numbers do not.  

The Triangle's rows are self numbers, lets not forget.  We use a Python generator to get them.  The entries get big fast.  

The Binomial Theorem hangs its hat here, as do several figurate and polyhedral number sequences.  Even the Fibonaccis may be discovered in the shadows.  

Pascal's Triangle has long been a Grand Central Station in our shared curriculum.  

Now AKS takes its place, along with RSA.  That's right, we're making a grokking of public key crypto an attainable goal by senior year.  By way of Fermat's Little Theorem and Euler's generalization thereof.  

Euclid's Algorithm kicks off the season.  

If this doesn't sound like any high school your remember, welcome to the club.  I'm sure you never learned about Quadrays, either.  During a summer enrichment course, we get to preview what most will have missed.

These are mostly well-trodden pathways, just not usually associated with high school in our more left behind Global University communities. 

Into the mix come my Four Flavors, per Heuristics for Teachers.  

I'm prone to think in terms of: 

  • Supermarket (logistics, databases)
  • Casino (probability, prediction)
  • Neolithic and (historical, visible)
  • Martian Math (futuristic, ephemeral)

From a science fictive Martian vista we pluck ideas for our Earthian markets today, and design programs around risk mitigation (prototyping, test piloting) and adoption (continuous integration).  

Our living standards, still thankfully Neolithic in some welcome ways, benefit from our projecting what we'll need to be packing for Mars.  Projecting about Mars helps us terraform Earth.

We're doing meetups twice a week online, over an eight week period.

Tuesday, June 29, 2021

Recap: The Modules of Synergetics

A & B Modules by Richard Hawkins

It would be great to have someone go over the modules with us, and Kirby has agreed to give us a short presentation.

                      Curt



That's one of my favorite posters (Curt's link above).  So clear.  So "elementary school" in flavor.  

Yet so not shared with many kids. And I don't think because of any invisible committee or meritocracy coming to a conscious conclusion. Inertia and reflex-conditioning (robotic thinking, AI) explains most of what we're up against, in my own sociological model of the global university student-faculty. 

We are the hollow men
We are the stuffed men
Leaning together
Headpiece filled with straw. Alas!


For those not on the call, here's a brief synopsis of my talk on the modules, with a few grace notes added, for this archived version.  

Curt let me screen share so that some of the web pages cited below were displayed in the course of my "lightning talk" as we call short Show & Tells in Python world (< 5 mins). 

====

On pg. 52 of Cosmography, Fuller mentions A, B, T, E and S "modules".  These are names he gives to tetrahedral wedge shapes that may be: 

(A) used in the assembly of other shapes (e.g. 24 A modules, 12 left and 12 right, build a regular tetrahedron of volume 1) 

and/or 

(B) treated solely as volume measures (like cups and spoons used for liquids) 

For example 24 x 3 = 72 A-modular thimble-fulls of water, would precisely fill a volume 3 cube with edges sqrt(2) and 2-R face diagonals inscribing our unit volume tetrahedron (where R = IVM ball radius; 4 such balls defining the tetrahedron). [0]

To actually assemble said cube from the modules (like a 3D jigsaw puzzle vs. just pouring grain or liquid) you'd need some B modules as well (same volume, different shape).

As & Bs together brick in the cube, rhombic dodecahedron and the Coupler. Both A & B have a tetra-volume of 1/24. Two As (left and right) plus one B (left or right) make the Mite (minimum tetrahedron), a space-filler of no outward handedness (yet left and right may be distinguished in dissection).

I pointed out this chart (Inchbald, Steel Pillow [1]) and table (by Michael Goldberg [2]) showing how the shapes Fuller defines and describes in Synergetics in terms of A & B modules (e.g. Mite, Rite, Coupler...) already appear elsewhere in the mathematical literature, sometimes in the context of answering the question "what tetrahedra fill space, and with no need of left and right versions?" That's a question Bucky took up as well.

Fuller's focus on space-filling tetrahedrons connects him to Sommerville, Hall, Goldberg etc. however Synergetics is not the type of book that footnotes / cites all the previous lit on a given topic.  Nor do mathematicians usually see any pressing reason to cite outsider Fuller on these topics and/or use his vocabulary, or think in terms of tetra volumes.  What peer group would reward such behavior?  An anthropological question.

In terms of outreach, these points of contact suggest possibilities for the interdisciplinary diplomats among us. 

Michael Goldberg intersects Fuller's research in other areas as well, around geodesic sphere classification and hexapents (another name for which are "Goldberg polyhedrons" [3]). E.J. Applewhaite got to meet him and liked him ("not a mean bone in his body" I recall him saying), even though citations to Goldberg seem to eclipse and occlude links to Bucky e.g. when Scientific American got around to narrating the discovery of the virus structure, and left Fuller out of its account, much to Bucky's chagrin (I had some access to EJA's archives).

Regarding the T & E modules, that's where I fit the "mind the gap" meme (a meme CJ has been using in a related context).  

Fuller had been seeking a volume 5 to join his family of volumes 1, 3, 4, 6 and 20, for tetrahedron, cube, octahedron, rhombic dodecahedron (RD) and cuboctahedron (VE) respectively (as "flower-arranged" i.e. "nested" in his "concentric hierarchy of polyhedra").  

At first he was attracted to some high frequency idealized sphere as his candidate volume 5.  But in retrospect, and after a battle with his "subconscious demon" [4] he glommed on to the rhombic triacontahedron (RT).  It would have a volume of precisely 5 if its radius were set at 0.9994... i.e. just shy of 1; the exact number may be expressed in closed form involving surds, notation which Fuller did not eschew, even though he did not subscribe to current axiomatic dogmas regarding the so-called Real Numbers.

120 T-mods assemble such an RT5 (30 diamond faces, volume 5), whereas 120 E mods assemble an RT5+ of radius 1 precisely i.e. the RT5+ "shrink wraps" (is precisely tangent to) the uni-radius ball of  the IVM (= CCP ball packing). [5]  We need them both.  The RT5, scaled up by 3/2 to volume 7.5, aligns with RD6 in terms of sharing vertices. T-mods have volume 1/24, just like A & B modules.

The concentric hierarchy is tight.  Compact.  Pregnant with so many relationships.  Worth sharing, even as a purely Platonic construct (pre-frequency, pre-time, pre-size, i.e. "eternal" in parochial-local synergetics nomenclature).

Finally, the S module bricks in the empty space between the octahedron of volume 4, and an inscribed, faces-flush icosahedron.[6]  I took us to a Koski Identities page.[7]  

Curt said David is enqueued to given a presentation sometime (he's vacationing in the upper peninsula these days) and had sent a bunch of materials -- including about phi pi (a close approximation of pi based on phi) which, of all David's research foci, I myself am not really into (I also tend to snub the snubs e.g. snub cube etc.).

I emphasized to the group that whereas Fuller endows his modules with energy-conserving and dispersing properties, and envisions cellular automata type studies that could somehow link his modules to CERN style particle physics, my own focus is on such low budget Platonic stuff, meaning I just stick to the pure geometry of it all and don't myself claim to be doing any high energy physics around the synergetics modules (I'm no Nassim).  I'm just a double-A battery low powered operation, like a wind-up toy bunny.

Should we have some breakthroughs in this area (where Synergetics meets CERN), that'd be another advance for modelability for sure.  For me, Tensegrity = Hypertext = WWW is already a CERN connection, i.e. the computerization of synergetics. [8]

Both Snelson and Fuller had high hopes their respective models would prove relevant to atomic studies.  Snelson focused on electrons, whereas Fuller hoped the atomic nucleus of transformable protons and neutrons could be modeled as closest packed spheres in some way with rhombic dodecahedra and his Coupler (8 Mites assembled in many different ways -- Chapter 2 discusses the permutations) in play.

====

ENDNOTES:

[0]  How could a cube of edges sqrt(2) have anything other than "sqrt(2) cubed" for its volume?  My slideshow on Fuller's meaning of "4D" begins there, by answering that question. Just as he challenges us on saying "up" and "down" instead of "in" and "out", he would have us question our most dogmatic (reflexive) use of "squared" and "cubed".

[1]  http://www.steelpillow.com/polyhedra/AHD/AHD_Chart.pdf (Archimedean honeycomb duals -- starting at its root with a handed half-Mite, what David Koski dubbed a "smite").

Table is from a 1972 paper i.e. pre the publishing of Synergetics.  


[4]  986.208  "My hindsight wisdom tells me that my subconscious  
demon latched tightly onto this 5 and fended off all subconsciously challenging intuitions." (cite Mistake Mystique -- something CJ harps on).

More about T & E modules:

[5]  That's another point of contact by the way: IVM = CCP = FCC but for minor nuances and connotations. Dr. Arthur Loeb was the interdisciplinary diplomat in this connection, in both what he taught, and in his prelude to Synergetics.


Some of the latest research on the S module.  E.g. not in Synergetics 1 & 2:  S:E == VE:Icosa (same ratio) where VE and Icoas are related by Jitterbug i.e. same edge lengths. 

S/E as a factor (about 1.08...) takes us to explorations of a Jitterbug-like transformation, also in Synergetics, wherein the icosa inscribed in the octa (faces flush) turns into a *smaller* VE, faces flush to the same octa. Multiply that VE by (S/E)(S/E) to get the corresponding larger icosa's volume.  Whereas Icosa * (S/E) --> larger VE by Jitterbug.

(hit green arrow to run the Python, eyeball the source code to see the groovy volume expressions for S and E modules:

φ = (rt2(5)+1)/2 # golden ratio
Smod = (φ **-5)/2 # home base Smod
Emod = (rt2(2)/8) * (φ ** -3) # home base Emod


Wednesday, June 09, 2021

Shooting the Breeze

About Python Properties and Goldberg Polyhedrons... Subgenius, Die Antwoord

Friday, May 21, 2021

Saturday, April 10, 2021

Asylum City Meme

Many an American suffers from a complication of Affluenza:  too much stuff.  If you have a garage or basement, so much the better, but many pay for storage lockers.  The standard way to cut down on stuff: Good Will.

An Asylum City along a train and/or truck route needs warehouses, apartment complexes, and scattered dwelling units.  EPCOT was a model (Walt's version, not the theme park).  We're envisioning "aerospace yurts" and "domed gardens of eden" for the dwelling units (Henry Ford Museum; Cornwall UK).  But do those moving in need to buy new stuff?  For the most part, they do not.  Bring your own stuff through the triage process, keeping most of what you want and contributing much of the rest of it to the commons.  

People come to Asylum City with a mindset of paring down, starting over, lightening up.  Those leaving have typically absorbed more "urban nomad" skills such that they're able to travel without a lot of stuff, but with appropriate gear.  You've got your yoga.  The dwelling units will increasingly go on a timeshare schedule, as original occupants decide to move on.  Golf carts from the bus terminal.  You didn't need to bring a personal vehicle.  Car ownership, like horse ownership, is mostly a drag.

Friday, April 09, 2021

Chinese Peace Corps

CPC is an old meme around here, by now.  The dire poverty of so many in the Western Hemisphere, is sometimes easier to address outside a competing hemispheric power, meaning India.  Getting exchange programs going on the basis of mutual aid, but also shared experience and language training.  Africa is just as worthy as Greater Detroit of course.

Monday, March 29, 2021

More Wikipedia Talk on Facebook

I don't see the A,B,T,E,S modules as an isolated topic in that they're constituents of the concentric hierarchy, itself defined in terms of the sphere packing lattice (IVM). The concentric hierarchy, with its Jitterbug Transformation, provides the beating heart core of Synergetics.

When we call Synergetics explorations of the geometry of thinking, we mean these streamlining, simplifying heuristics that have more whole number memorability than standard fare e.g. 10th grade "plane geometry" with polyhedrons in the back of the book and not always reached.

Descartes Deficit, Euler's V+F=E+2, and the spherical spin networks fit into the same tight little framework of interconnecting ideas, a "memory palace" of useful concepts. We get the language of systems, spheres of relevance (omnidirectional halo), concavity and convexity, frequency (time/size) and angle (eternal shape).

Given Fuller's (a) overall prominence independently of people reading and commenting on Synergetics and (b) folk fascination with polyhedral geometry, I'm somewhat shocked at how few papers since the 1970s, even if only about obscure corners of grade school pedagogy, deign to take up the concentric hierarchy from any angle. The volumes table in Wikipedia is practically nowhere echoed in the culture by any other authors. Yet that volumes table, which includes the modules, is what Synergetics is so much about.

Sure, there're a few of us, but way too few for comfort, who carry the torch. But I find it semi-incredible, yet true, that elementary and middle school teachers across the board have no exposure to A,B,T,E,S in the course of their training, either in math or in the American literature of the 1900s. People treat the concentric hierarchy as something deep that should be left to the specialists, whereas the actual subject matter is closer to kindergarten than college. By now, the 40 year gap in attention, the malign neglect of these innovations, has become the story, as much as the concentric hierarchy itself. What was the reason for this neglect?

A New Englander from Bear Island writes densely philosophical prose ala Poe's Eureka, wherein he celebrates the Individual, over governments and corporations, as the source of wealth and culture, and with a "hotline to God". Very Emersonian. And his great aunt was Margaret Fuller. To not classify Fuller as in the American Transcendentalist lineage would seem an error, not that such a classification is exclusive of other ways to compartmentalize. But for the sake of curriculum coherence, we've got a useful pigeon-hole. I've taken up the matter with a Transcendentalist group here on Facebook and received zero push-back. They're into it.

Probably the best argument that Fuller should not be considered a Transcendentalist is that by convention that chapter in literature has been tied off as a pre civil war phenomenon. The Buddhist idea of a "lineage" that goes for hundreds of years, does not seem to apply when telling America's story. Were it not for the convention of saying the age of the transcendentalists is over already, I'd say including Fuller within that lineage is a no brainer.

To my mind, Bucky waited until towards the end of his life to publish Synergetics because he knew a strong track record would help. Having people willing to work with you and take business risks with you is testament to their not thinking you're full of snake oil. We already have Applewhite and Loeb attesting from their two different angles that Synergetics is not a waste of time.

Ergo I think the Concentric Hierarchy was already sitting in clover (with color plates and everything) when a next generation showed up and maybe decided to neglect its cultural heritage.

This is not an argument from authority. I dove into the subject and checked the math. Koski has showed directions forward e.g. VE:Icosa = S:E isn't that spelled out. The whole game of using phi-scaled E and S modules to fill other volumes shows me his getting the Synergetics Explorer Award was not based on snake oil.

My story of Synergetics: The Invention Behind the Inventions is also plenty compelling, when you stand it up next to all the papers and lectures devoted to far less ambitious topics than Fuller's memory palace.

The reasons for all this malign neglect do not necessarily trace to shortcomings in Synergetics. Fuller himself put his finger on it in what Nature calls one of the most influential works on the topic of sustainability, Operating Manual for Spaceship Earth: he said overspecialization was the biggest threat i.e. no academic department sees fit to tackle anything so manifestly multi-disciplinary. Easier to attack the messenger with all these canards about Fuller's lack of intellectual integrity. Smear tactics and character assassination. The car flipped over, the domes leaked, and every idea he had was a popularization of someone else's. He became a target.

I choose to side with Applewhite and Loeb over these featherweight detractors who are losing the battle for hearts and minds.

Monday, March 22, 2021