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Yesterday, after coming across my teaching statement, a reader named Arber Borici sent me the following questions:

In your opinion and based on your experience at various institutions, what would you recommend to me (a young, inexperienced scholar) regarding on how to best remove students’ attention from the mediocrity of grading to the eagerness for knowledge or, at least, high culture? … I would also appreciate it if you could provide me with one or two guidelines in approaching students to appreciate what they are being taught and to teach them on how to seek knowledge for themselves.

It seemed like good fodder for a blog entry, so with Arber’s kind permission, I’ve decided to post my response to him here (with only light editing).

Dear Arber,Thanks for your thoughtful email!  I’m always delighted to hear from people who share my views about the inherent problems in combining teaching with evaluation.

Alas, your question of how to get students to focus on intellectual exploration rather than on their midterm grade is an incredibly difficult one, since it depends not only on you but also on your academic context (for example, you’ll probably be required to give grades by department policy).  I’ve been struggling with that question myself for the past three years, and still haven’t answered it to my satisfaction, but here are a few small tips I can offer.

(1) Some students didn’t come to college to learn, but for any number of other reasons: to party, get a high-paying job, satisfy their parents, etc.  Or they’re only taking your course because it’s required for the major, while their real interests lie elsewhere.  Treat these students fairly and with respect, but don’t kill yourself trying to awaken an intellectual curiosity that isn’t present.  Instead, identify the students who are in your class to learn, memorize their names and faces, and make special efforts to reach out to them—for example, by sticking around after class to chat with them about the lecture and answer their questions.  (In my experience, many intellectually curious students prefer sticking around after class to coming to office hours.  In many cases, students who come to office hours are there because they want you to do their homework for them!)

(2) Grade generously.  I usually give at least a B- to anyone who makes a serious effort in the course.  (In practice, that policy turns out to be compatible with giving a fair number of Cs, Ds, and even Fs.)

(3) Most importantly, if you don’t want the students to focus only on low-level boring stuff, don’t lecture only about low-level boring stuff!  Tell stories about Alan Turing and his codebreaking work.  Talk about the philosophy behind the Church-Turing Thesis, or the arguments for and against identifying “feasible” with “polynomial time,” or the implications for AI if it turned out that P=NP.  If a student asks a really good question, don’t be afraid to take a 10-minute digression to answer the question.  You’ll constantly feel pressure in the opposite direction—there’s so much “real material” that needs to be “covered”!  But think about what your students will remember from your course twenty years from now, long after the details of implementing red/black trees have been forgotten, and the right course of action will become clear to you.

I should point out that there’s a paradox at the heart of teaching, which your second question (which is actually a variation on your first question) makes clear:

I would also appreciate it if you could provide me with one or two guidelines in approaching students to appreciate what they are being taught and to teach them on how to seek knowledge for themselves.

To see the difficulty with what you ask, picture a classroom full of glazed-eyed students, dutifully taking notes on “how to seek knowledge for themselves,” so they can repeat back your tips on intellectual initiative for the test!

In my experience, probably the best (only?) way to teach people how to seek knowledge for themselves is to illustrate by example.  Let your students watch you in action doing all of the following:

1. happily admitting when you don’t know something.
2. looking something up and getting back to the asker during the next class meeting, rather than simply letting the matter drop.
3. thinking a difficult/novel question through on your feet.
4. eliciting help from the students in a “Socratic” manner.

Seeing a positive example will embolden the students who have a spark of any of these tendencies in themselves.

Anyway, I hope that helps!

Best of luck,
Scott

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(See also: Umeshisms, Anthropicisms)

Why, in real life, do we ever encounter hard instances of NP-complete problems?  Because if it’s too easy to find a 10,000-mile TSP tour, we ask for a 9,000-mile one.

Why are even some affluent parts of the world running out of fresh water?  Because if they weren’t, they’d keep watering their lawns until they were.

Why don’t we live in the utopia dreamed of by sixties pacifists and their many predecessors?  Because if we did, the first renegade to pick up a rock would become a Genghis Khan.

Why can’t everyone just agree to a family-friendly, 40-hour workweek?  Because then anyone who chose to work a 90-hour week would clean our clocks.

Why do native speakers of the language you’re studying talk too fast for you to understand them?  Because otherwise, they could talk faster and still understand each other.

Why is science hard?   Because so many of the easy problems have been solved already.

Why do the people you want to date seem so cruel, or aloof, or insensitive?  Maybe because, when they aren’t, you conclude you must be out of their league and lose your attraction for them.

Why does it cost so much to buy something to wear to a wedding?  Because if it didn’t, the fashion industry would invent more extravagant ‘requirements’ until it reached the limit of what people could afford.

Why do you cut yourself while shaving?  Because when you don’t, you conclude that you’re not shaving close enough.

These Malthusianisms share the properties that (1) they seem so obvious, once stated, as not to be worth stating, yet (2) whole ideologies, personal philosophies, and lifelong habits have been founded on the refusal to understand them.

Again and again, I’ve undergone the humbling experience of first lamenting how badly something sucks, then only much later having the crucial insight that its not sucking wouldn’t have been a Nash equilibrium.  Clearly, then, I haven’t yet gotten good enough at Malthusianizing my daily life—have you?

One might even go further, and speculate that human beings’ blind spot for this sort of explanation is why it took so long for Malthus himself (and his most famous disciple, Darwin) to come along.

Feel free to suggest your own Mathusianisms in the comments section.

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Recently someone asked me how to give funnier talks.  My first response was to recoil at such an insolent question: doesn’t everyone know that at the core of my shtick lies a unique and ineffable je ne sais quoi that can’t be packaged, bottled, or resold?  But the truth was not that I couldn’t give advice; it’s that I didn’t want to.  For if everyone knew how easy it was to keep an audience at least half-awake, how would people like me maintain their edge?  By proving better theorems?  Having something new and relevant and say?  These questions answer themselves.

But because I love you, my readers, so deeply, and because I feel guilty about abandoning you for so long, I shall now publicly deconstruct the main ingredients of seminar humor, insofar as I’ve been able to find them.  (A few ingredients are specific to theoretical computer science, but most are more general.)

1. Make fun of people in the audience.  (Of course, you have to do it in such a way that they’re flattered you’re ripping them and not someone else.)
2. Ridicule bogus claims related to your topic, particularly claims that received wide currency in the popular press.  (To be honest, I do this not so much because it gets laughs—though it does—but as a small service to humanity.  If I can make one budding crackpot think twice before hitting “Submit” on a disproof of Bell’s Theorem, I will not have lived in vain.  Of course, the ridicule should always focus more on ideas than people; and even then, a few in the audience will frown on it, considering it unscientific or unprofessional.  Forty or fifty crackpots ago, I agreed with them.  It’s only experience that hardened me into a vigilante.)
3. Incorporate the audience’s shared experiences into your talk (without making a big deal of it, as if it’s the most natural thing in the world).  For example, when it comes time to trot out an Alice/Bob scenario, have yours wryly comment on a previous talk, an excursion everyone went on, a current event (like an election) that everyone actually cares about more than the talk…
4. Self-deprecate.  (“My first conjecture was falsified.  The following conjecture hasn’t yet been falsified, and is obviously true…”)
5. Say things that recognize and comment on how neurotic the thought-process of theoretical computer scientists really is, by taking that thought-process to extremes.  (“That’s off by a factor of 10^{10^120}, which is only O(1) and is therefore irrelevant.” “For years, people tried unsuccessfully to prove this sort of impossibility result was impossible.  Our result shows the impossibility of their goal.”)
6. If your field is interdisciplinary, the humor potential is almost limitless.  Are you a physicist?  Ridicule the computer scientists.  A computer scientist?  Ridicule the mathematicians.  A mathematician?  Ridicule the economists.  Chances are, enough differences in notation, terminology, assumptions, and underlying goals will arise in the talk to give you a never-ending supply of material.  “Disciplinary humor” is a more refined, intellectual variant of ethnic humor, and is effective for the same reasons.
7. Explain your results in an unusually vivid or graphic way.  (“If, at the moment of your death, your whole life flashed before you in an instant, and if while you were alive you’d performed suitable quantum computations on your own brain, then you could solve Graph Isomorphism in polynomial time.”)  This type of humor is my absolute favorite: on a plot with laughter volume on one axis and scientific content on the other, it’s way out on the upper-right-hand corner.
8. If you’re using PowerPoint, take full advantage of its comic potential: wild animations, text that pops up on the screen to question or even flat-out contradict what you’re saying, a punchline at the bottom of the slide that only gets revealed when you press a key, etc.  I love doing this because I have as much time as I need to “precompute” jokes (though I’ll then often elaborate on them extemporaneously).
9. Banter with the crowd: if someone makes a crack at your expense, always respond, and even escalate the interaction into a “staged fight” (the rest of the audience will love it).  If someone catches you in a mistake, or you don’t know the answer to a question, make a self-deprecating joke that acknowledges the situation even as it wins you sympathy points.
10. Have high energy!  Loud, lots of moving around, emotion in your voice … like you can’t wait to invite everyone along to the most exciting journey in the history of the universe.  Not only is that good practice in general (at the least, it keeps the audience from falling asleep), it also creates a general atmosphere in which it’s okay to laugh at jokes.
11. Pause a few beats before the punchline.  (You can get better at this by watching professional comics.)
12. Experiment!  If a particular joke bombs, drop it from your rotation; if it brings the house down, recycle it in future talks.  Of course, you should drop a joke once it reaches its saturation point, where much of the audience has already heard it in previous talks.  On the other hand, if this particular audience hasn’t yet heard the joke, disregard your own internal sense of its being “tired”: it could go over just as well as the first time, or better.
13. Steal ideas shamelessly from other speakers.  (I mean their humor techniques, not their results.)  Just as importantly, study the lame jokes other speakers use, so as to avoid them.  (For example, I estimate that 94% of quantum computing talks include a heavy-handed comment about someone or something being “in superposition”; this has not yet gotten a laugh.  Or the talks repeat stories about Feynman, Bohr, etc. that everyone in the audience has already heard a thousand times.)
14. Tailor your jokes to the audience’s background.  For instance, I have some jokes that work great in the US, but sink in other countries.  Or work on physicists but not computer scientists, or vice versa.
15. Make jokes about the country you’re visiting.  Of course, this is subject to common sense: I’ve been known to resort to “zed” / “aboot” jokes in Canada, scone / royalty / powdered wig jokes in England, and neutrality / yodeling jokes in Switzerland, but I usually don’t make the first joke that pops into my head when visiting Germany or Austria.
16. Take risks!  Here’s an Umeshism: if some of your jokes don’t flop, then you’re not being bold enough.  Do things that people can’t believe anyone would actually do in a talk.  Most people seem to operate under the assumption that when they’re giving a talk, they have to be less funny than in regular conversation, when the truth is the opposite.  If something comes into your head that’s funny to you, and it passes the most flimsy and cursory of offensiveness checks … out with it, and worry later about the consequences!

Three final remarks.

First, reading over the list, I can’t help but feel sheepish about how much one can do with such a crude and obvious bag of tricks.

Second, I only wish I applied this crude bag more consistently!  Particularly when I have a new result and I’m excited about the proof, I all too often ignore my own advice and lapse into boringness.  But at least I notice I’m doing it, get annoyed at myself, and resolve to be crasser, less mature, and less professional the next time around.

Third, you might feel that adding shtick to your talks makes you “shallow,” that all that should matter is the content of your results.  In the relatively rare case where you’re addressing experts in your own sub-sub-subfield, that’s probably true: you can drop the funny business and get straight to the point.  In all other cases, I’m almost certain the audience will understand your results better if you incorporate some shtick than if you don’t.  But hey—it’s up to you whether you want to address an ideal Platonic audience (“more lemmas! no irrelevant distractions! yes! harder! faster!”) or the actual flesh-and-blood hairless apes who are dozing off in the seminar room while you speak.

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I know I’ve been gone from the shtetl too long—I even stood by as a P=NP goon performed a drive-by shooting through my comments section.  Part of the explanation, I’m ashamed to admit, is that I’ve been procrastinating by proving theorems and writing papers, rather than building up the massive corpus of blog entries on which my tenure case will undoubtedly rest.

But most of my absence has an unhappier source.  At an unknown time about three weeks ago, I crossed the Email Event Horizon—defined in General Unproductivity as the point beyond which you could literally spend your entire day answering emails, yet still have more emails at the end of the day demanding immediate attention than you had at the beginning.  Not spam or crank mail, but worthy missives from students, prospective students, high-school students, secretaries, TAs, fellow committee members, conference organizers, visit hosts, speakers, editors, co-editors, grant officers, referees, colleagues … everything, always, requiring you to do something, commit to some decision, send a title and abstract, pick dates for the trip, exercise Genuine Conscious Thought.  No one ever writes:

Please respond to the situation described above by cracking a joke, the less tasteful the better.  You will never need to deal with this matter again.

I don’t know the precise moment when I crossed the EEH—there was nothing to herald it, it felt like any other moment—but it’s obvious now that I’m in a new, unfamiliar causal region (and that, while I might have thought I’d crossed years ago, I hadn’t).  Communication from inside the EEH to the external universe is theoretically possible, but like Hawking radiation, it tends to be excruciatingly slow—and when it finally arrives, might simply regurgitate the incoming information in garbled form.

When I was a student, I used to wonder constantly about the professors who’d ignore my long, meticulously-crafted emails or fire off one-word replies, yet who might suddenly have an hour for me if I walked into their offices.  Were they senile?  Rude?  Did they secretly despise me?  Now I get it, now I understand—yet I doubt I could explain the warped spacetime Gmailometry I now inhabit to my own past self.  On the other hand, the recognition of what’s happened is itself a sort of liberation.  I’m starting to grasp what’s long been obvious to many of you, those who crossed the EEH before I got my first AOL account in seventh grade: that it’s useless to struggle.  By definition, the speed required to escape the EEH exceeds that of typing, while the mental energy required to accelerate a massive, resting theorist to such a speed is infinite.  So there’s nothing to do but blog, goof off, prove theorems, let the starred-but-unanswered inquiries pile higher and higher, and await the Email Singularity in my causal future.

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Whereas nerds stand to benefit, even more than normal people, from becoming more assertive, outgoing, optimistic, obamalike in temperament, and all those other good things,

Whereas the fundamental problem with nerds is that they’re constantly overthinking everything,

Whereas this means nerds are regularly beaten in life by people who think less than they do,

Whereas it also means that nerds can’t read self-help books without coming up with dozens of (generally sound) reasons why everything they’re reading is a load of crap,

Whereas there’s therefore a large unmet need for self-esteem-boosting, personality-improving materials that would somehow fly under nerds’ radar, disarming the rational skeptical parts of their brains,

This holiday season, as my present to all my nerd readers, I’ve decided to start an occasional series entitled Nerd Self-Help.

Today’s installment: What should you do when you find yourself asking whether you have any “right to exist”?

Pondering the problem this morning, I hit upon a solution: Ask yourself whether the integer 8 has any right to exist.

In first-order logic, existence is not even a property that can be predicated of objects.  Given a universe of objects, you can ask about properties of those objects: for example, is there a perfect cube which is one less than a perfect square?  But it’s simply assumed that when you use a phrase like “is there,” you’re quantifying over everything that exists.  (As many of you know, this was the basic insight behind Kant’s refutation of Anselm’s ontological proof of the existence of God: the notion of “a being that wouldn’t be perfect without the added perfection of existence,” said Kant, is gobbledygook.)

Similarly, I claim that if you were to formulate a theory of human rights in first-order logic in any “natural” way, then whether you have a right to exist is not even a question that would arise within that theory.  Such a theory might include your right to not be murdered, to get a fair trial, to engage in consensual sexual activities, to own property, etc., but not your “right to exist”: that “right,” to the extent it even made sense, would simply be presupposed by your being part of the universe of persons that the theory of rights was quantifying over.  In other words, the sequence of words “do I have the right to exist?” seems to me to dissolve on analysis, an ill-formed non-question.

Now, I don’t doubt that there are plenty of logical, metaphysical, and legal objections that might be raised against the above argument.  But here’s the key: don’t think about it too much!  Just trust that there’s a rational-sounding argument for why you shouldn’t doubt your right to exist, and be happy.

Merry Christmas, everyone!

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