Tuesday, June 21, 2016

The Tesseract, the Time Machine and the Tetrahedron


My title above is reminiscent of The Lion, the Witch and the Wardrobe, at least in terms of mentioning three rather disparate things.  That's intentional.  Welcome to Narnia, chuckle.

This campfire story, suitable for children, is about many great minds and how they grappled with their intuitions in different ways, coming up with different games, yet with overlapping memes, such as "dimension" and even "four dimensional".

We associate a Time Machine with H.G. Wells, who also wrote War of the Worlds, but also with Dr. Who I suppose, as what's that Tardis if not an inter-dimensional phone booth?  Milo had his Phantom Tollbooth with similar powers to transport.  If only Gulliver could have had one, to escape the Lilliputians.

However lets talk about Regular Polytopes and their rather gentrified neighborhood, in the sense of rectlinear, properly grided, with its main axial boulevards all meeting at right angles, as many as we need.  The upstanding L, as in perpendicular, rules in this multi-dimensional kingdom, of XYZ on steroids.  Abbott's Flatland helps us get comfortable with our higher dimensional mental powers.

Then Einstein came along with novel propositions about the relativity of simultaneity and therefore causation (as in "who made whom do what"), based on a new kind of dependency, that of one's own coordinate system.  One's point of view determined one's narrative more than we knew, even in physics.  Where you stand depends on where you sit.  Your angle on the action is therefore not "negligible" (nor off the table as a matter for peer review).

Linear independence in the Euclidean sense of XYZ was no longer sufficient, as no one God's Eye  coordinate system (interpreted by His duly appointed minions) could deny the others their physics, and yet these others might nevertheless tell the story in different ways, with different villains and heroes.  Blasphemy!

Logic was not forcing a unique or unitary result, and this seemed threatening to some, especially imperialists. Non-Euclidean geometry seemed subversive (Einstein was Jewish).  However the mathematicians were reassuring:  "we always promised as many rose gardens as you can manage" they said, "given the right fertilizing axioms."

Just the right set of axioms (no pun intended) or game rules, will fuel a fire that burns well, a game that plays.  Some won't become eternal favorites, whereas others may sit on a shelf pending rediscovery by players of matching mindset.  The time capsule effect.  Sleepers awaken.

Finally: the Tetrahedron, and a third chapter in our wandering story.

The primacy of the rectilinear orthodoxy was further called into question.  Why should right angles be so consequential at the end of the day?  They're unavoidable, true, but should they be that definitive?

On Planet Earth, two perpendiculars to the surface are not parallel to one another.  The smaller one is, relative to the planet, the less difference that makes.  But humans had outgrown their flat earth fixations by 1999.  What if the IVM tetrahedron played as well or better with others vis-a-vis the XYZ cube?

Well it turns out we have a choice of flavors.  Either / or is out the window (more a fallacy than a contradiction).  Enjoy them all, and more besides!

Really, I'm just retelling the story of 4D vs. 4D vs. 4D ("three scoops"), which is about three ways in which this 4D meme survived a 20th Century shakeout.  Different generalists commanded each namespace, keeping each coherent enough to avoid flaming out.

The polytope-minded gentry, many of them French, circled their n-dimensional wagons to protect their geometry from what they saw as time-degraded physics, the savage realm of Energy and Entropy.  Euclidean geometry is pre-Newtonian in its aloofness to temporal matters, almost Platonic in its relationships.

The Tetrahedron, meanwhile, wove back and forth somewhere in between, not needing a fourth perpendicular necessarily, for its additional degrees of freedom, yet sympathetic to the timelessness of Euclid and Plato.  The concentric arrangements of Platonics and their progeny was "pre-frequency" until some "frequency" was applied, giving spatiotemporal, special-case meaning.

Yes, this story is a deliberate simplification, as the "dimension" concept is slipperier than a slippery fish.  We have fractional dimensions today, perhaps even irrationally fractional (like pi).  The levels of indeterminacy and interdependency have also increased, with the discovery of quantum entanglement.

But hey, this was enough to get us going, and off to bed, to dream of swimming memes.

Visit your local science museum or library, for more information on the Tesseract (4D hypercube), the Time Machine (piloted by Einstein), and the Tetrahedron (4D in a different sense, just count the arrow tips).

Monday, June 20, 2016

Donate to CSN

[QR-code removed]

As a part of the #CodeCastle cryto-currencies initiative, it makes sense to walk the talk by both sending and receiving bitcoin as an authorized means of upholding one's end of a transaction.

I suggest making only small and non-anonymous donations if using the above QR-code for that. Claim the donation with your own public bitcoin address either just for that purpose or use your general wallet PK.

Do not assume anyone verifies these claims on our end, however the blockchain is public so there will be no doubt about the transaction itself, after some hours, and many donors are well-equipped to authenticate themselves in case their claim is contested.

Do not assume your donation is tax deductible, which is another reason to keep to small amounts. Contributions to a specific nonprofit's fund account would be through a different QR-Code.

The above is to CSN's marketing for CSN's promotion, an account controlled by the CMO (Chief Marketing Officer).  Feel free to earmark though, and to publicize your thinking on CSN in connection with your history of donations.

Come back to this web page for the best QR-code to use.  You can keep a snapshot of what it was at the time to verify your own blockchain transactions.

Sunday, June 12, 2016

HP4E Update

 :: link for more discussion ::

A decade ago, I started a media campaign known as HexaPents for Everyone or HP4E.  The Hexapent is another name for a BuckyBall or Fullerene.  The former, Bf, or C60 is the soccer ball topology, however more fullerenes of higher frequency (more hexagons) are conceivable.  There's a C72 and so on.

The gamer community is where HP4E took off, with or without my campaign.  Hexagons have long been a feature of two-dimensional game boards.

Seen from a gods-eye point of view, the player hovers over a plane of hexagons, moving assets around, building or destroying a civilization, as the case may be.

Many gamers realized that, given the Earth is spherical, there was maybe a way to have the hexagonal tiling close back on itself in all circumferential directions.  Those who explored the most deeply discovered the twelve pentagons needed for this closure to occur.

Proposals were floated on the Internet suggesting that Civilization itself, a popular commercial game, adopt this hexapent format.

The HP4E memeplex likewise has become a part of various global models of a more scientific bent, as carving the Earth into tetrahedral wedges, of which the hexagons and pentagons are composed, makes for a cellular data structure subject to various algorithmic techniques.

The mapping giants, Google Earth and ESRI, have offered somewhat muted support for hexapent displays.


The commercial mapping world is still fixated on spherical trapezoids, which become more square towards the equator.  These are no more equi-angular or equi-area than the hexagons and pentagons, but lat / long is what we're used to.

Fortunately, given the power of computer algorithms, it's not an either / or relationship and the hexapent matrix has a bright future even in the commercial sector (my prediction).

Finally, I've long been waiting for the crystal ball, also known as the "disco ball", to come out in hexapent form.

With CAD and laser cutters, getting the mirrors to be hexagons and pentagons, or even triangles, is not impossible.  A new brand could establish itself almost overnight.  I scan the Web for adverts.

Disco Ball

Monday, June 6, 2016


Is is still called anthropomorphism, even when they're not human?