Tetrahelix

We're still waiting for some enterprising blockchain company to choose the tetrahelix for a core animation. The successive blocks form the twisting path of face-bonded tetrahedra why not? Blocks are blocks. No one said the chained "blocks" have to be orthonormal, an aesthetic considered uncool in some circles, given the alternatives.

Gary Doskas is one of the current masters of tetrahelix lore and I ran the idea by him, but maybe he doesn't straddle the geomtech - fintech divide. Few do apparently, or we would have a lot more better toyz by now, counting computer games.

Clearly I've got tetrahedrons on my mind again, as I recently published a narrative to a couple listservs talking about the so-called "Goldberg Table" wherein Michael Goldberg summarizes what was known about space-filling tetrahedra up to the time of his publishing his paper.

The point of my Goldberg story was that Buckminster Fuller is repeatedly cut out of accounts where he's making serious contributions, either to virology, geometry, architecture or whatever, because there's always a convenient "inhouse luminary" better positioned to take the credit. From TrimTab (April 25, 2024):

It just so happened that Fuller's research carried him over territory being surveyed by professionals in many walks of life at the same time. Virology, the discipline, was bringing them together even more than architecture. 

The price RBF paid for his comprehensivity (anticipating CJ's book) was not being best of the best in any of the various fields he was visiting, meaning one could always swap in a home team star come trophy day [1], leaving "good at skipping rocks" his only real claim  to fame (I say that whimsic-sarcastically).

The dismissive attitude I'm circling is well-demonstrated by the lengthy reply we saw from Andrius:

The best we have is this Goldberg table. The point would be to show that polyhedra can fill space. Perhaps that would be useful for a model of dividing up conceptual space, which is actually what I do. But no, you have no interest in actually applying this math scientifically. Your interest is to validate Buckminster Fuller. An honest investigation would dive into that, what is that all about?

I have not been at all reticent to discuss my interest in validating Fuller's research. That America's premier futurist of the 1900s has been deplatformed by so many universities, after their milking his popularity when he could draw the big crowds, and paying students, is somewhat scandalous to say the least. Applewhite was always wondering how they got away with it, with impunity.

Quoting more from my TrimTab post:

Apologies if the ordering was confusing, between Fuller's compact vocab (mite, rite, bite...) and the Goldberg table of tetrahedral space-fillers coming to be known at the time. That slide (in my BEAST deck) is still evolving.

Speaking of Michael Goldberg, Applewhite said he'd met him (I recall asking him about Goldberg specifically, given his key role in our narrative) adding "he didn't have a mean bone in his body" meaning in that context Ed didn't believe the guy had any malevolent intention of deliberately messing with Fuller's self promotion / reputation i.e. he was no kind of villain or foe.

Easy to believe I'd say. "Space filling tetrahedrons" is a pretty obvious topic, when you get right down to bare bones and/or brass tacks, as are subdivisions of a sphere using variable frequencies. "Aristotle was right, remember the MITE" could be are our high school chant, in some weird sci-fi School of Tomorrow. Cue cheerleaders.

This was the footnote (see above):

[1] per Ed, Fuller was especially hurt when a certain Scientific American article summarizing recent breakthroughs in the field of virology, skipped mentioning him completely. I got to see some of the primary materials.

Catacombs

As some of you know, I've donned a Sociology hat and have been focusing on shaping relationships among "meetup-based" subcultures. I use "scare quotes" because of connotations around "meetup-based". Of course using Zoom a lot (a characteristic) is a recent development, galvanized by the SARS2 outbreak, and many of these subcultures were chugging along, sometimes famously, without the benefit of internet-based meetups for decades, if not centuries. Think churches, temples...

In tandem with these studies, I've taken up the topic of insect mentality, or shall we say dynamism. What are the deltas associated with an ant hive in particular? The metaphor of "tunnels under Disney World" has again arisen. I have to add: Catacombs. We're into the chthonic around here.  Mount Parnassus.

My thinking around the ants, inspired by Active Inference Institute faculty, DAF in particular, left me wide open to the sudden discovery of miner bees in my front lawn, at the base of the Tetrahedron, the pyramid of C6XTY beneath my front porch that makes helps Keep Portland Weird. Miner bees don't build a hive in a tree; they build individualized residences. Tiny mounds of dirt pop up, as a result of excavation. How catacombed these tunnels may be is a topic. Current answer: unknown. I'll read up on it sometime.

A household down the street was convinced it had a wasp infection and little warning signs went up everywhere, however I think it's likely merely a miner bee visitation for them as well, as the signs are now gone and, walking home last night, I saw a few tiny dirt mounds in the grass. This seemed to happen all at once around town (I say that now based on two data points), as if on a timer. 

YouTube says the world has over a thousand species of miner bee. They're not aggressive towards humans, don't or can't sting, and they cross pollinate. Gardners love them. They're not honeymakers though, so they're not usually "kept" in the beekeeping sense.

The Catacomb Codas. I've stuffed many a deep chamber with some of this Synergetics stuff. Detractors (or even entomologists) might picture me barfing up pabulum, weighed in tetra-somethings, anticipating this nurturing content will empower the colony going forward, the hive mind or whatever. 

At what level of consciousness does a hive operate? Put like that, the question is still a mirage, suggestive of a real question, still but a fevered dream. However, other questions might still be worth asking. Prompts get fine tuned.

Even though I've favored a Dark Theme in the Codas, a personal setting, I'm working to keep the subject matter non-turgid and easy breezy, partly because the purpose, architecturally, is transit, or liminal. Let's say vestibular. I'm meaning to sweep you onward, to your next flight, while providing a pleasant environment in the meantime. Enjoy your visit.

Think Tank Meetup

A lot of humans get born into high density population centers and scarcely have the opportunity to experience the opposite: low density areas. A theme in my blogs over the years has taken inspiration from Portland, Oregon's "outdoor school" institution: the public schools include an out-of-town camp-based experience wherein presumably light pollution is low enough to make the Milky Way visible.

I've tacked on the "make the Milky Way visible" tagline, i.e. I don't believe I'm cribbing it from official outdoor school literature, but if that's explicitly part of that program's mission statement, so much the better. Bill it as a psychological health requirement. You need outdoor living experience for that high school diploma.

Which brings me to our topic last night at the Think Tank (what we've taken to calling it): housing around Portland. My long term readers know I've hoped to get Portland into the "Refugee Tech" business, where "refugee" fades in and out with "camper" and "nomad". 

Some people hit the open road by choice, in a high end RV they've been saving for, and now have, in retirement. Others might fancy a pre-retirement business oriented vehicle that doubles as a place to stay, the so-called "business mobile" or BizMo option. Then you get people forced out of their homes by natural and/or economic disaster (e.g. war), and becoming reliant on social engineering, i.e. back to the "refugee" paradigm.

Portland has done some pioneering work along these lines, according to our guest, especially when it's not too proud to learn from other metro areas, and not just San Francisco and Seattle.

My approach focused on enrolling people into the business of shelter testing, with ideas flowing from the prototyping front lines to the commercial market as finished products. I used to send my little diagrams about it under the rubric of Project Renaissance. This was before public-private partnerships got such a negative reputation (long story).

Integrity Testing

Welcome to my journals. Welcome back if you're returning.

Let's recap: 

Facts I use as evidence, that Verboten Math is subversive include: 

(a) it's not taught 

(b) it won't go away

(c) it has practical applications

Most candidates are revealed to be (i) nonsensical (ii) false or (iii) trivially true. No such verdict has been established in this case, ergo it won't go away.

However, most people have no clue what Verboten Math even is (it's not taught), and calling it Martian Math instead doesn't really help matters. 

In fact, Verboten Math is a source of good ideas for the mainstream, once these ideas are sanitized, their  radical roots obscured.

In today's meetup (recorded) I mentioned Quakers had a history around creating schools, and with schools come their hallmark curricula and faculties. As Quakers, we need to compete in order to enhance our brand, and bring glory to God. We're not afraid to share Verboten Math. On the contrary, we relish the opportunity.

The New England Transcendentalist aspects, Margaret Fuller and so on, were always conducive to Quakers taking an interest, as is the inbuilt skepticism regarding Manifest Destiny style imperialist mindsets, a skepticism shared by Andrew Carnegie and Mark Twain of the Anti-Imperialist League.

In a move to repair the damage brought on by a narrow-minded and short-sighted global plutocracy, wrapping itself in the Stars and Stripes, American schools overseas have a special incentive to phase in elements of Martian Math, given both its highly geographic content, and its potency as positive PR, as Americana and as a vanguard for USA OS.

Refugee Planet

first published Oct 21, 2023

Meeting Notes

I was admiring the curriculum materials shaping up around ant colonies, their study. Daniel knows a lot about ants, and yet humanity on the whole still has a lot to learn. The study of ants is somewhat humbling, in terms of revealing our own ignorance.

Picture a queen ant, surrounded by layers of caretakers and apparent hangers on. We say "apparent" because in some theories the seeming passive crowds may store collective memories, ready to be expressed if triggered. The queen never ventures forth and workers tainted with experience of "the outside" don't get anywhere near her. If she serves a decision-making role (unclear) it's from within an abstracted layer where experience consists of pheromones.

Remembering that Andrius wants to "know everything" (the answer to the prayers of those with boundless curiosity), I'm eager to introduce him to CJ's work on comprehensivity. The commitment to "learn everything" is inherently problematic, and sounds like empty chutzpah unless qualified with self awareness and acknowledgement of the inherent paradoxes. 

"Tackling it all" is not only possible, but what we all do every day. It's just that, depending upon strategy, resources, and the practice of specific disciplines, how much we accomplish towards our impossible goal varies by orders of magnitude.

I took some time this morning, after feeding the dog, adding to my M4W repo on Github, where I chronicle recent progress. I haven't expressed a "know everything" goal, but I do value "comprehensivity" as CJ calls it, as many of the levers one needs to discover, as an activist, come to light only through considerable experience. Those into ML (machine learning) have a lot of concrete mathematics to show why quantity, not just quality, matters.

As a Quaker journalist, i.e. blogger, I need to keep twisting my strands together, and pulling tight, making a strong alloy, the way we often talk about our metaphorical language. The No More Secondhand God approach to religion means cutting out the middleman, a Buddhist teaching as well. We might be able to come up with more neurological-sounding explanations for why individuation is a positive. Transcendentalism here we come.

But we're also talking about sanitation and fish farms and Global Village communities. Where might we get to go, to gain all this leveraging experience?

On my end, I follow David Koski's research into phi-related topics. Phi (the golden mean) is already a hugely popular topic, but combined with Verboten Math it provides a goldmine of new material.

Knowledge Engineering Study Group

The story behind this meetup is we've started playing around with Coda more, "we" being the math4wisdom clique based around a figurative memory castle in Lithuania (not Transylvania).

Spring Retreat

If you've seen my Graph Theory slides, you might remember I toss my high school yearbook picture onto a slide next to Sam, likewise a younger man then, in the company of Bucky Fuller. They flew to the Philippines together, as guests of the Marcos family. I was living in Manila at the time, or perhaps was away for college. I was in Class of 1976 at International School Manila (ISM), which still exists but in newer digs.

Sam and I didn't know each other then. I learned of Sam Lanahan through Trevor Blake, who tracked him down as one of the owners of an original Tetrascroll, a very limited edition artifact. We set up an appointment to see it (but have yet to do so (it's still in its case)) and drove to Corvallis to meet the guy. We continued to hang out sporadically and undertake collaborations well into the future, especially during a chapter wherein Sam lived in Portland itself.

Sam's grandparents were pretty famous: F. Scott Fitzgerald and his wife Zelda, their daughter "Scottie" (Frances) being his mom and one time columnist for the New Yorker. Sam's dad, Jack Lanahan, had been a boxer in his Princeton years. After Frances died, he remarried. 

After moving from Corvallis to Portland, Sam moved a few more times, winding up in a well appointed farmstead in the Willamette Valley. Which is where I am right now, on retreat, working on projects, such as on Quadrays for M4W (math4wisdom).

My backyard in Portland is an outdoor museum for c6xty exhibits. The plastic sculptures become somewhat brittle after years in sunlight so we probably won't move them. 

These prototypes were meant to provide lots of feedback, about stressability, durability, replicability, constructability and so on. Several test materials were employed: plastic, steel, copper, aluminum. 

The farmstead is likewise decorated with specimens of each. C6XTY is a subtype of Flextegrity, which is adjacent to Tensegrity (ala Kenneth Snelson et al) but is more lattice-oriented.

What I've done around Flextegrity is develop my Python code base to render computer graphical versions, sometimes in the form of animated GIFs. My graphics generating pipeline involves using Quadrays sometimes, a type of vector akin to XYZ but featuring "basis vectors" at 109.47 degrees to one another. They're designed to make lattice work easy, as in closest sphere packing arrangements (Conway: Barlow packings). All the CCP balls (that's a specific packing pattern) have whole number 4-tuple coordinates, such as (2,1,1,0).

Nowadays I'm collaborating on Quadrays via the M4W Coda. We're seeing to what level AI might get involved, among other experiments. I'm taking advantage of the high level of fluency around mathematics I'm encountering at math4wisdom, which is anchored by Andrius Kulikauskas, a math PhD. 

Does a "vector space" have to have a dot product? Even if it doesn't, might it still include Euclidean Distance? 

Must basis vectors be unit length by definition? 

What if they span space without relying on negative mirrors of themselves, shouldn't that count for something?

In XYZ, we have three positive basis vectors that may be scaled by -1, which means reversed, which some might classify under rotation (i.e. to "face the other way" is to rotate by 180 degrees). 

Thanks to negation, -X, -Y, -Z will also participate in space-spanning, but as secondary, non-basis vectors. They're second bananas.  (4, -1, 0) entails adding an X basis vector, stretched to 4 times its original length of 1, added to a negated Y (so a -Y), and no Z involvement, giving this point in space, now uniquely addressed.

Thanks to vector reversal, the three positive basis vectors (X, Y, Z), abetted by their second bananas (-X, -Y, -Z), span all of space by means of addition and further stretching or shrinking, but without further need for rotation. (4, -1, 0) = 4X + 1(-Y) + 0 where X and -Y are vectors (pointy arrows, directed rays of definite length (i.e. not rays "to infinity")).

In the IVM, using Quadrays, we have four positive basis vectors that may optionally be scaled by -1 (reversed), but we don't need that "rotational" feature to have adding with scaling span our space. We never needed the help of a supplementary cast of negated basis vectors, to reach all the stars in our universe (points in our spatial volume). Just stretch or shrink at most three of these four Quadrays, without changing direction, add, and you're done. (4, -1, 0) is equivalently (4 sqrt(2), sqrt(2), 0, 5 sqrt(2)).

IVM = Isotropic Vector Matrix, Fuller's coin, but not unrelated to the Matrix of science fiction, since aberrations of Fuller's IVM give it "frequencies" (think of wind chimes) which are like immersive radio channels or scenarios in those Matrix cubicles. 

The IVM is like the Star Trek holodeck in other words, but with no exit or off switch. 

However, more prosaically, it's simply the skeletal scaffolding one gets from the aforementioned CCP (cubic close packing), a ball packing pattern of ball:space density of about 74%.

Sam's C6XTY (or c6xty) lattice places a compressive soccer-ball-looking element (same Adidas Telstar hexapent geometry) at every IVM hub, such that those most immersed all have twelve balls around one. But unlike in the CCP, these plastic balls do not touch one another. They're suspended in a network of connecting armatures, adding lots of flexibility, permeability and variability to the design. 

Flextegrities could be more like jellyfish, with thin yet stiff enough filaments holding sensors in a neutral buoyancy lattice submerged in water, perhaps in the open ocean. The sensors might be whole number addressed, as by Quadrays, and selectively illuminated or otherwise activated by Wi-Fi.

My dad and I took up scuba diving in the Philippines, so it's not unusual for my mind to drift to these undersea vistas. Sam had some experience in marine biology as well, as did my cousin Mary (who went on to get a medical degree). Therefore the posters Sam had made for Lattice Gallery (a West Broadway popup in that winter of 2019), showing off Flextegrity in its underwater context, did not seem as far-fetched to me as they might have for other visitors. Experiments with immersed flextegrity lattices could be undertaken today, and/or may already be underway without my knowledge.

Automatic Writing

Prompt: Is Kirby Urner a mathematician?

Bot: Kirby Urner is not conventionally recognized as a mathematician in the academic sense but rather as an educator and curriculum developer with a strong interest in mathematics, particularly in the context of educational reform and innovative teaching methods. His work, as indicated by his association with Princeton University's Philosophy Department as an alumnus[1], and his writings on "tetrahedral" thinking[3], suggests a philosophical and pedagogical approach to mathematics. Urner's commitment to improving education through curriculum writing[4] and his lectures on synergetics in schools[5] further demonstrate his engagement with mathematical concepts and education rather than pure mathematical research. Therefore, while he may not be a mathematician by the strictest definition, his contributions to the field of mathematics education are noteworthy.

Citations:

[1] https://princeton.academia.edu/kirbyurner

[2] https://www.linkedin.com/pulse/from-new-math-gnu-kirby-urner

[3] https://www.math4wisdom.com/wiki/Research/KirbyUrner

[4] https://www.linkedin.com/in/4dsolutions

[5] https://youtube.com/watch?v=Lzv30IKvfZs

[6] https://youtube.com/watch?v=g14mu4uWD4E

[7] https://github.com/4dsolutions

Asylum Cities

When people talk "billions for Ukraine" it's usually not with some accompanying breakout, meaning it's left to our imaginations how much is for hospitals and care units of various kinds. One might imagine an entirely civilian budget in other words, and then ask how far short of that are we willing to sacrifice. Another dime on mayhem might not be a dime well spent.

Actually there's likely a breakout and I'm just not seeing it when I make my rounds of the various channels and repositories I visit when harvesting information. Probably a pie chart or other visualization. We're told some of the biggest slices go to the prime contractor irrigation system (Beltway Mafia) and for a lot of family estates, that's reason enough to slobber, in anticipation of more lucrative contracts.

Out here in the Pacific Northwest, we're more concerned with preserving wetlands and salmon. As to whether Oregon could host some civilian construction operations (healthcare oriented), I'm not so sure. My nudging us in the direction of doing epcots, with university connections, encounters resistance, I'm guessing partly because of the negative Rajneesh Puram experience. 

So my sights turn to Canada, perhaps the Yellowknife area? These campuses could stay small. Breitenbush is an inspiration, but I'm thinking higher tech, maybe with electric ATVs powered from batteries charged by wind and solar. Lets just see if that's even doable. Computer animations and simulations don't replace reality outside of AI. We need the harsh realities of Mother Nature to teach us whether our designs are really worthy.

Which brings us back to Ukraine. Something like a flourishing peacetime economy is long overdue, by some decades. Any budget should recognize the need for military disengagement such that mature civilian undertakings might resume in earnest. There's no point trying to masquerade while stockpiling ammo, as these installations will attract tourists and journalists, other visitors. We're not about being secretive so much as role modeling the freedoms that come with keeping it transparently open source.

I'm not suggesting there's any real difference on either side when it comes to addressing civilian needs. The Russian side of the fence needs hospitals, working rail, trucking, internet, the whole works. Devastation is not the goal, for anyone in Greater Europe. 

If your mentality is purely punitive, you must be low ranking. Tales of feuding and revenge get to hog center stage for only so long, as the cast continues to roll over. Deeper themes, such as building new infrastructure, take one further, in terms of leaving a lasting legacy.

But then again, here in the Pacific Northwest we're more focused on the Pacific Rim economy, while those Atlanticist east coasters remain obsessed with their West Asia endeavors. We're East Asia facing, meaning towards Indonesia, the Philippines, Japan, Korea, China, of course Bali and Borneo, not forgetting the Aussies or New Zealand. Lots more. I was editor of Asian-Pacific Issues News there for awhile (AFSC, obscure), plus the Philippines was my home for some formative years.

To the north, Russia again, but more as an indigenous people than some EU foe, fellow Sibero-Alaskans.

Russian businesses have had their branch offices around here since well before Oregon attained statehood. They had dealings with Tulalip, the established resource keepers. Many Oregonians are ethnic Russkies to this day (even Stalin's granddaughter joined us a while back), plus we have ethnic Ukes too -- these are terms of endearment, we all get silly nicknames.