power laws like the pareto principle (that 20% of people are responsible for 80% of the outcomes in various organizations for good or bad) or the 1% rule of Internet culture are interesting to read.
are there power as that detail the productivity of scientists, engineers and mathematicians and if so does it follow these trends?
as an example in the us health care system, the most expensive 1% use 20-25% of all health spending. The most expensive 5% use 50% and the most expensive 20% use 80%. So despite the complaints about overutilization by healthy people, you have to target the most expensive 5% to save money.
I think wealth distribution in the us is similar. the top 1% have 20-25%,the top 20% have 80%,etc.
i used to think about a career in scientific R&D but realized I would never be anything but a low level cog. I assume in science there are similar trends, the top 1% come up with 20-25% of innovations, the top 5% maybe do 50, etc. by innovations I mean patents, discoveries, citations, new ideas, publications, products brought to market, etc.
i assume that like wealth there are a tiny number of hyperproductive outliers. Terence tao, Edward Witten, Charles lieber and Sheldon cooper.
can any math people tell me if there is a power law that applies to scientific productivity?
Productivity is incredibly hard to quantify. Yes you can count patents and citations, but both have problems. For one thing at many institutions a scientific paper might have 10 or more authors who contributed very unequally to the results in it. The authors names might be alphabetical, or in order of contribution, or by seniority so that may or may not help. Work in some fields may tend to be very much more cited that work in other fields because there are more people working in some field.
Having said that researchers and journals have looked into this issue and things like cite counts have been studied. There are various attempts to construct indicators of all this. One example is the h index. An author’s h index is the highest number such that s/he has h papers with at least h cites each. The Journal Impact factor is an attempt to quantify journals as to how important their published papers are.
Reviving this thread, I recently skimmed an article that attempted to discover if productivity (in science, art, sports, etc) followed a bell curve or more of a power law pareto principle shape. It was the latter by far.
http://www.tnonline.com/2012/may/26/guess-what-normal-abnormal
According to them, about 10% of people in science are ultra productive, another 10% are somewhat productive and the other 80% are below the average.
The paper is behind a paywall, and I don’t know if/how they break up the top 10% of performers. Like with the concept of the 1% (economically) in the US, that is misleading. It isn’t the top 1% (which includes families with two lawyers or doctors), it is more the top 0.01% who are growing far and away. So lumping in doctors with financial kingpins is a misleading way to characterize the 1% vs 99%. It is more the 0.1% vs the 99.9% or the 0.01% vs the 99.99%.
I have no idea if the top 10% in science is universally productive, or if it is an issue where the top 1% is ultra productive and the other 9% are highly (but not as much) productive. Or the top 0.01% are super productive, then another 1% who are extremely, then maybe 9% who are highly, or what exactly.
“Productive” is not quite the right word, I think. On the one hand, if you are not producing publishable papers at a fairly good rate you are not going going to be able to continue to get jobs and grants for very long, and will never get tenure.On the other hand, no matter how brilliant you are there is a limit on how many experiments you can get completed and written up in a year. The real difference comes in how influential you are, which can be at least roughly measured by how much your stuff gets cited. Some scientists get cited a lot, others hardly at all, and there is a positive feedback effect in that once you start to get a good reputation your subsequent publications are far more likely to be read and then cited than are otherwise equivalent (or even better) publications by some unknown.
In terms of influence (in the sense I outlined above), rather than productivity, I think it is much more likely to be the later than the former, at least in large fields where there enough researchers to make such statistics meaningful. I can’t point you at numbers (though they probably exist) but I have heard people at Caltech both gossiping and giving formal talks about this stuff. One guy (who was IIRC a Caltech Dean, with a non-negligible influence on national science policy) gave a talk in which he quite explicitly argued that most physics research labs at universities around the United States should be shut down, because their work almost never got cited by anybody, and the only people who did get cited significantly were at Caltech and, just maybe, a handful of other elite places (and yes, he had the figures to back this up). I asked if it was not important that there be a large heap, in order for Caltech to be able to be on top of it, but he did not think much of that idea. (Note, also, that Caltech is a very small university.)
What is more, even within an institution like Caltech (and, no doubt, other elité ones), there is an informal but very real hierarchy where some people are superstars and others are, relatively, grunts.
The field of scientometrics studies this:
Price’s Law says that 25% of scientists do 75% of scientific papers:
The impact of a scientific paper can supposedly be measured by the h-index:
Use of the citation index is total BS. The main citation index, ISI, appears to index only journals from major publishers, who presumably (they absolutely refuse to discuss it, so I can only presume) pay them to do so. The journal I help edit is free online. It referees papers in the usual way and probably turns down half of them. ISI will not index it. But they do index a Springer-Verlag journal called Homeopathy.
FWIW, I once read that for the average mathematician, the expected number of lifetime papers s/he will publish is double the number of what they have already published. (I am bringing the average down now, but I am 77 and probably won’t publish much more.) In particular, for the average guy who publishes his thesis, the lifetime expectation is 2. What this actually means is that most never publish another paper and a few publish a great many.
In the modern academic system published papers is not really a useful metric. When promotion or tenure is so heavily based upon publication rate, the system is skewed to the production of large numbers of only just good enough papers. Worse, there is significant incentive for the creation of poor quality forums for publication - and the little talked about, but clearly real - problem of circles of researchers who review and publish one anothers work with little to no external review of quality or even reality. A journal of Homeopathy an extreme, but clear, example.
Paper citation rate isn’t a good metric - it is usual practice to cite the work of the first publication that introduces something (which allows the citation trail to work well). This means that work that significantly extends the idea is often not cited nearly as much, making any metric of value of the paper badly skewed. (A friend of mine has the luck to have a such key paper. He doesn’t think much of the work published, he came up with an alternative model for some obscure physics, and as an alternative model, it gets cited with all the mainstreams ones, despite being of little value.)
Research funding has a habit of following success. So one successful round of funding, and you push out as many papers as is possible, and you can get on the gravy train. Next time around the number of papers defines an apparent “success” with your last grant, and off you go.
Different areas of science have fit and spurts of major progress at different times. Enabling technology, or a specific breakthrough, lead to times of significant discovery, and other times it is just plain slog work. And it is very hard to predict (essentially by definition.)
One criterion which is sometimes used to measure a researcher’s productivity is called the “impact factor”. A researcher has an impact factor of n if that researcher has written at least n papers, each of which has at least n citations. Thus, for instance, if I have ten papers with ten or more citations each, my impact factor is 10. I might have a whole slew of papers with fewer citations, and one of those 10 papers might have a great many more citations, but those don’t change my impact factor. This helps to weed out both those who just happened to have a single paper in the right place at the right time, as well as those who churn out huge quantities of junk.
Yes, Chronos, and if you’ll read my post, you’ll see that I linked to the Wikipedia article about that, which is usually called the h-index.
There are two laws I can think of:
1.) the more academic the work is, the less likely it is to be productive; and
2.) the more advances there have been in the past, the fewer there will be in the future.
I can attach numbers to them, unfortunately.
Ah, apologies, Wendell, I didn’t realize that was the same thing.
I take it that you meant to type that you can’t attach numbers, evidence, to them. That is entirely unsurprising, given that your “laws” are utter nonsense.
Well, they’re not nonsense at all. You can attach numbers to anything at all; that doesn’t mean the numbers mean anything important. I’m not against attaching numbers to things. I’m just saying attaching a number to something doesn’t automatically make it meaningful.
Take Marx, for example. An important economist, whose work was tremendously, world-changingly important. Of course, today, many people would say he was wrong, but it doesn’t change the fact that his work was important, but not academic. Or take Adam Smith. Many conservatives would say they agree with him (especially if they haven’t actually read his books), but his work was not academic, and I doubt (but don’t know) that his work his work has a high n-factor. Nevertheless, his work is tremendously influential, even foundational, in his field.
Modern academic economists, on the other hand, have work that’s hidden behind paywalls, is hardly ever read by anyone except other academic economists, and is not likely to have any impact on the world at all. Even if some of them (or even all of them) have high n-factors.
This is either meaninglessly pejorative, or tautological, depending upon your definitions.
Definition 1: relating to education and scholarship.
Is just pejorative - essentially saying any research that is scholarly is useless.
Definition 2. not of practical relevance; of only theoretical interest.
Makes the law tautological. Which is a waste of time.
This is just silly. It is only true if you can show ahead of time that there is a fixed body of knowledge to be found in the research area, you can define what it is, and show you are half way there. In almost any area of research endeavour there are fits and starts. Moribund areas get sudden new life with breakthroughs, new technology suddenly makes previously unviable areas rich grounds for new work.
Sure, if you are doing comparative literature studies on the work of Jane Austen, there is going to be a limit on what can be usefully done. But try telling anyone in any of the sciences your “law” and they will laugh in your face. Eventually, in some distant future, many areas will be mined out, but right now, in almost every area of serious research we are only beginning to get a grip on how big the questions are.
There is John Horgan’s interesting, and somewhat controversial book, The End of Science. He explored the idea of a limiting case of theories of everything, but unsurprisingly didn’t really read any startling conclusions. What makes the book a must read is the extraordinary list of people he interviewed, many of them very late in their lives, and his book captures some very important aspects of some of these people not otherwise understood.
Their work most certainly was “academic”. Smith was a professor. Marx had a doctorate and mostly wrote in a very difficult German academic style.
The very fact there are paywalls on stuff proves that enough people are willing to pay to read it to make the whole setup worthwhile and profitable for the publisher. Furthermore, many present day economists have a strong influences (for good or ill) on government policies right now, and who can say what influence their ideas might have in the future? Certainly not you.
Anyway, this thread is primarily concerned with the natural sciences, not economics.