(NOTES added 6/18/08) I thank  all the readers for their comments and remarks. I am traveling and have no access to Chinese writing hardware. Consequently, I cannot answer in Chinese or correct some minor inaccuracies in the Chinese translation of my article below for now. I intend to supplement this note upon my return.

  

Conventional wisdom portrays science as innovative (創新) and liberal in thinking in the sense that it is willing to consider all kinds of ideas. But in another sense, science is very conservative. Truly new ideas comes only once in a long while and often after a great deal of struggle for acceptance. This is actually not bad and the way it should be. The world is full of people with or without scientific training who believe they have discovered the truth or invented something remarkable, such as the perpetual motion machine. As a professor at Harvard, I have often received or have letters referred to me written by a person who either

1.       Feels that s/he discovered some new truth but received no support. S/he wants Harvard to look into this injustice, or

2.       S/he has invented a new device that will change the world in revolutionary ways. Would Harvard endorse this device?

Let me say that in my 46 years I have encountered many letters of the above type that are not worth the paper on which they were written. Even well educated people can sometimes delude themselves. As a result science often looks upon any claim of new discovery or breakthrough with a jaundiced eye particularly if such claims come from people one does not know.  Consequently really NEW results often have to face a considerable struggle for acceptance. The history of science has many of such incidents both positive and negative (e.g. the discovery of the pseudo planet PLUTO, and cold fusion results in the 1990s). And if science is under the supervision of politics and too closely tied to economics, then even more abuses can result. I don’t need to repeat well known historical examples. But even if science is free from politics and commerce, new ideas still must struggle to get accepted.

I shall relate a personal experience a generation ago that may be of some value to scholars who are facing similar situations.

First a bit of background. The successes of aerospace control including the moon landing in the 60s are based on modeling dynamic system by nonlinear differential equations and developing a class of control strategies using linearized (perturbed) equations of motion. During the 70s myself and others began to study non differential equation based dynamic systems, e.g. discrete manufacturing processes, communication networks, airport operations, et al. These systems, denoted as discrete event dynamic systems (DEDS), are governed by man-made rules of operation and traditionally belong in the domain of Industrial Engineering  and Operations Research (IEOR). But for me coming from control theory, the natural impulse is to see if we can duplicated our successes in differential equation based dynamic systems for these new DEDS. I also viewed this as an opportunity since researchers in IEOR up to that time  have not emphasized the dynamic aspects of these systems. Lastly, demand for my consulting expertise from industry also were coming from these areas.

Anyhow, my first thought was to see if it was possible to develop some sort of perturbation analysis for the motion of these discrete, nonlinear, discontinuous dynamic systems. The rationale behind this is to develop answer to the question “what will happen to the behavior and hence performance of these DEDS if I make a small perturbation in some design or control parameter of the system.” The significances of such question/answers are obvious. However, strangely enough traditional OR never bothered to ask such a question perhaps thinking that the obvious discontinuous nature of the system behavior renders such question meaningless at the time. The accepted practice is to make two separate experiments or simulations where everything is kept the same except for a small perturbation in the control or design parameter. The difference in observed performances in these two experiments when divided by the small parameter change gives the sensitivity (gradient) of the system performance with respect to the parameter perturbed. If sensitivity for n parameters are desired then n+1 experiments must be performed. The gradient thus calculated is also prone to numerical error and instability due to the fact that you are dividing a generally small and noisy difference by another small number. This is the state of the art when I first announced in 1981 that we have an entirely new way of computing this sensitivity using only ONE simulation experiment regardless how many sensitivities are required. Furthermore, the calculated sensitivity are numerically stable and much more accurate then those computed by differencing method traditionally. The basis of such a claim came from

1.       A real life consulting job starting in 1976 in connection with the manufacturing operations of a well known automobile company

2.       Through extensive simulations, experimental verifications, and intuitive commonsense ideas  we found we could actually accomplish the above claim for this particular manufacturing problem.

3.       I gradually realized that the idea embodied in the solution #2 above can be in fact be generalized to other simulation experiments. During travel in China in the summer of 1981, one afternoon in Wuhan I had an epiphany and came up with a “proof” (rather an intuitive but at the same time analytical understanding) as to why this scheme works in general. Of course by strict mathematical standards, my “proof” was far from rigorous. But it was back up by extensive amount of experimental evidence and is conceptually correct.

Of course to arrive at this point, we already had solved a real problem, accumulated a large amount of experimental evidence, and published a couple of engineering papers in our own field. Given #3 above, I felt I was ready to announce the “breakthrough” to the IEOR world.

The immediate reactions of the IEOR field was

1.       Who is this person we have not heard of before ? (although I was established in my own field, I have not published in the IEOR field nor have I attended their conferences)

2.       This new result cannot possibly be true. Otherwise we would have discovered it long ago. My paper submitted for publication in OR journals was summarily rejected

3.       When I appealed about the rejection, one editor in OR in fact took the trouble of writing to the editor of the control journal where I first published my early results telling the control journal editor that my results were wrong.

4.       Another person in OR took the trouble writing to the National Science Foundation complaining that the government was wasting taxpayers’ money in supporting my research.

If I was not already established and have credibility in my own field, imagine what #3 and #4 above would have done to me even in an environment where no politics nor commerce were involved.

Actually, these struggles were a blessing in disguise. Myself and others who believed in this were forced to come up with a more rigorous proof of the result and actually sharpened the conditions under which the result is mathematically correct and true. Eventually three books and over 1000 published paper came out of this struggle and the sub-discipline of Perturbation Analysis (PA) became established. Professor Xiren Cao of  the Science and Technology University of HongKong is the leading expert on PA and his new book on the subject just came out 2007. I bear no ill feelings towards the field of IEOR and in fact became an accepted member of the field if only grudgingly. I mention this in detail only to illustrate that the conservative nature of science is necessary and not a bad thing  in general. At the same time, my own opinions is to  recommend researchers in general look far and wide in neighboring fields and not spend ones whole career in one sub-discipline. There is much to be said for learning about a new field.

 

 

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