Algebra Redux

Algebra Redux

By Gene Wilburn

“On Algebra — We’re a month into it, and I’m planning to start a real protest movement, one to have X and Y removed from the alphabet. Z is also suspect as far as I’m concerned…Damn it! They put a man on the moon; can’t they find some way to end the scourge of Algebra?” ~ Huston Piner, My Life as a Myth

“I can explain to you why algebra is useful. But that is not what algebra is really for.” He moved his fingers gently on my temples. “It’s to keep what is in here healthy. PE [exercise] for the head. And the great thing is you can do it sitting down” ~ Mal Peet, Tamar

It pains me that math gets so little cred as a form of mental satisfaction. Oh, everyone respects it, in the way you respect quantum physics — good stuff, yup, the stuff of the universe, yup — just don’t get it near me! Crikey, there’s a horse that can count better than I can. I mean, are you serious? Mental satisfaction?

I don’t mean the satisfaction of the accountant whose books balanced, though there is likely a smattering of it there as well. I mean the pure pleasure of climbing the mountain of numeric relationships and reaching an understanding, and a point of view, you never thought you could. It doesn’t have to be advanced calculus. Mere algebra will do.

But first, a disclaimer. I really like algebra, though I’m aware that many of my friends would consider this a personal failing on my part. Yet when I was in grade school I deeply disliked math because I found arithmetic, such as doing long division on paper, indescribably boring. And frustrating, because I’ve never been very good at arithmetic. I’d nickel and dime myself on tests, making little arithmetic errors here and there even though I knew how to solve the problems. And I’ve never been very solid on the times tables either. Some part of my brain just doesn’t take to arithmetic, and those were the days before electronic calculators were invented. All arithmetic was done by hand.

So, what happened to make me like algebra? Two things: the math itself, and a fantastic high-school math teacher. When it’s introduced to you by an articulate, witty and cool teacher, algebra becomes almost electric.

I just got it, right off. It was ‘a’, ‘b’, ‘c’ and ‘x’, ‘y’, and ‘z’ used symbolically to store values. Just like numeric variables in a computer language (though I didn’t know about them at the time). That plus the sheer power of the equal sign (=). If you can determine equality in some mathematical relationship, you can then solve for its components.

And you can do anything to the equation and it’s still true as long as both sides get the same treatment. Factoring is just a way of simplifying the equation. And sometimes when two equations are related, you can work out the variables in common based on some tricky, but nifty logic. And then there are inequalities like “<”, “>”, “=<”, or “=>”, not to mention getting involved with “nots” and “ands”. Talk about sharpening up your logic circuits.

Of course algebra was considered an essential skill for anyone going into science or engineering. I thought, like many others in the late 50s, that I was Cape Canaveral bound as an engineer or scientist. There were two kinds of teenage boys when I was one: those who wanted to be James Dean, and those who wanted to be a younger version of Werner Von Braun. Alas, I was one of the latter. I was not one of the cool kids.

But, it was not to be. As Mae West said, “I used to be Snow White, but I drifted.” I spent a year in engineering, studying calculus among other challenging studies, but the tidal currents of my mind pulled me to the Humanities, especially literature, philosophy, and art, and I never saw advanced math again. At least not for many years.

Then I retired. Casting about for things that could challenge my brain to keep it healthy during retirement, I began doing sudoku and crossword puzzles, and although I liked them, I didn’t feel I was getting the right kind of challenge. A small tendril of memory teased my brain into thinking about math again and I began to wonder if I could get back into it. So I tried it.

My favourite book series in math and engineering is the Schaum’s Outline series. They’re terse but full of problems to be solved. They guide you through the first steps in solving equations after every new concept, then leave you on your own, only providing the correct answers. You learn a lot trying to reason out why your answer isn’t right, and feel good when you’re on target. It’s totally hands-on learning. So I started with Schaum’s Outline of College Algebra, regaining familiarity with math and undoubtedly growing a set of new neurons.

What I noticed, parenthetically, was that the more I studied algebra, the sharper my mind felt. It’s as if my brain highly welcomed a return to this side of its operations. But then, after a couple of years, for reasons I cannot remember, I drifted again, and quit studying math.

Recently I’ve begun to feel mentally sluggish, beyond just forgetting things and wondering why I’m staring at the pantry shelves. I’ve started to feel not as sharp. Then another new tendril of thought got through to me — I think tendrils may be how the subconscious communicates with the conscious mind — and I remembered how good studying math made me feel.

And so, the arithmetically clumsy me is going to return to studying algebra. Completing the square, here I come.

Whatever Happened to Ecology?

Whatever Happened to Ecology?

By Gene Wilburn

Words have lifetimes — some very long, some short. Many words are elastic and stretch from their original meanings to wider application or a more specialized meaning. Some words define and encapsulate eras. Think of disco and discotheque. Or flapper and Charleston. Eras gone by, and the only remaining life the words have is to give reference to the pop music of a different time. Another such word that comes to mind, from my earlier years, is ecumenical.

Ecumenical is a fancy word, imported in the late 16th century from Latin which in turn imported it from Greek and meaning, for the most part, “promoting or relating to unity among the world’s Christian churches” in the sense of “belonging to the universal Church.” The original Greek meaning appears to be something like “the (inhabited) earth,” meaning principally the Roman Empire.

The word came to renewed prominence in the mid–1960s and was especially popular on university campuses in the U.S. There were several ecumenical services that I and many others attended to see the ways the various branches of Christianity worshipped. It was the era of Pope John, folk masses, and Methodists, Catholics, Lutherans, Episcopalians, and Baptists getting together for pot-luck gatherings — perhaps the last such era of its kind before the echo of the Civil Rights marches and the ever-present war in Vietnam opened the rift that has continued to split the US into two separate, superimposed countries. Goodwill became less fashionable. Nixon was elected President. Goodbye ecumenical. Ceremonies of innocence were drowned.

It was around this time that many young people left the organized churches to find more contemporary ways of exploring their relationships to the universe. Transformations were in the wind — the times they were a-changing’. It rang through in the music, poetry, novels, hairstyles, and lifestyles of the young in what Mexican poet Octavio Paz called “an explosion of the spirit.” Its symbols were seen in peace signs, painted VW vans, concert posters, flowing hair, headbands, dance, and underground newspapers. Marijuana became the new communal sacrament, and LSD, mescaline, peyote, and magic mushrooms were portals to new kinds of perception. It was a heady time, unsustainable of course, and as with all things, tragic for some, but it was also a pretty time that, if experienced, can never be forgotten. Ah, the sunsets… but I digress…

It was in this time period that I first encountered the word ecology. The word, according to the Oxford English Dictionary first entered the language around 1875, in the original, scientific meaning of the term, “The branch of biology that deals with the relationships between living organisms and their environment.” The word grew gradually beyond its more limited definition to a broader sociological definition: “The study of the relationships between people, social groups, and their environment; (also) the system of such relationships in an area of human settlement. Freq. with modifying word, as cultural ecology, social ecology, urban ecology.

In the late 60s and early 70s it took on a more political flavour, meaning “The study of or concern for the effect of human activity on the environment; advocacy of restrictions on industrial and agricultural development as a political movement; (also) a political movement dedicated to this.” By this time ecology had become a buzzword and was frequently featured in such archives of the time as the Whole Earth Catalog, along with geodestic domes.

Ecology wasn’t a new concept — the interrelationship of organisms and their surroundings had been known for centuries — but the word gave clarity and weight to the concept, and in the world of DDT, Agent Orange, inappropriate dams, and urban sprawl, it began to take on an urgency as we learned of more species going extinct due to the clearing or altering of habitats and the encroachment of people.

Yet oddly, it’s a word I only hear now occasionally. One of the natural extensions of ecology is climate change. As the ecological and other studies added up, it became obvious to just about everyone in the world, except for a strange cadre of U.S. Republicans who have, for inscrutable political reasons, chosen to turn their backs on science and knowledge, that Earth, our very planet itself, is headed for a change that will not be good for the human species, much less the rest of the planet’s ecological systems.

Yet the word ecology is getting a new boost in usage, this time for the bacterial communities of our stomachs and intestines. Evidently we, and the bacteria in our bodies, co-evolved to make mammalian life, as we know it, possible. Our insides are literally crawling with them. The good ones help us digest food and contribute to our health. Whatever else our existence means, it is a life that, biologically, is only achieved by committee. Every “I” is literally a “we.” I’m glad to be seeing the word in use again because I always felt, in my gut, that ecology would make something of a comeback.

At a more abstract level, there is an ecology of the mind. The more you learn, ponder, and read, the more complex your mental landscape becomes and the more scope you have for ideas, counter-ideas, imagination, and insights. Who you read — which thinkers you have chosen to help guide you along the neuronal highways and byways of the brain — creates the type of mental ecosystem you live in, and determines whether it’s a rich, varied, healthy ecosystem, or a more limited ecosystem with poor mental soil. So, as the acolyte said to Indy, “Choose wisely.”

Flowers From Algernon

Flowers From Algernon

By Gene Wilburn

“What the Net seems to be doing is chipping away my capacity for concentration and contemplation. Whether I’m online or not, my mind now expects to take in information the way the Net distributes it: in a swiftly moving stream of particles. Once I was a scuba diver in the sea of words. Now I zip along the surface like a guy on a Jet Ski” ~ Nicholas Carr, The Shallows: What the Internet is Doing to Our Brains

I grinned recently at a cartoon of an elderly gentleman standing at the base of his stairway wondering if he had just come down the stairs or if he was about to go upstairs to get something. Welcome to my world: the world of cognitive gaps. Mix natural absent-mindedness with an aging brain and daily life becomes an adventure. It’s only through the grace of automated bank withdrawals that I’m still deemed credit worthy.

Sometimes cognitive gaps are embarrassing. About every two years or so I take a plane flight to the US to visit family. I always book an early morning flight and, due to customs protocols, have to arrive at the airport so early the ticket booths aren’t yet open. I’m not a morning person, so these dawn-tinged adventures require Olympic-level efforts from me, and to have it all shattered when the person I present my ticket to says, “Mr. Wilburn, I’m sorry, but your flight is booked for tomorrow,” is disheartening.

What worries me more is that my ability to concentrate on things is lessening. I’ve been living in the fast lane of Information Tech for years and years and despite the tsunami of new “stuff” coming down the pipe all the time, I think it was a kind of specialized narrowcasting of technical information that I had evolved, mentally, to swim in comfortably. I always kept an outside focus on things that interested me, such as books, music, and photography, but my main focus was tech.

Then retirement, and a gradual drift from computer services creator and provider, to computer services user. From techie to user — I’m left with a vague sense of having been demoted. Not that I miss the fast lane. I still write occasional snippets of code, but for the most part I’ve embraced my new overlords and have plugged myself into the Internet, like a bee into the hive mind.

In this world of Facebook, Twitter, Flickr, and other social media and news aggregators, information comes shooting at us as Carr said, “in a swiftly moving stream of particles.” It’s intense. And surely it must have consequences for the brain.

Our brains are wondrously adaptable and able to rewire themselves according to need, and as our needs shifts from deep reading to shallow reading, which they have to do to keep up with all the incoming, our brains compensate, perhaps, by borrowing from our deep-reading skills to adjust to our need to devour info in wide swaths. We adapt to quick, intermittent bursts of concentration rather than long sessions of concentration. In photographic terms, we’ve switched from macro lenses to wide angle.

I greatly admire people, like my wife Marion, who can concentrate on something for hours at a time. As I’m sweeping through the Internet with my net cast wide for nuggets of beauty, humour, and maybe even wisdom, she delves deep into genealogical data searching for clues that might provide links to her family tree. To the point where her hot drink grows cold because she forgets it’s there. I’m no longer capable of that kind of concentration.

It feels like a seismic shift, this dwindling ability to study anything hard and long, and a departure from the past when one sat in a favourite nook with a favourite book, savouring the thoughts and words of a voice from another time or place, perhaps in another language. It’s cutting us off from the past. While some people still read Jane Austen, and a handful read Dickens, there are few left who read translations of Homer or Marcus Aurelius, and fewer still who can read them in Greek or Latin.

The main culprit is the sheer volume of contemporary information we must process to adapt to living in an electronic age. We’re like baleen whales sieving for krill. To be a citizen of the Internet one is required to digest all sorts of facts and factoids and issues about everything under the sun and beyond. It’s enough to drive Southern evangelists to the mythic comfort of the Christian Bible (though even fewer of them appear to enjoy the rolling passages and magisterial tones of the King James translation).

Given that much of contemporary information feels like “a tedious argument of insidious intent,” we need more buffer zones — places or activities that shield us, at least temporarily, from the onslaught. Playing a musical instrument, cooking, drawing, having a picnic, walking in the park, meditating, reading for pleasure – all these things help, as long as you’re not on your cell phone.

Undoubtedly my brain is not as agile as it once was — not that I had any intention to read Spencer’s Faerie Queen — but as we head for what Nicolas Carr calls “the Shallows,” it’s apparent to me that age is not the only factor in my gentle demise. The zeitgeist, or spirit of the times, is reductive. Newsbytes, tweets, and click-bait headlines are conditioning us to view the world kaleidoscopically, reacting with “Oooh” or “Oh no” at each passing spark. And it’s not merely reductive. It’s addictive. It may even work as a form of mind control. Clearly there are implications.