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Mark Perakh's Web Site

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REINVENTING THE WHEEL

A personal report

By Mark Perakh

Posted August 17, 2004

The reason for writing this essay is the appearance of a paper by William Dembski wherein he introduces a measure of information he has dubbed "variational information" (the initial version of that paper has disappeared from the web but is available from the those who received Dembski's initial mailing, including me; modified version is at http://www.iscid.org/boards/ubb-get_topic-f-10-t-000086.html). Dembski emailed the initial version of that paper to a number of both his critics and supporters (I was one of the critics who received that email). In a remark accompanying the text of the paper, Dembski, among other things, wrote that he would appreciate critical comments, in particular because he would not like to "reinvent the wheel."

As it happened, Dembski indeed did just that – his "variational information" turned out to be a quantity known for over forty years as a particular case of Rènyi divergence (see http://www.cscs.umich.edu/~crshalizi/weblog/234.html).

In fact, there is nothing unusual in "reinventing the wheel." It has happened many times and even accomplished scientists are not guaranteed to be immune to such occurrences. Modern science and mathematics comprise such immense amount of material that rediscovering something long known happens now and then.

The situation is, though, not quite harmless if he who reinvents the wheel has been acclaimed as a great expert in a given field but in fact is shown to be unaware of significant developments in that field (as is the case with Dembski who is not only highly praised by his cohorts for his supposed breakthroughs, but also does not shy away from a self-aggrandizing claims (see, for example, www.talkreason.org/articles/revolution.cfm ).

Sometimes the existence of preceding results rediscovered by a researcher comes to light before his alleged discovery has been published. In such cases the "rediscovery" has little or no consequences besides a lesson to the researcher himself to do better next time. If, though, the announcement about the supposedly discovered wheel has been published, it may cause a considerable embarrassment for the re-discoverer.

If a scientist reinvents the wheel, the overall effect upon his reputation is largely determined by his behavior after his flop comes to light. If the researcher promptly admits his error, apologizes for it and does not insist that his work still is an important contribution to science, the embarrassment is usually mild, short-living, and easily forgiven. If, though, the offender tries to downplay his error and to wriggle out of the predicament by inventing casuistic arguments supposedly justifying his flop (as Dembski seems to be doing so far) it can only worsen his status even if his admirers continue fervently defend him.

All this reminded me how I once reinvented the wheel and what came out of it.

It happened in 1952. I was at that time a docent (which is the Soviet equivalent of the Associated Professor rank in the USA) at an institute in Dushanbe, the capital of Tajikistan (now an independent country but at that time part of the USSR)

One day my colleague, Yuri Nikolaevich Petrov, who was head of the department of machine repair technologies, approached me with a request. He and his assistants were conducting experiments wherein they studied ways to repair worn-out steel machine parts by reinstating their original dimensions through electrodeposition of iron layers on their surface.  Petrov showed me a steel plate upon which a layer of iron was electrodeposited. The plate, which was flat before the deposition of iron, now was bent. Obviously, the deposited layer of iron formed in a state of strong stress thus bending the substrate upon which it was deposited. Petrov asked me whether or not I could suggest a method for calculation of stress in the deposited layer on the basis of a measurement of its deformation.

At that time I was engaged in other projects. Tajikistan, like Japan, is a country where earthquakes happen for breakfast, lunch, and dinner. I was largely immersed in some problems of seismometry.  Still, I promised Petrov to think about his problem whenever I would have a window in my schedule.

The Party and the government took care of providing the necessary window: in a few days after my conversation with Petrov, the studies at the institute were temporarily suspended and all the students and instructors sent to the agriculture regions to pick cotton; the rain season was approaching and the cotton fields, as was usual for an economy ruled by five-year plans, remained unharvested.

While students picked cotton, we, the instructors, supervised them – and it would last for several weeks.

One day, during a lunch break, I found a semblance of shadow under the branches of a cotton plant, lay down and opened a notepad. By the end of the break I had a formula derived for calculation of stress in deposited metallic layers.  Satisfied, I ceased thinking of Petrov's problem. When we returned to the city, I went to Petrov and handed over my formula on a piece of paper torn from my notepad. I thought the matter was closed. I was wrong.

In a few weeks Petrov reappeared in my office. He displayed a bunch of graphs representing the stress in deposits as function of various parameters. He wanted to write a paper for a technical journal about his experimental data, and since he used the formula I derived for him, he thought I might be interested to be his co-author.

At that time I had a very few papers published (although I don't remember the exact count, it was certainly no more than around a dozen). The prospect of having a paper published was luring. However, I immediately realized that before writing a paper I needed to go back to my formula which was derived very hurriedly in a cotton field. I wanted to verify the formula's validity and to check whether or not a similar calculation of stress was conducted by somebody previously. At that time we had no PCs, no Google, no internet. A search of literature was a tedious and lengthy endeavor. I went to the library of the Academy of Sciences and solicited help from professional librarians versed in the required literature searches.  In a few weeks I had laid my hands on a paper that had a direct bearing on my problem.

The paper in question was published in the Proceedings of Royal Society in 1909, that is over forty years earlier. Its author was Gerald Stoney of the Cambridge University, the man credited with inventing the term "electron." (G. G. Stoney, Proc. Roy. Soc., A82, 1909: 172). Stoney had derived a formula for calculation of stress in deposited layers. To my astonishment my formula, derived under a bush on a cotton field, turned out to be an exact replica of Stoney's formula known for over forty years. I happened to reinvent the wheel.

I told Petrov that I could not be his co-author in the planned paper – he should simply refer to Stoney.

My feelings were ambivalent. On the one hand, I naturally felt a faint disappointment because of having reinvented the wheel. On the other hand I (also naturally for a beginning scientist) felt some satisfaction – I had effortlessly derived a formula which was deemed worth a publication in the Proceedings of the Royal Society!

I could hardly envision at that time that many years later (in 1978) the Royal Society would award me a prize for my research and invite me to come to England as their guest.

What happened, though, I became hooked on stress calculation. I started thinking about this problem and soon came to the conclusion that Stoney's formula, which I inadvertently rediscovered forty years later, was in fact wrong!  Stoney's (and my) error  was understandable, while its discovery required a rather deep analysis of the problem. Under the cotton bush, hurriedly deriving the formula, I simply repeated Stoney's error of forty years earlier.

Thus started my journey into the fascinating field of stress.  In 1966 I published (in Russian) a monograph on stress in films which in 1970 was translated into English and published in the USA by the National Bureau of Standards (now renamed NIST – National Institute of Standards and Technology). When this book came to attention of some IBM scientists, they arranged for my invitation as a visiting scientist to the IBM Research Center in Yorktown Height, NY. I came to the US and have been here ever since.

That is what came of my reinventing the (defective) wheel - a derivation of a long known and in fact erroneous formula under a bush in a cotton field.

So reinventing the wheel may not necessarily be a bad thing, even if the wheel is defective – what counts is how the wheel's re-inventor behaves when the facts come to light.