Sunday, October 15, 2017

Rainbow Gathering


And now for something completely different, as Monty Python would say, as they did some crazy segue.  Rainbow Gathering.  No, I've never been.  However, my long association with the two generations behind me (younger than) through Food Not Bombs brought me into many of the same circles.  They'd go.  I'd hear about it.

I've always been a browser, since before "web browsers" were a thing.  I dreamed of hypertext before the web was born.  So now, approaching 60, my idea of a good time is plowing through Youtubes about this and that, sometimes making one of my own, but mostly watching, er browsing.

Two themes tonight:
  • the 60 Minutes episode on the opioid epidemic (adding "opioid" to spellchecker), the one with the DEA whistle blower, focusing attention on big pharma as big drug pusher;
  • and Rainbow Gathering.
I don't premeditate, usually, about what I'm gonna browse about though I keep coming back to core topics.  A Dom Rosa post at Math Forum got me watching 60 Minutes.

Oh, and I listened to quite a bit of Bucky Fuller, like the interview below.  You might think I do that a lot given my interests, but I don't, probably because I feel pretty expert on that already (the Bucky stuff) and am more focused on filling holes (in my knowledge).

I'm doing laundry.  Today was First Day (Sunday) and I brought a car load of C6XTY stuff to share with kids.  Me, Ron and Carl were the adults.

Then Glenn and I had lunch at Hop House after which we decided to check out the newly installed wooden bar at Back Stage, McMenemins, literally back stage behind the main screen at The Bagdad.  An old Portland landmark, the Lotus Room, is closed and gone, however McMenamins rescued the bar itself, a sight to behold, and we enjoyed it, chatting with the bartenders while watching drag racing and soccer.

Tying things together more, in retrospect, Bucky Fuller was very respectful of the hippie "rebellion" from which such institutions as Rainbow Gathering derive. He was pretty in touch with the Zeitgeist himself, a fancy German word for the Holy Ghost if we're translating from Catholic.

The focus on artifacts and inventions, in the above video for example, is what his Design Science Revolution was all about, although in his case the initiative was to involve the aerospace industry in providing shelter solutions.

I was slightly post Boomer I think it safe to say, and my line is I didn't really get to know any true hippies until returning to Oregon post college and meeting Bead and Denise at the Gathering of Western Young Friends at Camp Myrtlewood, very Rainbow-like both in spirit and design, with a big focus on cooking (not assembled outdoors though, in a well-equipped camp kitchen).

My middle and high school years had been mostly in Italy and the Philippines.  At Princeton I lived with what I might call 2nd generation hippies (and Kirk) but that's a bit of a stretch given this was Princeton after all.  We hadn't dropped out.  We were definitely against Apartheid.

Sunday, October 08, 2017

Terminology and Scope

More Concentric Hierarchy

Scope relates to terminology. In computer programming, we're always looking to prevent "name collisions" which is like when everyone uses the term "vector" but defines it in different ways, ditto "quaternion" or "duckrabbit".  The Java language took your Internet domain and flipped it around, drilling down to some unique path, at the end of which your "vector" might append -- just yours.  Like I might have net.4dsolutions.quadrays.vector -- in Clojure.

Koski and I were yakking on Verizon tonight, mostly about terminology. I think it's fine to divide the RT's E-mod into "Fe Fi Fo Fum", reminiscent of the Jack and the Beanstalk story sure, but also of "Do Re Me Fa".

Let me unpack that a bit.  RT = Rhombic Triacontahedron (raise your hand if you thought Russia Today) and in having 30 rhombic (diamond) faces, each criss-crossed by face diagonals, it begets 120 of what we call E-mods in Synergetics, though the latter term relates to an RT of specific radius: same as that of a unit sphere.

The RT arises from combining two Platonics, dual to one another, the Icosahedron and Pentagonal Dodecahedron. Their edges provide the criss-crossing long and short diagonals respectively, of the 30 diamond faces.

The Icosahedron, when spun, around opposite vertexes, edge middles, face centers, generates a network of 31 great circles likewise consisting of 120 LCD (lowest common denominator) triangles, which may be superimposed on the RT, effectively slicing each E-mod into four sub-modules.  These are what David is naming the Fe, Fi, Fo and Fum (alternatively: Fee, Fie, Foe, Fum).

The Fi-mod, for example, has the volume of the containing E-mod with edges scaled down by precisely 1/Phi (0.618...), meaning its volume, a 3rd power of edge-length, has (1/Phi)(1/Phi)(1/Phi) the E-mod's volume. E weighs in as a tad greater than 1/24th (of the uni-volumed tetrahedron).

What we were discussing tonight is how one of the radii of the Fi is the S-factor, 1.08..., defined originally as the volumetric ratio between the S- and E-mods, or equivalently the ratio twixt the volume 20 cuboctahedron and its partner in Jitterbug, the volume ~18.51 Icosahedron.

Cubocta / Icosa == S / E == S-factor (S).

One of the Fi-mods radii is S.

We need to distinguish S from S3, the latter being the volumes ratio of the cube of edges R (= unit sphere radius) to the tetrahedron of edges D (D = 2R).  The former is a bit bigger by 1.06... or so.  S3 serves as our conversion constant between two systems of mensuration, the XYZ and IVM.

XYZ is the grid of cubes we're all used to from our math classes.  IVM, or "isotropic vector matrix" is the scaffolding (grid) defined by spheres in closest packing, consisting of tetrahedrons and octahedrons of volume ratio 1:4.  How we juxtapose these two is by convention and intelligent design.

Another math fact: the cuboctahedron of volume 20 times S3 gives the volume of the so-called "SuperRT" the RT formed from said ~18.51 volume Icosahedron and its dual.  The SuperRT derives from the aforementioned unit radius RT (of 120 E-mods) by scaling all edges up by phi (not fi) i.e. 1.618..., increasing volume by a factor of Phi to the 3rd power.

Such is the terminological world in which Koski and I swim around.  It'd be completely a private language were it not for it's tightly syncing with what's long been published and out there i.e. Synergetics itself, by the genius R. Buckminster Fuller.

The so-called E-mod is a part of a family, which includes the A-, B-, T-, E- and S-modules.  These are core to the Synergetics "concentric hierarchy", built around a duo-tet cube of volume 3. A-mods alone build the unit volume tetrahedron, whereas As and Bs build the octahedron of volume 4. Both A- and B-mod, like the T-mod, have volume 1/24.  They all have handedness (left and right versions).

For more information, about the S-module especially, my Coffee Shops Network blog.

Saturday, October 07, 2017

Thinking About Scope

Show & Tell


Thinking About Scope

For further reading:
Names Have Scope in CS (Math Forum)

Sunday, October 01, 2017

Number Sequences

eratosthenes
:: screen shot ::

Given I'm spending time with 5th and 6th graders as their Python teacher, I've been looking at Oregon's version of Common Core, and, sure enough, that's an age where students learn the difference between prime and composite numbers.

The so-called Natural Numbers, or Whole including zero, form a comforting world of integer types and operations, especially number sequences, like at OEIS (On-line Encyclopedia of Integer Sequences).

What I'd recommend to teachers are the two books Gnomon, by Midhat Gazale, and The Book of Numbers, by Conway and Guy as a way of motivating course prep around number sequences.

In addition to prime and composite, we have such as the triangular numbers, square numbers and then, off the plane (moving into space), tetrahedral and half-octahedral numbers.

Here's our transition to sphere packing and space-filling, analogous to tiling on a plane (tessellation -- already a favorite elementary school topic).  1, 12, 42, 92...

Back to primes, I'm also seeing 6th grade as a time when we pick up more keyboard skills.  Coding with Kids has them moving from block-based programming (sliding puzzle pieces around) to more lexical languages, such as Python.

To that end, I wrote yet another Sieve of Eratosthenes.  Such programs are an old standby in computer science, meaning I'm being very correct and conservative in my approach.

My agenda is to promote C-STEM or C-STEAM in a way that doesn't lose sight of Synergetics.

Good meetup with a NW Process Institute guy today over lunch.  I was hoping to catch Arnold Mindell in action on Friday but ended up working a new teaching assignment instead.