Some of you may have seen my last entry on the subject of good mentorship in CS/IT (11 Dec 2003), and my grade-skipping thread (29 Jan 2004 in my LJ and in this thread in 
cty_therapy). These were brought on by discussions with 
deire on professorial encouragement and discouragement, and with masteralida on the idea of taking students under one's wing.
Throughtout these threads, I have been thinking about virtuosity, to wit: how important are natural skill, talent, fluency and style?
For what they're worth, here are my personal thoughts:
Opinions? Comments?
1 As some of you know, chemical engineering, being about process planning, plant design, and applied mathematics and computational science and engineering, is a completely different field from chemistry, which deals with the theory and methodologies for analysis of reactions and substances. These are at least as different as computer science and computing.
2 My main area is more aptly described as applied probability, statistical computation, and even theoretical CS than combinatorics and graph theory.
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cty_therapy). These were brought on by discussions with deire on professorial encouragement and discouragement, and with masteralida on the idea of taking students under one's wing.Throughtout these threads, I have been thinking about virtuosity, to wit: how important are natural skill, talent, fluency and style?
- In technical fields such as software development, do they transfer across programming languages?
- In creative subjects such as mathematical theorem proving, does the skill really persist (like the oft-cited one of riding a bicycle) or does it burn out by age 35 in many cases, as the Chronicle of Higher Education postulated about a year and a half ago?
- Hypothetically speaking, is success in some "highly refined and rarefied" circles of math/CS research really constrained more by talent than hard work? Are students who beat themselves against the wall perseverant or in need of a reality check cf. American Idol, or is it the faculty member who pours a bucket of cold water on the aspiring and diligent student really the deluded one?
For what they're worth, here are my personal thoughts:
- Skill is as skill does: that is, skills transfer across fields when they reflect genuine aptitude. A case in point: my father is a chemical engineering virtuoso and a jack-of-all-trades in chemistry.1 But he's always been only competent or good at organic chemistry and biochemistry, and very good at inorganic and analytical chemistry. To really shine, he had to find his way through three iterations of physical chemistry, four graduate universities, a job, and a decade of grad school. Moral: don't give up doing what you love, but also don't give up looking for what you are best at. Or, as the late Prof. Dr. Edsger W. Dijkstra wrote: do only what only you can do.
- Virtuosity is overrated: Here, I have to disagree with Randy Jackson (who frequently asserts on American Idol that the contest is all about natural talent), or at least assert that at least in my field, virtuous practitioners and researchers are born and made, not born rather than made. As an example, I will use myself. I got scores around 90% on calculus exams in high school. As an undergrad, I got scores in the high 90s (even a couple of 100% scores, the only one in the class) on discrete math and combinatorics exams. I wasn't the best at the university, but I was best in the (small) class that year. I will state categorically that despite my ability being imperceptibly diminished since then, I am practially unrecognized as a discrete mathematician. Is it because I haven't published in this area? No, though it isn't my main area2; see my dissertation and the journal papers since. Nothing earth-shattering as combinatorics goes, but the mathematical content is there. Instead, I found something I was actually good at: spotting and addressing methdological gaps and needed syntheses of intelligent systems theory and practice. It's all about perception: your own, that of your colleagues and other peers, even that of your students.
- Teachers who quell ambition in the diligent and motivated are already doing a disservice to young minds: I will go out on a limb and just go ahead and say this. I'm not getting soft in my old age, it has nothing to do with saturation of the field, and it's not because I've been lucky enough to get only talented students. Those who have stayed are talented; I've had to screen many students and, yes, tell some they weren't suited certain research careers in the field. But as jereeza, the right kind of (art) teacher IMO, says: you don't teach by weeding; you don't protect the field from "dilution" by weeding; you reinforce strength where you find it, identify and correct weaknesses, and cautiously, carefully encourage talent. I have seen my share of both heartbreaking lack of confidence and insufferable arrogance that were brought on by bad discipline from an early age, as it were. Let us all resolve - every man Jack and woman Jill of us in educational disciplines - to avert the day when we have to say: I've created a monster. Monster.com is easy to come by; the Gojira emergency response team for overinflated egos - not so much.
Opinions? Comments?
1 As some of you know, chemical engineering, being about process planning, plant design, and applied mathematics and computational science and engineering, is a completely different field from chemistry, which deals with the theory and methodologies for analysis of reactions and substances. These are at least as different as computer science and computing.
2 My main area is more aptly described as applied probability, statistical computation, and even theoretical CS than combinatorics and graph theory.
Welcome to 9 new friends who added me in the last week:
11 Feb 2004 - 2:
consilience, othercriteria10 Feb 2004 - 1:
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wiliqueenPlease feel free to reply here and introduce yourselves!
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Comments
Thanks!
The responses have been interesting too, so far.
I think I teeter between 'heartbreaking lack of confidence' and 'insufferable arrogance' on a day-to-day basis.
LOL!
You're not alone, Deborah - not by a long shot.
:-)
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Banazir
A teacher is never a giver of truth - he is a guide, a pointer to the truth that each student must find for himself. A good teacher is merely a catalyst. - Bruce Lee
Not sure it's completely relevant to what you want to say but it does ring true.
--
Danger is my middle name
Not sure it's completely relevant to what you want to say but it does ring true.
That it does, but Li Xiaolong was actually paraphrasing a precept that dates back to Confucian times: lao shi ling jing men..., i.e., "the teacher leads [one] through the door..." (one must continue on the path by oneself).
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Banazir
(or, the Road Goes Ever On and On * sorry, on 4 hours' sleep here)
As for burn-out, it might, it might not. The Fields Medal can only go to those younger than a certain age, right? I'm not absolutely sure as to what age it is (35 seems to come to mind). However, didn't Wiles finally solve Fermat's Last Theorem at 50 or thereabouts?
Ultimately, I think hard work can solve a lot of things. When I was a kid, I was tested to go to this program for the academically talented. Ultimately, I didn't make it, and the reason they gave my parents was "his math skills are far too weak." Since then, I graduated with high honours in computer science, and I took the "pure honours" program rather than the software engineering one, which meant courses in computational complexity, advanced algorithms, advanced formal AI, and so forth. That's mostly hard work right there. Then again, for my master's, I'm doing work in a fairly applied area (semantic web services), making use of what I feel is a natural talent of mine (programming). So I'm not sure. Both? Can I ride the fence on this one?
Well, yes, but there I think you have to chalk it up to deficient (non-logical, non-mathematical) conditioning. Like a lot of music students, math/CS students have a lot of unlearning to do by graduate school. For example, the continuous and discrete math dichotomy runs all the way down to primary school in some East Asian and South Asian educational traditions. Some of the most brilliant discrete mathematicians I know come from India (out of a semi-westernized tradition); a few can't do it worth a lick. Similarly, I have Chinese students who are whizzes at differential and integeral calculus, calculus of variations, differential equations, numerical analysis, and engineering mathematics, but turn into complete incompetents when posed with original problems involving number theory or counting, graph theory, or even a new twist on some symbolic logic or probabilistic reasoning problem.
You get a lot of students from Asia who learn about the Three Prisoner's Puzzle or Monty Hall by rote, but who can't really grok conditioning. Conversely, a lot of American students have the qualitative grasp but can't work a hard calculus problem (I'm more in this category, IIRC from my struggles with volumes of revolution - bear in mind I never had a course in abstract algebra, real and complex analysis, or topology).
As for burn-out, it might, it might not. The Fields Medal can only go to those younger than a certain age, right? I'm not absolutely sure as to what age it is (35 seems to come to mind).
40 ar present. That's a pragmatic matter of interpretation, though, just as with the Presidential Young Investigator (PYI) awards, which used to have an upper age limit of 40 years.
However, didn't Wiles finally solve Fermat's Last Theorem at 50 or thereabouts?
41, and that was after an erroneous proof at age 39-40. This scenario shows that you can persevere and continue, or come back. But does show that 40 is pretty old for a working mathematician. Then again, as
Here's the Chronicle article by Lila Guterman from the December, 2000 issue. As this AMS survey summarizes, "Guterman quotes the findings of Dean K. Simonton, an expert on the question: mathematicians make their best research contributions, on the average, at 38.8 (biologists: 40.5; physicists 38.2; chemists 38.0)". So, the finding actually contradicts what I've come to call the Tyrell Effect after the android designer Eldon Tyrell in Blade Runner, who famously said: "the flame that burns twice as fast burns half as long, and you have burned very brightly indeed, my boy" to the replicant, Roy Batty (Rutger Hauer).
(continued)
Offhand, I think that:
1) Virtuosity will only get you so far: at some point everyone reaches something that innate talent can't overcome, and people who are used to relying only on "I'm smart, I can do this easily" can kind of fall apart when this sort of thing happens to them. Motivation and diligence when things get tricky matter way more than being able to intuitively grasp concepts or a general natural aptitude. I know someone who, despite her innate talent, flunked out of CS grad school because she couldn't muster up the motivation and diligence to study for and pass her qualifying exams, even on the third time. Innate ability doesn't matter much if you're not willing and able to work, and that's something that people who *are* naturally very talented don't always learn to do.
2) Sometimes love just isn't enough. Being motivated or diligent or really interested, but with absolutely no aptitude for the subject does happen sometimes. And it's the role of a mentor to... not discourage it, maybe, but try to channel that enthusiasm into a different and perhaps more fruitful direction. I don't think that you can go on hard work alone with no results -- that seems to be the path to burnout.
3) Insufferable arrogance. Oh, it infuriates me, even (especially?) when I see it in myself -- and I think that it's bred into the virtuoso during ones' learning career. "You're so talented. You can do everything." I would love to see a world where everyone recognizes that they have limitations. (Although I'd lose the inadvertent humor in listening to people who, in their insufferable arrogance, makes incredibly stupid comments while thinking that they're smart.)
So, in other words, I think I agree with you.
I'd say more, but can't really think of anything to add.
Though I may be inspired to write something similar regarding my own field, which has oddly similar issues configured in different ways.
And thanks for the welcome! :-D
Thanks!
I'd say more, but can't really think of anything to add.
Though I may be inspired to write something similar regarding my own field, which has oddly similar issues configured in different ways.
Please do!
I'd like to read about it.
And thanks for the welcome! :-D
You are welcome!
Your icons... so amazzling.
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Banazir
Found it very amusing.
Smile!
Was there a mean judge who told the lesser idiots that they were "not dumb enough"?
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Banazir
Natural talent does carry one only so far. We can point to scores and tests, but in the end, what matters is how that is applied.
But as
A very wise method, indeed!
That is high praise indeed.
I will do my best to live up to it, better than I have been doing.
Natural talent does carry one only so far. We can point to scores and tests, but in the end, what matters is how that is applied.
That's quite true.
But as
A very wise method, indeed!
It's easier said than done, is what it is, but she has the right idea. And she learned the hard way as I and
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Banazir
One corollary issue. I often find that adults assume erroneously that they have no talent because they can't do something they've never tried right out of the box. You can't, for instance, draw well without practice, including muscle training, no matter your underlyign talent. We wouldn't expect a child with no experience or teaching to do something. It's not that much more reasonable to expect such of an adult.
Thank you; same here, on and off.
Mostly triggered by observations of ill effects of discouragement and encouragement/neglect gone awry, unfortunately - though this has usually been from watching other people's "kids" rather than my own (students).
Firm answers not going to happen, at least for me.
Fair enough; I'm not expecting them from anyone, including myself, though I do appreciate all the dialogue - it's an "invitiation to an internal debate", as you called it a while back.
One corollary issue. I often find that adults assume erroneously that they have no talent because they can't do something they've never tried right out of the box.
Well, that is part of the "virtuosity" fallacy (the expectation that virtuoso-level skill will obviate practice - at least by accelerating, if not invalidating the Power Law of Practice. But you're quite right, it is a fallacy.
You can't, for instance, draw well without practice, including muscle training, no matter your underlyign talent. We wouldn't expect a child with no experience or teaching to do something. It's not that much more reasonable to expect such of an adult.
Just so. There's also the Precocious Virtuosity Corollary, witnessed by many a figure-skating Chinese child or Russian gymnast in Olympics past, but also by your American tronkie CS student ("because Suzy's so good with a {VCR|notebook|cell phone}"), Asian-American premed, etc.
(Your stereotype here)
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Banazir
Perhaps it's also an unhappy comment on the work world that folk assume that something that requires work can't possibly be a joy.
How true!
Actors and singers, for instance, spend years of hard work learning their craft. You don't become a performer by singing along with the car radio.
No indeed; and while there are a few who can play instruments without formal music education (or even how to read sheet music), "natural" virtuosity is (a) a popular legend and (b) the exception rather than the rule.
I really do think that the myths of
are quite fallacious if not outright pernicious, and have to be corrected many times in the course of a student's career. Sometimes the teachers and parents have to be corrected, too (especially the parents, who in some cases are really the only reason some people are majoring in CS).
I'm quite glad you are doing CS work because it's something you are finding worth while on your own, for example. That is becoming a minority situation, if not an altogether rare one.
While it's seldom true that such skill is unattainable by mere mortals, neither can it be had by closing one's eyes and wishing for 5 minutes. I'm not sure why people often go to either extreme.
"Wishful thinking" is one answer. The other (related to your internal debate) is a little more unhealthy IMO: I think that people who dabble in certain arts as a hobby and reach some modicum of success often blind themselves to the existence of the next levels of aptitude, chalking "famous" virtuosos up to flukes of history. Poetry, graphic arts, and music suffer infamously from this. I compare it to people programming as I sometimes do (rustily and "at need") and as some of the "I can if I have to" physical science majors do. It's a far cry from the cut-and-paste programmer and casual script hacker to the Larry Walls and Bill Joys, or even the Linus Torvalds, Richard Stallmans, and Eric Raymondses of the IT disciplines.
Perhaps it's also an unhappy comment on the work world that folk assume that something that requires work can't possibly be a joy.
You are very much correct IMO, and I'm going to have to think long and hard on what a plausible "solution", if any, might be.
I was told once by a graduate advisor that I treated work (programming language semantics) as play. This was meant critically in that I couldn't take it seriously, which was indeed a problem, but insofar as I dared to enjoy work... I still disagree somewhat with his general philosophy of education, even though I see his point about having the maturity to tough it out and surmount difficult topics rather than evading them or leaving "gaps in understanding". I had many in programming language theory (and still have some); I had fewer in the theoretical foundations of intelligent systems. So, I switched. In retrospect, it isn't too surprising. But I don't feel as if I traded down; far from it.
Thanks for your comments; they were very astute and helped me focus my thoughts, at least. If you have more comments on this line of reasoning, I look forward to reading them (and continuing the discussion) in your LJ.
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Banazir