J.D.
Phillips
18
April,
2003
How does it happen
that there are people who do not
understand mathematics? . . . If mathematics invokes only the rules of
logic,
such as are accepted by all normal minds; if its evidence is based on
principles common to all men, and that none could deny it without being
mad,
how does it come about that so many persons are here refractory? . . .
That not
everyone can understand mathematical reasoning when explained appears
very surprising
when we think of it.
—Henry Poincare,
From
the
Margins.
Who has ever, in all these millennia, seen men acting solely for the sake of advantage? What's to be done with the millions of facts that attest to their knowingly—that is, with full awareness of their true interests—dismissing these interests as secondary and rushing off in another direction, at risk, at hazard, without anyone or anything compelling them to do so, but as if solely in order to reject the designated road, and stubbornly, willfully carving out another—a difficult, absurd one—seeking it out virtually in the dark?
—Fyodor
Dostoyevsky,
Notes
from Underground
It is a very great
pleasure, indeed, to join you today. Thank you for the opportunity.
Before
I turn to a consideration of Poincare's
quote, I should note that the
sorts
of institutions and departments that we all come from are decidedly
different.
Those of you at large European research universities are up to
something
markedly different with your students than we who are at small,
American
liberal arts colleges are with our students. My remarks, then, are
grounded in
a particular understanding of undergraduate education that is part of a
very
old liberal arts tradition, a tradition that, alas, is becoming
increasingly
marginal in the wider higher education landscape. In my department for
instance, our teaching activities are focused mostly on exploiting our
disciplinary expertise as research mathematicians to prepare students
for
post-graduate studies in mathematics (this is easy) while at the same
time
trying to overcome the significant limitations this same disciplinary
expertise
imposes as we try to serve the much broader aims of a liberal arts
education
(this is difficult). And I note that by liberal arts education, I do
not mean mathematics
classes for humanities
majors. I mean something rather different, which will hopefully begin
to
emerge, slowly, in the body of my talk. All of this is to say that I
hope my
remarks have some bearing on your own teaching.
I should also mention
that I view my remarks today as a report on part of a larger and
on-going
project, funded by Wabash College's Center for Inquiry. As such, I
would
welcome comments on this talk that might inform my larger project, and
indeed,
I look forward to conversations with you this weekend and beyond. Yours
is a
new group for me, and I thank you for your warm collegiality and for
the
prospects of new horizons of discourse for me.
Finally, I hope that
you will detect a gleefully polemical tone in this talk. This is a bit
heavy-handed, I suppose, but it is in the higher service of my awkward
attempts
to enact the dialectic. Thus, I will focus my remarks on, even exploit,
those
few areas where we might disagree, and not dwell on places of
widespread
agreement.
"How does
it happen?"
Let no one
ungeometrical enter here.
—on the gate of Plato's
Academy.
Geometrical inquiry . . . . then, will be that which draws the soul to truth and produces a philosophical disposition for tending upward where we now tend downward, as we ought not. —Plato
The
Republic
Indeed, how does it happen, that most
people don't
understand mathematics? The Greek root of the word mathematics translates roughly as
"that which is
learnable." One can come to know something in
mathematics; one can learn it unlike, say,
politics, where one
simply weighs competing opinions. Mathematics is thus
paradigmatic of learning itself; as such,
the ancients understood mathematics to be a necessary propaedeutic to
philosophy, as the quotes above suggest. And what is more human than
the
appetite to learn, the desire to know, philo-sophy?
It is instructive,
but not surprising, to note that while Meno's slave boy learns about
geometry
and numbers with Socrates, by the time we reach Poincare such learning
is no
longer on the horizon of conceivability, and we are reduced simply to
wondering
about what went wrong. While Plato inquired directly about the nature,
the eidos, of number, unmediated
by technique
or method, by the time we reach Husserl, sedimentation—the inevitable
result of the march of the scientific project to higher states of
abstraction,
rendering its intelligible origin forgotten, nearly inaccessible—makes
this all but impossible. What went wrong? Or, as Poincare (a trope, of
course,
for a commonly held position amongst mathematicians today) puts it,
"How does
it happen?" this failure in mathematics. Is learning mathematics
too difficult
for most people? Do students today resist learning mathematics out of
various
psychopathologies that represent a sickness, a crisis, in our larger
culture?
Or is it just that there aren't enough Socrates' around anymore to
teach them?
These are hard
questions. And I note here that they are especially difficult without
attending
carefully to the subtle distinctions between the ancient conceptions of
logisitik and arithmos. But this would take us
too far
afield for this talk. And in any event, it would be hard to improve on
Jacob
Klein's work on this in his masterly Greek Mathematical Thought and
the
Origin of Algebra.
And this seems like
the right place to mention my good fortune on rereading Camus' The
Fall
and Dostoyevsky's Notes from Underground as I was preparing
this talk.
The form of this talk emerged as I read these two novels, as will soon
become
apparent.
Pursuits.
Because all I could do
was only play around with words, dream a
bit in my mind.
—Fyodor
Dostoyevsky,
Notes
from Underground
And the worst of it is that I have begun to justify myself before you. And even worse, that I am making this remark now. But enough, or there will be no end to it: whatever I say or do will be cheaper and nastier than what has gone before. . . —Fyodor Dostoyevsky,
Notes
from Underground
Mathematicians pursue
proof. But when we teach mathematics, we do not pursue proof.
Nor,
generally, do we direct our students toward the pursuit of proof. As
mathematics teachers, our energies
are directed elsewhere, toward what a friend of mine calls the
assertive
pursuit of scientifically intentioned problem sets.
I know of no area of
current mathematics research that is regularly a part of the
undergraduate
mathematics curriculum. Still, in spite of this, I suppose that,
strictly
speaking, the pursuit of proof is still possible in undergraduate
mathematics.
But, alas, this possibility actually realizes itself only in those rare
activities that are entirely marginal in the landscape of undergraduate
mathematics education. More on this shortly. First, though, I should
remind you
of what actually goes on in undergraduate mathematics.
Mostly, what goes on
is conditioning, as above, via the pursuit of problem sets. Jacob
Klein's
colleague, Eva Brann, describes this activity as the asking and
answering of
sham questions. Of course, a genuine question is one that the
questioner
doesn't know the answer to; in fact, a genuine question is nothing more than the desire for an
answer. It
leaves uncertainty in its wake and generates genuine conversation in
which none
of the participants knows the answer, but all desire it. A sham
question—a problem set, for instance—on the other hand, is one that
the questioner already knows the answer to, and hence, cares very
little about;
for instance, from a typical problem set in the calculus, "What is the
derivative of the sine function?" And this—namely using problem
sets
(sham questions) to condition—is what mathematicians do when we teach.
It
bears no resemblance to what we do as mathematicians. So there is a
tension,
then, between our two primary activities—"doing" mathematics and
teaching
mathematics.
By the way, as an
aside, I note that this tension is present even in very sophisticated
classes
at the graduate level. For instance, consider John Thompson's
celebrated
theorem: "A finite group with a fixed point free automorphism of prime
order is
nilpotent." Now, it's certainly true that most of us couldn't
prove this
theorem on the spot. But it is true that we could all simply look
up the
proof and follow it.
More
importantly, we all know it to be true; it is simply not the object of our desires—you don't
desire to know what you already know. And in this sense, the only way
you can
ask about something as sophisticated as even Thompson's theorem, is as
a
problem set, not as a genuine question.
I think this
tension is not resolvable. Sham
questions are a necessary part of mathematics education, and they
necessarily
interfere with genuine questions. I do, however, think we can respond
constructively to it. One way is by reading books—like Euclid's Elements—in
addition to simply working through problem sets in textbooks. Books
like this,
ancient mathematical books, invite reflection in a way that modern
textbooks do
not and cannot. Ancient synthetic mathematics is different from modern
mathematics (a la
Jacob
Klein). It systematically allows for, even invites, the sort of radical
and
profound questions about the nature of mathematics and mathematical
objects
that students care about. But more on this later.
Method.
When one has no
character one has to apply a method.
—Albert Camus,
In the absence of
genuine questions, that is, in the absence of actual inquiry, a fetish
for
method invades our thinking and our teaching. After all, when
"teaching"
becomes nothing more than revealing what we already know to those who
do not
yet know, what's left but method? Classroom
management, projects, computer applications,
textbooks, and so on, become the heart of the matter. The professor
merely
searches for the most effective technique for dispensing information;
he or she
becomes coordinator, facilitator, and manager of "materials".
And ultimately
the students themselves become material, to be shaped, cast, and
manufactured
by the professor. Of course, no one wants to be used in this way, to be
materials; students rightly resist it. And so we respond with renewed
and
intensified reliance on materials, a feverish pursuit of a better
method. And
students dig in their heels and resist even more ferociously. Ad
infinitum.
The failures that
haunt the mathematics landscape are apparent. But clearly, the project
of
"fixing" them is mistaken insofar as it relies on this or that method
to repair what it imagines is broken, instead of attending to the
cultivation
of certain habits of mind proper to legitimate inquiry, to mathematics.
Of
course, some problems can't be "fixed". And even more importantly, not
everything that we don't like is a problem. Maybe it's good that most people resist
mathematics;
it's not a problem, and there's nothing to "fix". Our failure is most
acute, and its effects are most pernicious, when we forget that
intellectual
virtue, that learning, emerges only from these
habits of mind, and that it is resistant
to prescriptive methods or techniques. Thus enters Eros and thymos and their commingling.
But more on
this later.
Tyranny.
Good
God, what do I care about the laws of nature and arithmetic if, for one
reason
or another, I don't like these laws, including the "two times two is
four"? Of
course, I cannot break through this wall with my head if I don't have
the
strength to break through it, but neither will I accept it simply
because I
face a stone wall and am not strong enough. . . Two
times two will be four even without my will. Is that what you call
man's free
will?
—Fyodor
Dostoyevsky,
Notes
from Underground
It is a form of
tyranny to treat students as course material, as a means and not an
end. And as
above, students, always smarter than we think they are, recognize when
we treat
them as a means, and they resist. But I think there's another, more
fundamental, sort of tyranny that students often feel, a tyranny that
we don't
see at all, because it rules us so thoroughly. I'm thinking here of the
tyranny
of logical necessity, the tyranny that Dostoyevsky's underground
man—and
our most spirited (thymotic) students—refuse to
submit to.
I notice this spiritedness in my own children. They are still quite young, two and three-years-old, respectively. And they have a more difficult time acquiescing to the tyranny of the laws of nature than they do acquiescing to the rules that my wife and I set for them. Physical obstacles that interfere with play, nightfall and darkness ending play, tiredness and hunger, are all much more oppressive to them than are the seemingly arbitrary laws that my wife and I lay down. The laws of nature and the law of logical necessity are inflexible, unflinching. They are mightier than, and uncompromising toward, human will. But people don't like to have their will thwarted. At least with people, there's a chance the law will bend; you recognize your oppressor; your will might prevail. But logical necessity simply and completely snubs your will. If you fight, you will lose. You may give your assent and be governed by it, or you may dismiss it completely. But you cannot fight it.
There's something naive and precious, even delusional and self-flattering, about mathematicians—Poincare and us—emoting about why people don't master mathematics. Small children know why. So did Dostoyevsky. But mathematicians don't. And so what of our students? By the time they reach us, they often conflate the tyranny of logical necessity with the tyranny of bad (often very bad) mathematics instruction (i.e., with tyrannical mathematics professors). And our precious emoting, as above, makes it even harder for us to recognize that we encourage this conflation. Our students feel oppressed by the tyranny, both of logical necessity and of us. But we see neither, and are left to wonder about simply "fixing" things.
Utility.
Nowhere else are vigorous efficacy and dreary operationalism so much each other's obverse, so that beauty is forfeited to blind efficiency. . . The paradox of instrumental learning—power wrecks pleasure—is a most serious problem of modern pedagogy that can be resolved only by making frequent returns to the intellectual presuppositions of such learning.
—Eva
T.H. Brann,
Paradoxes
of Education in a Republic
One way we "fix" things is by cultivating an obsession with utility, both in what we teach and in how we teach. At its crudest, this obsession realizes itself in the view of mathematics as chiefly a useful and practical utensil. But of course, as an actual utensil, mathematics is useful mainly to the professional scientist, a complex and arcane world out of reach to most students. To these students the practicality of mathematics is relegated to the simplest of childish arithmetic. And so our obsession with utility is oppressive or banal to most students.
Our obsession with utility is also seen in our relentless campaign to defend undergraduate education on the grounds that it guarantees both economic success and good citizenship. (Sociologists even tell us that the former might actually cause the latter!) The connection between love of money and love of knowing is unclear at best. And claims about guaranteeing good citizenship are even more puzzling. A school that devotes itself to authentic education, one that esteems freedom, is a radical and dangerous institution, as it systematically incorporates into its assumptions the possibility that eventually those whom it educates will turn away from all of the virtues it cherishes and embrace instead all that is subversive and threatening, to the school and to the state. That is, it is necessarily potentially self-undermining as it allows for the possibility of its own demise. Good citizenship? The state thought Socrates was such a good citizen that it executed him.
Ultimately this obsession with utility in higher education is especially pernicious in that it nullifies our claim—a claim, ironically enough, unique to higher education—that a life devoted to actual inquiry, study, and thought is an end in itself.
This obsession also guides how we teach. What could be more useful and
practical
than measuring our "effectiveness" at teaching the utility of
mathematics? And
so we flatter ourselves by "assessing student learning outcomes". But of course, as Eva Brann puts it, "When
learning is measured, the measurable is eventually what is
taught." And
the measurable is very easy to teach effectively.
Teachers.
They are free and hence have to shift for themselves; and since they don't want freedom or its judgments, they ask to be rapped on the knuckles, they invent dreadful rules. . . Each of us insists on being innocent at all costs, even if he has to accuse the whole human race and heaven itself. —Albert Camus,
The Fall
After all of this,
why would anyone want to teach mathematics? Even Plato's Gorgias takes
a shot
at us, saying that those who neglect philosophy for the busy-work of
teaching
mathematics are like the wooers of Penelope, who settled for her maids.
And it
gets worse!
Education—especially an education in
the
liberal arts—is (and I will argue necessarily is) burdened with a number of
conflicting
tensions. For instance, there is the tension between the inexorable
press of
politics on education (from Meno asking Socrates "can virtue be
taught" to "education for citizenship" in our own time—to
say nothing of programs, from the NSF to the DOD, that reward
achievement in
mathematics based exclusively on mathematics' ability to serve
political aims)
against the freedom an education, especially a liberal arts education,
both
requires and aims for. By the way, understanding the tension like
this—teaching virtue versus a liberal arts education's required (and
aimed for) freedom—helps explain why conservative moralists,
politically
correct professors, and religious fundamentalists are up to the same
thing,
more or less, in education: straightening us out morally; teaching
virtue.
Politics indeed makes for very strange bedfellows. And in this case it
means
that the deep-seated desire to remain morally unchallenged itself challenges freedom. And of course as
above, there
is another tension, specific to mathematics: what we do as mathematicians bears little resemblance to what we do
as
mathematics teachers.
A friend of mine
likes to rant about the arrested emotional and intellectual development
of
anyone who views the teaching of mathematics as an end, especially the
all-too-common banal sorts of busy-work that we often teach today.
Imagine the
level of depravity and confusion it takes to actually devote one's life
to "teaching" mathematics in this fatuous way, more distraction
than propaeduetic.
I don't know if I agree with my friend. But I am sure that he's not
completely
wrong. And I know this from students, who all too often end up agreeing
with my
friend. It's no wonder then that these students resist.
Students.
Because I longed for eternal life, I went to bed with harlots and drank for nights on end. . . True debauchery is liberating because it creates no obligations. In it you possess only yourself.
—Albert Camus,
But I repeat to you
for the hundredth time: there is only one
occasion, one only, when man may purposely, consciously choose for
himself even
the harmful and the stupid, even the stupidest thing—just so that he
will
have the right to wish the stupidest thing, and not be bound by the
duty to
have only intelligent wishes.
—Fyodor
Dostoyevsky,
Notes
from Underground
So, what of these
students? Do you remember
when the
so-called "reform" calculus was just coming in to fashion 15
years ago? I was a
graduate student at the time, and so quite naturally, and quite
naively, I
observantly attended to its birth. Its most zealous proselytizers—of
which
there were legions—pitched it as a way to get around students' myriad
algebraic infelicities by focusing on the deep, subtle and profound
aspects of
the calculus sans
computation.
Phlegmatic traditionalists thought it was all a game of smoke and
mirrors, and
balked. The calculus wars erupted. Papers, books, editorials, and
letters to
the editor were written. Conferences and workshops were convened.
Careers were
made. Some were ruined. But what of the students? Some of the initial fervor has
mercifully subsided,
but a core residue remains, a fine vantage point from which to inquire.
Prior to learning, of course, is intentionality. That is, one must intend to learn before one can learn. One must desire to know before one knows. And what do calculus students desire? Naturally, students are not all alike. Some, a few perhaps, desire to know, but only in an inchoate way. And these, if the circumstances are right, might come to know the calculus. But most students, though, even very good students, do not desire to know the calculus. The mathematician's desires to understand the profound subtleties of mathematics—desires that have been stoked and cultivated over a bloody march of years of difficult study—are not students' desires. Students, young and spirited—like Dostoyevsky's underground man, full of will, full of thymos—do not yet know how to desire to know mathematics. Their desires lie elsewhere.
If you listen to students, if you attend carefully to their words, the object of their desire begins to reveal itself. Students speak of the pleasure of doing well, of mastering a difficult subject, of the erotic desire driving them to complete a complex computation or proof that culminates in its intended object, of the thymotic desire for honor in having mastered something complex and difficult. So students desire the self-assertive pleasure of mastery, especially of a technically demanding subject like mathematics, and the honor bestowed on them when they succeed. And a great deal of effort on our part is spent in depriving them of this pleasure. What remains is anxiety.
Anxiety
and Inquiry.
If pimps and thieves were invariably
sentenced, all
decent people would get to thinking that they themselves were
constantly
innocent.
—Albert Camus,
We even feel it's too much of a burden to be men—men with real bodies, real blood of our own. We are ashamed of this; we deem it a disgrace, and try to be some impossible "general human". . . What made them imagine that man must necessarily wish what is sensible and advantageous?. . .Perhaps a normal man should be stupid, how do we know? Perhaps it's even very beautiful that way. —Fyodor Dostoyevsky,
Notes
from Underground
There are, of course,
many constructive ways to respond to this anxiety, to the many tensions
I've
already outlined. Here I'll only mention one, and leave the others for
another
time. One way then, to respond constructively to this tension and
anxiety is
with books. And
this response
is so uncommon as to be almost entirely marginal. So it seems like a
good place
to remind you of Abel's famous dictum:
It
appears to me that if one wants to make progress
in
mathematics one should study the masters.
I should qualify
this. Recall from above that mathematics is
paradigmatic
of all learning. And so built in to every mathematics class is the
possibility
that bracing and accompanying all of the other efforts in the class
will be the
purposeful attendance to nothing less than learning itself, (re)learning how to learn. This is hard to
do if you're
just pursuing problem sets. But
it's not
hard to do if you're reading, say, The Elements.
Reading The
Elements demands the student's careful attention to the details of
actually
working through the demonstrations. And this, in turn, opens up the
conversation to the sorts of questions we're all familiar with. Why
will those
two circles intersect? Why is there only one triangle with this
property? And
so on. Of course, mathematics textbooks and problem sets might allow
for these
sorts of questions, but unfortunately most textbooks and problem sets
answer
these questions before students have a chance to actually struggle with
them
for themselves.
But The Elements,
as you know, inevitably generates another sort of genuine question—the
question about the deductive apparatus and the axiomatic system itself.
What is
the difference between a postulate and a common notion? What is a point? Do points exist? Are the propositions true? Can you tinker with the
axioms and
still prove some of the propositions? If so, what recommends one set of
axioms
over another? I suppose good textbooks and problem sets can generate
these
sorts of questions, but it is rare.
Ultimately, though,
if you read The Elements attentively, you might get the feeling
that
Euclid is up to something more than just presenting "results"
(as in a typical
mathematics textbook), that he is actually working toward something: The prime
number theorem? A
commentary on the Platonic solids? An insight into the nature of logic
and
deduction? These are genuine questions. They demand genuine
conversation. And
this, in turn, stokes passion. [As an aside, I should note that it is
this
passion, by the way—the passion to find the truth about things, to
satisfy the simple desire to know—that drives us as mathematicians, not
the assigning and grading of problem sets.] And finally, all of this
invites
reflection on the nature of human learning, to say nothing of giving
the
student an authentic taste, not contrived, of what we actually do as
mathematicians. Textbooks and problem sets—even the seemingly
"sophisticated" activity of working through Thompson's
nilpotence
theorem—don't do this. Textbooks and problem sets can't do this. By the
way, notice that the root
of the word "sophisticated" is the same as the root of the word
"sophistry".
So certain books can
generate precisely the sort of erotic uncertainty necessary for a
genuine
conversation that stokes the passion for mathematical discovery that
drives us
as mathematicians. This conversation, by the way, is part of a
tradition that
fosters habituation toward truth and beauty by first liberating
students from
slavish devotion to their own parochial opinions (opinions formed
against the
backdrop of nothing more than tribalism and bloodlines). Certain books,
not
just the pursuit of problem sets, are particularly well suited to this.
This
approach recognizes the "skills" and
"competencies"—developed via the pursuit of problem
sets—as means, subordinate to other ends, for instance, wisdom and
freedom. And as above, the slavish devotion to technique and training
that is
part of the pursuit of problem sets mistakes these skills and
competencies as
ends, and thereby expresses contempt for wisdom and freedom. It is
self-undermining insofar as the wisdom required to see through all this
is
grounded, at least in part, in mathematics.
I don't mean to say
that the pursuit of problem sets shouldn't be part of a mathematics
education.
In fact, it must be; remember, I claimed that the tension in
mathematics is
irresolvable. I am suggesting, though, that the anxiety can be
tempered—and again, only in an entirely marginal way.
Pleasure,
Pain and Suffering.
It's in despair that you find the sharpest pleasure, particularly when you are most acutely aware of the hopelessness of your position. . . [during the painful course of a toothache] your recognition of the whole array of natural laws, which you, of course, don't give a hoot about, but which nevertheless make you suffer, while nature itself doesn't feel a thing. They express your realization that there is no enemy to blame, yet there is pain.
—Fyodor
Dostoyevsky,
Notes
from Underground
After all, man may be fond not only of well-being. Perhaps he is just as fond of suffering? Perhaps suffering is just as much in his interest as well-being? . . . As for my personal opinion, it's even somehow indecent to love only well-being. Whether it's good or bad, smashing something is also very pleasant on occasion . . . I am convinced that man will never give up true suffering—that is, destruction and chaos. Why, suffering is the sole root of consciousness. . . Consciousness, for example, is infinitely nobler than two times two.
—Fyodor
Dostoyevsky,
Notes
from Underground
Have you ever noticed how unusual academics are? Students sure notice it. A friend of mine thinks that one of the primary purposes of the university is to provide gainful employment to people who otherwise would be unemployable. There is some truth to this.
Why are academics so unusual, so
abnormal?
And what is it about them that students notice? I think they notice
that
professors, completely devoted and pious as they are to disciplinary
expertise,
to their arcane and narrow area of specialization, are alienated from
the rest
of intellectual life, from an authentic and full human life. Combinatorial
group theory, or
lattice gauge theory, or Chicano literature, or medieval Chinese poetry
is not
the proper end of a full human intellectual life. But we treat each of
them,
quite blindly, as if it were. In this way we are wounded. (And by the
way, in
this case we are quite like Oedipus: arrogant and clever, but quick to
anger
and self-pity, with a self-inflicted blindness. But let's keep our
parents out
of it!)
Students see this
wound, our pain, and our afflicted yearning for healing. Students,
unlike us,
recognize that the proper ends of intellectual life are not arcane and
specialized disciplinary expertise. They yearn for something else, for
something more; they resist overtures from the blind and wounded. And
the way
all of this plays out for students in mathematics is especially thorny.
As I
mentioned earlier there is the student's self-assertive pleasure in
mastery,
almost unique to mathematics among the disciplines. There is the sweet
promise
of Eros—the
desire to know. And complicating it all is the seductive, and
ultimately
misleading, allure of the power of proof.
The "certainty" of
proof tricks us. Our unspoken desire for power, control, and autonomy
leads us
to flatter ourselves by taking the certainty of willfully fashioned
proof (or
demonstration, for the ancients) as knowledge. But as Socrates reveals,
genuine
proof, demonstration, is always negative. Defining virtue is hopeless.
But you can recognize what virtue is
not.
So the pleasure of proving is seductive
and often misleading. Recognizing this is painful and difficult. But
from the
effort, hopefully you emerge a little less foolish. And this places
mathematics
in a very privileged position, indeed. If we recognize it.
Desire
and
Deception.
You see, gentlemen, reason is unquestionably a fine thing, but reason is no more than reason, and it gives fulfillment only to man's reasoning capacity, while desires are a manifestation of the whole of life—I mean the whole of human life, both with its reason and with all its itches and scratches. . . Because all of man's purpose, it seems to me, really consists of nothing but proving to himself every moment that he is a man and not an organ stop! Proving it even at the cost of his own skin. . . . What is better—cheap happiness, or noble suffering? Well, which is better?
—Fyodor
Dostoyevsky,
Notes
from Underground
Ultimately, of
course, intention precedes learning. As above, before you can know, you
must desire to know. Students won't
learn if they
don't first intend
to. So, how do we teach? Mostly we devote our energies to fiddling with
curriculum, cooking up problem sets, fussing with course materials,
tinkering
with web and multi-media technologies, and the like. But we rarely
think
about students, how
they learn, what their appetites are, how to cultivate habits of mind,
the
possibility of inquiry.
So we flatter
ourselves by treating our students as course material to be shaped by
us, in
our own image. It is a form of tyranny. But students are free, and they
resist
tyranny. Students' self-assertive desire for mastery (thymos), might eventually grow
into a desire
to know (Eros).
Or, in response to tyranny, it might remain shunted by simply
resisting, by
drowning in adolescent rebellion.
Learning is a
mystery. How is it possible at all? But we are teachers of
mathematics; we are supposed to know. To
Socrates, of course, the ultimate foolishness is the willful belief in
your own
wisdom.
And finally, there are things he is afraid to reveal even to himself, and every decent man has quite an accumulation of them. In fact, the more decent the man, the more of them he has stored up. As regards myself personally, I have in my own life merely carried to the extreme that which you have never ventured to carry even halfway; and what's more, you've regarded your cowardice as prudence, and found comfort in deceiving yourselves.
—Fyodor
Dostoyevsky,
Notes
from Underground