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已有 8515 次阅读 2009-9-5 22:57 |系统分类:教学心得

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The popularity of an earlier article How to Supervise Yourself (怎么自导博士论文) (visit count 8758 as of 9/5/09) made me realize how desperate for help Chinese ph.d students and young scholars are. Thus, here I pass on another bit of personal experience – how do know you have got a good research result? You need to be able to answer this question BEFORE you write a paper, prepare a presentation, and/or write to outside experts for recognition and help.
 
Indicators of Good Research Results – Simplicity in Science
 
It is almost an universal belief in science that a good result must be SIMPLE to state and its significance easy to understand. In big physics just compare Einstein’s formula vs the standard model of subatomic particles you will understand as to why we are not satisfied with the latter. Darwin’s theory of evolution is simple to grasp yet its generality covers the entire biological world. Of course the dictates of Occam’s razor is well known. Statistically, we are taught from day 1 that we must be parsimonious in the use of our modeling parameters.
On a much mundane level, I have always told my students that if during my exams they find themselves deriving complicated formula or detailed calculation, they can be sure that they are on the wrong track and should stop. My exams are always open book –thus one does not need to commit to memory anything except understanding. The really good students need not bring any books/notes/laptops to my exams. My questions are basically to test understanding of concepts. Most concepts worth teaching are simple because their essences have been distilled by many over the years. In fact, while innovation and discovery are important in basic research , another worthwhile task is to codify and simplify them so that they can be passed onto the next generation. To use a metaphor, a piece of raw granite is valuable, but carving, shaping, and polishing must be added to make it into a foundation stone for a beautiful edifice.
 
The same can be said for a piece of research one carries out. You must have an AHA moment (恍然大悟). It is in my opinion, a necessary condition for having done something worthwhile. At the very least, you should have learned that your struggle for the past few months now can be understood and taught in a few paragraphs of writing. It is what most scientists call “AN ELEGANCE RESULT”. This is something that defies definition and must be understood on an intuitive basis (只可以义会不可以言传). A conscientious advisor will consider teaching this appreciation to his student one of the most important duties. Or as when the US supreme court justice Potter Stewart was asked to define pornography, he famously said, “while I cannot define it, I know it when I see it”.
 
Finally, you may raised the question “what about research in complex systems or something fundamentally complex?”. Well, this should not stop you from trying for simple explanations and models. Probability is one way to hide complexity or capture complexity via simple formula/models. Everyone is familiar with the use of simple pseudo random generators to create random sequences; Steve Wolfram’s – a new kind of science – is another attempt to describe complex systems; lastly the negative result of No Free Lunch Theorem I mentioned in an earlier article “Why most things fail?” are additional examples of keeping complex things simple.
I end this article by listing a series of quotations
o   "Things should be made as simple as possible, but no simpler." — Albert Einstein (1879–1955)
o   "You can always recognize truth by its beauty and simplicity." — Richard Feynman (1918–1988)
o   "Our lives are frittered away by detail; simplify, simplify." — Henry David Thoreau (1817–1862)
o   "Simplicity is the ultimate sophistication." — Leonardo da Vinci (1452–1519)
o   "Simplicity is the direct result of profound thought." — Anon 
Good luck in your work!


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