Of late I find myself getting into several discussions on "mastery". One example was here, where the topic under discussion was poetry, and my opinion was this: "To break the rules you need to know the rules. I'd say you need to do more than know the rules: you need to master the rules." (I also promised a longer write-up on my views on the subject, but this is not that write-up: it's more of a trial run.)
Here, however, I want to talk about a different question: does mastery of a field imply exclusion of ability, or interest, in other fields? The specific motivation is Sunil Mukhi's post today on mastery. He expresses his skepticism on the current scientific/academic trend favouring "interdisciplinarity" and "being a well-rounded individual" and "all that", and adds that "serious achievement requires concentration, knowledge, technique and depth."
Now, there is absolutely no doubt about that. Achievement in any field requires all of the above. But he cites as his example Sachin Tendulkar, saying that Sachin "single-mindedly focuses on what he does best" and suggesting that he has no interest in any other form of expertise.
But in Sachin's case this is not true. He is a fine bowler. To date he has 154 ODI wickets, 44 Test wickets, but those figures don't reveal his value: he is not called to bowl long spells as specialist bowlers do, but as a change bowler to break up a well-set partnership, and his success rate there is extraordinary. He seems to extract as much turn, sometimes, as Shane Warne or Mutthiah Muralitharan. I am convinced that if he had applied a part of his batting focus to bowling, though he wouldn't have been the greatest batsman in history, he would have been by far the greatest allrounder -- greater than Gary Sobers. Ne is also an outstanding fielder. As for other sports: very few sportsmen -- in Tendulkar's class or not -- attempt more than one sport professionally, but I am sure Tendulkar has an amateur interest in several other sports. In particular, he has been photographed playing table-tennis (with concentration writ large on his face).
I have a big problem with the view, widespread in India, that mastery in one field requires exclusion of interest in other fields. Many Indian parents discourage their children from pursuing any other activity during the dreaded Board exams: anything other than study is viewed as a distraction. I read the complete Sherlock Holmes, cover to cover, and I don't think my results suffered. Nearly all great scientists that I can think of have had strong interests in other fields, and not just in other sciences. Far from distracting them, I think it has strengthened their primary work -- even if they never went fully "interdisciplinary".
Which brings me to Sunil's other example: Srinivasa Ramanujan. Says Sunil:
Recently a colleague, talking about his institution's undergrad admissions process, observed that "with the kind of breadth requirements we have, one wonders if Ramanujan, who only knew mathematics, would even get admission". That's basically my point, and I think Sachin's achievement validates it.
But Ramanujans are very rare and not replicable. I'd like to think that if a Ramanujan showed up at my institute, or Sunil's, his ability would be immediately recognised by the scientists there and we would make every effort to help him bypass the usual educational requirements. But it is terrible advice to a young mind to try and become a Ramanujan. Such a creature comes along once a century, or
even more rarely.
Most of the great Indian scientists I can think of were multidisciplinary. Visveswarayya had an extraordinary range of civil engineering achievements, from irrigation to flood protection to roadways. Jagdish Chandra Bose made significant contributions to plant physiology, membrane biophysics, and other fields, and is now recognised as Marconi's predecessor in wireless communication. C V Raman made contributions in light scattering, acoustics of musical instruments, crystal dynamics and properties. Subrahmanyan Chandrasekhar was famous for switching fields every ten years and achieving mastery of the new field: he wrote classic books on stellar structure, stellar dynamics, radiative transfer, plasma physics, and hydrodynamics. Yet Ramanujan seems to capture the popular imagination much more than these figures. His is a unique and romantic story, but should not be held up as an example to follow. He is not someone who broke the rules after first having mastered the rules: he seems to have never learned the rules, but achieved mastery all the same.
To me, "mastery" does not imply "singlemindedness". Nor does it imply remaining in the same field all one's life. And, in fact, I think Sachin Tendulkar is an excellent example of the former point, and I suspect he will continue to be an important figure in whatever he chooses to do after he retires from cricket.
Sachin Tendulkar is no Ramanujan. He has natural talent, yes, but is the product of a fine coach (Ramakant Achrekar), a school system that has produced many other fine cricketers, and, of course, his own hard work and study. Ramanujan barely knew how he produced his own results (which he largely supplied without proof, keeping mathematicians busy for the following century), and often attributed his insights to the Goddess Namagiri. Tendulkar's achievements are the results of extremely conscious hard work, and he is eminently worthy of emulation.
17 comments:
Rahul, I think your interpretation of "single mindedness" is too narrow. I don't think "single mindedness" mean having no other interests. It only means that you spend most of your time (say 90%) on one goal. With his talent, Sachin could have chosen to be either the greatest batsman, greatest bowler or the greatest all rounder of all time. If he had chosen to become the greatest all rounder, I am sure he would not have scored as many runs/centuries. At any given point of time, for most mortals, in order to achieve mastery, they need to focus on one thing. Like S. Chandrashekhar, what they choose to master can of course change with time.
Vikram: I don't think that's what Sunil meant (but perhaps he'll comment, here or on his own blog, and clarify). As is clear here, I found the comparison to Ramanujan particularly irksome. Ramanujan could perhaps be compared to Bobby Fischer -- an entirely untutored genius that burst on the world -- but Sachin is not only the product of much hard work besides talent, but appears to be an exceptionally "well-rounded" individual, to use the phrase that bothers Sunil.
And I don't think you should build policies to cater to potential Ramanujans. Ramanujans -- or even Sunil Mukhis -- will get noticed despite the system. For the average person, though, in any field, breath of interest and education is an enormous advantage. Sunil himself has deep interests outside of physics/science, as is obvious from reading his blog. Some scientists develop deep interests in science, outside their speciality. Others change their specialities altogether and focus on a new field. Nothing wrong with either of those. Nothing wrong, either, in giving the kids a broad education (as the IISERs are doing) so that they will know what options are available to them down the line.
I think what Dr. Mukhi implied was, with the existing "broad" requirements, to be even considered eligible to "show up" at any institute may be tough enough for people like Ramanujan. I liked your article though, it was a good, distinct viewpoint from that of Dr. Mukhi's.
I think the difference in viewpoint about interdisciplinary research (IDR) is also a matter of which field you are talking about. You will notice that most of the people sceptical about IDR are high energy physicists for most of whom IDR is tantamount to dabbling in a field without getting one's feet wet. The reason for this is that HEP has become a super specialised field -- so much so that a person in Condensed Matter or Biology or Chemistry would find it impossible to get into HEP without a very large amount of effort. This is not, let me hasten to add, because HEP people are smarter than the rest (though I know that some of my HEP colleagues might want to believe so) but because it requires just an enormous amount of background training. String Theory requires a fair amount of esoteric mathematics (to the extent that I, despite being a high energy physicist, find even the titles of string theory papers nowadays indecipherable, let alone their abstract), collider physics too has become specialised to the extent that a simple one semester course in Field Theory is nowhere near to being sufficient to start working in it - one needs very specialised techniques to do calculations that haven't already been done. Witness the discussion in our institutes where some of our HEP colleagues want course work even in the fifth semester.
Compared to this, the preparation needed in other fields, particularly those that are 'amenable' to IDR is substantially less. After all, how many people would want to spend a year and a half or even more just to learn the basics to get into a new field, let alone be able to do original research which would probably require even more time and effort.
I don't wish to get into controversial discussions into what is more fundamental and deeper, but I think it is the nature of the field which has made HEP very specialised and therefore less amenable to being casually 'practised'. Or to use a favourite word that is being bandied about -- 'mastery' of the field requires substantial effort, hard work and persistence. The result of this is that HEP people generally tend to view IDR with a healthy dose of scepticism. It is probably a narrow viewpoint in the present day world and perhaps we are dinosaurs, but there it is.
My point of view is, there is good science and bad science. However comprehensive the "background training" required, it is possible to do both creative science as well as profoundly unimaginative science with that training. Equally, with IDR one can do superficial work as well as insightful work.
I think the problem comes when (some) scientists make a blanket judgement of IDR, essentially amounting to the following chain of logic: "X does interdisciplinary research in field Y which is not his/her original field, which happens to be Z. My own field A is very complicated and needs lots of training before one can even understand the notation, but that is not my impression of field Z. Thus, X must be doing something trivial under the guise of IDR, especially if he/she sees the need to advertise what they are doing as exciting, which isn't my personal style. If he/she had stuck to Z, that might have been OK. In fact, I might even have been OK with all the IDR stuff if they talked less about it."
Parsed in this manner, a number of implicit assumptions that are often made become clearer. I may be wrong but this seems to me to be a fairly accurate breakdown of arguments I have been having around these parts.
Regarding IDR, there are some more examples, a prominent one being the French Nobel laureate de Gennes. He worked on superconductivity, superfluidity, magnetism, liquid crystals, polymers, membranes, wetting, biophysics and - towards the end -neuroscience, making huge impacts in these fields (all except possibly the neuroscience) as he went along. His Nobel citation called him the "Newton of our times" or something similar. I don't think he was ever accused of being superficial, but he was, of course, a very special case.
Taatya -- since I know a rough idea of the quality of students we normally get, I'd guess that if a student is a fraction as good as Ramanujan and focussed only on one field, he/she would still get a lot of help, rules would be bent, etc.
Gautam - nice summary!
Rahul, Gautam -- well, I didn't really want to get into all that too much: I've already been accused (though not by Sunil) of overstating what Sunil was trying to say. I would fully agree that, even if you switch fields, you need dedication, discipline and time in the new field to make a non-superficial impression. At the same time, one can (easily) ignore the carps of the sort of scientists that Gautam caricatures, who believe that because their science requires years learning a new mathematical language before you can even read the titles of their papers, it must be more significant than anything you are doing.
Very interesting post, Rahul. I am currently having my students read Adam Smith's Wealth of Nations, and some of his reflections in Book 1 seem relevant here. First, he describes how manufacturing occasions naturally the division of labor, and then applies this insight to "philosophical speculation," saying that "Each individual becomes more expert in his own peculiar branch, more work is done upon the whole, and the quantity of science is considerably increased by it." But then, in a subsequent chapter, he also provides a qualification. He argues that the size of the market limits the benefits of such division of labor - "When the market is small, no person can have any encouragement to dedicate himself entirely to one employment." What are the implications of this for scientific endeavor? What is the equivalent of "the market"? Smith does not speculate on this, but it is not hard to extrapolate. Perhaps, starting around Smith's time, and well into the 20th century, the market for scientific ideas multiplied even as it divided up into sub-fields and sub-sub-fields, each of which mushroomed via the division of labor, the application in other words, of what you are calling mastery and singlemindedness. But perhaps, now we are reaching a point where those markets are not multiplying fast enough (string theory is a good example), and many fields of science are naturally gravitating towards a taking stock of what we know (macroeconomics/finance is a good example), and upon discovering that the answer is "not much!", are beginning to look towards other disciplines for guidance. The role of interdisciplinarity today may be quite different from its role 100 years ago. So the requirement of mastery in one's own field, before one can feel ready to take on another, seems moot to me.
From a personal perspective, as a scientist, I care less about whether I will be published, and more about feeding a genuine curiosity about some of the deepest puzzles in my field. If this requires gaining a certain level of mastery in a new field, I will make the effort, but, to even start, to believe that such effort will ultimately pay off in finite time, I have to believe, for example, that I do *not* have to be a wizard at operator mathematics in order to apply quantum mechanics to finance (turns out the Black-Scholes PDE is a "wick-rotated Schrodinger equation," something I'm still trying to understand).
ws - thanks for bringing the economics perspective -- very relevant since a lot of the "interdisciplinary science" that I see seems to involve economics these days.
I suppose part of the problem is that science is not a free market: it's largely funded by the government, around the world. So the funds go to the people who are the most persuasive (and, often, most numerous), not necessarily to the most deserving people. It becomes "the rich get richer". I think sciences -- especially theoretical sciences -- should be funded similarly to the arts: they are not directly useful and are not money-spinning but a cultural necessity. But in some areas of science, the funding has gone well beyond that.
I think HEP has had a problem since the 1970s, that theory has been far ahead of experiment. String theory in particular has been divorced from experiment since the beginning. (Nothing wrong with theory that was not driven by experiment -- Einstein's theory of gravity was driven purely by his theoretical considerations and not by any known shortcoming of Newton's theory at that time -- but experimental validation is needed down the line, and in Einstein's case it didn't take too long.)
So your observation of the "markets" for certain sciences "not multiplying fast enough" is, I think, a consequence of this. If it turns out that string theory has a totally unexpected application in some other areas of science, that would guarantee an enormous wave of interest in it. But then that would be an example of "interdisciplinary" research, which some people despise.
Interesting that the Black-Scholes equation is similar to the Schrodinger equation -- I just looked it up and the similarity seems to be that it is second order in the price (space for Schrodinger) derivative, and first order in the time derivative. This is also true of the diffusion equation in classical physics. The Schrodinger equation has an imaginary factor for the time derivative, so its solutions are wave-like rather than diffusion-like.
But I don't think the Schrodinger equation is the essence of quantum mechanics. Differential equations occur everywhere, and if that's all there is to the analogy, I'd say engineers are much more expert at solving such equations. The essential ideas of quantum mechanics are that observables are "operators", not numbers; observable values are given by the "spectrum" of those operators; systems can be in pure states (where an observable has a definite value) or in superpositions of states (with complex coefficients); in a superposition, the probability of observing any value is proportional to the weight (the absolute square of the coefficient) of the "pure state" component in the superposition corresponding to that value; and, finally, the time-evolution of a state is given by Schrodinger's equation -- and, in particular, if it is a "pure state" for energy, the evolution is simply a complex exponential factor, while if it is not a pure state, it can be decomposed into pure states each of which has its own time-evolution factor.
I'd be astonished if all of this had an analogy in economics. But this is what a quantum physicist does. I'd say very few physicists actually spend time solving the differential Schrodinger equation. They diagonalise matrices, often with layers and layers of explicit or implicit approximations: nobody cares about the "true" wave function of a many-body system, it's just intractable. And I'd be surprised if any of those skills are transferrable to economics.
Physicists have a mathematical ability and a propensity to form "minimal models" of everything, and those are useful. But coming into a new field with preconceptions is not useful.
Unfortunately Gautam, not only is your caricature of what many people say about IDR true, occasionally the caricatured statement is in itself true. Just think about it. Of course, it is also almost trivially true and you and Rahul S. also say it, that one can always do something badly and one can do things well. It doesn't help to give examples of Newton or de Gennes. The vast majority of scientists are NOT de Gennes, let alone Newton, and it is hard not to get the feeling sometimes that many people make the shift to quickly get a paper out, particularly if it is a field where it is not necessary to do too much of background study.
Rahul B: I find it hard to see why one would switch fields to get papers out: surely it is easier to stay in a field where one has a certain comfort level. But it depends on what one means by IDR or switching fields. I, of course, am most familiar with computational biology. Some physicists (and computer scientists) have a nice technique in their original field, think up a biology analogy, and throw it in to their paper. Others work closely with biologists and find out exactly what the biologists are looking for (and, usually, learn a lot of biology on the way). The former process takes minutes, the latter takes years. Also, the former gets published in physics or CS journals, the latter in biology journals. Physicists like elegant, minimalistic toy models (put proteins on a lattice, with two kinds of amino acids, and watch it fold), and computer scientists like efficient algorithms (finding common substrings in linear time). But to do biology you need to fit your model or algorithm to the biological system, not the other way around.
The same applies to any form of interdisciplinary research, I would say. Doing something that is useful to the guys in the "other" discipline is hard. But the reason so many people are doing the "hard" kind of computational biology is that the rewards can be so great.
Rahul S. : Good points. The intriguing thing, though, is that the Schrodinger equation maps (without the i) directly to the heat equation, where the uncertainty is modeled as Gaussian. In fact there seems to be something fundamental about the Gaussian assumption that "generates" the uncertainty principle. This was a pure math result proved in the 1950s, but physicists, I am told, are largely unaware of it (see, for instance, Eq. 3.14 on Page 52 of Chorin and Hald's "Stochastic Tools in Mathematics and Science"). Now, the connection to finance is that the uncertainty is again modeled as Gaussian, and that the resulting Black-Scholes PDE looks very much like the heat equation in physics.
What all this means, I do not know for sure yet. But I will need more time to reflect on what you have said as well.
As to the "true" wave function of a many-body system, I have a colleague who is a nanochemist, and when I discussed my research with him, he sounded very excited because apparently in his field, understanding the quantum mechanics of many-body systems is par for the course. As he said - "we like to play dirty!"
Haha.
ws - well, the heat equation is the diffusion equation. Not sure what you mean by "generating" the uncertainty principle -- I'll look up the book you mention -- but in QM, the uncertainty principle is basically the same as the following linear algebra result: two linear operators have a complete set of simultaneous eigenstates if, and only if, they commute. This follows from the statements I made in the previous comment, on observables and eigenvalues.
I meant nobody cares about exact many-body wavefunctions. Of course people care about approximate solutions: it's a major industry (which didn't start with nanomaterials -- it started with Hartree-Fock theory in the 1930s). In most cases these are constructed from products of single-body wavefunctions. In no case (that I know of) is it the exact solution of the Schrodinger equation for N particles in a fixed potential -- except when the particles are non-interacting (not true of electrons).
ps - my summary of QM is full of holes (eg, I forgot to say the operators must be Hermitian, so that their eigenvalues -- the observables -- are real). Don't use that to learn the subject :)
pps - what I wanted to say two comments ago is that, in QM, the uncertainty principle has nothing to do with Schrodinger's equation per se: it only has to do with the fact that the operators for position and momentum don't commute. This is also true for many other pairs of operators, eg different Cartesian components of angular momentum, which also cannot simultaneously have exact values (except the special case where they are both zero).
I have to agree that interdisciplinary research is a welcome romp towards the roots of science. Scientific specialization is really a product of the last one hundred years. Before that, while there certainly were specialists, most famous scientists were interdisciplinary researchers. There's another interesting point here; that interdisciplinary reserch then was somewhat easy because there was a lot of low-hanging fruit in many areas. But it's also true that as you progress in science, low-hanging fruit in other areas (such as neuroscience and nanotechnology in the present era) again becomes visible.
Off topic. I have been reading off and on, but not completed yet "Evolution in Four Dimensions" by Jablonkaand Lamb, "TheAccidental Brain" by David Linden. They are both interesting and seem closer to your research interests than mine. I wonder whether you can talk about them at some stage. Thanks.
gaddeswarup - thanks for the pointers. As you can probably tell from the frequency of my updates, I'm less active on the blogosphere, but will look out for those books. (BTW, I enjoy your blog too, but rarely comment for the same reason I rarely post on mine...)
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