Tuesday, September 19, 2017

GNU Math = Math + CS

[first shared on math-teach, Math Forum @ Drexel, with no pictures ]

Factor an Integer
:: factors(84729293) ::

Rhymes with "New Math"...

I think we all know the pun by now: GNU stands for GNU is Not Unix.

However in being recursively defined, it's also an allusion to Lambda Calculus.

GNU came along around Gen 2.0 of the C-STEM Epoch, which Epoch started around PLATO (1960) and rolled through at least two revolutions: PC (personal computer) and Liberation (free / open source).

Liberation was a long fought battle pitting the likes of GNU / Linux against SCO. I'm sure some here remember those years, followed by Browser Wars...

Where C-STEM starts hybridizing with the contemporary public schools math sequence is around the Fundamental Theorem of Arithmetic, that every integer has a unique prime factorization.

I'm going with Conway's suggestion that we throw in -1 as a factor along with 1, go ahead and call the former prime if you like.

A prime has only itself and 1 as a factor, and -1 if negative. 1 itself is not prime.

When we say factors, we may include or omit the 1 (identity element) depending on context.

factors(42)
(1, 2, 3, 7)
factors(100)
(1, 2, 2, 5, 5)
factors(-12)
(1, -1, 2, 2, 3)

When students are ready to write code, in whatever language, to deliver these unique prime factorizations, that's when CS starts to meet Algebra. The Sieve of Eratosthenes, Trial By Division, Euclid's Algorithm, start phasing in here, as things to code.

Yes, we're still doing arithmetic, using the four basic operators plus modulo (%), but we're also introducing functions, the composition of which will be our basis for getting work done.

Algebra has much to do with controlling the components of a function, one might say inputs, arguments or parameters. The specifics are often fixed with constants, as in:

A sin (Bx + C) + D

the paradigm oscillator. Only x is considered the dependent variable at the end of the day, as A, B, C, D are used to construct a special case function.

Polynomials are the same way. The coefficients fix the function, and then x or t do the heavy lifting.

A*x**3 + B*x**2 + C*x + ... we have notation for arbitrarily long lists.

CS is good at this: providing an executable language wherein functions have the ability to construct other functions.

CS profs further along in the pipeline will be grateful if we start writing functions that build functions earlier.

C-STEM has a bright future.

The Pumpkin Knows
:: (1, 11, 31, 248473) ::

Saturday, September 16, 2017

Gala Gathering


I tried to explain this event to people by saying we were shooting raw footage for future commercials.  That might not be quite it, certainly not it entirely, however people understand the movie shoot, complete with retakes, and that's what this was, as well as a party.

Sam Lanahan has been planning this event for some time, blending his personal genius with that of the many he's come to collaborate with.  Jeff is the talented engineer.  We carried the four frequency tetrahedron together.  Steffan is the talented magician, working with Hope, the athlete.  Polara brought their considerable abilities to the scene, as did the professional drone camera operator.  No, I'm not forgetting the crane.

Barry Redd and Glenn Stockton have been helping Sam build C6XTY sculptures, which show off a non-cubic lattice, not BCP.  All the examples were CCP, but each colored and "carved" (in the sense of omitted balls) to create a landscape of clearly unique pieces.  One was for stress testing.  Others were for display on a grassy yard.  The biggest was for hoisting by crane so that Hope could dangle and twist therefrom, ushering in the Tension Age.

I should explain the plot a little.  Steffan Soule had it worked out, with a stage magician's brick, symbolizing compression, and a bright pink and black ball of C6XTY, matched in color by Hope's harlequin outfit.  During several takes, Sam both received, and handed over, the plastic ball, the icon symbolizing Tension in this picture.  The receding Age of Compression was about the Cube.

Yes, this all sounds esoteric and to some level indecipherable, the entropy is high, potentially.  However, I'm connecting the themes that go back years in these blogs, so in a way I don't feel I have the burden, in one post, to compress all these years of thinking and running experiments.  That's partly what "tension" means:  not having to re-invent the wheel every day.  I'll be referring back to this HP4E event again, don't you worry.

Many thanks to Derek Bridges for additional photography and a twitter stream, to Tim Hitchcock (bizmo pilot) and Trevor Blake (a Fuller archivist, among other roles).  Thanks to Patrick Barton for helping move pieces from my patio to the rented truck, and to Diane for having some ideas about what all this could be about.  We're still figuring that out.  The Age of Tension is often suspenseful, but perhaps less awkwardly melodramatic?

Monday, September 11, 2017

Back to School

Patrick has been working out.

I'm expecting my mentor and personal trainer, Patrick, to come over and remind me how it all works through his control panel.  I've only "flown" (piloted) his rig once and remember Mac shortcut combos were translating to surprising combos on the Windows server.  I need to practice which combos to avoid next time.

Patrick and I were co-workers through many of the O'Reilly School of Technology years.  We're both friends with Steve Holden, a former neighbor, and citizen of the UK.  Steve was a major player in getting the early flagship Pycons off the ground, imitating EuroPython which came earlier.  A nonprofit named the Python Software Foundation grew up around Pycons as the organizing entity and eventually became what it is today, with Steve one of the first directors, later chairman.

I've been dividing my attention between hurricanes and quaternions, not as distant-apart concepts as that may sound, though granted hurricanes are energetic phenomena whereas quaternions are metaphysical assets, a tool in the computer graphics library for making things rotate, around any axis, in what in XYZ-talk we call 3-space.

XYZ-talk extends into Coxeter type n-space, wherein real number-lines are imagined to be mutually independent through a common origin, as many as we need.  IVM-talk is different, is what Bucky hatched in Synergetics, with a little help from his friends.  IVM-talk has only a toe-hold, or beach-head or one of those, vis-a-vis contemporary academia.  We're more likely to read that Bucky was crazy (quirky) or Synergetics is pseudo-math here in 2017.  I've got the two talks somewhat mixed together.

OK, Patrick has come and gone.  We sat on the back deck overlooking the C6XTY sculpture garden. The truck will be here tomorrow, to haul most of it away.

I then went upstairs to watch CBS Evening News, to get some overview on Irma.  Today is of course September 11, my wedding anniversary, as well as a day the metaphysical climate changed dramatically.

Friday, September 08, 2017

News Room

Remembering a Friendship

What's amazing is how in a few decades, the personal workspace (PWS) has evolved into a newsroom.  Instead of a few papers having these telex machine feeds, we get this blizzard of news reports, some half baked, others slickly misleading, all ready for editing in the virtual studio.

The CSN CRO and I were checking out the Florida freeway system this morning, using Google to suggest where the worst logjams are, then pulling up stories.  How many freeways have committed all four lanes north?  Any concept of "evacuation bus"?  What's up with the trains?  Why not commit railways to getting people out?  Insufficient rolling stock?

Houston decided to hunker down, more than evacuate, yet more freeways fan out from that hub, going inland, then you get leaving Florida.  The two sides of the peninsula provide the two main arterials.

It'd be easy enough to get all these computers on different channels with several sources per screen.  Then it'd look more like a newsroom or monitoring station.  Like a control room.

I took public transit out to PDX last night for a meetup with a JetBlue pilot's sister (she was flying JetBlue).

He's retiring today, or at least bringing in his final flight, from Fort Lauderdale as it happens.  They're having a gate party at JFK today, a JetBlue tradition.

I used to live full time in Florida, in a mobile home park in Bradenton.  A lot of the news stories are focused on changes to building codes since Hurricane Andrew but what's special about Florida is how much of it is mobile home estates.  Lets not just focus on fancy beach side apartments and condos.