Visual Harmonies

:: by synergetics explorer david koski ::

Multiplying is often a scaling operation such as when edges or volumes are doubled in size.  Given an unchanging shape, meaning central and surface angles are held fixed, a doubling in edge lengths results in a two to the second power or four folding in area, and a two to the third power or eight folding in volume.

Starting with a cuboctahedron of edges root-of-two i.e. ~1.414214 and multiplying all those edges by phi (φ) results in a phi-to-the-third-power increase in volume.  The cuboctahedron's 24 surface edges and 12 radials (24 if seen as doubled) will now be root-of-two times phi. φ = half of one plus root of five or approximately:

>>> (1 + sqrt(5))/2
1.618033988749895

Finally, halving the difference in radial increase between these two, results in a third cuboctahedron that "harmonizes" with the icosahedron of edge-length-two.  The harmony consists in having both intersecting edges and coincident facial areas.

This "geography" of differently scaled versions of these polyhedrons has been variously mapped, including by R. Buckminster Fuller in his "explorations in the geometry of thinking" (or "synergetics" for short).  A "highway" between "places" may be a transformation, such as the Jitterbug Transformation, or, as above, a simple resizing.

SuperRT:                21.2132034
VE    (edge 2):         20.0000000
Icosa (edge 2):         18.5122959
SmallGuy:               15.8606454
RD6:                     6.0000000
RT5+:                    5.0077580
RT5:                     5.0000000 

SmallGuy will seem an idiosyncratic name, but then maps often contain folk names.  "SuperRT" is a rhombic triacontahedron scaled up by phi from its original size of 120 E-modules, a shape well-defined in Synergetics.  Said SuperRT embeds our Icosa of edges two as its long diagonals.  This same Icosa intersects and shares facial area with SmallGuy.

In sum SmallGuy, in this map, is a cuboctahedron "half way between" (edge-wise) the rt2-edge cuboctahedron and the phi-times-rt2-edge or say (rt2)(phi)/2 is the scale factor.  Starting with the same SmallGuy volume and multiplying by the sFactor * sFactor gets us the Icosa of edges 2 in volume, whereas one more application of the sFactor gets us the Cuboctahedron of volume 20, edges 2 (at the start of our Jitterbug Transformation).

Using some rational approximations in the Python shell:

>>> 15.8606454 * 1.0803630269509035 * 1.0803630269509035
18.512295822967804

>>> 18.512295822967804 * 1.0803630269509035
19.999999951112063

That's SmallGuy * sFactor * sFactor = Icosahedron (a volume expression)
Icosahedron * sFactor = Cuboctahedron (same edge lengths as Icosahedron)

Note that we're using tetravolumes as our standard (same as Synergetics).  Four unit radius spheres closest pack to define a tetrahedron of edges 2R (1D) and volume one.  The Icosahedron of volume ~18.51 and cuboctahedron of volume 20 both have edges of this same length (2R).

Another "harmonizing" to map is the edge-crossing of the rhombic dodecahedron of volume six, Kepler's favorite space-filler and a "voronoi cell" for our unit radius spheres, and the volume 7.5 rhombic triacontahedron, inflated (scaled) by a factor of 1.5 from it's T-module beginnings.

The T- and E-modules have a "same shape" relationship with the E a tad larger in size (T-volume is 1/24).  The sFactor, used above, is the ratio of the S-module to the E-module or about 0.045084/0.041731.  More output from a Python program:

Amod volume = : 0.04166666666666668
Bmod volume = : 0.041666666666666595
Emod volume = : 0.04173131692777366
Tmod volume = : 0.04166666666666668
Smod volume = : 0.045084971874737034
================
sFactor (Svol/Evol) =    1.0803630269509035

Blues Festival 2014 (Portland, Oregon)

More Fun with Phi

 :: Fun on July 4th by David Koski ::

Mario Livio, aka "phi guy" in my blogs, helped me catalyze this Philosophy Shop (network) some years ago.

Appropriately, we're still going strong with the Phi Stuff.

 :: Early Insights ::

:: The E-module ::

vZome @ Work

Some of us were privileged enough as children to have Zome Tool, a construction kit for exploring geometric relationships.  David Koski is like a polyhedralist of old, playing not so much with Archimedean honeycomb duals as with phi-scaled versions of what Bucky Fuller called the T, E and S modules or SET.

He uses a tool called vZome by Scott Vorthmann, a virtual version of Zome Tool.  You can see for yourself that it has an elegant GUI and the Zome hubs may be rendered in almost photographic detail if need be.  Scott's faithfulness to the physical kit is astounding and yet with vZome one may build with greater fluency and fluidity in some dimensions.

Don't worry if you hear something that sounds off, as David ad libs and maybe transposes a number or two.  The visuals more than make up for any soundtrack glitches.  Take your time.  Background reading about the SET modules will help, if this all seems too alien (as in remote / esoteric).

GI Coffeeshops Tour 2014

:: GI Coffeeshops Tour / PDX ::

Their bizmo was traveling from San Diego, CA to Everett, WA with many stops in between, to share with the public about the reality and sorrows of empire.

The movie Sir! No Sir! was mentioned a few times, to help orient a general audience as to where these folks were coming from.

I was a muted presence in a packed meetinghouse, bringing copies of the Wray Harris Authority & Expectation DVD to the three coffeeshop owner-representatives, courtesy of Recruiter Watch.

The coffeeshops are / were Coffee Strong outside Lewis-McChord near Tacoma, WA, Under the Hood in Killeen, Texas, and the The Clearing Barrel coffee bar in Kaiserslautern, Germany.

Worthy Projects

Two worthy projects came to my attention at Multnomah Meeting today.

Ann Hyde gave me a copy of When a Peace Tree Blooms, a telling the story from the Japanese side, of being atom bombed.  Yet good relations are restored with the perpetrators, a representative of whom brings a gift of seeds that grow into beautiful and fruitful trees with healing powers.

I'll pass this book to Carol and the Disarmament Day (August 6) Committee.  More libraries and gift stores than ours might be interested in this slender tome, the story by Hideko Tamura Snider, and illustrations by Mari Kishi.

All profits will be donated to charities supporting the children of Fukushima. ISBN: 978-0-9894858-0-7.

Even as Ann was sharing about this project, Lew Scholl was setting up the projector for our invited speaker, Dana Iglesias, MD MPH.

This young yet already experienced family practice doctor has done stints in Haiti, Peru and Nigeria, as well as in the US in some hardship areas.  Her parents hail from Panama.  She grew up in New York and started her medical training in North Carolina.

After testing the waters and searching her soul, Dana feels ready to commit fully to the Egbe Hospital Revitalization Project.  Her participation is being organized by SIM.  She needs to fund her own way, about $50K a year which covers travel.  The positive multiplier effects have huge potential.

Dana is especially focused on mothers giving birth and pediatric care, though she practices the full gamut of cradle-to-grave medicine.  She is skilled at several kinds of surgery, such as delivery by C-section.  However she feels she makes an even bigger long term difference when able to help influence public health through improved infrastructure and education.

As of this writing, she was just getting started on her website.

I adjourned to a Peace and Social Concerns Committee after Dana's presentation, in my capacity as AFSC Liaison.  We'd had our meeting of the Area Program Committee since the last meeting and I was to report back.

Didactic Visualizations / Animations

I'm glad I caught the Tomi Ungerer bio, Far Out is not Far Out Enough.  Like me, he's a pioneer in the edgy cartoons area and sees andragogy as distinct from, yet inter-mixed with, pedagogy.  We have ratings for a reason.

What caught people off guard is he was spanning G (General Audience) to MA (Mature Audience) with the same aesthetic, unifying the levels in some sense.

Was that interference in childhood innocence?  The Puritans thought so.

My agenda is a little different:  to impart technical content but to not eschew the animated form, even the demented or unrated.

Take these excellent lectures by Sapolsky at Standford for example, and imagine the animated reveries that could go with them, ala this movie on Chomsky, or these well-known RSA lectures.

Or I think of the more Bakshi / MAD style in the Morton Downy documentary.

Having a "movie track" for a lecture adds value.   Using animations is not "dumbing it down" even where higher and lower math, and quantum physics is concerned.

In our coffee shops, I don't necessarily want to monopolize the audio track, though an ear buds "airplane seat" setup might be used.  You get the reveries disconnected from the anchoring lectures and maybe spliced together by enthusiasts.

That's OK, as our coffee shop is more trafficking in a "meme soup" than in any particular subject or discipline.  We're providing ambiance, an atmosphere conducive to study and / or daydreaming, but we're not necessarily directly competing with the Apollonian Academy.   We're complementary.