Bridging from STEM to PATH

Bridging to STEM

New Circuit Designs for Motherboard Earth

Part 1

Part 2

Geodesic Domes

 

featured artist: 

王德祥

Imported from Twitter

From the archives: The fact that he thought a whole number volumed tetrahedron and octahedron, combining in what he called an IVM scaffolding, could help serve a C.P Snow Chasm bridging function, thereby countering what he regarded as paralysis-inducing overspecialization...

— Kirby Urner (@4DsolutionsPDX) November 7, 2021

... is sufficiently interesting as historical fact, to meet the bar of shareability -- whether or not Bucky was ultimately correct in his analysis.

— Kirby Urner (@4DsolutionsPDX) November 7, 2021

Public Schools Embrace Design Science

Not all at once mind you. A blend of computer science + the humanities is ready to roll forward without disturbing the math teaching rank and file, which are boxed in by standards. 

Our impact on other STEM subjects is more by osmosis and organic growth than because of any top-down campaign led by think tanks, not that we don't have our own think tanks and ways of advertising. 

Some public schools have more freedoms than others, when it comes to sharing American and/or World Literature and History. We do not all share the same notion of "cultural literacy" and the resulting diversity is considered a positive.

School of Tomorrow. Oregon Curriculum Network. 4D Solutions.

American Philosophy 101: The Bucky Stuff

 

:: pyramid scheme:  Descartes' deficit = one tetrahedron ::

Featured Artist Shares Goldbergs Galore

 

王德祥

More About S3

Halloween Theme

Memo re S3

Note that if I build an XYZ skyscraper and an IVM space station side by side, there's no implied scale factor until we start adding the little human construction workers and/or cosmonauts or whatever. The XYZ and IVM scaffoldings each float free of one another in the imagination with no necessary strategy for entangling them. Creating a conversion constant required a designer's touch, as there was no one right answer to mathematically deduce, nor any empirical answer for scientists to uncover.

What's revolutionary about a tetrahedron unit is not its size  relative to the XYZ system, but its shape. The tetrahedron stabilizes the cube and provides an ecosystem in which both have an integer volume, versus only the cube when it's allowed to hog the limelight. The tetrahedron is simpler, topologically, and stronger, structurally. Making it also be unit is a streamlining maneuver that XYZers get awkward about, forgetting to walk their own talk i.e. different axiomatic underpinnings were never verboten nor even defended against. We welcome this example of an alternative paradigm. 

Fuller figured out a way to bring a cube and tetrahedron within 6% of each other by making XYZ edge 1 be a CCP ball radius, and making IVM prime vector (tetra edge) be edge 2, i.e. twice XYZ's. The unifying concept, like the cosmonauts above, is the unit radius CCP ball. Make its radius define the XYZ unit cube  and make its diameter give the edges of the IVM unit tetrahedron. 

 It's a simple story, linking the two scaffolding strategies, the skyscraper and the space station skeletons.

One may also introduce the TetraBook at this point, the one triangular page book, with triangular covers open wide open flat. The page wages back and forth in an arc.

When the page is vertical to the covers, the two right tetrahedrons described, symmetric around this vertical partition, are each equal to that of a cube of edges R, shown in green down below. That's XYZ's unit cube, in the background. In this IVM world (call it Mars), we're modeling the unit cube's volume as a right tetrahedron of all edges D, except for the "hypotenuse" which is even longer.

Tilt the page a little further, either way, and you get a regular tetrahedron and its equal-volumed complement. That's the unit of volume in the IVM system, shown below in blue.

 

High School in the Silicon Forest (Mites Make Rites)

Dissecting Volumes

In Synergetics we closest pack (densely pack) a lot of ideas together. Arthur C. Clarke mentions that in his blurb, on the back of the volume. 

Much of that work is done using tetrahedral wedges or volumes known as modules, sometimes known as "quanta modules" because they quantify discretely. You're welcome to keep it Platonic by not hopping over to quarks right away. 

Fuller is entitled to speculate, but we're likewise free to think more in terms of a game of cellular automata in 3D, using Mite-shaped cells, ala Stephen Wolfram (a new kind of science) and J.H. Conway (a game of life). 

Mites fill space with clones of themselves, possibly by way of other space-filling shapes they build along the way, such as the Cube (3), Coupler (oblate octahedron, volume 1) and the Rhombic Dodecahedron (6).

Bucky himself links his Mite to Donald Coxeter's Regular Polytopes in one of his captions (see below), where Coxeter introduces an orthoscheme of the cube made of half-Mites, or Smites as we might playfully call them (as in "smitten, into semi-Mites").  

Coxeter was into kaleidoscopic reflections, and an orthoscheme, kaleidoscopically reflected, often tends to make a characteristic shape. 

The A module reflects to make a tetrahedron of 24As, 12+ and 12- (left and right), and As are orthoschemes, meaning there's a way to visit all four of its verts by making only 90 degree turns. 

If three right angles meets at a single vertex, it's a trirectangular tetrahedron, but not an orthoscheme.

The B module alone is not an orthoscheme, but an A and B face-bonded together make the 1/48th orthoscheme of the regular octahedron, canonically our volume 4.  1/48 of 4 = 1/12 = 1/24 + 1/24.  A and B are both 1/24.

Fig 950.12 Three Self-Packing, Allspace-Filling Irregular Tetrahedra: There are three self-packing irregular tetrahedra that will fill allspace without need of any complementary shape (not even with the need of right- and left-hand versions of themselves). One, the Mite (A), has been proposed by Fuller and described by Coxeter as a tri-rectangular tetrahedron in his book Regular Polytopes, p.71. By joining together two Mites, two varieties of irregular tetrahedra, both called Sytes, can be formed. The tetragonal disphenoid (B), described by Coxeter, is also called the isosceles tetrahedron because it is bounded by four congruent isosceles triangles. The other Syte is formed by joining two Mites by their right-triangle faces (C). It was discovered by Fuller that the Mite has a population of two A quanta modules and one B quanta module (not noted by Coxeter). It is of interest to note that the B quanta module of the Mite may be either right- of left-handed (see the remarks of Arthur L. Loeb). Either of the other two self-packing irregular tetrahedra (Sytes) have a population of four A quanta modules and two B quanta modules, since each Syte consists of two Mites. Since the Mites are the limit case all space-filling system, Mites may have some relationship to quarks. The A quanta module can be folded out of one planar triangle, suggesting that it may be an energy conserver, while the B quanta module can not, suggesting that it may be an energy dissipator. This gives the Mite a population of two energy conservers (A quanta module) and one energy dissipator (B quanta module).

Did Fuller think the Mite and its derivative Sytes (Bite and Rite) where the only self-packing allspace-filling irregular tetrahedrons?  He appears to miss both the half and the quarter Rite, as a self-packing space-fillers.  

In these vZomes by David Koski, the tan triangles are Rite halvers, whereas the two blue planes in the bottom canvas (one of darker shade) slice the Rite into four clone quarters.

The Mite and two Sytes, Rite and Bite, plus the half- and fourth-Rite summarize the five space-filling tetrahedrons known, right before Michael Goldberg introduced a new family.

David Koski has helped us cross-index the Smite's volume in terms of the concentric hierarchy, as also equal to that of the 1/4 Rite, and also to that of each of the 120 E-mod shapes (but bigger) building the rhombic triacontahedron of volume 7.5.

This RT of volume 7.5 (not focused upon in the first two volumes of Synergetics) is sized up by 3/2 (or by a 3rd root of same as a linear scale factor) from the RT of volume 5 (a star of Synergetics 2) which latter is made of 120 T modules (likewise volume 1/24, same as A and B).  

The 7.5 RT pleasingly shares verts with the volume six space-filling RD, another "circuit closer" in our geometric, mnemonic spatial mandala, i.e. the concentric hierarchy.  Four Rites make the Coupler.

Turning Left (Open Source)

This Old House (School of Tomorrow)

A Meta Meetup: Esoteric Memes in Cyberia

Check the Youtube description for related links. 

Also, for that story on Medium, click here, make me rich.

Heuristics for Teachers (continued)

From Agora on Quora

Are the philosophical needs of Americans being met?

Not really.

For one thing, “philosophy for children” is still considered arcane and off beat. Montclair University has been a key player in that movement.

We do teach metaphysics to children however, ancient Greek metaphysics. We call it mathematics and dress it up as not-philosophy.

But at the fundamental level, when you introduce points, lines, planes and volumes, as 0, 1, 2, 3 dimensional, you’re doing metaphysics. Philosophical debates belong here, not authoritarian commandments to not question the authorities.

It’s a “spooky” metaphysics, this ancient Greek stuff, in that you’re told you’ll never meet or experience the reality of some of these lower dimensional phenomena.

Even 3D can’t happen outside of Time (they’ll tell you).

So it’s like you’re learning about ghosts.

Since you mention Americans, and since the people who like to call themselves Americans the most are the North Americans who conquered the several territories and turned them into 48 states plus Canada, I should point out that some of the most important American philosophers are not studied as philosophers.

For example, Doctor of Philosophy (PhD) programs tend to overlook Ralph Waldo Emerson as a philosopher of note, and even though Nietzsche admired him.

Walt Whitman studied some Hegel.

The New England Transcendentalists, as they’re called, were imbued with German Idealism and came to their anti-slavery / anti-imperialist views without the influence of Marxism.

One of the few American philosophers who acknowledges this lineage is the late Richard Rorty in his slim tome Achieving Our Country. He’s a leading pragmatist who incorporates the later Wittgenstein’s anti-representationalism when it comes to his philosophy of language.

Finally, American philosophy departments are horrible when it comes to Buckminster Fuller, grand nephew of the Transcendentalist Margaret Fuller. They typecast him as some kind of Technocrat who had naive beliefs about politics and who simply popularized others’ great ideas.

My view, in contrast, is if you haven’t studied his Grunch of Giants and its precursors, you’re missing out on some of the greatest philosophy of the 20th century — a bold claim I realize. That’s the satirical work wherein he declares the USA bankrupt and extinct, around the same time he gets the Medal of Freedom from president Reagan. Who knows about that?

This all ties together in that the spooky metaphysics we teach in grade school, without admitting it’s philosophy in disguise, forms the perfect segue to alternative ideas in geometry, including Bucky Fuller’s alternative paradigm regarding our use of the word “dimension”.

He champions the tetrahedron over the cube as the more secure basis for our logic. Who ever learns that in their wonky PhD academy?

The old bridge to German Idealism is still there too, only now it’s to Bubbles, Globes and Foams by Peter Sloterdijk.

Thanks to Youtube and Cyberia in general, I think Americans are waking up to their denied heritage and will not so gullibly enroll in degree programs that perpetuate this sad state of affairs.

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American Philo

From a Facebook group, Transcendentalists 2021.

Rorty invented "linguistic turn" to mark when philosophy turned on language itself with new suspicion, starting big time with Nietzsche. "How is it that we mean stuff?" became the new question, which Wittgenstein dove deeply into, and the result is a break with ancient Greeks at another level. Cracks and crumbles are par for the course though, this isn't a tragedy. Rorty carries the later Wittgenstein forward under the banner of pragmatism. Not sure his detractor Haack is up on that aspect, nor the importance of "meaning as use" to that of "namespace" (as in: Synergetics is a namespace i.e. set of language games).

For further reading on Quora:

Are the philosophical needs of Americans being met?

Bridging From the Humanities (Quadrays on Colab continued)

Seven Wonders of the World per Arthur C. Clarke

Martian Math

Thinking with Mike Episode 5:  My Favorite Martian Mathematician

Show Promo

 

experimental ad for Kirby Urner (CSN CMO) on Thinking with Mike

Remembering Prohibition

The Coffee Shops Network is not a face of Prohibition. 

Our well-trained baristas know their "poisons" and speak easily of their properties.

Mapping Our Curriculum: Lambda vs Delta Calc (School of Tomorrow)

Recapping Themes (School of Tomorrow)

Celebrating a Design Science Decade (2021 - 2030)

Featured Artist

Synæsthetics by Amanda Gregory- (Excerpts)- Live Virtual Performance

Soundtracks for Hypertoons.

Synergetics Meets Archimedes (School of Tomorrow)

Remembering Manly P. Hall

Curriculum By Osmosis: Concentric Hierarchy (of Polyhedrons)

I'm glad we get a pioneer tale, with all the elements (protests, slavery, native Americans) interwoven with the esoterica.  That gives me and east to west context and setting, from the Atlantic-Euro Basin (I know, not usually called a "basin") to our Pacific Rim.  

In this one, I show off our Russian flavors (fly our Russian colors) on some literary circuit.  Russia likewise spans the same range, twixt Europe to the one side, Asia to the other, and each other, America and Russia almost touch.

No Synergetics scholar can contradict me, regarding the relative conductance, to energy, of the different tetrahedron wedges, as a theme running throughout. The Coupler gets dissected, in all possible ways, into A & B arrangements, presumably with consequences in energetic terms.  That's where we cross the line, from Pre-frequency to Frequency.

For those just joining us, I'm talking about the inner workings of an esoteric, literary work, bequeathed to us by American futurist-poet, R. Buckminster Fuller.

Here's a sequel over in Control Room.

Curriculum Advances (School of Tomorrow)

Rehabilitating American Futurism

Explaining CSN on Facebook

My scheme is to heist "church bingo" to where you go to a bar and play video lottery or any wired arcade game, but your winnings such as they are go to charities the circuit supports. Micro-philanthropy coinciding with moments of heroism. 

A dopamine rush right when you give in a strategic manner (as time goes on, more strategic). Now these winnings could all be in crypto, and good against specific catalogs... anyway, I brainstorm and open source the circuits. 

Don't forget to save profile when you donate winnings, as your profile is what builds reputation score, something money can't buy.

Riding the Wave (School of Tomorrow)