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.
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:
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). 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. 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 notation).
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 assignment).
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 ).
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 ).
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!
 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).
 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."