Essays, reviews, sketches, remembrances, counsel, and other writings.

Month: May, 2012

Physics at St Stephen’s in 2035 – a Vision

Later this year it will be twenty-five years since I graduated from college. If I had spent this quarter-century in the wilderness and then returned to St Stephen’s, I would certainly have noticed a few changes – more cars, more women, more Hindi –, but the ovewhelming perception would have been – nothing’s changed! Now let’s look twenty-five years into the future.

You are in your mid-forties, and have not revisited college since you left. In fact you’ve been in the wilderness yourself, cut-off from the world of education, working, let us say, with the tribal people in Bastar. But you’re back in Delhi after two decades, and yesterday when you called up one of your classmates she told you her daughter was hoping to get into St Stephen’s. You’re drawn back to the old days – you have to go back to College. You park your rented car in the underground parking lot where the shooting range used to be, and walk in through the Allnutt gate. Rohtas’s dhaba, you notice immediately, is gone, replaced by a large vending machine. But the cafe is still where it was. You step in; how clean it looks! And no, of course not, that can’t be Bhayyan over there. You decide not to stop for a snack; you never liked the mince cutlet anyway, and you’ve finally outgrown Maggi. Outside, eternal, is the tree and its ring of beautiful people, sitting delicately, legs crossed, like ballet dancers. On the Allnutt Court you see groups of students in the sun. The flowers look beautiful.You walk on, down the lane by Allnutt South. Is it still a girls’ block? you wonder, and then you notice both boys and girls going in and out freely.

You walk into the main cor. The ramp has been re-built, thank god. It has a guard-rail now, and a considerate slope. You look eagerly into Room C. Every student has a small computer, you notice. This doesn’t surprise you – you’re not that disconnected. You rush past rooms C, B, and A, turn quickly into the main foyer and look in through the open door of the hall. The seating is rather plush. You look up. Jesus said, I am the Light of the World … – it’s still there. You go back out into the main corridor, and have a look at Today’s Engagements: the Planning Forum invites you to meet Mr Rahul Gandhi, leader of the Opposition; the Choreo and Music Societies will hold a combined audition this afternoon for their annual musical (wow, you think, they’re really moved on since my time). You walk past the Principal’s office, and turn right. You look into the library. It’s now one vast computer centre. Looks like something out of Star Trek, you think.You can’t wait anymore: you must see what’s happened to the science block. You rush past Rud North, give the old chapel hardly a nod, and then, as you reach Mukh West you begin to run. You’re startled to see a dome-like fibre-glass roof floating over the basketball court, but you don’t stop.

Oh my god – a second storey! And the corridors have been glassed in. You turn left, push open the door, and enter the cool, air-conditioned space outside the NPLT. You look in. The classroom has no ramp anymore, and that huge desk in front is gone. So is Dr Popli’s picture. There are about twenty students sitting in a ring. They’re looking intently into wafer-thin screens. Ah, you think, the teacher must have given them some exercise to do.

You look in through the open door, at the nearest computer screen. Electricty & Magnetism, it says at the top of the page. Old Maxwell’s Equations, you think. Hmm, let’s see: div E equals rho by epsilon naught, …. There’s a video running on the screen. A white man draws a horizontal line, quickly inscribes some positive signs under it, and a vertical arrow – a vector, an electric field –, and then draws a flat little box – a Gaussian pillbox! Yes, of course: the change in epsilon times the the normal component of the electric field is equal to the surface density of free charges. You smile foolishly, aglow with pleasure. You start looking around. Then you notice something funny: there are different videos on different computers. But as you watch you notice that they all seem to be saying the same thing: they’re all about boundary conditions, only some explain them with pictures, some with equations, some talk a lot, some just write enigmatically. No one looks bored. Wow, what a great idea, you think; I could never understand Dr Phookun’s long-winded explanations.

A bell rings. The students take off their headphones. They talk to each other for a while, and then most of them type furiously into what looks like a chat-box. You peer in. I don’t get it, the student is writing, how come only the free charge density appears on the RHS? Ah, questions, they’re posing questions! And you see the answers popping up in the lower panel. Now you can’t stop yourself; you walk into the classroom, and look into a couple of the screens in front of you. At one of them a sardarji is sitting quietly. Then, slowly, with one finger, he types out something. After a pause, you see this message on the lower panel: The data bank bank does not have any answer matching your question, but it will be passed on to Grandmaster Walter Lewin Jr at MIT. If he approves of your question, you will get your answer tommorrow, plus ten bonus points on your Universal Academic Rating.

The class ends. Some of the kids smile at you, and you begin talking to them. You think, let’s see, who would still be around? Dr Garg, Dr Cherian, Dr Phookun, Dr Sanjay, Dr Sangeeta – they must all be gone by now. Maybe Dr Gupta is still here; he looked so young then. You ask after your old teachers. The kids look puzzled. Then someone tells you – but there are no teachers here! No teachers? You mean this isn’t a college any more? Of course it is – it’s a self-learning college. You mean teachers don’t exist any more. They do, but only in, like, really remote areas, and special colleges for the handicapped. And of course there are the Grandmasters at MIT and Caltech; they’re the ones who make our lessons, and our answer banks. But who looks after the college? Well, there’s an administration, but we help too. But why come to college at all then? The discussions really help. And often old students and visitors come and tell us about what’s happening out there. Then there’s ECA. Besides, if we didn’t come to college, how would we meet?

You stagger out.

March 2010.

Isaac Newton (1642/43 – 1727)

Outside the British Library in London there is a bronze statue of Isaac Newton, by Sir Eduardo Paulozzi, based on an engraving by the English mystical poet and artist William Blake. It shows Newton naked and muscular, sitting on a block and bent double, eyes focussed on a divider with which he marks out something – presumably the order of the universe, in a poet’s understanding of the scientist’s vocation. Blake lived in the century after Newton, at the same time as Pierre-Simon de Laplace, the French mathematician whose great work on celestial mechanics started where Newton’s Principia ended and demonstrated, among other things, the long-term stability of the solar system. On being presented this work Napoleon is supposed to have asked Laplace what role God had to play in his scheme of things, to which Laplace replied that God was a hypothesis of which he had no need, since it explained everything but predicted nothing! The supposed ability of the Newtonian mechanics to predict the course of the world was a shock to the religion-infused Middle Ages in Europe, where God’s supervisory role in everyday life was taken for granted. It is the disdain of a mystic for the man ultimately responsible for this worldview that Blake’s engraving of Newton is thought to represent. I like to think, however, that what stirred Blake was an inkling that behind the cold front of Isaac Newton, this god of Godless science, there was a heart that sought out ultimate order with just as great a passion as his own.

Isaac Newton was born on Christmas Day 1642 (which, when the Gregorian calendar was adopted by England in 1752, became 4th January 1643), two months after his father died, to Hannah Ayscough of Woolsthorpe, Lincolnshire, England. When he was two, his mother remarried and left him to the care of her parents. Isaac was unhappy at this abandonment. He was briefly re-united with his mother in 1653, when her second husband died. Shortly thereafter he was sent to nearby Grantham to attend its Free Grammar School. His mother withdrew him from school when reports came in that he was “idle” and “inattentive”, and sent him to manage the considerable properties left to her by Isaac’s father (a well-to-do but illiterate man of farmer stock), a task at which he proved inept. He was sent back to the school about 1659, at the instance of his uncle William Ayscough and the headmaster of the school, and there prepared for admission to university.

In 1661 he went up to Trinity College, Cambridge, to study the Law. He was enrolled as a sizar, i.e. a student who earns an allowance as a servant or helper to another, in this case Humphrey Babington, a distant relative who did not make much of an imposition on Isaac. At any rate, he had time enough to read extensively – not just the canonical Aristotle, but also Descartes, Hobbes, Boyle, Galileo, Kepler, et al. He also learned mathematics seriously – from Euclid and Descartes, and from Wallis, whose work on algebra inspired Isaac to try proving theorems his own way (“Thus Wallis doth it, but it may be done thus…”). By 1665, when Isaac graduated from Cambridge, his mind was ripe for the two-year hiatus from university life that followed when Cambridge had to be closed for the duration of the Great Plague of London (which spread to Cambridge). Isaac returned to Lincolnshire, and in the two following years cultivated in solitude the many ideas that Cambridge had sown in his fertile mind. From this emerged the great work for which he later became famous – on calculus, gravity and mechanics, and optics.

Newton returned to Trinity in 1667, where he was elected Fellow in 1668, giving him the freedom to continue his researches. Though Newton was reluctant to publish, his extraordinary discoveries in mathematics and natural philosophy soon became known to the scientific community at Cambridge and beyond, especially as a result of the interest and encouragement of Isaac Barrow, the first Lucasian Professor of Mathematics, and of Barrow’s correspondence on Newton’s work with the mathematician John Collins, who forwarded it to the President of the Royal Society.

In 1669 Barrow resigned from the Lucasian professorship, recommending Newton as successor. In 1670 Newton delivered his first lectures – on optics – as Lucasian Professor. The work that Newton did on optics at this time – both experimental and theoretical – led to the publication in 1704 of his famous work Opticks (the thirty-year delay in publication being partly the result of Newton’s feuding with Robert Hooke, after whose death the book was published). Newton continued his work on mechanics and astronomy, corresponding with well-known astronomer Edmond Halley, who had been able to show that Kepler’s third law implied an inverse-square law of attraction. Halley discovered that Newton’s researches went much deeper, and strongly encouraged him to publish his work. This led in 1687 to the publication of Philosophiæ Naturalis Principia Mathematica, the preface to the first edition of which begins with the words “Since the ancients …made great account of the science of mechanics in the investigation of natural things; and the moderns, laying aside substantial forms and occult qualities, have endeavoured to subject the phænomena of nature to the laws of mathematics, I have in this treatise cultivated mathematics so far as it regards philosophy.” In this – the cultivation of mathematics so far as it regards philosophy – Newton succeeded so completely that his methods became the archetype of the physicist’s practice. The watertight logic of mathematically reasoned natural philosophy also had the effect of making God an unnecessary hypothesis.

Yet Newton was a deeply religious man. In the Middle Ages in England it was taken for granted that everyone would be affiliated to the Church. But Newton’s interest in religion went far beyond affiliation to a church. In the General Scholium, an essay that was included in the 3rd edition of the Principia, he wrote “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being” and then went on, at some length, to deduce the qualities of an omnipresent God. He wrote extensively on religion, engaging himself not just in interpretations of Christian concepts like the Trinity but also in practices that today we would associate with cranks and charlatans, e.g. numerology based on numbers appearing in the Bible.

In fact there was a strain in Newton that was deeply sympathetic to the supernatural. In 1936 a trunk filled with Newton’s notebooks was auctioned by Sotheby’s and acquired by the economist John Maynard Keynes. These notebooks had been examined by the Royal Society after Newton’s death, and deemed unfit for printing. Keynes was fascinated to discover that they contained, in great detail, accounts of Newton’s secret researches on alchemy, carried on during the very years when he was becoming famous as a mathematical philosopher. Keynes was invited by the Royal Society to speak at Newton’s tercentenary celebrations (which took place in 1946); though he died before the event, the text of his proposed lecture, entitled Newton, the Man, survives and contains the famous lines: “Newton was not the first of the age of reason. He was the last of the magicians …”

The received image of Newton the Sage of Reason was perfected after he left Cambridge in 1696 to become Warden of the Royal Mint. As Master of the Mint from 1699 onward he was a powerful, active, and very successful civil servant. For twenty-four years he was the also reigning monarch of the Royal Society (to which he had been elected Fellow in 1672). He was the first scientist to be knighted, in 1705. In his home in London – of which his brilliant and charming niece Catherine Barton was hostess (Newton never married) – he received the greatest intellectuals of Europe. Jonathan Swift wrote about Catherine. Alexander Pope wrote Newton’s epitaph when he died – “Nature and Nature’s laws lay hid by night: / God said Let Newton be! and all was light.” Newton was buried in Westminster Abbey. The pall bearers to this farmer’s son were three earls, two dukes, and the Lord Chancellor; they were followed by the Fellows of the Royal Society. The rather elaborate monument at his grave bears the inscription “Hic depositum est, quod mortale fuit Isaaci Newtoni.” The immortal remains of Isaac Newton cannot be so neatly contained. Pope’s anodyne epitaph speaks only of Newton the master of self-consistent natural philosophy. Yet this reasonable Newton was only a part of – and perhaps a result of – a complex and contradictory creature whose measure we cannot easily take. Perhaps a more appropriate epitaph to Newton would be the defiant words of the mystical American poet Walt Whitman in Song of Myself “Do I contradict myself? Very well, then, I contradict myself. I am large, I contain multitudes.”

The Fear, and the Use, of Mathematics and Physics

The two areas of human enquiry that inspire the greatest terror in the hearts of students are undoubtedly Mathematics and Physics. You may find history, or chemistry, or economics difficult, but your reaction to these subjects, and most others, is almost certainly not fear. On the other hand, when you encounter an equation, your first reaction is to escape to more amiable company. If you compare subjects to people, you will realize that your reaction to maths or physics is very similar to you reaction to a stern, quiet person who is famous for his wisdom but who makes you very uncomfortable indeed. When he speaks you listen dutifully, because you’ve been told his words contain a lot of meaning, but you understand almost nothing, and you end up feeling foolish and exposed; and what is worse, this person does not need to shout to make you feel this way – he just has to look at you. When you see an equation or a mathematical expression you react in the same way. Let us try to understand what mathematics is and why it is so difficult.

Pure mathematics is a kind of language: its symbols carry meaning and these symbols can be combined into expressions in well-defined ways to carry more complex meaning. The rules for constructing expressions in mathematics are very precise and well-defined. As a result it is possible in mathematics to start from simple ideas and rapidly build up mathematical structures that are unbelievably complex and far-reaching. Even to a professional mathematician, the heights that can be reached by this method are astonishing; in fact a true mathematician never loses his joyful amazement at the power and reach of mathematics.

In applied mathematics, of which theoretical physics is the most outstanding example, the meanings carried by the mathematical structures are closely reflected in the physical world. In a typical piece of reasoning in physics we start from a universal law, e.g. Newton’s second law, which relates the acceleration of an object to its physical interactions with other objects. When we throw a ball, its acceleration is due to its gravitational interaction with the Earth. We express this in mathematical form, and, once we do that, we have all the power and reach of pure mathematics at our disposal – i.e. we can now use the rules of mathematics to travel far away from the apparently simple physical facts expressed by our original equation. But because the physical situation has been captured in some fundamental sense by our original equation, the results we arrive at using mathematics remain representations of actual physical situations – including ones that we may never have guessed. For example, in the case of the ball thrown up, our mathematics tells us that if the velocity of the ball is more than 11.2 km/sec, it will escape the gravitational pull of the earth. So, starting from a mathematical representation of an apparently simple situation – a ball thrown upward – we arrive at the conclusion that rockets and interplanetary travel are possible!

This description of pure and applied mathematics also reveals the various reasons why they are reputed to be – and indeed are – so difficult. First, if you see just the final result of a long process of mathematical reasoning, it is virtually impossible to see how it could have been arrived at from its simple origins. Second, if you decide to go through the process of reasoning yourself, you have to make sure that you walk only along the paths allowed by the rules of mathematics – else you fall! When a mathematical structure is first being built there are often big gaps in it, and seasoned mathematicians must therefore become adept at leaping across these gaps, rather like a monkey jumping from tree to tree. In pure mathematics, as the structure is completed, mathematicians try to ensure that every gap is closed – the tree-tops are linked by a network of sky-bridges – and that it becomes possible for anyone with basic skills and courage to walk from one point to another. In physical mathematics, on the other hand, it is common practice to leave many of the gaps unclosed – we are expected to use our “physical intuition” to leap across the gaps. A mathematician is more sensitive to the beauty and intricacy of the structures that they have built, many of which seem to float in the air. A physicist is more interested in how he can get from one point in the forest to another, and to do that he moves sometimes along the ground – this is called reasoning physically – and sometimes high above the ground – this is called mathematical physics.

From my description above you can deduce that someone wishing to be a pure mathematician must possess two distinct abilities: first, he must be able to guess what kinds of mathematical structures can be built – is this conjecture provable? – and are worth building – is it mathematically important? –; and second, he must have the ability to build them, i.e. he must learn the necessary techniques. To be able to walk along mathematical structures that others have built is no mean ability, and certainly a very useful one, but a creator of mathematics must do much more. On the other hand a physicist must be able to walk boldy along the ground level of physical reality, climb up the elevated network called mathematical physics and walk along it, and always keep in mind the connection between the two.

There are of course many areas outside physics in which mathematics is indispensable. All branches of engineering use a combination of physical and mathematical reasoning, much as physicists do. Theoretical computer science is pure mathematics. Even in some areas of science that have traditionally been practised without mathematics, it is beginning to make inroads. For example, biology, once the most non-mathematical science, has recently begun to discover that mathematical reasoning can go a long way in explaining its phenomena. As a result, physicists are moving into biology in droves, leading to the a new area called biophysics. In chemistry too sophisticated mathematical models are used to determine the details of the chemical bond. Economics and its offshoots, e.g. finance, have of late become increasingly mathematical. The stock market and its various goods – options, derivatives, etc – are priced according to mathematical models. The increasing complexity of these models means that many people with PhDs in mathematics and physics and computer science have begun working in finance, especially in the US.

You may ask what role mathematics and physics have to play in the ordinary lives that most of us lead. Is it necessary for an IAS officer or journalist or a doctor to be familiar with the methods of mathematics and physics? One sometimes reads articles condemning the common man for being mathematically and scientifically illiterate in a world where our technology depends so much on advanced mathematics. I feel, however, that this line of argument misses the point in one way. When calculators didn’t exist, most of us knew our multiplication tables. Now that calculators are available to everyone, do we insist that everyone still remember their multiplication tables? Of course not. Music compression using mp3 depends on a beautiful and powerful mathematical idea called the Fourier transform. Does that mean that all of us must learn about Fourier transforms? Of course not.The experts must of course know their mathematics, or our computers and mobile phones will not work, but it is not just futile but pointless to insist that everyone should be familiar with the mathematics that underlies computers and mobile phones and other conveniences. Of course, everyone is welcome to learn about such mathematics, and feel enriched and inspired by it, but it is unlikely to help administer districts better or write more vivid reports or heal patients more effectively.

Does that mean I think mathematics and physics can be dispensed with altogether by the ordinary person? Not at all. If we believe that an educated person should be familiar, at some level, with the world in which he lives, then perhaps we should encourage him to develop an appreciation of some ideas in mathematics and physics – ideas that are reasonably simple yet convey the spirit and the methods of these disciplines. For example, the idea of the proof, so central to mathematics, is conveyed by fairly simple theorems in geometry, of the kind that used to be taught in all schools when I was a child. The subtlety of the concept of number can be appreciated by trying to undertand why mathematicians are so taken up with prime numbers. The idea of symmetry, which is fairly intuitive and physical, leads to the beautiful and abstract mathematics of group theory. Similarly, in physics the average person can try to learn from popular sources some of the central ideas of physics. A ball follows a path, but an electron does not – this is the strange world of quantum mechanics. One can never catch up with light – this is electromagnetic theory, optics, and relativity –, and so on. You can go beyond the basics too, and discover from popular sources what the major areas of research in mathematics and physics are. A large number of books explain these ideas for the non-scientific reader, and of course the internet is an inexhaustible resource for someone who wishes to learn.

That brings us to my final point. Suppose that you do not wish to spend your time appreciating mathematics and physics. What you want to know is whether they can help you in your day-to-day life. If I were asked to choose one area of mathematics – beyond addition and multiplication – that could help virtually everyone, it would be statistics. And one idea from physics that every minister and IAS officer and journalist should learn is how to make an intelligent estimate.

The basic ideas of statistics appear in virtually all areas of life, though we are often unaware of them. Consider for example the result of a blood test. You find that your cholesterol is 190. Unhappy that it is close to the danger mark, you get it tested again. This time you find that it is 180, and you feel reassured. Being an “optimist” you prefer to believe the second result! But suppose instead that you tried to understand this disparity in test results; then you would have to learn about the basic ideas of a statistical distribution and its mean and standard deviation. You would realize that if you got your blood tested a very large number of times, the results would yield a distribution, which would resemble the famous bell curve. Its mean would tend towards your true cholesterol level. More importantly – and this point is usually missed, even by doctors – the width of the distribution, or its standard deviation, would tell you how far you can trust the number produced by any one test, and help you to distinguish a significant difference between two test results from a insignificant difference. Another important statisical idea is that of a correlation: if you have data on two variables in a populations – e.g. height and weight –, how do you test whether they are related? Obviously, taller people are, on the whole, heavier than shorter people (in spite of the existence of short fat people and tall thin people). If you make a plot of height versus weight of a population, this correlation between height and weight will show itself as a band. If you understand this method, and it refinements, you can use correlations between variables not so obviously connected, to understand how much one factor influences another. And by looking at the way correlations change with location, and with time, you can draw important conclusions on how to invest resourses. For example, if you plot an indicator of health, say longevity, versus income, you are likely to find that in a sample of poor countries longevity increases with wealth, whereas in a sample of rich countries, longevity is not as strongly correlated with wealth. Whether you are talking about medical tests, the census, average rainfall, change in prices, variation in nutrition levels – the ideas of statistics will help you to draw useful conclusions from the information you have.

The idea from physics that I choose as the most useful for the common man is intelligent estimation. Before embarking on a calculation or an experiment that may consume a lot of time and resources, it is often important to have some idea where one is headed. For this, physicists must learn to do what they call “order-of-magnitude” calculations. The great physicist Enrico Fermi expressed this in his own way: he said that every physicist should know how to estimate the number of barbers in the city of Chicago! Let us try to estimate the number of barbers in the city of Delhi. – The average man has one haircut a month, i.e. one-thirtieth of a haircut per day. The male population of Delhi is between 60 lakhs and 90 lakhs, which means that there are 2 to 3 lakh haircuts per day. The average barber probably cuts 15 to 20 heads of hair in a day. … Put these together and you will find that the city of Delhi has between 10,000 and 20,000 barbers. To determine exactly how many barbers there are you need a survey, but notice how easily you can deduce that the number can’t be 1000 (or Delhi-ites would have to grow their hair like sadhus) or 100,000 (or the barbers would be mostly unemployed). A problem that when first posed sounds impossible to answer becomes simple when broken appropriately into parts. The same method can be used to estimate the power consumption or the petrol consumption in a city, the appropriate fare for a half-hour autorickshaw ride, the amount of grain needed to feed a population, the number of doctors needed in a district – the questions are endless. Normally one looks to experts for answers to these questions – and indeed experts are needed for precise answers –, but if you learn the physicist’s science of intelligent estimation, you can check whether the authorities know what they are talking about, and you don’t always have to wait for their answers.

A Letter of Recommendation

In the fourteen years since I joined the Physics Department of ________ I have written several hundred letters of recommendation – to Indian and foreign research institutions and to foundations providing scholarships. The most substantial ones are those written in support of applications to graduate programmes. I would like to share in this note the process of writing one.

What an institution seeks from you, in addition to your marks etc, is a statement of purpose, which is your perception, given your past and present, of the direction your life could take. What they seek from me, the recommender, is the perception of an expert who, knowing you and others like you, can discover your potential and place you in the spectrum of possibilities. There are a hundred questions they might have about you. Some are posed explicitly, but there are many others to which I imagine they might want answers. I try to answer at least a few of them.

Are you eager, attentive, interested? – even when the teacher isn’t observing you? Can you see past the exams? Do you always put in your best, or only when your enthusiasm is aroused? Can you sustain your enthusiasm? Will it survive the rigours of undependent physics? Are you a classroom star or a proto-scientist? Are you capable, resourceful, cooperative, flexible? – independent, open-minded, alert, observant, curious, playful? Do you find possibilities in confusion, or are you afraid of it? Do you face difficulty with courage and humour? Do you have an unusual take on things? – make interesting observations, ask probing questions? Do you follow up on the questions you pose? Do you have the confidence and ability to try out things on your own? (“Thus Wallis doth it, but it may be done thus…”, said Newton, as an undergraduate at Trinity.) Do you stay with a problem until it opens itself to you? Do you enjoy solving problems at all? – even when the answers aren’t given? Do you try to make sense of what you did and what you got? Can you catch a hint and take it further? Can you make connections between different areas of physics? – between physics and the world around you? Can you estimate the number of barbers in the city of Delhi? Do you know why you’re doing the experiment you’re doing, or do you just want to finish the damned thing? Do you ever make discoveries when doing experiments or is your work always perfect? Do you like trouble-shooting, or do you run for help when the BG shows no deflection? Are you interested in instruments and electronics? Do you like taking things apart and putting them together again? How about ideas – do you like taking them apart? Are you comfortable with abstraction? Do you think mathematically or physically? Can you describe a physical situation mathematically and then find physics in the mathematics? Are you quick, or slow but interesting? Do you find different solutions to the same problem and the same solution to different problems? Do you know the thousand names of the simple harmonic oscillator? What if it isn’t simple? Can you solve it on the computer? Do you know enough physics and mathematics for the programme you’re applying to? Are you versatile, drawn in different directions by your many talents? What turns you on? What do you do best? Do your inclinations meet your abilities? Do you manage your time well? Are you ambitious? Do you have any idea what it means to do research? Have you done any interesting projects in college? – summer projects elsewhere? Do you work well with others? – and alone? Do I have any feedback, from you and from your guides? Have you given talks on them? Did your talks seem well-prepared, clear, insightful? Do you like discussing physics? Would you make a good teacher? Are you helpful? – humble enough to admit your mistakes? – honest, intellectually and otherwise? Do you add to the classroom? Anything else? – Do you have any special qualities? Are you disconcertingly direct? Are you unusually logical? Do you always spot my mistakes? What about your mistakes – are they enlightening? Do you jump to the right conclusions?

You may wonder how on earth I can answer all these questions about you (though at other times you’re furious with me for not acknowledging your subtlest abilities and fathoming your deepest desires). For most of you, I would be able to answer no more than two or three of these questions. For some rare students I might be able answer more than two-thirds of them. With even a few significant answers I may be able to make a recommendation that counts. Where do I find my answers? In tests: If your written answers are uncharacteristically lucid, get straight to the point, show a different way of thinking, explain what you’re doing instead of brandishing formulas; if you always attempt the challenging questions and not just the standard ones; if I say to myself, “She can read my mind!” or “Wow, I never thought of that!” – I will remember. In the classroom: If you are always attentive, participate in discussions, make unusual observations, are willing to take risks, ask thoughtful or startling or deep questions, make a presentation that takes my breath away – I will remember. In the lab: If I ask you about your potential divider, or your error calculations, or whether you know your result’s in the right ball park, and I see you thinking; if your circuits are beautiful; if you get caught up in trying to figure something out; if I see you trouble-shooting or handling equipment joyfully; if you’re unusually regular in submitting your file – I will remember. In the Physics Society: If you show initiative, get others excited, take the lead, keep your commitments, organize something well, give a good talk – I will remember. Elsewhere: If we meet and you tell me that you’re really enjoying the maths, or that electronics is, really, fun, or that you’re writing this intricate programme; if I see you following a trail like a bloodhound; if your summer project made a big impact on you; if another teacher says something that makes me change my mind about you; if I am taken aback by your integrity; if I see you helping your classmates – I will remember. If your summer-project adviser says to me, “______, that guy was amazing: I just outlined what needed to be done, and he did the whole thing and came back. He was better than my PhD students” – I will remember. Hell, if I see you take one step off the straight and narrow path, one chance in the wilderness, I will remember. But if you always hold back, lest you make a fool of yourself and earn my scorn, I won’t know very much about you. And if you approach me for a letter of recommendation, I may not have the heart to refuse, because I don’t want you to feel rejected, but what I write will not win anyone over.

One question you probably ask yourself is – “Does Dr _________ like me?” My affection for you, real or imagined, is not as important as you think. It is true that on very rare occasions I have been swayed into writing a stronger recommendation than, in retrospect, I think the student deserved, but this happens very rarely indeed – and to the extent that it happens my recommendation is compromised. It may be difficult for you to accept this – but my recommendation is credible to the extent that it is not swayed by the ease with which you and I converse. Nor must it be swayed easily by your self-perception. What is asked of me is a kind of doctor’s view of a patient he knows well. I must know what you think and say of yourself, which is why I listen to you and ask you for your statement of purpose, but I must be able to see you not just as the unduplicable person you know yourself to be but also as one of many who have gone through this process – this suffering! – before and will go through it again in future. So it’s more important that I know you well than that I like you well. That said, I must add that I do not appreciate requests for recommendation from students who have made it amply clear that my teaching – in its broadest sense – has meant little or nothing to them, or from former students who, having snapped all links, reappear only to seek a recommendation, and then plunge back into the darkness from which they emerged. I usually agree even in these cases, and write fairly and perhaps knowledgeably, but I do so with a feeling of being used.

I like to write a letter of recommendation with goodwill and enthusiasm, at least the former. I was on one occasion asked by a student whether I would write him a good recommendation, and if not would I please tell him in advance. I explained that a recommender was not bound to write a good recommendation, only an honest one. However, as a personal policy – probably the policy of many other referees as well –, if I feel I cannot write a recommendation that is on the whole positive, I try to let the student know in advance. This I do especially if the student happens to be someone who, on the basis of his academic standing or for other reasons, would automatically expect a strong recommendation. Most of my letters, however, will, explicitly or through silence, convey not just your strengths but also your weaknesses. Here is how I organize a typical letter of recommendation.

In the first paragraph I establish my credentials, by specifying how I know you – what classes and labs I have taught you, whether I have interviewed you, talked to you outside the classroom, talked to others about you, observed you giving talks, etc. Then I write about your strengths as an undergraduate student. If I am writing to an institution that is unfamiliar with St Stephen’s College, I describe what makes a physics degree from Delhi University, and especially from St Stephen’s, stronger than degrees from other places; I also inform them about the weaknesses of our programme – lack of problem solving and of computational physics. If you have done anything to overcome the weaknesses of the curriculum, e.g. if you are an expert at programming or love problem solving, I mention that. If you have gone on to another institution after St Stephen’s, say IIT or Cambridge, I add a line or two about the ways in which your education there is likely to have complemented what you learnt at College. Then I go on to those of your characteristics that are less student-like and more scientist-like, e.g. the way you do projects or other independent work. I give them my perception of your maturity, self-confidence, ability to do a sustained piece of work, ability to work alone or in a group, and so on. If you are applying to a course outside physics, and I know something of what it requires, I say a word about how your training in physics may lead to it. If there are lacunae in your training, e.g. if you know little programming and are not used to problem solving, I may be quite explicit about them. If you’re easily distracted, a last-minute crammer, I may mention that, but I will normally put it in the the context of a system that encourages such qualities, if I think that you’re capable of focussed hard work in the right circumstances. If I don’t see in you certain other traits of character and mind that graduate study requires, I usually convey that through silence or by pointing to the possibility of growth. However, there are certain character traits that I may try to forewarn them about; e.g. if you are someone who needs to be handled delicately, I may let them know. If you are someone who I think is very capable but who has so far been resolutely unadventurous, I may state that as well. On the whole, though, I am far more gentle about your weaknesses than you might imagine. I try to see you as you might be. If it is a letter to a foreign university, I add a line about your fluency in English. If I know someone who is already in the programme to which you are applying, I compare you with him or her. I do not usually write about your achievements outside physics, but if you are unusually gifted at something and I feel that it says something essential about you, I add that a word about that, and how it connects with, adds or takes away from your commitment to physics; if you are applying for the Rhodes Scholarship, then of course I write a little more about your extra-curricular activities. I finish with an overall recommendation – strong, very strong, etc. In addition to information I try to communicate through tone, emphasis and example a picture of you as a whole person; I may tell a story or two to show how I discovered something about you. Sometimes I go a little overboard. (“_______, on the basis of your recommendation, we could get her married.”) But on the whole I think I do a pretty good job. I may be tempted to tell you what I wrote about you, but, though I may discuss your strengths and weaknesses with you in another setting, I desist from revealing the contents of my letter to you.

I believe strongly that a letter or recommendation to be effective must be confidential. I am required in it to express opinions about you that in normal circumstances would not be explicit. There is no reason, for example, for you to know in what respect I think you are superior or inferior to X or Y, but such information is essential to the institutions to which you are applying; in fact openly bandying such knowledge would destroy or seriously endanger the relationship of which this act of recommendation is a part. Asking for a letter of recommendation is ultimately an act of trust.


There are certain protocols that go with the act of asking for a letter of recommendation. First, ask yourself whether I have had the chance to get to know you well enough to write a convincing letter. If you think so, approach me in person if you are in College, or write to me or call me if you are elsewhere. Do not provide my name as a referee without my explicit permission, no matter how sure you may be that I will agree. Provide me with the information I seek, usually your statement of purpose, your CV, etc. I will usually want to talk to you about your application, and may want to interview you. If you are handing me a printed form, make sure your details are complete, and that you provide, as a courtesy, an envelope with your name and the name of the programme written clearly on it. Do not wait until the last moment to ask me for the reco: I do not appreciate being asked to provide a letter tomorrow; I recommend that you let me know month or so in advance that you intend to ask me for a letter, and then forewarn me and hand me the required material at least two weeks in advance. (For summer programmes I can fill a form at short notice, but even there I prefer to have some time.) After the letter is complete I will inform you, and if you are in College I expect you to come personally and collect it. If the letter is to be sent online, I will let you know after I have submitted it. Have the courtesy, in either case, to acknowledge my letter with a word of thanks (if you can’t resist giving me a blinding smile, that will quite in order, but nothing more is needed); remember, I don’t like being taken for granted any more than you do. When you hear back from the institutions to which you have applied, once again be so kind as to let me know what happened; I am interested. I do not expect you to write back to me from Cambridge or Cornell, but if you do, I’ll be happy to know how you’re faring in the programme to which I have recommended you. Besides, the information you provide will prove useful to other students who will, after you, come to me for counsel and recommendations.

Good luck.

December, 2010.