manuelb1

Advice to a Beginning Graduate Student or What is Research? or The 4 R's of Graduate School: Reading, Rithmetic, Research, and Writing Outline of the talk: READING, STUDYING, THINKING, STARTING OFF on the PhD, DEEP in the MIDDLE of the PhD, WRITING it all up. YOU READING: Books are not scrolls. Scrolls must be read like the Torah from one end to the other. Books are random access -- a great innovation over scrolls. Make use of this innovation! Do NOT feel obliged to read a book from beginning to end. Permit yourself to open a book and start reading from anywhere. In the case of mathematics or physics or anything especially hard, try to find something anything that you can understand. Read what you can. Write in the margins. (You know how useful that can be.) Next time you come back to that book, you'll be able to read more. You can gradually learn extraordinarily hard things this way. Consider writing what you read as you read it. This is especially true if you're intent on reading something hard. I remember a professor of Mathematics at MIT, name of BERTRAM KOSTANT, who would keep his door open whenever he was in his office, and he would always be at his desk writing. Writing. Always writing. Was he writing up his research? Maybe. Writing up his ideas? Maybe. I personally think he was reading, and writing what he was reading. At least for me, writing what I read is one of the most enjoyable and profitable ways to learn hard material. STUDYING: You are all computer scientists. You know what FINITE AUTOMATA can do. You know what TURING MACHINES can do. For example, Finite Automata can add but not multiply. Turing Machines can compute any computable function. Turing machines are incredibly more powerful than Finite Automata. Yet the only difference between a FA and a TM is that the TM, unlike the FA, has paper and pencil. Think about it. It tells you something about the power of writing. Without writing, you are reduced to a finite automaton. With writing you have the extraordinary power of a Turing machine. THINKING: CLAUDE SHANNON once told me that as a kid, he remembered being stuck on a jigsaw puzzle. His brother, who was passing by, said to him: "You know: I could tell you something." That's all his brother said. Yet that was enough hint to help Claude solve the puzzle. The great thing about this hint... is that you can always give it to yourself !!! I advise you, when you're stuck on a hard problem, to imagine a little birdie or an older version of yourself whispering "... I could tell you something..." I once asked UMESH VAZIRANI how he was able, as an undergraduate at MIT, to take 6 courses each and every semester. He said that he knew he didn't have the time to work out his answers the hard way. He had to find a shortcut. You see, Umesh understood that problems often have short clever solutions. There will come a time when you work on a problem long and hard but UNsuccessfully :( And then you learn that someone else found a solution. See this as the GREAT opportunity it is to learn something important. Don't let it pass you by. Ask yourself: "How SHOULD I have been thinking to solve that problem?" I have found that doing so is a powerful exercise. Danny Sleator tells me that BOB FLOYD independently recommended exactly this exercise to his students. He would lead them into asking themselves: "How COULD I have led myself to that answer?" Take the time to think it through. It's worth it. There will come a time when you work on a problem long and hard and SUCCESSFULLY :) And then you learn that someone else already published. :( Hard as that may be for you to take, you must view this too as a great opportunity. Don't turn off. Read what got published. You will be surprised how often the published paper turns out to be different in some significant way. Roughly 50% of the time, it is NOT at all the same as what you did. 25% of the time, it is the same but not as good. 25% of the time it is better. This means that 50% of the time or more, you can still publish. And what about the 25% time that what got published is better than your own? In that case, you have a great opportunity to learn. Ask yourself: "How SHOULD I have been thinking to solve the problem in this fine way?" This is how I discovered, as a young engineer, that I should learn something enormously powerful called "Modern Algebra." It's one reason I switched from Electrical Engineering as an undergraduate major to Mathematics as a Graduate major. Of course, this was before there existed anything called Computer Science. Still on THINKING... The importance of PARADOX and CONTRADICTION. When you can prove that a statement S is true, and you can prove that the same statement S is false, then you KNOW that that you're on to something: Something is wrong somewhere. Never underestimate the power of a contradiction. It is one of our most potent sources of knowledge. Examples include the Liar Paradox "This statement is false." with its applications to Set Theory and our understanding of language. There are the seeming paradoxes of countability and uncountability, In CS, there is the apparent paradox that leads to The Halting Problem. Physics has lots of paradoxical material: Quantum Theory. The Einstein-Rosen-Podulsky Paradox. The relativistically speeding Twins. The wave and particle nature of matter. Here's an ASIDE on my current work, also based on paradox: I am personally interested in the Paradox of consciousness. Compare the following two views: 1. the view that the human is a MECHANISM, an automaton with substantial but finite internal memory, programmed like any computer to do whatever it does, and/or 2. the view that the human is a thoughtful observant creature with a God-like free will; that it is a CONSCIOUS ENTITY at the controls of a highly complex highly capable mechanism, choosing what to do from among options served up by/from its vast unconscious below. In my view, both these views are correct. How can that be? In his "Life of Johnson," James Boswell quotes Samuel Johnson as saying: "All theory is against the freedom of the will; all experience is for it." Johnson was 18 years old when Newton (age 85) was buried. Johnson knew that F=MA implied that humans are mechanisms. "All theory is against the freedom of the will; all experience is for it." This ends my ASIDE. Make a list for yourself of good ways to pursue a problem. My own favorite is to try small examples. By comparison, DAVID GRIES's favorite is to put himself in the middle of a (presumed) solution. An example is his coffee can problem: Given a can of black and white coffee beans, do the following: Pull out two beans: if both are the same color, replace them with a white bean. If the two are different, replace them with a black bean. What color is the last bean? Or try out the two methods on the Hershey Bar problem [Give an optimal algorithm to break an mxn Hershey bar into 1x1 pieces. At each step, you can choose a single rectangle of chocolate and crack it along one of its vertical or horizontal lines. A single crack counts one step. You are to make the fewest number of cracks] Brains are muscles. They grow strong with exercise. And even if they're strong, they grow weak without it. In the months before Kasparov lost to Deep Blue, his mother came after him. She was worried that he wasn't spending enough time exercising himself (on chess). Her worries proved well-founded. THE PhD: GETTING STARTED I remember a great summer job I once had at IVIC (Instituto Venezolano de Investigaciones Cientificos). A top neurophysiologist, name of Svaetichin, gave me a splendid problem... one that I unfortunately could not solve. The problem was to find a way to focus light on a single cell of a goldfish retina so that the light would not spill over onto any of the adjacent cells. Svaetichin had tried making a pinhole in a sheet of black tin, and shining his light thru the hole. This worked for moderate size holes, but failed for really small holes, which caused the light to diverge, to form diffraction patterns. Since Svaetichin couldn't solve the problem, I decided I couldn't. Or perhaps it's that I thought his problem physically unsolvable. In retrospect, I should have taken out books on physics, especially optics, read as much as I could, talked to others and kept on talking to him. Svaetichin would have helped me if I had shown him I was reading thinking working. Don't expect your thesis advisor to give you a problem that he or she can answer. Of course, she might. * She might give you a problem to which she already knows an answer. * She might give you a problem that she thinks is answerable, but that she hasn't actually answered. * She might give you a problem that is deadly hard. * If the problem she gives you is hard enough, I suggest you look for a NONSTANDARD answer. More on this later after I get done cooking the thesis advisor. Your thesis advisor may encourage you to work in an area that she feels completely comfortable in... in which case you can rely on her for sage advice and sound guidance. Or she may encourage you to work on something she knows little or nothing about, in which case it will be up to you to inform and teach her. In the latter case, you will have to learn all you can for yourself... You will have to learn from other faculty, from courses, from books, from journals. from peers. Both kinds of advisors can work out for you. I don't know that one is necessarily better than the other. But you should know which you got. Whatever you do, you got to like doing it.... You got to like it so much that you're willing to think about it, work on it, long after everyone else has moved on. THE PhD: DEEP IN THE MIDDLE OF IT. There's a wonderful quote from ANATOLE FRANCE: "A University Student" -- and this is especially true for a PhD Student -- "should know something about everything and everything about something." You know the jokes about PhD's...