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Topic: Of Backpacking and Sphere Packing
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kirby urner

Posts: 3,514
Registered: 11/29/05
Of Backpacking and Sphere Packing
Posted: Dec 3, 2010 5:14 PM
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I published a first issue of GeekOut! yesterday. Clearly I need
more of an editing staff as some typos sneaked (snuck?)
through. This was a digital preprint and I could take it down
and redo it, but I rather dramatize the "one man show" aspect.[0]

The thesis of this new 'zine is that whereas Portland prides itself
on being a geek mecca, the local press pretty much shies
away from gnarly geek topics, for fear of scaring off more generic
readers. That spells: a niche market for a shop-talking rag.

Doing it as a hardcopy 'zine in selected coffee shops and
bookstores is just retro enough to catch the eye. Takes some
of us back to the early days of BBSs and FIDOnet. Check
your local library.

The top topic in Vol 1 No 1, even before I dove into the politics
around IronPython, a computer language, was Sphere Packing.
This was a topic in my recent meeting with an educator from
Alaska as well.

During my IEEE lecture at Portland Center Stage, I essentially
jeered at the engineers for not doing more around Sphere Packing
and Polyhedra, leaving all the fun to Circus Geeks like me. This
was election night, as I was recounting to Haim:
(see the ** for a link)

I have a long history here on the Math Forum of following in the
footsteps of the figurate and polyhedral numbers trailblazers. These
folks go way back, to ancient Egypt and "gnomon studies".

Midhat Gazale has been influential, with his books 'Gnomon' and
'Number'. Conway and Guy, with their 'The Book of Numbers' are
likewise near the top of our syllabus.

As Allen Taylor, author of 'SQL for Dummies', was recently saying
"gee, I could see where STEM recruits might indeed find these
topics attractive" (paraphrasing)[1]. Adding Anthropology to
STEM gives us STEAM and more sensitivity as to how our
R&D and implementation process is going over in the
humanities departments.

Anthropology is a sweeping cover-all that reminds us of our
responsibility to keep that bridge open, the one over the C.P. Snow
chasm twixt the engineers and the theater people.

But do we agree that Sphere Packing is an engineering topic?
I think looking across the letters S T E M that most would drop it
into Science first, maybe thinking of crystallography (CCP vs
HCP vs any Barlow Packing), then maybe math (where the topic
turns hyperdimensional), maybe thinking of recent density studies,
for both spheres and for regular tetrahedra (at Princeton).
Computers were essential tools in both studies.

There *is* a link to E though (Engineering) and that's through the
octet-truss, at one time considered the only true candidate for
an extended space frame in the literally orbiting sense, as in
"space station". Once you know what you're looking for, you'll
find this skeletal arrangement or scaffolding all over the place.
Architects use it frequently, in airports, in public buildings.

This arrangement makes a quite dramatic appearance in the
engineering career of Alexander Graham Bell. This is where
the NCTM tends to pick up the story, with its Kite lesson plan
at the official web site (so back to math again).

The octet-truss is basically just the CCP with neighboring sphere
centers connected, and then with the spheres disappeared or
simply rendered invisible. You're left with a skeleton outlining both
regular tetrahedral and octahedral voids, with provably twice as
many of the former in the general case.

This is what any technical writer (any curriculum writer) needs
to know if writing for the K-12 spatial geometry market, which
is intensely competitive. Learn your Ps and Qs. Know that the
CCP and FCC are the same thing, and may be taught with dots,
like on dice. 4-5-4 == 12-around-1.

That's the 4-pattern from a gamer's die (like a dradle) with a 5-pattern
atop, then another 4-pattern. Ask your mentor to project the relevant
animation (assuming you're in teacher training, which some zine
readers are).

I don't actually spend more than a few sentences on this topic in
the actual zine. Then, in the treasure hunt follow-ups, readers go
geocaching through the net, looking for more in-depth write-ups
such as this one. Not everyone is teaching STEM subjects these
days, I realize. However, if we count the military as STEM (seems
a reasonable inclusion) then more probably more are than aren't
(teaching STEM). Adding Anthropology to STEM to get STEAM
reminds us to consider the real people involved, and the impact
of our in-theater behaviors. To that end, we recommend a lot of
training in anthro, simulations as a prelude to actual field deployments.
Journalists might enjoy attending one of our boot camps.

And that brings me to backpacking. You may have heard of the
book 'Packing for Mars' by Mary Roach. She came through
the Bagdad Theater here in 97214 and enthralled the neighbors
(including my family) with brilliant excerpts from her research.

A lot of that research is retrospective, is about how astronauts have
had to deal with issues of excrement, other bodily effluvia. There's
that definite link to Grossology which kids groove on, as I explicitly
point out in my Europython slides (Vilnius).

The audience was all-ages and wildly amused. We also developed
a very healthy respect for these pioneers willing to endure new
extremes of mental and physical suffering, pushing the envelope
of what humans might do and live to tell about.

My own 'Martian Math' course had only a little of this lore. On a
next pass, I'd be strongly tempted to put Mary's book on the
syllabus. We watched videos about the recent Mars probes and
their discoveries. Mostly our perspective was retrospective (like
hers), to even earlier science fiction about Martians attacking,
War of the Worlds especially.

There's an odd yet telling similarity between the tripods (the attack
vehicles) and the micro-architecture of the virus.[2] Those who
remember the ending of that H.G. Wells story, inspiration for
films, will realize how appropriate a mnemonic this is. The
implications are real world as well: if Mars has primitive life
forms, what will this mean for the Earthian immune systems?
Some engineers would argue this has likely been tested
already, as the two planets already share their dust with
each other, all human-crafted space probes aside.

I bring up the virus advisedly, and in connection with Sphere Packing.
We're back to the cuboctahedral numbers and the progression
1, 12, 42, 92... according to the rule 10 * F**2 + 2, where F is
a variable (sometimes called "frequency" in geodesic dome
architecture) and ** stands for exponentiation (using Python

That same progression turns out to be the icosahedral numbers
as well, and why this is true may be cleverly shown by means of
what's called the Jitterbug Transformation.

A regular cuboctahedron (often pre-defined to have volume
20) smoothly morphs into an icosahedron with the addition
of 6 edges to its 6 square faces, now forming into diamonds
and creasing along their short diagonals. Given it had
8 triangles to start with, and all 6 squares have become
two triangles, we now have 8 + 12 = 20 triangles, where
the meme "icosa" comes from (means) 20. The volume
has decreased, from an initial 20 to around 18.51. And
note that the 12 radial vectors from the origin are now a
tad shorter than they were than when reaching to the
surrounding 12 vertexes of the cuboctahedron as defined
by the CCP (or "octet-truss" as NASA might describe it).

Viruses tend to come in the form of icosahedra with a
tail or docking mechanism. As you know, a virus contains
genetic material which it injects into a host bacterium.
This is generally considered parasitic behavior which
casts the virus as a "bad guy" -- not surprising given many
viruses have lethal effects. The virus is said to be
"hijacking" the bacterium, and might be considered a
"hacker" or "pirate" in the negative (less romantic) sense.
On the other hand, upgrading genetic material might
mean starting with said material in viral form. If you're
studying biology, knowing about these studies will help
bring you up to speed. Here's an example article:

(exercise: find 4 more "good virus" articles, filtering out
"computer viruses" as irrelevant for the purposes of this

So Sphere Packing and virus morphology definitely intersect.

"All of these numbers are in fact found in actual viruses,
12 for certain bacteriophages, 42 for wart viruses, 92 for
reovirus, 162 for herpesvirus, 252 for adenovirus and 812
for a virus attacking crane-flies (Tipula or daddy-long-legs)"
- - The Natural History of Viruses by C.H. Andrews
(W.W. Norton R Co., 1967).

This is where journalists need to focus if wanting to get up to
speed on what our experimental prototype curriculum of
tomorrow might look like. Picture a buckyball as its symbol.

Why did we give that cuboctahedron a default value of 20 just
now? Remember Alexander Graham Bell's Kite and the NCTM
lesson plan that goes with it. The tetrahedral and octahedral
voids have a relative volume ratio of 1:4. If you pick any hub in
the CCP, the 12 arms radiating therefrom will give you six
half-octahedral voids (the square faces) and eight tetrahedral
voids. If we set the tetrahedron = volume 1 (an opening gambit
in Martian Math), then the half-octahedra have volume 2.
6 * 2 + 8 = 20, the volume of the cuboctahedron of 12-around-1
(remember: 4-5-4 from Casino Math).

Each of those spheres has its own domain or neighborhood,
meaning it "owns" slices of the between-sphere voids shared with
12 neighbors. The most equitable partitioning of these voids gives
us a hive-like packing of rhombic dodecahedra, and these have
a volume of 6 relative to the cuboctahedron's 20.

These simple whole number volumes are a well-kept secret in
Geekdom, giving us an edge when advertising our own favorite
brands. If your advertising is exclusively XYZ-looking in flavor
(i.e. obsessively rectilinear) then chances are you're sending a
more subtle turn-off message that you didn't intend. Viewers
pick up on these vibes though, even if only "subliminably" (to
play off one of GWB's little gaffs).

Imagine you're in 10th grade, flipping through your geometry
textbook. It immediately becomes apparent: these people
aren't geeks and apparently they don't have a clue. That's why
GeekOut! is so useful. Get your advertising in there, and it
might actually look like you know something about the future.
Find that hot readership. Place that "help wanted".

So what about backpacking again? How does that fit? Readers
here on math-teach may recall my fascination with what I've
variously called: "off your duff math", "army math" and "girl
scout math". I've tended to favor the latter of late, though want
to avoid trademark issues, using lowercase to suggest scouts
of any nation, perhaps Chinese (such as shown in this picture [3]).

Then I'll use GSM as the abbreviation and link it to both XRL
and GST. XRL = eXtreme remote livingry i.e. livingry for use in
extremely remote circumstances, or perhaps for extreme living
in only moderately remote circumstances (there's variability).
GSM includes topics in navigation (getting around), resource
use (efficient heating and cooling), camping out under the
stars (with planetarium simulations back in the city). The word
"livingry" is itself a neologism coined by Mr. Spaceship Earth
himself, Bucky Fuller. He coined it in tandem with "killingry"
to indicate two ways some artifacts may be used (so-called
"dual use" artifacts) -- whereas other artifacts may have only
one obvious purpose, be that pro-life or pro-death (lots of
Anthropology here). GST = general systems theory, a
swap-in for Economics if you want to stay deeper in STEM.

When you backpack into some camp site, you typically set
up your tents and then adjourn to a fire pit or campfire of some
variety. Some camps have an outdoor theater platform, with
room for an audience. This is where the more programmed
theatrical activities might occur which theater, on a Geek Outing,
that might include Lightning Talks, somewhat on the pattern
of those Ignite events (Portland has had several Ignites, including
an Ignite Gov at the most recent GOSCON [4]).

The ability to project films may not be at all far fetched, depending
on base facilities. Some training grounds even blanket the
terrain with signal, serving wifi devices (as already modeled in
some computer games). Oregon's native populations (aka "tribes")
include many geeks among their ranks, in part thanks to their
large data centers and IT shops (aka "casinos"). GSM might take
you to a "reservation" as a part of your work / study as an
eco-tourist (a growing industry in Oregon).

Campfire tellings will include screenings about Celilo Falls and
its 1957 damming, other lore (the great flood that created the Gorge
in the first place, and the explosion of Mt. Mazama, St. Helens
more recently). Geology is included in STEM, and provides the
grander time-lines against which to link the astronomical trajectories,
such as that of the Sun around the Milky Way's center, and the
Earth's precession about its own axis (the Pole Star used to be
the star Thuban in Draco, and will be again around 21000,
according to sources).

Those following my Flickr Photostream may have noticed some
GSM XRL showing up through the parcel delivery services.
Snow shoes for example (somewhat retro in flavor, like in
Toon Town). Army surplus mostly. Girl scout math has a
paramilitary flavor. Part of it is budget (being responsible with
funds). Your "coven leader" (FOSS geek talk) might wanna
double check that credit card and make sure you didn't buy
irresponsibly (this isn't a cash card in any case, is pre-certified
with authorized sources, at least in some of the implementations
- -- more like coupons and/or meal tickets). No sense getting
a solar panel that doesn't work with the charger your rechargeable
batteries will need. That kind of thing. You get held back if
you can't gear up properly, for your own safety and that of
your peers. Pure uniformity is not required. Girl scouts like to
express their individuality, perhaps even more than boys do.

These anthropological circumstances, of women camping out
and learning wilderness skills, will be taken into account by
those customizing the curriculum front end. These would be
your school's own faculty members in typical circumstances,
your parents and guardians, your peers, mentors, members
of your local community.

If your company, class, or coven is actually not women but
mostly or even all men, then your work / study content may
only partially overlap. You might share the Martian Math piece,
along with the other three components of the Digital Math
curriculum (see Oregon Curriculum Network's Heuristics for
Teachers on Wikieducator), but not then not apply the GSM
abbreviation to your coursework. Choose a more gender-
neutral synonym?

XRL and/or GST still might make sense though. Your faculty
will be looking for guidance from the district, which is
supposedly loyal to higher education on the one hand
(e.g. OSU), and political pressures (e.g. Salem) on the other.
There's also local industry to consider, and its need for
skilled STEM people. The Silicon Forest is somewhat
ravenous for geeks with enough self discipline to keep
things interesting within the state. Some of us would like
to keep living here.

"Goof off geeks" encourage transmigration, which in Cyberia
is quite a simple matter: wake up some morning, and
you're working for a Swedish company through VPN. Many
of the geeks around Portland actually count clients overseas,
which is why you'll find them in coffee shops at all hours,
skyping with other time zones (I've got just such a Skype
session next Tuesday, though with a neighboring time
zone in that instance).

So here in Portland, as a STEM teacher, you might get some
guidance from Geeks (plus you might be a geek). Check
out GeekOut! for some of those reality checks. Read about
the curriculum ideas we favor (like that volume six rhombic
dodecahedron, like that Jitterbug Transformation -- topics
for upcoming issues).

Don't worry if a lot of the information seems esoteric (it is).
Popular culture feeds off of esoterica as anyone in Hollywood
might tell ya. Those "good viruses" should give you a clue.
When it comes to memes and word of mouth, you want to
bring good things to the world, i.e. lotsa livingry. That's what
Free and Open Source is all about, at least if you've studied
your geek heritage, your Stallman. So don't get left behind.
Go to Barcamps. Get that backpack packed and do your
homework around sphere packing why not? Before ya know
it, you'll be geeking out too!



[0] Small startup zines often begin in this way, as do underground
comics. Geek hits such as Logicomix (out of Athens) then emerge
and gain a following. Not that different from the music business,
which uses Myspace quite a bit (including my own 4D Studios,
which helped produce several important live performances --
now freely available in recorded format, with transcripts).

[1] What he actually said was: "Sure the octet truss is useful, and
more generally, it is useful to know how forces and loads are
transmitted between connected objects. These are the kinds of
things that might cause students to think about pursuing a
career in engineering, if they are presented in an engaging way."

(note similarity of virus and tripods)

(Chinese girl scout) Photo-journalism by Glenn Baker, the documentary
film artist

(GOSCON slides featuring official Python mascot (with which I was encharged)

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