What Is Research?

June 1, 2007

Research and funding — some questions to be answered later

Filed under: Places and events — vipulnaik @ 8:26 pm

Today, I attended a Psychiatry Seminar at College of France. This was a seminar meant for the public, with short 15-20 minute lectures by a number of eminent people in psychiatry research (most of them working with INSERM in various colleges and universities in Paris, but there were also two outsiders who have talks in English).

The talks were about research in psychiatry, mainly focussing on the following things: schizophrenia,bipolar disorder, and suicide. Issues like the cause of these (genes versus environment), the relation between psychiatry and neurological symptoms, the incidence of these in the population, and the effect on behaviour and emotional pattersn, were discussed. Though I didn’t really follow all of them (both due to language and subject gap) I definitely got a good general idea.

I noticed some fairly basic differences between the way psychiatry stuff was presented, and the way I have seen mathematics stuff usually presented. For one, almost every slide of the psychiatry talks had references to studies! In fact, every claim made was substantiated by the name of some study, and usually a lot of effort was made to establish the credibility of the study for important claims.

Mathematicians also enjoy cross-referring to one another, but in mathematics, it is not mandatory to refer to a past paper or publication whenever using results first mentioned in it. This is probably because mathematical arguments (at least, the simpler among them) can usually be explained and followed on the spot; it is hard to do the same for psychiatric arguments.

The problem with psychiatric arguments is that almost any statement about human behaviour can be justified, or made to appear convincing, to at least some people. While in mathematics, the problem may be that intuition is hard to get, it is probable that in subjects like psychiatry, one may have too much intuition — only it may not always square with reality! Further, personal experience and beliefs, while they may be a very reliable way for making personal decisions, cannot be quoted authoritately at other people. Which is why psychiatrists need to use established studies to justify, or establish, any statement.

Another thing I was struck with, initially, was the fact that a lot of the psychiatry research seemed to be about fairly pointless things, or at least, about things that didn’t seem to have much of a direct impact to actual psychiatric treatment. However, a little shake revealed that I had no right to say such things as a mathematician! Which led me to some general introspection about the research world.

The world of research and academia usually functions like this sort of closed system, that takes funds from outside regularly at the one end and supplies the other end with some tidbits of knowledge and information at the other end. But the system doesn’t just work in the way that it takes funds from outside and sells back knowledge or information — it’s not just like selling things in the market. It is more like keeping an entire system alive, throwing in money in it at times, getting rewards from it at times.

And the system of research and academia, like any other, develops its own tentacles, its own bureacucracy, its own hierarchy, its own conventions. For instance the world of mathematics research can be thought of as having tentacles in math departments across the universities of the world, special math-dedicated institutes, journals devoted to mathematics, special research groups, and others involved in doing mathematics. There are whole hierarchies of thought, whole resources devoted to mathematics. There are conventions of whta is good mathematics and what isn’t. In other words, the world of mathematics research is some huge ecosystem of its own — except that it needs its supply of money from outside, because it can’t directly make money, and also that often the results it produces shake the workd a few deacdes down the line.

In some other subjects, the relation with the outside universe may be more intimate, and hence the inputs as well as the output may be more closely correlated. For instance, when the French government sponsors a study on the causes of autism in children, they hope that the study will produce results that will help improve the quality of children’s lives. Or at any rate, they hope it may do so. On the other hand, when the government sponsors CMI people to do research in complex algebraic varieties, they aren’t hoping for any immediate gains to anybody, rather, they are just hoping that the general body of knowledge would have improved.

Which leads to the question: what if those who are keeping the ecosystem alive by pumping in the moeny, suddenly realize that they’re not getting their money’s worth out of it? Or what if they ask the research world to change its practices for greater apparent gains in results? Or to put it another way” how much is the research world, or research community, making sure that those who are pumping resources into it are kept satisfied with its performance, viz they get their results?

I think this is where the small differ from the big. When one asks big money, and promises big results, one is basically saying — “Okay, we’ll create a flourishing ecosystem if you pump stuff into us, and this is what you’ll get out of it!” On the other hand, if one asks small money, and zero interference, one is basically saying — “Okay, give us whatever spare money you have, and don’t ask us any questions”. The first is asking for an investment, the second is asking for alms or charity.

It is an interesting puzzle to me how mathematics research has been lasting for so long — is it simply on the chiarity basis, or do people view it as a worthwhile investment? My feeling is that mathematics research has grown too big, and too influential, to be simply cut down or removed. Thus, even if mathematicians do not produce any direct results of use, they are so closely tied to the other ecosystems (which are of very direct use) that it’s best to keep them alive!

For instance, work by mathematicians in number theory, algebraic geometry, and group theory, is used in areas of computer science like algorithms, complexity and cryptography. The relation isn’t just of one output being processed as another input, rather, it is the fact that the comuter scientist working in these areas often seeks to learn the mathematics, and actively engage in discussions with the mathematician, to progress on his or her work. Similarly a lot of work in differential and riemannian geometry, as well as much of Lie group theory, has profound relations with physics in the new era, and the physicists (thouh they useslightly differernt jargon) are always keen to understand more of the mathematics involved.

So basically, suppose somebody decides not to fund the mathematics department to do mathematics research. As such, there may be no immediate loss. However, the people in the physics department may suddenly find that there is nobody to teach courses to their physcis students in Lie groups and Riemannian geometry. the people in the computer science department may find themselves unable to get a good supply of new ideas in their areas.

In some sense, the security of mathematics as a research discipline lies, not so much in the direct utility of its results, but in the link with at least two disciplines: physics and computer science. Another important reason why people do not want to destroy mathematics departments, of course, is that people who graduate from mathematics departments often do well on a number of areas involving finance and statistics, and investment/actuaries! And these are sure big money!

For instance, a fair bit of CMI’s funding comes from companies which hope to get recruits into CMI after the Masters program in Computer Science. Actually ,the Masters program in Computer Science, while fairly good, is not the highlight of CMI’s programme, and definitely, most of the CMI faculty and resources do not go into it! But by having this one crucial likn with the outside world, CMI helds keep itself afloat, gets a certain amount of sponsorship.

Thus, in some sense, mathematicians are the cleverest, they get their funding from people, not as charity or investment, but rather as a kind of indirect investment, which means they are not accountable to anybody directly! The mathematician may be imagined as the person who says — “You need me to be around, but I can’t be around unless you give me food to eat, and unless you give me a car to drive in, and unless you give me a house to live in. I don’t need these for your work, but these are my conditions.”

Unfortunately, this, though definitely a better attractor than charity, stil doesn’t get huge funds (which is true, after all, for the mathematics departments). The best funds will come in if the mathematician makes a case that the particular research being done is of use, rather than the give me the money to keep me happy line. I am not sure which mathematical projects qualify for loans and grants because of their particular importance. I am sure there are a few, but it certainly doesn’t seem to be something that most mathematics projects can boast of!

In coming blog posts, I will look at how unuversities, and funders, decide to support research, and how this differs across various subjects, with particular emphasis, of course, to mathematics.

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