Where Coding Meets Math

I was tempted to use the British spelling of "math", which is "maths" (plural), however my spellchecker immediately flagged it and I was feeling insecure in betraying my regional roots as an "Amerish" speaker.

I put that unfamiliar word "Amerish" in quotes, with a tip of my cap to poet Gene Fowler (author of Waking the Poet), who anticipated needing a word for an English different enough from the British parent to merit this newfangled alt-English, with the accent on "mer" (for mermaid?).

The Economist has a publication, 1843 Magazine, in which Python, the computer language, recently figured. Andrew Smith, the author of Code to Joy, is a fully functioning Liberal Arts major who decides to tackle Learning to Code, but not from a bottom up kids-oriented approach, which actually might be a good idea, going forward.

Part of the ethic in contemporary coding communities, such as Python's, is "giving back" meaning contributing to the stash of dharmas or teachings, that help perpetuate the language, by facilitating learning it.

Harvard's famous CS50 2016, on Youtube, starts with MIT Scratch before moving through C and then some Python, if I got the order right. Andrew, our guinea pig adult learner, flirts with C, but follows good advice and eventually comes to understand the freedom from machine-specific knowledge such a high level language affords. Dive into C later why not? The reference version of Python is itself is a C language creation.

Said 1843 Magazine article also mentions Nicholas Tollervey as one of Andrew's key advisors. Nicholas has been a keynote presenter at recent Pycon EduSummits, in turn a vibrant source of new thinking in K-12 circles.

"K-12" is what we in the Lower 48 call "elementary through high school" and probably we call it that in Hawaii and Alaska too, in Puerto Rico, in the Virgin Islands.

I used to hang out in K-12 circles outside the Federation all together, on the Philippine Islands. I visited mainland China in the company of K-12 teachers, from military bases in the Asian Pacific. I joined a family working with what was then the USIA, formerly USIS.

Back then there were Expos and Worlds Fairs, which the old US (Uncle Sam) would be a part of, with the USIS eventually playing a big role. Then the US decided to get out of the Expo business, perhaps as too European. Then later the US itself morphed into some kind of Banana Republic, or maybe DC did. We're still reeling from all the changes, here in 2018.

Remember the Montreal Dome of 1967? Actually, my memories begin at the Space Needle in 1964, in Seattle, as my family was living in nearby Portland, Oregon back then (I'm here now, having returned in the 1980s). I was in elementary school, about six years old, when the World's Fair happened in Seattle. We moved to the Philippine Islands (a Republic, but under then martial law) much later in the early 1970s, when I was in 9th grade. I finished high school there.

Pycon is a flagship conference organized by the Python Software Foundation (PSF), a non-profit based in Delaware, with an elected board. I'm one of the voters and also, these days, a volunteer listowner for edu-sig, the Special Interest Group for educators especially interested in using Python.

We're interested in using Python not just as an end in itself, but as a means to an end. In other words, once you know Python, why not use it to improve your understanding of mathematics, or transportation infrastructure, or cryptography?

"Python opens doors" is one of our advertising slogans.

[ "Python is like a skeleton key" is likely too scary for advertising purposes, as many people are queasy about snakes to begin with, whereas adding a skeleton to the picture might just push them over the edge. On the other hand, we might attract more coder Goths. ]

"Python" was named for "Monty Python" by the way, by its famous Dutch inventor Guido van Rossum. He was soon joined by a rag tag knights of the round table, variously abled and gendered, willing to share his quest for that Holy Grail of computer programmers: a general purpose language that is both readable and writable, one that scales.

[ Hah hah, another pun. "Scales" get it? Nod nod, wink wink. We're encouraged to allude to said Pythonic comedy troupe's skits in our "About Python" documentation. ]

I followed Pycon around mid-career, somewhat like a Dead Head in a micro bus, who never gets enough of Jerry Garcia and company. I'd show up in Washington DC, in Chicago, and of course in Portland. I eventually befriended Steve Holden, one of Pycon's founding organizers, who later went on to produce ApacheCon and DjangoCon, even a GOSCON (government centered).

However I didn't make it to Texas, nor Montreal. Nor should we assume I'm giving a talk, even a Lightning Talk, when I attend. I've had many turns at bat, hit a few out of the park, and now have retired to make the most of past glory, while making room for the newer young stars. Like Nicholas Tollervey for instance. Lets rejoin that thread.

The Federated States of North America, and Hawaii, have nothing quite like the BBC. I can imagine the avuncular Walter Cronkite wanting every kid in CBS America to have a micro-chip to practice programming, some programmable "thing" that might join the internet "of things" at some point. Certainly the Raspberry Pi may be programmed in that way.

But sending every kid a Pi would be cost prohibitive, even for the BBC. Too many would end up shelved by Muggle parents, not wanting their little darling to become a "hacker" (witch or wizard).

Keep the Pi on a higher rung, for those ready to take advantage. Make the Micro:bit entry level. But make it Python programmable. That's what the BBC did then: mailed a lot of Micro:bits to BBC subscribers.

Again, the zip codes around here don't receive those kinds of mailings. We get stuff from Newsmax, about needing to help our president kill the Deep State. That sounds pretty exciting, but there's no hands-on programming aspect. This "Kill the Deep State" is a soap opera one watches on television, or reads about in the news.

So that's all about Coding, so now what about Maths? There, I said it. Plural.

You may want to read my article on so-called "Gnu Math" here on LinkedIn. That's where we avail of the GNU-spearheaded free software revolution, to endow your children with greater and more powerful algorithmic tools.

I know some of you think Al Gore invented the Algorithm, not just the internet, but actually that honor was bestowed on a Persian sage, denizen of Baghdad, faculty of the Wisdom School.

However Al Khwarizmi was in turn capitalizing on knowledge coming from other centers of learning. He passed down such algorithms as we know them today, for adding, subtracting, multiplying, dividing, on paper, free of any abacus.

Then many centuries later, Ada Byron shared her dream of "programming" said algorithms, to "run" on something such as Charles Babbage was inventing, a geared affair, some kind of engine.

Then, within a few short generations, we were staring into the eyes of AIs, feeling all Frankensteinian. What had we wrought? Would AI prove our undoing? A lot of us felt our jobs were threatened, as AIers would work for free and never give guff to the boss.

Pythonic Andragogy is my game. Helping adults learn to code in Python might be the easiest interpretation of that tagline.

But then I like to take this word Pythonic, which means pithy (using language and gesture to maximum advantage) and apply it to other topics outside of computer programming.

I too like to be a learner oft times, not just a teacher. I appreciate the efficiently Pythonic nature of specific teachers and teachings, trainers and trainings. We all benefit, when even just a few of us really learn what's on tap that's super valuable. A few here, a few there, it all adds up. That's what universities are supposed to give us: the positive effects of synergy, as the many differently endowed learn to work well together.

I'm now suddenly cutting to Dr. N. Wildberger in New South Wales, a research mathematician who has been prolific on Youtube. He wants school teachers at the high school level to be OK with questioning authority, meaning long established dogmas, regarding such "things" (sets?) as the Real Numbers. Question yourselves, and let your students question. There's no need to keep the lid on philosophical debates.

The breakthroughs leading to our present ways of talking about such fundamentals as the nature of number and counting, may not stop with Set Theoretic approaches, championed by Ludwig Wittgenstein's chief mentors. Russell, Whitehead and Frege were among the early stalwarts of Propositional Calculus (as some then called it), a Philosophers' Stone, a Logic. Their agenda was to rest mathematics soundly on some Foundation, which they would build under, displacing a veritable catacomb of speculative tunnelings with a mint condition basement, not at all leaky. Cracks in the new Foundation appeared even before publication.

Dr. Wildberger somewhat regrets mathematicians' willingness to outsource Foundations in the first place, to a neighboring discipline, Philosophy. He proposes what amounts to a stock buyback, wherein mathematics itself would undertake the serious work of rebuilding its own foundations.

That's a bold dream, however I'm thinking Dr. Wilderberger is not entirely alone in dreaming it.

But then the other shoe is: he thinks mathematics under some new management might tilt its Foundations rather strongly towards Finitism, and away from the infinite subdivisibility of the Real Number line. The Continuum would become more "quantum" (digitized).

Since Russell's time, our world has gotten a lot friendlier to quantum mechanics in the sense of discrete mathematics. That the limits would appear more as gear teeth, as bits, than as perfectly contiguous continua, helped restore the legitimacy of computation, which of necessity involves energetic phenomena, such as digital circuitry and digital memory.

Let's move our Sets into combinatorics (or "Casino Math" as I call it, in Heuristics for Teachers) and not posit a Foundations made of such data structures, proposes Dr. Wildberger.

Wittgenstein's language-games-based investigations deserve more focus, for the clarity these investigations make possible.

What I expect will happen is K-12 teachers, math teachers in particular, will be feeling the winds of change most strongly, as generalists, whereas as the specialists are largely insulated from Zeitgeist storms.

The Learning to Code movement is stirring some mathematicians to see new freedoms to seize the day. We're not trapped in a static framework. Every Renaissance worth its salt eventually comes to this same conclusion. The urge to innovate, reinvent, alter, becomes unstoppable. But not every backwater gets it at first.

What we suppose to ourselves, perhaps unconsciously, is the winds are strongest at the tippy top of the Ivory Tower, whereas rank and file grade school teachers are tucked safely behind some bluff, some craggy cliff that shelters them from the open ocean, its tempestuous seasons.

However that's not a believable picture.

Young minds are archetypally active and engaged in sweeping searches, across multiple media, constructing their own realities to the extent they're at liberty, or under the gun (pressured) to do so.

What a math teacher says in the classroom gets compared and contrasted to everything else that's being said by others outside the classroom. The relevance of math itself, or a specific pedagogical technique, gets questioned, by various peer groups.

Parents may bring strong views to the table.

We've had what many have called the Math Wars. Passions have run strong.

Politicians would love a bigger piece of the action, but how to gain traction? The jargon of mathematics is difficult to grab a hold of.

We've seen the New Math, the New New Math... What is this Gnu Math again?

Partly what keeps the conversation shallow and therefore unsustainable is in the nature of journalism. Who has time for Foundations when there's so much juicy gossip to spread around? The supremacy of the unit volume cube goes unchallenged, as the public focuses on Stormy Daniels (long stories, especially the unit cube one).

What's happening is concerns about Terminator scenarios (big budget movies), and AIers "pushing the button" (supposedly by mistake but who can be sure), are forcing Philosophy out of the utility closet and into the foreground.

Engagement with philosophical topics, in some existential earnest, is in turn dredging up "how do we know what we know" type questions, raising the specter of Foundations coming back to haunt us, given how much they may be seen to have crumbled.

Will the public take kindly to our level of uncertainty, in the face of chaos?

Skittish adults, needing more solidity themselves, will want teachers to help them drum home a healthy folk wisdom, but what is that wisdom in this case?

Is AI our best friend or worst enemy? We're getting mixed messages, and that's stirring the pot, waking people up to the "deep questions" once again.

Python opens doors.

Figuring out what AI is all about, leads to forays into Machine Learning, then Deep Learning. Python might prove elucidating.

The tools prove not that hard to master, and the grownups, having seen the light, having tackled climbing the learning curve, come back to the table insisting the K-12 not wall itself off from these latest algorithms.

Junior needs to learn about hierarchical clustering and K-means testing, even if that just means eyeballing some Jupyter Notebooks and watching a few Youtubes (which might be therein embedded). Come back for more hands on at a later date? When you have a safe space to study?

Here's the good news: Junior needs more than a scientific calculator, and a bigger screen than a cell phone provides.

The middle class ideal, and nuclear family standard, wherein every member of the household has their own private space, is in contrast to the locker-only, or backpack-only ambience of room-to-room lecture mode.

Get the lectures online, with rewind and even re-edit potential (for quoting and citing), and build a personal workspace that's at least as good as a cubicle (minimum standard) or even better, contains a whole bed (work and crash pad), even a kitchen (cafeteria the other option).

If I'm going to need a bigger screen and a "home theater" ambience (headphones?), then why am I sitting here in school, not building equity? Is it either / or? May I have both please?

Now that the main site for learning has become an electronic desktop, the emphasis on building schools is more commensurate with building homes or home schools, or school homes.

We don't necessarily want junior spending hours on a bus, only to land in a library with less bandwidth and concentration potential than was already available at the starting location.

With teachers less in a position to proctor behavior, their focus becomes less disciplinary.

So does that mean adult guardians are needed within the home? We've tried to escape from that equation, but history suggests the family unit, with a low adult to child ratio, is not so easily circumvented.

"Two working parents plus day care" simply leaves the home empty all day, with rush hours wasting more fuel than the day jobs really pay for.

That's an extreme interpretation of the data, as we do need workers other than telecommuters.

But let's get real: we're cresting on peak oil and need to give people more ways to enjoy their electronic devices and back off having two homes (one called "work") separated by a crazy commute.

This trend towards the Personal Workspace, starting with a Personal Computer, has been moving to the personal bubble and cell. Now we're advancing to the studio apartment and shared MakerSpace. How it all plays out is matter worthy of further speculation, and I have quite a few Medium essays devoted to the topic. However I'm more into watching and reporting at this point. Now that I've identified the trend, I'm content to play the observer role.

My purpose here was to suggest that futurism is infusing through the math classroom, and Ivory Tower types have little to do with it, and even less to say about it.

The impulse is coming from Philosophy, which is getting a new lease on life thanks to emerging concerns about AI.

Those seeking clarity on the whole AI question find themselves diving into coding, and returning to K-12 with new ideas.

Junior needs more room than mere classrooms provide.

Not that it's either / or, just that curriculum concerns, the focus of curriculum writers, will increasingly include "at home" and/or "at the office" types of content.

The student will be expected to have at least a cubicle, with room to store projects, prototypes, supplies.

The student will also have space in the cloud and the means to create websites, file stashes (including encrypted).

Learning to manage such spaces is what schooling needs to be about, as it has been. Filing, keeping records, logging, blogging and now vlogging, have always gone together.