Archive for the ‘Education’ Category

The Politics of Perplexity in Twenty-First Century America

Friday, July 17th, 2020

In the context of twenty-first century America, “politics” is perhaps one of the most curiously irritating words in the English language. I know from personal experience – whether from observing others, or from paying attention to myself – that there is a visceral reflex to feel something between annoyance and disgust upon hearing the word. If politics rears its ugly head, you may think something along the lines of “I’ve had enough of that, thank you!” before rapidly extricating yourself from an unwanted intrusion into an otherwise perfect day. Alternatively, I suspect many of us know people who hear the word “politics” or some related term and can immediately launch into an ambitious lecture on what is wrong and what should be done that somehow promises (implausibly) to solve all our social, political, and economic problems in one fell legislative swoop. We’re surrounded by bitter disputes – online and on television, in print and in person – over political issues, to the extent that it can be hard to stomach contemplating (much less discussing) politics without feeling a little irritated, even disgusted, with both our neighbors and ourselves.

These powerful emotional reactions should give us some pause for reflection. In theory, if not always in practice, the United States of America is a democratic republic, ruled by representative officials in the name of its citizenry. Even without considering the matter deeply, it should be clear to us that such a government cannot function if its citizens are entirely disengaged, as radical factions across the political spectrum will be left to do the politicking on our behalf. Whether we like it or not, our nation’s political life will likely remain interested in us even if we are uninterested in return. We might as well make the best of it, and get down to the business of figuring out where, exactly, we went wrong, and what might be done to repair the damage.

Since the early twentieth century, the predominant approach to teaching American students about their form of government has been in the form of what is known as political science. This perspective is primarily (though not exclusively) concerned with educating students about the practical mechanics of their government and the political dynamics of the American electorate – in short, the branches of the United States government, their differing roles and jurisdictions, group behavioral dynamics, and so forth. All of these political institutions and phenomena are generally treated as abstractions that can be measured and predicted with some degree of accuracy using scientific methodology and data analysis.

The meaning of political science must be carefully qualified and defined. Science is derived from the Latin scientia, or knowledge. The majority of ancient, medieval, and early modern political thinkers used the term political science to refer to the study of politics as a domain of the humanities. They studied politics in light of inquiries in philosophy and history: they did not, as a general rule, conceive of the art of government as something that could be understood as an institutional abstraction that operated independently of the deepest human needs and desires (such as for law and virtue), or the eternal problems that confront every human individual and society (what is justice and truth, and how de we find them?). Above all else, classical political science aimed at cultivating self-governing (moderate) individuals that would be capable of wielding political power responsibly while refraining from tyrannical injustice. Hence, in the conclusion of Plato’s Republic, Socrates teaches Glaucon that the highest end of political science is to teach the soul to bear “all evils and all goods… and practice justice with prudence in every way.” (Republic, Book X, 621c).

Modern political science operates on an entirely different basis and different assumptions about human beings and political life. It begins with the premise that human beings, like all natural things, are subject to mechanical laws that render them predictable. Once these laws are understood, the political life of human beings can be mastered and directed towards progress (understood as material comforts and technological innovation) to a degree that was never remotely possible in prior eras of human history. This view of political science emerged first among certain thinkers of the Enlightenment, and became a close companion to the development of the entire field of social science in the late nineteenth century. Both modern political and social science emerged from a common intellectual project that aimed to apply modern scientific methods and insights to the study of very nearly every aspect of human communal life – economics, social dynamics (sociology), religion, sexuality, psychology, and politics, among others.

This application of human technical knowledge to endemic social problems, economic systems, and political institutions (among other domains of human life) was expected to deliver unprecedented advances that would mirror and eventually surpass the tremendous technological and intellectual achievements of the Scientific Revolution. Max Weber, a social scientist of incredible imtelligence and one of the most brilliant minds of the early twentieth century, fully expected that the complimentary discoveries of both natural and social science would ensure that human “progress goes on ad infinitum.” For many intellectuals in Europe and the United States in Weber’s day, human social and political life had become like a machine that could be kept in a perpetual state of inexorable forward motion. This view remains a powerful one within certain spheres of the social sciences and general public, and has been articulated perhaps most eloquently in the public sphere by the Harvard psychologist Steven Pinker, among others, even if it is gradually declining in popularity among the greater mass of the American citizenry.

Academically, this modern scientific approach to understanding American government had many apparent advantages that explain both its widespread acceptance and its continued influence within the academy. For one, it enabled teachers to focus on explaining the structure of U.S. government with a focus on the technical mechanics of government that can be mastered intuitively by most students, regardless of their particular political views and prejudices. Similarly, it relieves teachers and students of having to focus on tiresome historical minutia or obscure philosophical debates that bear no obvious relevance to contemporary issues: students can study their government based on recent experiences that are more easily comprehensible for them than those of, say, two hundred years ago. Above all else, contemporary political science treats the study of American government in utilitarian and mechanistic terms, thereby minimizing occasions for awkwardly passionate or unsolvable confrontations over thorny issues that touch on moral as well as historical and philosophical complexities. What many students will learn from this education is that the American form of government is perfectly reasonable, orderly, and balanced, with predictable mechanics that ensure its stability and perpetuity; in short, it makes sense. And not only does the American government operate like a well-oiled machine, but it also leaves individuals tremendous room to define themselves and act within an ever-expanding horizon of freedoms. Government exists mainly to resolve practical matters of policy and administration, leaving moral questions largely to the domain of the private sphere.

Many may rightly ask: if this model is true, then why does the American government function so poorly in practice? And why are Americans so remarkably inept at finding common ground for resolving pressing political issues? Indeed, there are alarming trends that should inspire us to doubt the viability of this interpretation. Polling conducted over the past decade consistently shows that Americans of all political persuasions are increasingly distrustful of both their governments and of their fellow citizens who hold opposing views. Rigid ideological voices have emerged among both liberal and conservative parties that insist that dialogue is impossible and compromise on any issue is a sign of political weakness, and that a candidate’s quality should be determined by ideological considerations rather than by competence and experience. As electoral politics have devolved into brutal slugging matches between increasingly extreme views, the actual levers of political power have gradually shifted into the hands of a theoretically subordinate but frequently unaccountable and inefficient bureaucracy.

The fruits of this widespread culture of distrust has been the breakdown of civic life and political order amidst frustration and mutual recrimination throughout American society. Many are understandably frustrated with a system of government that seems incapable or unwilling to fulfill its most basic functions. For that matter, generations of young Americans have now grown up in the shadow of a dysfunctional government that leaves them with little incentive for acting as responsible and engaged citizens. It should be no wonder that there are now voices who now ask questions such as the following: if our current Constitution is a product of eighteenth century political circumstances and ideals, should we not perhaps craft a new political system that is better adapted our contemporary needs and values?

Perhaps these are all passing fads, and some bearable equilibrium will return in short order. I am doubtful that such an event is likely in the near future. Recent events have shown that contemporary Americans of all political stripes are divided not merely by petty partisan differences over policy decisions and electoral contests, but even more importantly by fierce disagreements over fundamental questions about the nature of political life and American civic identity that transcend mere partisan disagreement, and we are not remotely close to resolving these disputes. What is it to be a human? What is freedom? What is justice? We do not have common answers for any of these fundamental questions, nor do we seem (at least, as of this writing) to have a clear direction for amicably resolving these disputes in the public sphere.

Yet these disputes, however unpleasant and acrimonious, provide us with a hint of where, exactly, we may have gone wrong. Far from liberating us from antiquated concerns, our modern political education (and the novel mode of thought that created it) may lie at the heart of our perplexity. Modern political science has worked tremendous wonders in allowing us to track the chimerical shifting of public whims in opinion polls or understand the psychology of group dynamics, but it has also obfuscated our ability to grapple with and comprehend problems that are part of the permanent condition of our species. Political institutions and policy alone cannot solve America’s most vexing problems. And we should remember that representative government depends ultimately on the qualities of both officeholders and voters to function properly; institutions abstracted from the body politic cannot rule themselves. Our government, as John Adams observed in 1798, “was designed for a moral and religious people. It is wholly inadequate to the government of any other.” Adams thought that republican government could not exist without some degree of self-government among the citizenry, or else it must devolve into a mass of petty tyrants; we are, perhaps, in the process of proving his point for him.

I suspect that the root of modern American political dissatisfaction is not so much in our continued subjection to an apparently antiquated form of government, nor merely in our frustration with the peculiar idiocies of our political parties, but rather in our own failure to accurately comprehend and utilize our form of government. In an era of change and tumult, we would do well, as the American novelist and essayist John Dos Passos put it in 1941, to “look backwards as well as forwards” as we attempt to extricate ourselves from our current political predicament. While we may face many distinctly twenty-first century problems in certain respects, our most pressing problems – justice, love, truth, goodness, and so forth – are as old as the human species. We live in troubled times: but so, too, did prior generations of Americans. I hope that, if we can find it in ourselves to turn back and reconsider the first principles of American government, its deep roots in English political life and philosophy, we may yet discover a firm foundation that will give us a lifeline from our current perplexity, and enable us to engage more fully in a life of dutiful, informed, and responsible citizenship that can be passed on to future generations.

Mr. Spock, Pseudo-scientist

Wednesday, April 15th, 2020

I’m one of those aging folks who still remember the original run of Star Trek (no colon, no The Original Series or any other kind of elaboration — just Star Trek). It was a groundbreaking show, and whether you like it or not (there are plenty of reasons to do both), it held out a positive vision for the future, and sketched a societal ethos that was not entirely acquisitive, and not even as secular and materialistic as later outings in the Star Trek franchise. The officers of the Enterprise were not latter-day conquistadors. They were genuine explorers, with a Prime Directive to help them avoid destroying too many other nascent cultures. (Yes, I know: they violated it very frequently, but that was part of the point of the story. Sometimes there was even a good reason for doing so.)

It also offered the nerds among us a point of contact. Sure, Captain Kirk was kind of a cowboy hero, galloping into situations with fists swinging and phasers blazing, and, more often than not, reducing complex situations to polar binaries and then referring them either to fisticuffs or an outpouring of excruciatingly impassioned rhetoric. Dr. McCoy, on the other hand, was the splenetic physician, constantly kvetching about everything he couldn’t fix, and blaming people who were trying to work the problem for not being sensitive enough to be as ineffectual as he was. But Mr. Spock (usually the object of McCoy’s invective) was different. He was consummately cool, and he relied upon what he called Logic (I’m sure it had a capital “L” in his lexicon) for all his decision-making. He was the science officer on the Enterprise, and also the first officer in the command structure. Most of the more technically savvy kids aspired to be like him.

It was an article of faith that whatever conclusions Spock reached were, because he was relying on Logic, logical. They were the right answer, too, unless this week’s episode was explicitly making a concession to the value of feelings over logic (which happened occasionally, but not often enough to be really off-putting), and they could be validated by science and reason. You can’t argue with facts. People who try are doomed to failure, and their attempt is at best a distraction, and often worse. 

Up to that point, I am more or less on board, though I was always kind of on the periphery of the nerd cluster, myself. I suspected then (as I still do) that there are things that logic (with an upper-case or a lower-case L) or mathematics cannot really address. Certainly not everything is even quantifiable. But it was the concept of significant digits that ultimately demolished, for me, Mr. Spock’s credibility as a science officer. When faced with command decisions, he usually did reasonably well, but when pontificating on mathematics, he really did rather badly. (Arguably he was exactly as bad at it as some of the writers of the series. Small wonder: see the Sherlock Holmes Law, which I’ve discussed here previously.)

The concept of significant digits (or figures) is really a simple one, though its exact specifications involve some fussy details. Basically it means that you can’t make your information more accurate merely by performing arithmetic on it. (It’s more formally explained here on Wikipedia.) By combining a number of things that you know only approximately and doing some calculations on them, you’re not going to get a more accurate answer: you’re going to get a less accurate one. The uncertainty of each of those terms or factors will increase the uncertainty of the whole.

So how does Spock, for all his putative scientific and logical prowess, lose track of this notion, essential to any kind of genuine scientific thinking? In the first-season episode “Errand of Mercy”, he has a memorable exchange with Kirk: 

Kirk: What would you say the odds are on our getting out of here?

Spock: Difficult to be precise, Captain. I should say approximately 7,824.7 to 1.

Kirk: Difficult to be precise? 7,824 to 1?

Spock: 7,824.7 to 1.

Kirk: That’s pretty close approximation.

Spock: I endeavor to be accurate.

Kirk: You do quite well.

No, he doesn’t do quite well. He does miserably: he has assumed in his runaway calculations that the input values on which he bases this fantastically precise number are known to levels of precision that could not possibly be ascertained in the real world, especially in the middle of a military operation — even a skirmish in which all the participants and tactical elements are known in detail (as they are not here).  The concept of the “fog of war” has something to say about how even apparent certainties can quickly degrade, in the midst of battle, into fatal ignorance. Most of the statistical odds for this kind of thing couldn’t be discovered by any rational means whatever.

Precision and accuracy are not at all the same thing. Yes, you can calculate arbitrarily precise answers based on any data, however precise or imprecise the data may be. Beyond the range of its significant digits, however, this manufactured precision is worse than meaningless: it conveys fuzzy knowledge as if it were better understood than it really is. It certainly adds nothing to the accuracy of the result, and only a terrible scientist would assume that it did. Spock’s answer is more precise, therefore, than “about 8000 to one”, but it’s less accurate, because it suggests that the value is known to a much higher degree of precision than it possibly could be. Even “about 8000 to one” is probably not justifiable, given what the characters actually know. (It’s also kind of stupid, in the middle of a firefight, to give your commanding officer gratuitously complex answers to simple questions: “Exceedingly poor,” would be more accurate and more useful.

This has not entirely escaped the fan community, of course: “How many Vulcans does it take to change a lightbulb?” is answered with, “1.000000”. This is funny, because it is, for all its pointless precision, no more accurate than “one”, and in no situations would fractional persons form a meaningful category when it comes to changing light bulbs. (Fractional persons might be valid measurements in other contexts — for example, in a cannibalistic society. Don’t think about it too hard.) 

Elsewhere in the series, too, logic is invoked as a kind of deus ex machina — something to which the writer of the episode could appeal to justify any decision Mr. Spock might come up with, irrespective of whether it was reasonable or not. Seldom (I’m inclined to say never, but I’m not going to bother to watch the whole series over again just to verify the fact) are we shown the operation of even one actual logical operation.

The structures of deductive reasoning (logic’s home turf) seldom have a great deal to do with science, in any case. Mathematical procedures are typically deductive. Some philosophical disciplines, including traditional logic, are too. Physical science, however, is almost entirely inductive. In induction, one generalizes tentatively from an accumulation of data; such collections of data are seldom either definitive or complete. Refining hypotheses as new information comes to light is integral to the scientific process as it’s generally understood. The concept of significant digits is only one of those things that helps optimize our induction.

Odds are a measure of ignorance, not knowledge. They do not submit to purely deductive analysis. For determinate events, there are no odds. Something either happens or it doesn’t, Mr. Spock notwithstanding. However impossibly remote it might have seemed yesterday, the meteorite that actually landed in your back yard containing a message from the Great Pumpkin written in Old Church Slavonic now has a probability of 100% if it actually happened. If it didn’t, its probability is zero. There are no valid degrees between the two.

Am I bashing Star Trek at this point? Well, maybe a little. I think they had an opportunity to teach an important concept, and they blew it. It would have been really refreshing (and arguably much more realistic) to have Spock occasionally say, “Captain, why are you asking me this? You know as well as I do that we can’t really know that, because we have almost no data,” or “Well, I can compute an answer of 28.63725, but it has a margin of error in the thousands, so it’s not worth relying upon.” Obviously quiet data-gathering is not the stuff of edge-of-the-seat television. I get that. But it’s what the situation really would require. (Spock, to his credit, often says, “It’s like nothing we’ve ever seen before,” but that’s usually just prior to his reaching another unsubstantiated conclusion about it.)

I do think, however, that the Star Trek promotion of science as an oracular fount of uncontested truth — a myth that few real scientists believe, but a whole lot of others (including certain scientistic pundits one could name) do believe — is actively pernicious. It oversells and undercuts the legitimate prerogatives of science, and in the long run undermines our confidence in what it actually can do well. There are many things in this world that we don’t know. Some of the things we do know are even pretty improbable.  Some very plausible constructs, on the other hand, are in fact false. I’m all in favor of doing our best to find out, and of relying on logical inference where it’s valid, but it’s not life’s deus ex machina. At best, it’s a machina ex Deo: the exercise of one — but only one — of our God-given capacities. Like most of them, it should be used responsibly, and in concert with the rest.

The Sherlock Holmes Law

Friday, April 3rd, 2020

I rather like Arthur Conan Doyle’s Sherlock Holmes stories. I should also admit that I’m not a hard-core devotee of mysteries in general. If I were, I probably would find the frequent plot holes in the Holmes corpus more annoying than I do. I enjoy them mostly for the period atmosphere, the prickly character of Holmes himself, and the buddy-show dynamic of his relationship with Doctor Watson. To be honest, I’ve actually enjoyed the old BBC Holmes series with Jeremy Brett at least as much as I have enjoyed reading the original works. There’s more of the color, more of the banter, and less scolding of Watson (and implicitly the reader) for not observing the one detail in a million that will somehow eventually prove relevant.

Irrespective of form, though, the Holmes stories have helped me articulate a principle I like to call the “Sherlock Holmes Law”, which relates to the presentation of fictional characters in any context. In its simplest form, it’s merely this:

A fictional character can think no thought that the author cannot.

This is so obvious that one can easily overlook it, and in most fiction it rarely poses a problem. Most authors are reasonably intelligent — most of the ones who actually see publication, at least — and they can create reasonably intelligent characters without breaking the credibility bank. 

There are of course some ways for authors to make characters who are practically superior to themselves. Almost any writer can extrapolate from his or her own skills to create a character who can perform the same tasks faster or more accurately. Hence though my own grasp of calculus is exceedingly slight, and my ability to work with the little I do know is glacially slow, I could write about someone who can look at an arch and mentally calculate the area under the curve in an instant. I know that this is something one can theoretically do with calculus, even if I’m not able to do it myself. There are well-defined inputs and outputs. The impressive thing about the character is mostly in his speed or accuracy. 

This is true for the same reason that you don’t have to be a world-class archer to describe a Robin Hood who can hit the left eye of a gnat from a hundred yards. It’s just another implausible extrapolation from a known ability. As long as nobody questions it, it will sell at least in the marketplace of entertainment. Winning genuine credence might require a bit more.

Genuinely different kinds of thinking, though, are something else. 

I refer this principle to the Holmes stories because, though Mr. Holmes is almost by definition the most luminous intellect on the planet, he’s really not any smarter than Arthur Conan Doyle, save in the quantitative sense I just described. Doyle was not a stupid man, to be sure (though he was more than a little credulous — apparently he believed in fairies, based on some clearly doctored photographs). But neither was he one of the rare intellects for the ages. And so while Doyle may repeatedly assure us (through Watson, who is more or less equivalent to Doyle himself in both training and intelligence) that Holmes is brilliant, what he offers as evidence boils down to his ability to do two things. He can:

a) observe things very minutely (even implausibly so);


b) draw conclusions from those observations with lightning speed. That such inferences themselves strain logic rather badly is not really the point: Doyle has the writer’s privilege of guaranteeing by fiat that they will turn out to be correct.

Time, of course, is one of those things for which an author has a lot of latitude, since books are not necessarily (or ever, one imagines) written in real time. Even if it takes Holmes only a few seconds to work out a chain of reasoning, it’s likely that Doyle himself put much more time into its formation. While that probably does suggest a higher-powered brain, it still doesn’t push into any genuinely new territory. Put in computer terms, while a hypothetical Z80 chip running at a clock speed of 400Mhz would be a hundred times faster than the 4Mhz one that powered my first computer back in the 1982, it would not be able to perform any genuinely new operations. It would probably be best for running CP/M on a 64K system — just doing so really quickly.

It’s worth noting that sometimes what manifests itself chiefly as an increase in speed actually does represent a new kind of thinking. There is a (perhaps apocryphal) story about Carl Friedrich Gauss (1777-1855), who, when he was still in school, was told to add the digits from one to a hundred as punishment for some classroom infraction or other. As the story goes, he thought about it for a second or two, and then produced the correct result (5050), much to the amazement of his teacher. Gauss had achieved his answer not by adding all those numbers very rapidly, but by realizing that if one paired and added the numbers at the ends of the sequence, moving in toward the center, one would always get 101: i.e., 100 + 1 = 101; 99 + 2 = 101; and so on. There would then be fifty such pairs — hence 50 x 101: 5050. 

A character cannot produce that kind of idea if the author doesn’t understand it first. It makes the depiction of superintelligent characters very tricky, and sometimes may even limit the portrayal of stupid ones who don’t think the way the rest of us do.

For readers, however, it is different. Literary works (fictional or not) can open up genuinely new kinds of ideas to readers. While a writer who has achieved a completely new way of thinking about some technical problem is less likely to expound it in fiction than in some sort of a treatise or an application with the patent office, fictional works often present ideas one has never considered before in the human arena. It need not be a thought that’s new to the world in order to be of value — it needs merely to be new to you.

Such a thought, no matter how simple it may seem once you see it, can blow away the confines of our imaginations. It’s happened to me at a few different stages in my life. Tolkien’s The Lord of the Rings awakened me when I was a teenager to something profound about the nature of language and memory. C. S. Lewis’ “The Weight of Glory” revolutionized the way I thought about other people. Tolstoy’s War and Peace laid to rest any notion I had that other people’s minds (or even my own) could ever be fully mapped. Aquinas’ Summa Theologica (especially Q. 1.1.10) transformed forever my apprehension of scriptureThe list goes on, but it’s not my point to catalogue it completely here.

Where has that happened to you?

Reflections on Trisecting the Angle

Thursday, March 12th, 2020

I’m not a mathematician by training, but the language and (for want of a better term) the sport of geometry has always had a special appeal for me. I wasn’t a whiz at algebra in high school, but I aced geometry. As a homeschooling parent, I had a wonderful time teaching geometry to our three kids. I still find geometry intriguing.

When I was in high school, I spent hours trying to figure out how to trisect an angle with compass and straightedge. I knew that nobody had found a way to do it. As it turns out, in 1837 (before even my school days) French mathematician Pierre Wantzel proved that it was impossible for the general case (trisecting certain special angles is trivial). I’m glad I didn’t know that, though, since it gave me a certain license to hack at it anyway. Perhaps I was motivated by a sense that it would be glorious to be the first to crack this particular nut, but mostly I just wondered, “Can it be done, and if not, why not?”

Trisecting the angle is cited in Wikipedia as an example of “pseudomathematics”, and while I will happily concede that any claim to be able to do so would doubtless rely on bogus premises or operations, I nevertheless argue that wrestling with the problem honestly, within the rules of the game, is a mathematical activity as valid as any other, at least as an exercise. I tried different strategies, mostly trying to find a useful correspondence between the (simple) trisection of a straight line and the trisection of an arc. My efforts, of course, failed (that’s what “impossible” means, after all). Had they not, my own name would be celebrated in different Wikipedia articles describing how the puzzle had finally been solved. It’s not. In my defense, I hasten to point out that I never was under the impression that I had succeeded. I just wanted to try and to know either how to do it or to know the reason why.

My failed effort might, by many measures, be accounted a waste of time. But was it? I don’t think it was. Its value for me was not in the achievement but in the striving. Pushing on El Capitan isn’t going to move the mountain, either, but doing it regularly will provide a measure of isometric exercise. Similarly confronting an impossible mental challenge can have certain benefits.

And so along the way I gained a visceral appreciation of some truths I might not have grasped as fully otherwise.

In the narrowest terms, I came to understand that the problem of trisecting the angle (either as an angle or as its corresponding arc) is fundamentally distinct from the problem of trisecting a line segment, because curvature — even in the simplest case, which is the circular — fundamentally changes the problem. One cannot treat the circumference of a circle as if it were linear, even though it is much like a line segment, having no thickness and a specific finite extension. (The fact that π is irrational seems at least obliquely connected to this, though it might not be: that’s just a surmise of my own.)

In the broadest terms, I came more fully to appreciate the fact that some things are intrinsically impossible, even if they are not obvious logical contradictions. You can bang away at them for as long as you like, but you’ll never solve them. This truth transcends mathematics by a long stretch, but it’s worth realizing that failing to accomplish something that you want to accomplish is not invariably a result of your personal moral, intellectual, or imaginative deficiencies. As disappointing as it may be for those who want to believe that every failure is a moral, intellectual, or imaginative one, it’s very liberating for the rest of us.

Between those obvious extremes are some more nuanced realizations. 

I came to appreciate iterative refinement as a tool. After all, even if you can’t trisect the general angle with perfect geometrical rigor, you actually can come up with an imperfect but eminently practical approximation — to whatever degree of precision you require. By iterative refinement (interpolating between the too-large and the too-small solutions), you can zero in on a value that’s demonstrably better than the last one every time. Eventually, the inaccuracy won’t matter to you any more for any practical application. I’m perfectly aware that this no longer pure math — but it is the very essence of engineering, which has a fairly prominent and distinguished place in the world. Thinking about this also altered my appreciation of precision as a pragmatic real-world concept. 

A more general expression of this notion is that, while some problems never have perfect solutions, they sometimes can be practically solved in a way that’s good enough for a given purpose. That’s a liberating realization. Failure to achieve the perfect solution needn’t stop you in your tracks. It doesn’t mean you can’t get a very good one. It’s worth internalizing this basic truth. And only by wrestling with the impossible do we typically discover the limits of the possible. That in turn lets us develop strategies for practical work-arounds.

Conceptually, too, iterative refinement ultimately loops around on itself and becomes a model for thinking about such things as calculus, and the strange and wonderful fact that, with limit theory, we can (at least sometimes) achieve exact (if occasionally bizarre) values for things that we can’t measure directly. Calculus gives us the ability (figuratively speaking) to bounce a very orderly sequence of successive refinements off an infinitely remote backstop and somehow get back an answer that is not only usable but sometimes actually is perfect. This is important enough that we now define the value of pi as the limit of the perimeter of a polygon with infinitely many sides.

It shows also that this is not just a problem of something being somehow too difficult to do: difficulty has little or nothing to do with intrinsic impossibility (pace the Army Corps of Engineers: they are, after all, engineers, not pure mathematicians). In fact we live in a world full of unachievable things. Irrational numbers are all around us, from pi to phi to the square root of two, and even though no amount of effort will produce a perfect rational expression of any of those values, they are not on that account any less real. You cannot solve pi to its last decimal digit because there is no such digit, and no other rational expression can capture it either. But the proportion of circumference to diameter is always exactly pi, and the circumference of the circle is an exact distance. It’s magnificently reliable and absolutely perfect, but its perfection can never be entirely expressed in the same terms as the diameter. (We could arbitrarily designate the circumference as 1 or any other rational number; but then the diameter would be inexpressible in the same terms.)

I’m inclined to draw some theological application from that, but I’m not sure I’m competent to do so. It bears thinking on. Certainly it has at least some broad philosophical applications. The prevailing culture tends to suggest that whatever is not quantifiable and tangible is not real. There are a lot of reasons we can’t quantify such things as love or justice or truth; it’s also in the nature of number that we can’t nail down many concrete things. None of them is the less real merely because we can’t express them perfectly.

Approximation by iterative refinement is basic in dealing with the world in both its rational and its irrational dimensions. While your inability to express pi rationally is not a failure of your moral or rational fiber, you may still legitimately be required — and you will be able — to get an arbitrarily precise approximation of it. In my day, we were taught the Greek value 22/7 as a practical rational value for pi, though Archimedes (288-212 BC) knew it was a bit too high (3.1428…). The Chinese mathematician Zhu Chongzhi (AD 429-500) came up with 355/113, which is not precisely pi either, but it’s more than a thousand times closer to the mark (3.1415929…). The whole domain of rational approximation is fun to explore, and has analogical implications in things not bound up with numbers at all.

So I personally don’t consider my attempts to trisect the general angle with compass and straightedge to be time wasted. It’s that way in most intellectual endeavors, really: education represents not a catalogue of facts, but a process and an exercise, in which the collateral benefits can far outweigh any immediate success or failure. Pitting yourself against reality, win or lose, you become stronger, and, one hopes, wiser. 

Crafting a Literature Program

Saturday, February 22nd, 2020

The liberal arts are, to great measure, founded on written remains, from the earliest times to our own. Literature (broadly construed to take in both fiction and non-fiction) encompasses a bewildering variety of texts, genres, attitudes, belief systems, and just about everything else. Like history (which can reasonably be construed to cover everything we know, with the possible, but incomplete, exception of pure logic and mathematics), literature is a problematic area of instruction: it is both enormously important and virtually impossible to reduce to a clear and manageable number of postulates. 

In modern educational circles, literary studies are often dominated by critical schools, the grinding of pedagogical axes, and dogmatic or interpretive agendas of all sorts — social, political, psychological, or completely idiosyncratic. Often these things loom so large as to eclipse the reality that they claim to investigate. It is as if the study of astronomy had become exclusively bound up with the technology of telescope manufacture, but no longer bothered with turning them toward the stars and planets. Other difficulties attend the field as well.

We’re sailing on an ocean here…

The first is just the sheer size of the field. Yes, astronomy may investigate a vast number of stars, and biology may look at a vast number of organisms and biological systems, but the effort there is to elicit what is common to the diverse phenomena (which did not in and of themselves come into being as objects of human contemplation) and produce a coherent system to account for them. Literature doesn’t work that way. There is an unimaginably huge body of literature out there, and it’s getting bigger every day. Unlike science or milk, the old material doesn’t spoil or go off; it just keeps accumulating. Even if (by your standards or Sturgeon’s Law) 90% of it is garbage, that still leaves an enormous volume of good material to cover. There’s no way to examine more than the tiniest part of that.

…on which the waves never stop moving…

Every item you will encounter in a study of literature is itself an overt attempt to communicate something to someone. That means that each piece expresses its author’s identity and personality; in the process it inevitably reflects a range of underlying social and cultural suppositions. In their turn, these may be common to that author’s time and place, or they may represent resistance to the norms of the time. Any given work may reach us through few or many intermediaries, some of which will have left their stamp on it, one way or the other. Finally, every reader receives every literary product he or she encounters differently, too. That allows virtually infinite room for ongoing negotiation between author and reader in shaping the experience and its meaning — which is the perennially shifting middle ground between them.

…while no two compasses agree…

I haven’t seen this discussed very much out in the open, though perhaps I just don’t frequent the right websites, email lists, or conferences. But the reality — the elephant in the room — is that no two teachers agree on what qualifies as good and bad literature. Everyone has ideas about that, but they remain somewhat hidden, and often they are derived viscerally rather than systematically. For example, I teach (among other things) The Odyssey and Huckleberry Finn; I have seen both attacked, in a national forum of English teachers, as having no place in the curriculum because they are (for one reason or another) either not good literature or because they are seen as conveying pernicious social or cultural messages. I disagree with their conclusion, at least — obviously, since I do in fact teach them, but the people holding these positions are not stupid. In fact, they make some very strong arguments. They’re proceeding from basic assumptions different from my own…but, then again, so does just about everyone. That’s life.

…nor can anyone name the destination:

Nobody talks about this much, either, but it’s basic: our literature teachers don’t even remotely agree on what they’re doing. Again, I don’t mean that they are incompetent or foolish, but merely that there is no universally agreed-upon description of what success in a literature program looks like. Success in a science or math program, or even a foreign language program, is relatively simple to quantify and consequently reasonably simple to assess. Not so here. Every teacher seems to bring a different yardstick to the table. Some see their courses as morally neutral instruction in the history and techniques of an art form; others see it as a mode of indoctrination in values, according to their lights. For some, that’s Marxism. For some, it’s conservative Christianity. For some, it’s a liberal secular humanism. For others…well, there is no accounting for all the stripes of opinion people bring with the to the table — but the range is very broad.

is it any wonder people are confused?

So where are we, then, anyway? The sum is so chaotic that most public high students I have asked in the past two decades appear to have simply checked out: they play the game and endure their English classes, but the shocking fact is that, even while enrolled in them at the time, almost all have been unable to tell me what they were reading for those classes. This is not a furtive examination: I’ve simply asked them, “So, what are you reading for English?” If one or two didn’t know, I’d take that as a deficiency in the student or a sudden momentary diffidence on the subject. When all of them seem not to know, however, I suspect some more systemic shortfall. I would suggest that this is not because they are stupid either, but because their own literary instruction has been so chaotic as to stymie real engagement with the material.

It’s not particularly surprising, then, that literature is seen as somehow suspect, and that homeschooling parents looking for literature courses for their students feel that they are buying a pig in a poke. They are. They have to be wondering — will this course or that respect my beliefs or betray them? Will the whole project really add up to anything? Will the time spend on it add in any meaningful sense to my students’ lives, or is this just some gravy we could just as well do without? Some parents believe (rightly or wrongly: it would be a conflict of interest for me even to speculate which) that they probably can do just as well on such a “soft” subject as some program they don’t fully understand or trust. 

One teacher’s approach

These questions are critical, and I encourage any parent to get some satisfactory answers before enrolling in any program of literary instruction, including mine. Here are my answers: if they satisfy you, I hope you’ll consider our program. If not, look elsewhere with my blessing, but keep asking the questions.

In the first instance, my project is fairly simple. I am trying to teach my students to read well. Of course, by now they have mastered the mechanical art of deciphering letters, combining them into words, and extracting meaning from sentences on a page. But there’s more to reading than that: one must associate those individual sentences with each other and weigh them together to come to a synthetic understanding of what the author is doing. They need in the long run to consider nuance, irony, tonality, and the myriad inflections an author imparts to the text with his or her own persona. Moreover, they need t consider what a given position or set of ideas means within its own cultural conversation. All those things change the big picture.

There’s a lot there to know, and a lot to learn. I don’t pretend to know it all myself either, but I think I know at least some of the basic questions, and I have for about a generation now been encouraging students to ask them, probe them, and keep worrying at the feedback like a dog with a favorite bone. In some areas, my own perspectives are doubtless deficient. I do, on the other hand, know enough about ancient and medieval literature, language, and culture that I usually can open some doors that students hadn’t hitherto suspected. Once one develops a habit of looking at these things, one can often see where to push on other kinds of literature as well. The payoff is cumulative.

There are some things I generally do not do. I do not try to use literary instruction as a reductive occasion or pretext for moral or religious indoctrination. Most of our students come from families already seriously engaged with questions of faith and morals, and I prefer to respect that fact, leaving it to their parents and clergy. I also don’t believe that any work of literature can be entirely encompassed by such questions, and hence it would be more than a little arrogant of me to try to constrain the discussion to those points.

This is not to say that I shy away from moral and religious topics either (as teachers in our public schools often have to do perforce). Moral and theological issues come up naturally in our conversations, and I do not suppress them; I try to deal with them honestly from my own perspective as a fairly conservative reader and as a Christian while leaving respectful room for divergence of opinion as well. (I do believe that my own salvation is not contingent upon my having all the right answers, so I’m willing to be proven wrong on the particulars.)

It is never my purpose to mine literary works for “teachable points” or to find disembodied sententiae that I can use as an excuse to exalt this work or dismiss that one. This is for two reasons. First of all, I have too much respect for the literary art to think that it can or should be reduced to a platitudinous substrate. Second, story in particular (which is a large part of what literature involves) is a powerful and largely autonomous entity. It cannot well be tamed; any attempt to subvert it with tendentious arguments (from either the author’s point of view or from the reader’s) almost invariably produces bad art and bad reading. An attempt to tell a student “You should like this work, but must appreciate it only in the following way,” is merely tyrannical — tyrannical in the worst way, since it sees itself as being entirely in the interest of and for the benefit of the student. Fortunately, for most students, it’s also almost wholly ineffectual, though a sorry side effect is that a number find the whole process so off-putting that they ditch literature altogether. That’s probably the worst possible outcome for a literature program.

I also do not insist on canons of my own taste. If students disagree with me (positively or negatively) about the value of a given work, I’m fine with that. I don’t require anyone to like what I like. I deal in classics (in a variety of senses of the term) but the idea of an absolute canon of literature is a foolish attempt to control what cannot be controlled. It does not erode my appreciation for a work of literature that a student doesn’t like it. The fact that twenty generations have liked another won’t itself make me like it either, if I don’t, though it does make me reticent to reject it out of hand. It takes a little humility to revisit something on which you have already formed an opinion, but it’s salutary. It’s not just the verdict of the generations that can force me back to a work again, either: if a student can see something in a work that I have hitherto missed and can show me how to appreciate it, I gain by that. At the worst, I’m not harmed; at the best, I’m a beneficiary. Many teachers seem eager to enforce their evaluations of works on their students. I don’t know why. I have learned more from my students than from any other source, I suspect. Why would I not want that to continue?

Being primarily a language scholar, I do attempt to dig into texts for things like grammatical function — both as a way of ascertaining the exact surface meanings and as a way of uncovering the hidden complexities. Those who haven’t read Shakespeare with an eye on his brilliant syntactical ambiguity in mind are missing a lot. He was a master of complex expression, and what may initially seem oddly phrased but obvious statements can unfold into far less obvious questions or bivalent confessions. After thirty years of picking at it, I still have never seen an adequate discussion in the critical literature on Macbeth’s “Here had we now our country’s honour roofed / Were the graced person of our Banquo present (Macbeth 3.4.39-40).”  The odd phrasing is routinely explained as something like “All the nobility of Scotland would be gathered under one roof if only Banquo were present,” but I think he is saying considerably more than that, thanks to the formation of contrary-to-fact conditions and the English subjunctive.

My broadest approach to literature is more fully elaborated in Reading and Christian Charity, an earlier posting on this blog and also one of the “White Papers” on the school website. I hope all parents (and their students) considering taking any of my courses will read it, because it contains the essential core of my own approach to literature, which differs from many others, both in the secular world and in the community flying the banner of Classical Christian Education. If it is what you’re looking for, I hope you will consider our courses. 

[Some of the foregoing appeared at the Scholars Online Website as ancillary to the description of the literature offerings. It has been considerably revised and extended here.]

Autonomy of Means Again: “Best Practices”

Wednesday, January 1st, 2020

When our kids were younger and living at home, they also frequently had dishwashing duty. Even today we haven’t gotten around to buying a mechanical dishwasher, but when five people were living (and eating) at home, it was good not to have to do all that by ourselves.

But as anyone who has ever enlisted the services of children for this job will surely remember, the process needs to be refined by practice. Even more importantly, though, no matter how good the process seems to be, it can’t be considered a success if the outcome is not up to par. At different points, when I pointed out a dirty glass or pan in the drain, all three of our kids responded with, “But I washed it,” as if that had fully discharged their responsibility.

The problem is that though they might have washed it, they had not cleaned it. The purpose of the washing (a process, which can be efficacious or not) is to have a clean article of tableware or cookware (the proper product of the task). Product trumps process: the mere performance of a ritual of cleansing may or may not have the desired result. Inadequate results can at any time call the sufficiency of the process into question.

This is paradigmatic of something I see more and more these days in relation to education. The notion that completing a process — any process — is the same as achieving its goal is beguiling but false. Depending on whether we’re talking about a speck of egg on a frying pan or the inadequate adjustment of the brakes on your car, that category mistake can be irksome or it can be deadly.

In education it’s often more than merely irksome, but usually less than deadly. I’ve already talked about the “I translated it but I don’t understand it” phenomenon here: ; the claim has never made sense to me, since if you actually translated it, that means that you actually expressed the sense as you understood it. No other set of processes one can do with a foreign-language text is really translating it.

Accordingly I’m skeptical of educational theorists (including those who put together some of the standards for the accreditation process we are going through now) buzzing about “best practices”. This pernicious little concept, borrowed with less thought than zeal from the business world, misleadingly suggests — and to most people means — practices that are ipso facto sufficient: pursuing them to the letter guarantees a satisfactory outcome. And yet sometimes the dish is dirty, the translation is gibberish, or the brakes fail.

It’s not really even a good idea in the business world. An article in Forbes by Mike Myatt in 2012 trenchantly backs up its title claim, “Best Practices — Aren’t”; in 2014, Liz Ryan followed up the same concept with “The Truth about Best Practices”. Both articles challenge the blinkered orthodoxies of the “best practices” narrative.

The problem with any process-side validation of an activity is that, in the very act of being articulated, it tends to eclipse the purpose for which the task is being done. Doing it the right way takes precedence over doing the right thing. Surely the measure of an education is the learning itself — not the process that has been followed. The process is just a means to the end. In Charles Williams’ words, which I’ve quoted and referred to here before (here  and here), “When the means are autonomous, they are deadly”.

Of course they may not in any given situation cause someone to die — but means divorced from their proper ends inevitably subvert, erode, and deform the goals for which they were originally ordained. This is especially true in education, precisely because there’s no broad consensus on what the product looks like. Accordingly the only really successful educational process is one that’s a dynamic outgrowth of the situation at hand, and it can ultimately be validated only by its results.

Liz Ryan notes, “They’re only Best Practices if they work for you.” There are at least two ways of understanding that phrase, and both of them are right: they’re only Best Practices if they work for you, and they’re only Best Practices if they work for you. Their utility depends on both the person and the outcome. Nor should it be any other way.

Socrates’ Argumentation — Method, Madness, or Something Else?

Monday, July 31st, 2017

The common understanding of basic terms and ideas is often amiss. Sometimes that’s innocuous; sometimes it’s not.

Many in the field of classical education tout what they call the Socratic Method, by which they seem to mean a process that draws the student to the correct conclusion by means of a sequence of leading questions. The end is predetermined; for good or ill, the method is primarily a rhetorical strategy to convince students that the answer was their own idea all along, thus achieving “buy-in”, so to speak. As rhetorical strategies go, it’s not really so bad.

Is it also good pedagogical technique? I am less certain. The short-term advantage of persuading a student that something is his or her own idea is materially compromised by the fact that (on these terms, at least) the method is fundamentally disingenuous. If the questioner feigns ignorance, while all the while knowing precisely where these questions must lead, perceptive students, at least, will eventually realize that they are being played. Some may not resent that; others certainly will, and will seek every opportunity to disengage themselves from a process that they rightly consider a pretense.

Whether it’s valid pedagogically or not, however, we mustn’t claim that it’s Socratic. Socrates did indeed proceed by asking questions. He asked them incessantly. He was annoying, in fact — a kind of perpetual three-year-old, asking “why?” after each answer, challenging every supposition, and never satisfied with the status quo or with any piece of accepted wisdom. It can be wearying to respond to this game; harried parents through the years have learned to shut down such interrogation: “Because I said so!” The Athenians shut Socrates’ questioning down with a cup of hemlock.

But the fact is that the annoying three-year-old is probably the most capable learning agent in the history of the world. The unfettered inquiry into why and how — about anything and everything — is the very stuff of learning. It’s why young children learn sophisticated language at such a rate. “Because I said so,” is arguably the correct answer to “Why must I do what you say?” But as an answer to a question about the truth, rather than as the justification of a command, it’s entirely inadequate, and even a three-year-old knows the difference. If we consider it acceptable, we are surrendering our credentials as learners or as teachers.

The difference between the popular notion of this so-called Socratic method and the method Socrates actually follows in the Platonic dialogues is that Socrates apparently had no fixed goal in view. He was always far more concerned to dismantle specious knowledge than to supply a substitute in its place. He was willing to challenge any conclusions, and the endpoint of most of his early dialogues was not a settled agreement, but merely an admission of humility: “Well, golly, Socrates. I’m stuck. I guess I really have no idea what I was talking about.” Socrates thought that this was a pretty good beginning; indeed, he claimed that his one advantage over other presumed experts was that he at least knew that he didn’t know anything, while they, just as ignorant in fact, believed that they knew something.

Taken on this view, the Socratic method is really a fairly poor way of training someone. If you are teaching people to be technicians of some sort or other, you want them to submit to the program and take instruction. It’s arguably not the best tool for practical engineering, medicine, or the law. (There is now a major push in resistance to using any kind of real Socratic method in law school, for example.)

But training is precisely not education. Education is where the true Socratic process comes into its own. It’s about the confrontation of minds, the clarification of definitions, and the discovery and testing of new ideas. It’s a risky way of teaching. It changes the underlying supposition of the enterprise. It can no longer be seen merely as a one-way download of information from master to pupil. In its place it commends to us a common search for the truth. At this point, the teacher is at most the first among equals.

This makes — and will continue to make — a lot of people uncomfortable. It makes many teachers uncomfortable, because in the process they risk losing control — not necessarily behavioral control of a class, but their identity (often carefully groomed and still more zealously protected) as oracles whose word should not be questioned. It opens their narrative and their identity to questioning, and may put them on the defensive.

It makes students uncomfortable too — especially those who are identified as “good” students — the ones who dot every “i” and cross every “t”, and never seem to step out of line or challenge the teacher’s authority. These are the ones likeliest, in a traditional high school, to be valedictorians and materially successful, according to a few recent studies — but not the ones likeliest to make real breakthrough contributions. (The recent book Barking up the Wrong Tree by Eric Barker has some interesting things to say about this: one can read a precis of his contentions here. Barker’s work is based at least in part on Karen Arnold’s Lives of Promise, published in 1995, and discussed here.)

In practical terms, education is a mixed bag.

There is a place for training. We need at least some of the “download” kind of instruction. Basic terms need to be learned before they can be manipulated; every discipline has its grammar. I really do know Latin, for example, better than most of my students, and, at least most of the time, what I say is likelier to be correct. But my saying so neither constitutes nor assures correctness, and if a student corrects me, then, assuming he or she is right, it should be my part to accept that correction graciously, not to insist on a falsehood because I can prevail on the basis of my presumed status. If the correction is wrong, the course of charity is also to assume good intention on the student’s part, and clarify the right answer in my turn. Either way, there is no room for “alternative facts”. There is truth, and there is falsehood. The truth is always the truth, irrespective of who articulates it, and it — not I or my student — deserves the primary respect. We must serve the truth, not the other way around.

At some point in their education, though, students should also be invited to get into the ring with each other and with the teacher, to state their cases with conviction, and back them up with reasoned argument and well-documented facts. If they get knocked down, they need to learn to get back up again and keep on engaging in the process. It hurts a lot less if one realizes that it’s not one’s own personal worth that’s at stake: it’s the truth that is slowly coming to light as we go along. That’s the experience — and the thrill of the chase that it actually entails — that constitutes the deeper part of education. That’s what the true Socratic method was — and still should be — about.

Two modes of learning are prevalent today in colleges, especially — the lecture course and the seminar. In the lecture, the students are, for the most part, passive recipients of information. The agent is the lecturer, who delivers course content in a one-way stream. It’s enshrined in hundreds of years of tradition, and it has its place. But a student who never moves beyond that will emerge more or less free of actual education. The seminar, on the other hand, is about the dialectic — the back-and-forth of the process. It requires the student to become, for a time, the teacher, to challenge authority not because it is authority but because truth has the higher claim. Here disagreement is not toxic: it’s the life blood of the process, and it’s lifegiving for the student.

At Scholars Online, we have chiefly chosen to rely on something like the seminar approach for our live chats. We have, we think, very capable teachers, and there are some things that they need to impart to the students. But to large measure, these can be done by web-page “lectures”, which a student can read on his or her own time. The class discussion, however, is reciprocal, and that reciprocity of passionately-held ideas is what fires a true love of learning. It’s about the exchange — the push and pull, honoring the truth first and foremost. It may come at a cost: in Socrates’s case it certainly did. But it’s about awakening the life of the mind, without which there is no education: schooling without real engagement merely produces drones.

Getting Started Asking the Right Questions

Wednesday, April 13th, 2016

Recently on a homework assignment for my Natural Science course, I asked students to identify which solar system planets it would be possible to explore from Earth-based telescopes, which from space-born but Earth-orbit telescopes (like the Hubble), and which would require space probes sent to the planet. The results were fairly telling about the approaches students take to open-ended questions. Several students left the question blank, because (as they explained in emails and chat), they “couldn’t find the answer” in the assigned reading. Most students explained in very generic terms that while Venus and Mars (closest to Earth) could be viewed from Earth-based or Earth-orbit satellites, more distant objects would require probes. None addressed the question of Earth-based vs. Earth-orbit telescopes implied by listing the two options, and only one considered planetary characteristics other than distance, and identified Venus as a candidate for a probe because its dense atmosphere blocks any attempt to view its surface from Earth-bound telescopes.

Although I had warned the students repeatedly that some of their homework questions would require them to think through the answer and not simply look it up, at least some of my students felt this was unfair: they couldn’t be held responsible for what they couldn’t not look up and quote from the assigned reading. Most of my students were game to tackle the question even without finding the words “we can use telescopes to look at Mars but need probes for Pluto” in their reading, but they still did not study the question carefully enough to realize they needed to think about the advantages and disadvantages of each option, and consider the individual planet itself, as criteria for determining the best method of observation. They immediately seized on finding a single uniform answer, which would let them complete the assignment quickly, without worrying too much about whether the situation was more complicated.

From the perspective of classical education, this is backward, because classical education, and in particular Christian classical education, is not fundamentally about finding right answers to practical questions. Its goal is to develop the skills required by a free citizen who would be responsible for discerning God’s will, then making decisions for himself and for the state. It recognizes that there is no set formula for “getting the right answer” to the questions of real life; the most important first step is to make sure we can even formulate or recognize the important questions. Then we can look at how these questions (or ones like them) have been answered before, in literature and in history. Although Greek philosophy in particular developed rigorous methods of rational analysis, classical education still depends on story to convey the complexity of real decisions in real circumstances. Greek drama and history constantly throw out examples where individuals must decide between personal integrity, duty to the gods, and duty to the state. Latin literature is full of examples of individuals who sacrifice themselves to fulfill their civic duty. The Greeks and Romans of the classical period studied their own history, read their own literature, and produced often conflicting philosophical reflections because they realized that determining the right questions to ask was a citizen’s responsibility, and it was no use seeking answers until one had the right questions.

St. Clement of Alexandria, in his Stromata calls rational philosophy God’s divine gift to the Greeks, identifying direct revelation as God’s gift to the Jews. The early Christian Fathers, like Clement, who found inspiration in and supported the study of pagan classical literature recognized the development of reason and logic as an important skill in witnessing to and defending the Christian faith — and for distinguishing important questions that were worth pursuing from questions that were merely divisive and distracting. For nearly twenty centuries, western civilization depended on these stories and philosophies to help students form the values that would let them determine the wisest course in a difficult situation, both for themselves and for those they were expected to govern: personal integrity, loyalty, charity, civic duty, duty to God. The questions it forces us to ask are the most important questions of our lives: who am I? what do I want? what is God calling me to do?

If classical Christian education is about questions, then, how do we get students to learn to formulate or recognize the questions they need to ask? And equally important, how do we get them to develop passion for their studies and the courage to overcome the sense that asking questions is somehow an admission of failure to study correctly?

I believe that we need to make asking questions the most important job a student has to do: not completing the homework, not skimming the reading, but thinking deeply about the ideas they encounter and formulating questions about them. Every student (and teacher) needs to come to class full of questions. We meet in discussion to bring up these questions and to hear each other’s questions. As a teacher, I usually have a stock set of questions for a given chat to get the ball rolling, but these are based on my own experience and my own values and they are essentially “plan B” material for the chat. The most successful discussions occur when the students raise questions about their own understanding, based on their own concerns. When they voice those questions and we explore possible answers, we all find new ways of thinking about the material, and new insight on the questions that pester us.

While ultimately we need to address the important questions of our lives, we have to start somewhere, so here are some of the questions even novice students ought to be asking themselves constantly as they read both factual material and literature. Most important, to put this into practice, students should be writing down notes to bring up in class if they are puzzled or don’t have answers, or want to test their own assumptions:

Do I know what all the words mean? Does a term (even if I know its dictionary definition) seem vague or misapplied to the topic? Do all the parts of this graph or illustration make sense and can I see how they are related?

Can I follow all the steps of an example? Do I know what all the assumptions are, and how they are justified? Can I follow the calculation or reasons given for making a conclusion?

Is the author making an argument for a general conclusion or interpretation? Is the author’s claim valid? Do I understand the evidence used to support it? Does it apply to the cases given? Is it too general? too narrow? Can I think of any contradictory examples?

If several things are described, what characteristics, values, or processes are used to distinguish them? Do I understand how these distinctions are made, and can I use these methods myself to make distinctions among similar things?

If a process is described, can I follow the process? If not, why not — where do I get confused? If I do understand the process, do I accept it as valid, or do I think it skips important steps or considerations?

What does the author think are the most important points to make or take away from his or her presentation? What criteria does he or she use to make this evaluation (and do I agree)?  Can I make an outline of the important points and identify the supporting details? Does the author skip points I think are important? Can I figure out why — what values or assumptions am I making differently from those the author is making?

If I am translating a sentence or a paragraph, does my English translation make sense in English? Does it reflect something an intelligent person would say, or is it gibberish? Do I understand what each word means and how it functions in the sentence?

These questions force us to be honest with ourselves in two ways. One is making sure that we actually engage with the materials, not just pass our eyes over the reading, and that we seriously  attempt to comprehend the knowledge presented. The second is making sure that we are also applying our own developing system of values to what we are learning, that we are not simply agreeing blindly to what is presented, but trying to develop ways to determine for ourselves what is right, pure, lovely, admirable, and worthy of praise.

Failure as a good thing

Friday, March 11th, 2016

People tout many different goals in the educational enterprise, but not all goals are created equal. They require a good deal of sifting, and some should be discarded. Many of them seem to be either obvious on the one hand or, on the other, completely wrong-headed (to my way of thinking, at least).

One of the most improbable goals one could posit, however, would be failure. Yet failure — not as an end (and hence not a final goal), but as an essential and salutary means to achieving a real education — is the subject of Jessica Lahey’s The Gift of Failure (New York, HarperCollins, 2015). In all fairness, I guess I was predisposed to like what she had to say, since she’s a teacher of both English and Latin, but I genuinely think that it is one of the more trenchant critiques I have read of modern pedagogy and the child-rearing approaches that have helped shape it, sometimes with the complicity of teachers, and sometimes in spite of their best efforts.

Christe first drew my attention to an extract of her book at The Atlantic here. When we conferred after reading it, we discovered that we’d both been sufficiently impressed that we’d each ordered a copy of the book.

Lahey calls into question, first and foremost, the notion that the student (whether younger or older) really needs to feel that he or she is doing well at all stages of the process. Feeling good about your achievement, whether or not it really amounts to anything, is not in fact a particularly useful thing. That seems common-sensical to me, but it has for some time gone against the grain of a good deal of teaching theory. Instead, Lahey argues, failing — and in the process learning to get up again, and throw oneself back into the task at hand — is not only beneficial to a student, but essential to the formation of any kind of adult autonomy. Insofar as education is not merely about achieving a certain number of grades and scores, but about the actual formation of characer, this is (I think) spot-on.

A good deal of her discussion is centered around the sharply diminishing value of any system of extrinsic reward — that is, anything attached secondarily to the process of learning — be it grades on a paper or a report card, a monetary payoff from parents for good grades, or the often illusory goal of getting into a good college. The only real reward for learning something, she insists, is knowing it. She has articulated better than I have a number of things I’ve tried to express before. (On the notion that the reason to learn Latin and Greek was not as a stepping-stone to something else, but really to know Latin and Greek, see here and here. On allowing the student freedom to fail, see here. On grades, see here.) Education should be — and arguably can only be — about learning, not about grades, and about mastery, not about serving time, passing tests so that one can be certified or bumped along to something else. In meticulous detail, Lahey documents the uselessness of extrinsic rewards at almost every level — not merely because they fail to achieve the desired result, but because they drag the student away from engagement in learning, dull the mind and sensitivity, and effectively promote the ongoing infantilization of our adolescents — making sure that they are never directly exposed to the real and natural consequences of either their successes or their failures. Put differently, unless you can fail, you can’t really succeed either.

Rather than merely being content to denounce the inadequacies of modern pedagogy, Ms. Lahey has concrete suggestions for how to turn things around. She honestly reports how she has had to do so herself in her ways of dealing with her own children. The book is graciously honest, and I enthusiastically recommend it to parents and teachers at every level. If I haven’t convinced you this far, though, at least read the excerpt linked above. The kind of learning she’s talking about — engaged learning tied to a real love of learning, coupled with the humility to take the occasional setback not as an invalidation of oneself but as a challenge to grow into something tougher — is precisely what we’re hoping to cultivate at Scholars Online. If that’s what you’re looking for, I hope we can provide it.

A Fine Thing

Tuesday, February 9th, 2016

Nearly two years ago, disquieting rumors hit my work group: our jobs were moving out of the area, across the country.

I did not want to move out of my home, away from my friends and family, or face restarting our home business in another state, especially since I would just be trading one earthquake zone for another one, but one with worse winters, more flooding, and tornadoes. So I let my bosses know that I wouldn’t be following my work assignment backwards along the Oregon Trail, and starting thinking about what I wanted to do with the rest of my life.

As usually when requiring clarity of thought, I turned to Dorothy Sayers, who recounts in one of her addresses how she came to learn Latin:

“I was rising seven when [my father] appeared one morning in the nursery, holding in his hand a shabby black book, which had already seen some service, and addressed to me the following memorable words: “I think, my dear, that you are now old enough to begin to learn Latin.” … I was by no means unwilling, because it seemed to me that it would be a very fine thing to learn Latin, and would place me in a position of superiority to my mother, my aunt, and my nurse-though not to my paternal grandmother, who was an old lady of parts, and had at least a nodding acquaintance with the language.”

I already know a little Latin, but I do not know classical Greek. My husband does, and my children do, so far from being in a position of superiority to my own children, I am somewhat at a disadvantage when they talk about finer points of Homer’s style, or the interpretation of a passage from Luke. It seemed to me that it would be a very fine thing to learn Greek, and would place me on something of a more level position with my husband and my children, at least, so far as classical languages are concerned.

Besides, there are some Byzantine commentaries by John Philoponus and John of Damascus on Aristotle’s de Caelo that I ran across when researching my dissertation on medieval astronomy forty years ago, and I have never been able to read them, since the only available printed editions are in Greek and 19th century philosophical German. Of the two, Greek seemed easier to master.

I happened to mention my sort of vague yearning to start classical Greek to a few friends and some family members. This may have been a mistake, but it’s too late now. Scholars Online posted its Greek I course for 2016-2017, and I enrolled, thus putting an end to well-meant but incessant encouragement that I actually indulge myself in the joys of ancient Greek. Mr. Dean kindly agreed to accept me into his course.

It’s been interesting, to say the least.

Latin has seven noun cases, forms of nouns that indicate how they will be used in a sentence as subject, direct object, indirect object, and so on (nominative, genitive, dative, accusative, ablative, locative, and vocative). Greek has five, lacking the ablative and locative, whose functions still exist but are rolled into one or another of the other cases. Plowing through the explanations in Unit I, I thought, this I can do: Greek is simpler is simpler than Latin!

So for the first unit, I put my time into learning paradigms for three nouns: a first declension feminine: ἡ ἀρχή: beginning, from which we get the English words “archaic” and “archeology”; the second declension masculine ὁ λόγος, word, from which we get “logic” and “theology”; and a mixed bag word which could be either masculine or feminine — you have to pay attention to the attached article: ὁ θεός, ἡ θεός, god or goddess.

I’m sure those of you reading this who know some Greek are mentally nudging one another with barely-disguised glee, the kind novelists invoke with the well-worn phrase “little did she know….” Yes, the plot twist is coming.

With the next unit, we hit the verbs. Greek has all the Latin tenses, plus one more. It has all the Latin verb moods, plus one more. It has an extra voice. It even has an extra number, distinguishing between singular, plural, and dual (just two). That’s a lot of verb forms to learn.

Let me spare you the details, but for the first time since I was in high school, there are 3×5 cards in stacks all over the house, wherever I happened to leave a set the last time I found a few minutes to study, minutes that usually add up to at least an hour every day. The ones with green edges have the principal parts of verbs, the ones with yellow edges give the cases for nouns and adjectives, the multicolored ones hold details on prepositions and which cases they take and how the meaning changes with the case. The blue-edged ones have grammar rules for conditional phrases with wonderful names like “future more vivid”, clauses of purpose with different levels of purposefulness, summaries of all possible endings, and rules for accents that give new meaning to the concept of mathematical chaos. I’m sure there’s a connection, since my teachers insist there’s a pattern even if I can’t find it. The blue-edged cards are the most bent and draggled of the bunch, because for some reason, I can’t keep straight whether the future passive indicative uses the un-augmented aorist stem or the augmented perfect stem with an extra syllable thrown in so you don’t confuse it with the perfect passive, and I have to look up which verb stem is used when, even if I remember the six stems and the proper endings for the tense and mood and voice in question.

There was a time when I thought sequence of moods meant something like the sequence of emotional states on getting a new software program that doesn’t quite do everything you hoped — anticipation, joy, frustration, resignation. Now I realize the “sequence of moods” depends on the verb tense used in the independent clause to govern the tense in the subordinate clause. There is probably some philosophical observation to be made there, but at the moment, I’m just trying to keep my tenses straight. I sometimes feel that if I manage to get the pluperfect endings lodged firmly in my head, the aorist ones will fall out the other side.

But there is more to learning a language than memorizing forms or appreciating its contributions to one’s own native vocabulary. The next step is translation, and while forms may be approached with rigorous method (even if there are lots of niggling details), translating is rarely straightforward.

That’s because words don’t just have meaning in some one-to-one correspondence between languages, any more than chartreuse, lime, Kelly, or Lincoln all mean the same green, even though they all mean “green” at some level.

After centuries of use in philosophical, scientific, and theological works, ἀρχή and λόγος have become loaded terms in Greek, words that absolutely defy a one-word decoding translation.

  • ἀρχή can mean beginning, or the first principles or elements on which all else is built, or the source of power, and by extension an empire, realm, authority, or even command.
  • λόγος can mean the story one tells in words, a speech one makes — that is, the spoken-out-loud-word that stirs others to action (one of Aristotle’s three modes of persuasion), or the reason why one does something, or the root or basis behind an action.
  • θεός is more direct: it unambiguously means a god, a deity; it cannot be used for something merely divine or spiritually-inclined.

We did a lot of sentences with the vocabulary words in different situations, partly to learn the different forms, but also to gain by experience appreciation for the nuances of meaning.

  1. Homer taught the men with words (using speech).
  2. The poets teach well by means of stories (skillful use of rhetoric).
  3. The young men learned skills with words (learned to reason clearly or speak clearly).
  4. The messengers from the enemy destroyed the peace with words (of persuasion).

On December 24, I could sit down and work out out the Gospel for the first Eucharist of Christmas in Greek: Ἐν ἀρχῇ ἦν ὁ λόγος, καὶ ὁ λόγος ἦν πρὸς τὸν θεόν, καὶ θεός ἦν ὁ λόγος.

I know the English translation, “in the beginning was the word, and the Word was with God, and the Word was God.”, but the Greek means more than that, so the author of John meant more than the plain English. In a word-for-word translation, the text arrives in English naked, stripped of all the nuances the author surely reasoned out when he chose those words to begin his story and lay out the foundations of his faith so long ago.

And that’s the reason for learning Greek: to read and recognize what Homer and Aristotle, Herodotus and Sophocles, Plato and the authors of the New Testament really said, and to get closer to what they still have to say to us today, in all its complexity.

Learning Greek is hard work, and that’s okay. Learning anything, and learning it well is hard work. It takes time and effort and repetition and review and thought and puzzlement and clarification.

I make lots of mistakes, and that’s okay, too. My mistakes in class provide harmless amusement to my teacher and classmates and they don’t hurt me. In fact, I usually remember the points I’ve flubbed better over the long run than the ones I somehow, and often accidentally, got right the first time.

But the very best part of my own personal Greek journey is something I haven’t mentioned yet: my teacher was once one of our own students.

And for a teacher, it doesn’t get much better than this: to sit at the feet of your own student, and learn something new.

It turns out that taking Greek really is a very fine thing.