I was a high school mostly-math teacher fresh out of university (hey Joe, is that you? — new follower here on Medium) and I’ll say up front I loved the work. I also taught some world history. Having just returned from a summer in Egypt, I tried to share from my personal perspective.
I’d decided in my senior year at Princeton that I’d like to do that, and the guidance counselors expressed skepticism.
I joined in renting a small house behind Loew’s Theater, in Jersey City, with some of my schoolmates. This was a stepping stone for all of us, a waystation. Some were seeking lives in New York City. I ended up staying the longest, as I found my teaching job just down the street, on Kennedy Boulevard.
I’d been goofing off as a privileged liberal (as some might see it), diving deeply into Liberal Arts, going so far as to specialize in Wittgenstein’s later philosophy (the topic of my thesis).
I had not done any of the responsible things a person would do, if expecting to actually work for a living, and as a teacher no less. What about certification? Did I expect to just waltz in without paying dues, just because I’d gone to some big name Ivy League school?
I’d say I was more oblivious to such judgements. During my two year career as a high school teacher, I also continued with what I considered to be philosophy, volunteering many hours a week at local est Centers (remember those? — The Landmark Forum was to come much later). Thanks to Walter Kaufmann et al, I’d seen how philosophy and my nascent interest in psychology might converge, in a commercial setting.
Growing up outside North America, I had nurtured the stereotype that Americans were into “out there” kinds of experimentation, beyond the bounds of what was possible in conservative Catholic societies (Italy and the Philippines had been my pre-university places of residence). Once stateside, I was eager to sample some innovative program, and as it turned out, est was it.
I’m going into that part of my autobio to underscore the point that I wasn’t really seeking a lifetime career in high school teaching. I don’t think it’s a bad design to have some jobs mostly suited to quite young people, not long out of high school themselves, who then “burn out” and move on. The “burn out” part sounds bad, but we’re taught since birth, or I was, that we could expect to switch careers several times in a lifetime. Sure, it was tempting to stay and grow old in place, but thanks to my dreams of becoming an est Trainer or something approximate, I was setting my sights to step out as an entrepreneur. This was the Reagan Era.
Actually I had done a lot with computer science, studying the evolution of the human-computer language. I mix the two (human and computer language) because mouse clicks and swiping are just as human gestures, as is keyboarding. Yes, we’re in a cybernetic loop with our machinery, a kind of I-It conversation (to sound more like Martin Buber about it), evolving our cell-silicon interface (the implant idea sounds so primitive, compared to using pre-existing peripherals as we’re doing now, but I understand about needing prosthetics in case of injury or deformity sure).
The piano has a keyboard. Programming is like writing music, in more ways than one. That computing is now a full keyboard activity, versus punching calculator keys, is a victory for typing skills and for keyboards. Computer languages took advantage of everything QWERTY and with APL went beyond. APL was the first computer language I fell in love with.
These days, decades later, I still teach programming quite a bit, including to high and middle schoolers, as well as adults. I’ll be sixty two like next week.
These days I’m feeling the urge to stay with data science and pick up a lot of the statistics I’d neglected in the university. I’ve been learning about Z, T and F tests, Poisson and Exponential probability curves, Markov Chains, Bayesian versus Frequentist semantics. I’m not getting a PhD in it or anything, as I already consider myself a philosopher to some degree n, where n is some integer, I just want to stay germane.
I’m thinking back to high school math teaching, and asking myself why, when we cover the calculus (delta calculus, not lambda calculus), we don’t jump back and forth between probability distributions (PDFs) like the Bell Curve, the their cumulative area-under-the-curve counterparts (the CDFs). Yet the CDF is the integral of the PDF and vice versa.
When kids ask “what is this used for” and we don’t show them statistics, we’re being too intellectually austere, too ungenerous, for their, and our, own good.
Instead, the way I was taught in high school, statistics was partitioned off as a math track elective divorced from calculus.
From an historian’s view, I’m seeing how Statistics clearly bears the metaphysical marks, the scars, the traces, the memetic codes, of the calculus revolution.
Coin flips and card hands form specific countable events, their relative frequencies shown in a histogram or tally.
But other measures presumably come from a theoretical world that becomes infinitely smooth (versus bumpy?) at some elusive limit we can only dream about in practice.
In special case reality, we would need to sample and make do. We say x-bar (sample average) instead of mu (population average). The infinite deserves the respect of a separate vocabulary, much as some monarchies attract their own set of verbs, such that royals never do commonplace activities (the language guards against it).
Going from the discrete to the continuous, from sigma notation to Riemann sum notation, means going from “mass functions” (discrete) to “density functions” (continuous).
The whole “discrete versus continuous” theme permeates the culture and continues to deserve foreground treatment in the History of Ideas. We’re not obligated to “solve the puzzle” or “terminate the debate”. The History of Ideas reveals that when it comes to expressing eternal verities, our language must stay deliberately open-ended and ever-engaged in a dialectic.
I see lots of weaknesses like this calculus-statistics disconnect in our Global U curriculum, a lack of tethering, of connecting the dots. Sure, some more elite academies will attract teachers with the confidence to address such weaknesses and develop new curriculum. That place I taught in Jersey City was an elite academy, and I had a lot of leeway to explore my pedagogical ideas and theories.
Looking back on what we’ve been through in sixty years, I’d say containing the knowledge explosion has not been easy.
The actual knowledge we’ve gained, we might use, eventually, however the process of acquiring and digesting it has not been glitch free. Climbing the learning curve itself has been difficult.
We’ve passed some of our stress tests and failed others. Trial and error is our modus operendi.
We’re taking long term biospheric trends more seriously and as a matter for human planning and responsibility, even if we dumb it all down to talk about “climate change” in some circles (as if global temperature and sea levels were all that mattered).
Back to est, I was impressed to what extent the Erhard enterprise was mixing it up with the Buckminster Fuller legacy. Werner and Bucky were making co-appearances and splitting the door 50–50, neither propping up the other (Fuller’s endorsements would not have been genuine were he not a co-venturer and “partner in crime” so to speak).
To this day, I remain curious what the consequences would be for humanity were the concept of tetravolumes (core to Fuller’s Synergetics) to percolate more thoroughly through the culture, and I believe I’m witnessing a slowly manifesting answer to my question, although it could be one of those “too little too late” situations who knows. A lot of hindsight I don’t yet have, to sound Yoda-like about it.
The contribution of the Koski Identities, like Quadrays, is to further elaborate on the Synergetics project Fuller started (continuing his own subculture). The Koski Identities bring back phi to the equations whereas Quadrays suggest a less hyperdimensional use of the “4D” meme, which Fuller too had done a lot to popularize (he’s always “a popularizer” in contemporary accounts, less an inventor or discoverer of anything).
I don’t see myself solving the “mystery” of consciousness, per some of these speculative quantum gravity models, so much as investigating the “impact on consciousness” of what I consider high school level innovations, not beyond the grasp of ordinary individuals and not the stuff of great genius once one comes to understanding it.
“Why didn’t I always know this?” would be more the reaction I’m expecting, when people re-enroll in high school again (say every ten years?).
That the Concentric Hierarchy is so high school accessible is partly why it’s so untouchable, it’s not Brahmin class higher dimensional quantum mechanics, on the verge of explaining quantum consciousness.
It’s more like architecture or mechanical drawing, something to take up in vocational school as a set of skill-building exercises, like a programming language.
Consciousness is accepted, not explained as the sum of its parts, and speculatively given teleological role — nothing the Jesuits haven’t been teaching for some hundreds of years, or the Sufis.
You don’t get to be “the next Einstein” just because the Concentric Hierarchy makes total sense to you. A useful heuristic helps you organize your head, but that’s not sufficient to score you a Nobel Prize. And that’s a good thing. The discoverers of buckminsterfullerene got Nobel prizes. Those who know what a “hexpent” is (like a soccer ball), thanks maybe to learning some Synergetics, have less trouble following the relevant science.
Synergetics itself, being a philosophical literary prose kind of thing, is more about organizing and preparing the mind of an humanitarian, a philanthropist, a technical writer, for doing more technical readings in the several sciences. Philosophers sometime provide “glue languages” the have strong mnemonic qualities. These languages fold up like proteins, magnetically attractive to themselves, to give us the memetic tools we need to appreciate and operate within nature’s energetic geometry.
The strong distinctions drawn between shape and size (angle and frequency), exceptionless eternal and specialcase (mind and brain), all the focus on spatial and spherical trig, bespeaks of a more well rounded global U student of tomorrow, more confidant for the better mastery of science (including psychology).
But not because Synergetics somehow proved we were wrong about bosons or something. Or that mathematics to date was somehow invalid. Those are projections.
True, Bucky the polemicist thinks the tetravolumes thing is big and deserves attention, and he knows in this age of overspecialization, money-making nonsense talks the loudest. He engages in techno-invective, sends out some verbal volleys.
If only we still had some great pirates… what we have is The Grunch (the Global U).