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There's something about phi - Chapter 7 - Phi, the enneagram and the platonic solids

Javier Romañach

Chapter 7 of the series "There's something About phi". Video on the number phi, golden number, divine proportion or golden ratio and its relationship with the golden segments. Dedicated to the enneagram, its relation with the platonic solids, and the construction of an unknown figure for me tha I've named as the divertahedron.

Navigating the Lattice

You have no doubt played a 2D game on a grid of squares, chess or checkers for example. Not every piece moves the same way perhaps, however in principle each square has four neighbors over the edge, and four more along the diagonals.

Bishops know those diagonals...

...whereas Knights move over one and then two, at ninety degrees.  The horse-mounted cavalry has surprising moves.

Fewer casual gamers, but most ardent players, know the hexagonal grid just as well. A lot of tank games, drawing from our dark ages history, take place on a board of hexagons.

With the advent of computer games, the job of moving and tracking position, went from piece on the board, to avatar.  The games themselves went from 2D to 3D, with ever more elaborate floor plans.

However, consider the humble 2D chess board and tank wargame terrain.

What would be the 3D correlates?

The chess board suggests a 3D world of cubes, hexahedrons.

The tank game suggests a 3D world of dodecahedrons, diamond faced.  From every position in space, twelve possibilities suggest themselves.

What keyboard keys should we use?  One possibility: ERT for three "above", ASDFGH for six on the "same plane", and XCV for "three below".

When R. Buckminster Fuller took up the topic of "the will" in Synergetics, he stayed in his own namespace and shared his input in game playing terms.

Game Theory was already an accepted academic area of focus by that time, with World Game branching off as Fuller's innovation, and inheriting from War Games as well (logistics savvy and operations research).

"I always have twelve directions to choose from" Fuller explained (paraphrasing).  He imagined himself as a chess piece, an avatar in the IVM.

It is clear to me that most humans tend to think in a linear, Go-or No-go, greenlight-redlight manner. To me, will is an optionally exercisable control by mind over brain^__by wisdom over conditioned reflex-that becomes realizable when mind is adequately convinced regarding which of the 12 alternatives will produce the most comprehensively considerate vital advantage for all. (Synergetics 537.52)

In the Flextegrity system, both the 3D cubes and dodecahedrons feature together.  The cube domains encase the compression islands, interconnected by springs or struts.

Given every move from Icosahedron X may be represented by a single vector, perhaps represented in Quadray Coordinates, the game engine should allow multiple frequencies to interpenetrate, multiple webs, each with its avatar spider.

via GIPHY

Koski's Kiosk

Koski's Kiosk is great alliteration and will go forward in the literature, website or no.

Perhaps a synonym for "module" in the "tetrahedral wedge" sense, could be "kiosk". A tetrahedral voxel within a family consisting of family members E&T, S, A&B. Or these could be subway lines.

At the stations, the Kiosks appear as actual newstands with "read all about it" headlines regarding the Koski Identities. 

Picturing like Japanese anime, hypertoons with chill beats.

Zonohedron Zone

hollowed out

Another classic from Koski, an ongoing dissection of an interesting combo:  the greens are in the six IVM directions, whereas the reds come from five-fold world. You can see the reds in action, building the rhombic triacontahedron (bottom left).  The overall shape (transparent) is all reds and greens.

The colors refer to Zome, the construction kit, and the screenshot above is from vZome or the virtual Zome builder.  It's a standalone Java application.  Feel free to grab.

One of David's fascinations has been breaking down all these tetravolumes into sums of phi-scaled modules, the S and E modules in particular.  You'll find out more about these tetrahedrons in this blog and elsewhere.

filled in

Hypertoons on 3DTV

I've usually shared hypertoon reveries as a flat screen experience, as if on an HDTV.  You'll find an earlier blog post on LCD aesthetics.  However we need not confine our imaginations to such prosaic devices.  Won't 3DTV be here soon?

When you imagine a pixelated surface, do you think of squares or hexagons?  We can tell a lot about your personality based on that, just kidding.  As when tiling a bathroom floor, we have our reasons for going with one or another tiling pattern.

Space comes with "tiling" patterns too.  Instead of pixels, we have voxels?

When you imagine a voxelated volume, do you think of cubes or rhombic dodecahedrons?  I'd say a majority will think of cubes and don't know much about that other thingamajiggy.

However rhombic dodecahedrons are more neighborly in the sense of sharing more faces.  Cubes share six faces with neighbors (why we call them hexahedra).  Dodecahedrons (of this space-filling voxel kind) share twelve.

As soon as you start filling space with some repeated shape, you're likely to think "honeycomb" or even "lattice" whereas an engineer might think "space frame".  Different professions teach different words, but we all know what it means to "brick a volume" with some shape, even if said shape has all diamond faces.

The sculptors at Flextegrity Labs, the informal name for your builders' skunkworks, know all about modeling sculptures in 3D, given C6XTY and its progenitors came from a 3D imagination in the first place, via CAD and industrial processing.

Having the CCP (another name for our lattice, not a political party) pre-implemented in software, with each icosahedron or ball position selectively illumined, is a kind of 3DTV in its own right.

The sculpture supports its own weight.

We don't need to wait, to experiment with sound and light shows.  Our gallery was in the nightclub district, after all.

Who knows, perhaps 3D hypertoons could be in our future?

Or shall we say 4D, switching to the Bucky brand, wherein the Tetrahedron anchors our sense of "dimension" in a four directional volume, our "space"?  We've learned that "namespaces" coexist and that an either/or mindset may be unnecessary in the long run.

So sure, 4D it is.  Too.

Ramanujan Rocks!

You know me, I'm back to harping on some abstract stuff, wanting to make aesthetics matter.  Today I was talking about Ramanujan saying, in response to a Medium story:

Good one, got me thinking of the ballads, plays, sagas and epics that have mathematics in them. I favor bringing in some Ramanujan because now we have arbitrary precision software available (beyond calculators), so why not check out some of his wild convergences to thousands of places?

There's a lot of history (storytelling) behind just how far we can push our algorithms, to how many digits of accuracy. From Al Khwarizmi to Wolfram. 

We may not have proved why a given convergence works (some of Ramanujan's were famously opaque to proof) yet we're free to test them in empirical reality... 

https://archive.org/details/Ramanujan (actual ballad about the guy)

You probably know what I'm thinking of right?

Self Booting Startup

Everyone believes in the dream of booting, as we somewhat do that through being born, and we hope making it to adulthood.  All from a couple of cells.  We intuit that organizations work somewhat the same way, to develop critical mass and then take off somehow.  We explore for the right business model designs, the right chemistry.

Philanthropy for Everyone

The Coffee Shops Network is a philosophy based in the idea of Philanthropy for Everyone, meaning no matter how meager your means, you deserve opportunities to commit to projects that express your values in some way.  That your contribution might be amplified through higher scores, within some exciting game playing experience, is an added bonus, one could say thrill, giving you that added "chance to win big" possibility.

For those used to a Video Lottery, perhaps state permitted and used to raise funds for the state, winning the lottery is akin to having a fortune to divvy up among your lucky recipients. Their job, as a partial consequence, is to live up to their potential and prove their worth to investors.  However charitable ventures are not designed to reward with interest.  They're aiming to achieve specific results.  Successful projects tend to come with metrics:  ways to evaluate their success.

Gambling for Charity

Say I walk into a Coffee Shop and buy a bagel.  The purchases feed my gaming account, which I may pay into outright.  Once I've chosen a game, I have some ability to amplify more gift in accordance with performance, and some games help build skills I need anyway, such as typing faster, or recognizing rare birds.  I buy more coffee and play some more.  I rack up winnings for beneficiaries.  I am literally a hero.  The psychological benefits of giving to charity are well known.

You might object that I'm actually describing a lot of church operations here, in giving opportunities to amplify prayers with the right add-ons.  Philosophy has always been a close neighbor of the religions, given its focus on ethics and aesthetics.  Believing your contributions are actually doing some good requires some trust in the framework.  Do you actually see the crypto-currency going over the wire?  What assurances do you have that the transaction has gone through?

Clearly for a Coffee Shops Network to build out, it has to partake of solutions pioneered by FinTech, giving organizations ways to channel some token of value in ways that make sense to the power brokers.  If you're thinking "someone, somewhere is making money" you're probably thinking in terms of whether your generosity is being exploited or taken advantage of.  Possibly so.  In other words, we're back to whether you have trust in the organization. Those organizations that fall apart over time seem too much like pyramids.

Your Profile

Don't forget your profile matters.  Your record as a donor of winnings, a contributing player, may come back to haunt you, and take you into "deleted tweet" territory.  The social media aspect of backing effective projects is worthy of much exploration.  You may well develop imitators, but then some designs may give you backers.  In committing their winnings to your kitty, you get all that much more to forge ahead with.