It amazes me how long an insight can take to fully develop, sometimes simmering for years while the pieces fall into place. I feel like this when it comes to the importance of context. I presume I’ve known the word since I was a youngster, thrown in with a jumble of other words I might occasionally see fit to use. Over the past decade, I have become increasingly aware of its relevance and value. At this stage, I can think of few more important words or concepts.

In this post, I’ll extract highlights on my path to greater awareness of contextual importance, and its relevance to the present predicament—using a few metaphors to help paint the picture.

Application to Learning

Perhaps an appropriate beginning to the story is in connection to my role as an educator. I constantly strove to recreate for students the relevance I myself found in new concepts that I stumbled upon as a young student. Admittedly, a large fraction of those stumblings took place outside of the curriculum, as a result of my own motivated explorations.

The Early Years

A few early examples will help illustrate the “warehouse” framework I’ll describe in a bit. First, as a teenager, I had a poster on my wall of the Moon’s face. I noticed that the lines of longitude—each 10° apart—were broadly separated in the center and got closer together toward the edge. I had an intuitive understanding for why this must be so, as a matter of the projection of a sphere onto a plane. But I wanted to understand how to describe it mathematically. Careful measurements and plotting revealed an elegant curve, but my attempts to get a parabola (poor) or hyperbola (better) to match it left me unsatisfied, so I shelved the problem (emphasis will later become clear).

Some months later, as a junior in high school, my first-ever physics class introduced sines and cosines. Most of my fellow students groaned with displeasure at these uninvited guests, but I wondered. I could see how they might connect to the mystery of longitude spacings. I scaled the sine to my measurements, and viola! Perfection! Delight! I had a new best friend! While other students continued to resent these interlopers, I had all kinds of fun with them, understanding how they connect to real problems.

Later in the same year, I noticed in my growing collection of Sky & Telescope magazines that the subtracted time between successive new moons (times of each month’s new moon were listed to the minute) was not the same from month to month. The various subtractions collected across several months (issues) seemed to cluster around the nominal 29.53 days, but varied by a surprisingly large fraction of a day, showing what looked like an annual cycle. In the process of trying to figure it out—ultimately relating to non-uniform angular velocity in an elliptical orbit—I needed to compute the velocity at a point on the orbit. Having acquired a way to compute position as a function of time, I reasoned that the difference in two computed positions divided by the time separating those two instances would approximate a velocity. Moreover, I recognized that the smaller I made the time interval, the more exactly I would converge on an instantaneous velocity (rather than the average of a value that changes over the interval), up to computational rounding error. I carried out my calculations using this technique.

So, the next year when my math class introduced some calculus preliminaries, a key concept underlying the derivative involved ratios in the limit where the amount of change (in the denominator) went toward zero. Literal-minded students had a fit with this, as everyone knows that dividing by zero yields infinity nonsense. The calculator confirms it! But I was able to keep my cool: “No, no, this is exactly what you want in order to get at the rate of change at that exact moment or place.”

In a word, I had context! I had already laid a foundation of connections to the broader world. The abstraction had immediate, larger relevance—rather than sitting on its own, as it does for many students. As others crammed for math exams, I didn’t bother, because I owned the concepts, thanks to a rich contextual framework.

The Warehouse

I only appreciated the importance of such context as an educator when trying to understand how my approach differed from that of students in my classes. I developed a metaphor for how the brain works. Firstly, I recognized that the physical basis of learning must come down to rearranging (re-weighting) neural connections, you know, in the brain. Connections are an expression of context (the two words are indeed hard for me to separate). Thinking of the brain as a warehouse in which to store knowledge and concepts, I realized that my various experiences had worked to prepare labeled shelf space waiting for new deliveries, pre-loaded with contextual connections to things that had personal meaning for me. When a class delivered new information, I either already had a space waiting for it (at last!), or recognized that I needed to work proactively to contextualize the new piece so that I might know where to put it and what other things I might connect it to (picture yarn criss-crossing the shelves making a web; not very unlike the actual neural network in your brain).

My mental picture for how education works for most students is that every day a forklift arrives bearing a new load of material. The driver asks: “where do you want this?” Whereas I might say: “I have just the place…over here—see, it’s already labeled and has ready-made connections,” I sense that a lot of students say: “Umm, I dunno. Dump it right there, I guess.” When it comes time to take an exam, they find themselves kicking around the pile looking for something that might suit the problem at hand. “Is this equation going to do what I need?” You can imagine the result, and the anxiety that a pile of decontextualized information produces.

I began encouraging students to build a bank of their own questions—motivated by genuine curiosity—that would essentially prepare labeled shelves awaiting future deliveries. I taught freshman seminars where every session involved reading questions submitted by every student, centered on some fundamental curiosity about the physical world (it was a physics seminar, after all). By reading them aloud, I hoped to spread the seeds of curiosity all around: more shelves for everyone! I have no idea if it made a bit of difference, but sessions were entertaining, mostly spent tackling the less trivial and most richly contextual of the topics.

More than a Number

I also noticed that many students had an unhealthy relationship with numbers. To them, numbers were fixed, exact, literal, untouchable. To me, they’re only as good as their context. Numbers become fluid, fungible, friendly. Approximate estimates are sort-of my thing, and usually the inputs are too crude to worry about the difference between π, √10, 10/3, or 3. They’re all “three.” To make math easier to carry out in my head, I might round up here, down there, striving to maintain approximate balance in the process—not stressing about inconsequential imprecision. Professionally, meanwhile, I was measuring Earth–Moon distance to millimeter accuracy (loads of digits!). Contextually, both approaches have their place.

For students, if the calculator says it, it’s sacrosanct. They’ll write down all the digits, because they are not keeping in mind what the number represents in its original context. To these students, “significant digits” is just an annoying practice required (only) in chemistry classes that has no relevance elsewhere: just more rules to follow when grades depend on it.

Algorithmic Bots

Student reactions to my textbook—which is meant to expose general-education classes to highly contextual quantitative reasoning—often expressed distaste over integrating math (equations) into prose in a back-and-forth “codeswitch” format. Such students want math relegated to side boxes in recipe form so that they can replicate the steps when given a problem whose setup appears to parallel a boxed case. I understand why. Not only is this an easier process of pattern-matching—requiring less cognitive heavy lifting—but their educational experience has prepared them for little else. They do not instinctively see equations as I do: as precise, compact sentences that communicate tons of relationships (within some limited context) and that can both ground and echo intuition. Surrounding sentences bring the equation-sentence to life, contextualizing it to the world: why it’s useful, what it says, and when its use is appropriate.

Students seem to resist my efforts to provide context. It’s harder; messier; less cut-and-dried; less algorithmic. Our educational system has, unfortunately, reduced thought to robotic forms—emphasizing exactness, uniformity, repeatability, standardization (thus ease of grading), recipes. Students are not practiced at the art of contextual understanding, where numerous particulars might come into play and ambiguity looms. How would we measure and produce boatloads of students on ambiguous, contextual turf? Machine no likey.

Context’s Opposite

I would say that the opposite of context is abstraction. Both have their uses, but abstraction deliberately strips away particulars to leave a clean, universal, compartmentalized, prescriptive form. Such a bare remnant of reality becomes easier to conceptualize and manipulate. In many modern concerns, the result pays off, which is why the practice has been encouraged. The fundamental building blocks of the universe indeed appear to operate by such well-defined and repeatable rules (physics), so that the act of abstraction facilitates powerful application.

However, beyond a certain degree of complexity, abstraction loses its grip and can even become a liability as an over-simplification that misses critical subtleties. You drive a car based on some mental model of traction, tuned by experience. However, invisible black ice changes the context, so that application of the usual model will result in tires losing their grip on the road and putting you in peril. Abstraction is necessarily incomplete, and the simplification is sometimes frighteningly consequential. Likewise, we build an abstraction of the society in which we operate based on observations and its history. The abstraction does not prepare us for new developments outside of the model, like the waterfall we now approach. The abstraction might be great at capturing the current patterns in the river, but does not incorporate broader truth outside the zone of focus.

I should briefly mention that this whole topic gained even more relevance recently upon reading Iain McGilchrist’s The Master and His Emissary, about hemispheric specializations stemming from clinical research.  While much of the focus is on which hemisphere does which kind of thinking, the most important lessons from the book have little to do with assignment to a particular hemisphere, but elucidate keen insights on different ways of thinking and their values vs. limitations.  It’s helped me to more clearly see the faults in modernity’s mindset (and in my own tendencies), and underlies a number of the points in this post.

Example Contextual Metaphors

Metaphorical thinking might be considered to be the counterpart to algorithmic thinking. Metaphor aims to build a picture that is graspable in its entirety as a ready-made insight—in a flash. Once implanted, it needs no words or step-wise elaboration for its value and applicability to be perceived. The following metaphors help illustrate the importance of context.

Clueless Cats

House cats often find that furniture suits very well as scratching posts for claw maintenance. All they know is that it’s convenient, feels right, performs a function, and that sometimes their house brutes get loud, clap, and throw things at them. They cannot appreciate the context leading to your dislike of their actions. What are aesthetics? What are visitor opinions, and why do they matter? What is money (then get more, stupid)? What is a job? Why do you do things you don’t want to do? There is no logic in this place.

How much context are we missing in our destruction of Earth’s furnishings, oblivious to the larger picture? We’re sawing the branch we’re standing on, marveling at the technology and power without appreciating the dire consequences.

Riderless Bike

If you were like me as a kid, you sometimes pushed your bicycle down a hill to see how far it would go without you. Like the cat, you failed to grasp the context that would make your parents steam at this careless action. We could go on and on about adolescent misdeeds as failures of contextual understanding.

In any case, the bike might go for a while (or sometimes not very far at all) before colliding with something, getting tripped by a bump, or just pathetically leaning over. The riderless bike is a bike out of context. It might appear to work for a while, but failure is virtually assured. Humans are a species out of context, as Wes Jackson put it. We might go on for a while in the current mode (modernity), but we can’t stay out of context forever.

Look Out the Window!

Context relates to the whole world, as it is presented—rather than an impoverished, abstracted facsimile (representation) of the world. The artificial version is attractive, as it is easier to grasp, while the full picture defies facile reduction.

In this sense, let’s say you were presented with a particular car, having access to all its specifications down to the last detail: engine efficiency as a function of revolutions per minute; transmission gear ratios; drive train parameters and tire size; fuel delivery mechanism and control linkages; aerodynamic performance data; frictional forces. You are asked to figure out how fast the car ought ought to travel, optimizing performance.

Given all these clear pieces, it would be possible in principle to compute the ideal speed and indeed how much pressure to apply to the accelerator pedal (alternatively, how far to depress it) to achieve this speed. The calculator delivers a number. Make it so.

The model seemed to be complete. What’s missing is any indication of the external conditions. Is the road straight or diabolically curvy? Is it flat or hilly? How far does the road go? Is there even a road? The context matters. A focus on the technical aspects failed to ever look out the window to see what’s out there.

Our society likewise tends to focus on the small bits, without looking out to see what the external world tells us. A look out the window gives cause for alarm.  Modernity motors forward, accelerating, with little regard for whether this road even continues (hint: it can’t).

I am reminded of the movie Men in Black, in which Will Smith’s character repeatedly outperforms other job applicants by displaying a broad contextual understanding of his environment, rather than focusing on the more obvious but narrow tasks to which he and the other applicants are set. That’s the kind of thinking we need in novel situations like the one presented to us today by the predicament.

Contextualizing the Predicament

I recognize that a very large part of what I have consistently tried to accomplish in my communication efforts is a matter of contextualization. Why not growth? Why not space? Why not fusion? Why not renewable energy? Why not modernity? What’s so bad about our current path? Each case is a battle against narrow-boundary thinking. Our society has become ever-more compartmentalized, and the “paid thinkers” (academics) along with it—each field in its own silo.

The experience is like a whack-a-mole game, as it is impossible to convey all the contextual elements in one go, including: time, space, energy, ecology, economy, sociology, psychology, etc. But I keep trying, as in a recent article for The Physics Teacher. In a way, each attempt targets some narrow sector of the overall predicament and tries to bring contextual understanding. Tools of language, logic, and math are deployed to engage on the turf of the narrow concern, immediately at a disadvantage.

Context is about the whole. It’s about the simultaneous consideration of everything at once, which is nearly impossible—especially when having to communicate in a plodding, serial, language-constrained format. Context happens in a flash. It’s behind the “exploding brain” phenomenon, when so many thoughts or objections crowd in at once that words can’t spill out quickly enough. As indicated above, metaphor can be a better delivery system for a contextual whole. An image or cartoon can convey complex, nuanced thinking in one shot (worth a thousand words, simultaneously processed).

Caesar’s Dictum of divide and conquer is a fine route to power and subjugation, but not germane when the goal is long-term cooperative sustainability. One group working on renewable energy, another on fusion, another on forest management, another on social justice, another on infrastructure, another on political grass roots, etc. will not likely result in a viable existence, as each effort is decontextualized and lacking a shared set of values and priorities. Moreover, without placing top priority on ecological health, the result will not accidentally be viable, somehow. Lacking the appropriate contextual appreciation, it is hard to see how modernity could survive the real world for very long.

So, here is some context for the predicament. Humans are: a biological species; one of millions; relatively new to the planet; needed by few but needing many; part of nature; belonging to Earth and no other place. Moreover, many humans on the planet are: only very recently experimenting with modernity; operating without explicit regard for ecological consequences; rapidly spending a material inheritance; boasting a population temporarily swollen on the fruits of that inheritance; carrying out enormous ecological damage as a thoughtless by-product of energy and material expenditures; running a system predicated on something as obviously and inherently unsustainable as growth; purposefully decontextualizing our lives by separating further from nature; powerful enough to have initiated a sixth mass extinction; collectively arrogant enough to think we’re getting away with it; short-lived enough to not appreciate the magnitude of the insanity; unaccustomed to thinking about context, as lives are increasingly structured around narrow concerns.

Oh, if more people could hold all these things in mind at once. But let’s try, shall we?

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