Recently, I was looking at the various costs involved in different research activities. I was thinking of questions like: what is the intrinsic cost of doing mathematical research? Why do research institutes require such high/lavish research funding when all that research basically needs is smart minds? Are all the grand architecture, good food, high pays, transport facilities etc. provided to researchers reflected in better research output?
For instance, in a time when land is scarce, when travel is expensive, are the huge amounts paid to have people from all across the world attend a research conference really justified? In a time when printing and publishing costs are high, are the huge costs that institutes spend on having well-stocked libraries worth it in terms of increased research output. Given the high costs involved in transportation, is it worth it for an institute to offer regular transportation
facilities to its students and faculties? Given the high costs involved with food and accommodation, why should institutes sponsor part of the costs?
These questions are particularly relevant in an era where many of these expenses could be cut down on significantly through the use of technology (at least in principle). A hundred years ago, communication across countries invariably meant physically going here and meeting; now, communication can happen over Internet, the phone, and voice/text chatting and conferencing. Of course, needless to say, these things don’t carry the same romantic flavour as meeting up physically and discussing problems over tea or coffee, but is the slight advantage
gained thus worth the tremendous extra costs incurred?
Really, how much is an atmosphere worth for research? How much are we willing to pay for things that “feel better” even though they involve greater costs in terms of time, money, and organizational power — like going out there and meeting feels better than communicating over a long distance?
Interestingly, I think it is still worth the high costs, the reason being, interestingly, that being at a place and in a right atmosphere is very critical to getting one started along the right path of thinking. Living in a ghetto even with a distant access to the greatest resources in the world, one may not develop the same ways and patterns of thinking that are needed to utilize those resources. Further, being in a place means that you and the others are “forcefully exposed” to each other, to an environment, to an atmosphere where “serendipity” occurs. The use of the word “serendipity” stems here from a write-up on the onsite library at the University of Chicago, where all volumes are kept onsite with the hope and belief that serendipity occur. Interestingly, analysis of book usage patterns at the University of Chicago also indicates that those who use Internet resources more also tend to use the print books in the library more. In other words, greater use of the new technology correlates positively with the good old print books.
However, the main issue (problem) with the old way of doing things (viz going nad meeting, holding physical conferences) is that it doesn’t scale. That is, it may be worth it to invite the top 40 people to an international conference, and they may genuinely get a
lot of benefit that justifies the costs and efforts. But one can’t invite the top 4000 people for the same: there are decreasing returns to scale.
On the other hand, the newer technologies and the approach of “each to his/her own” without grand institute funding, can scale effectively. To take an example, consider that an organization wants
to spread greater awareness in a particular area of cryptography. The organization could consider the following approaches:
- Start an organization/department that conducts research in this area: Great returns, but a lot of investment and hassles, high risk, and a long gestation-period.
- Hold a conference, workshop, or summer school: This can be done with less effort, and with more immediate returns. But a conference or workshop or summer school means travel expenses for the participants, accommodation and lodging expenses, and it requires people to shell
out a huge chunk of their time. Further, one cannot call a very large number of people to a conference.
- Encourage colleges/universities to start courses in those areas: Here, the scaling is more. The investment from the side of the organization is less. The focussed return on investment is also less — it is possible that many of those who benefit may benefit too
little or too late or may never “pay back” for the benefits.
- Prepare a series of books/lecture notes in the subject and throw them into the market: Again, this requires effort, but the advantage is again that the effort is far more distributed, the focussed investment may be less, and the reach is wider. Again, the effect may be diluted: after all, how many people will actually read the book?
- Put a free online resource on the subject: This again requires effort, which may in many ways be much less than the effort needed to prepare a book. The advantage of a free online resource is that the reach is much greater, the costs per person reached may be much less. On the other hand, the focussed impact may also be much less. Online resources, however, scale. It’s much easier to take an online resource from 40 to 4000 people than to take a conference size from 40 people
to 4000 people.
There are all sorts of approaches at different scales, with different kinds of immediate and long-term impacts, with different degrees of investment and different degrees of return to investment. Some of these, being newer, have not been tried so far, and so people may feel
reluctant to invest in them.
For instance, many people in the research profession find themselves shuttling from place to place, attending one conference after that, giving one lecture after another, following time-tested practices of knowledge dissemination and sharing. They may spend hours correcting
and solving homework problems. Yet, the amount of time they may want to shell out towards writing a book or creating a definition resource for general consumption could be much less.
Since individuals are invariable overworked and have to meet performance criteria, it is up to the institutes to say :do we want to scale up and reach out? If so, should we focus on creating resources that can be used far and wide, so that people are attracted towards our work? Or should we concentrate on financing only those things that are tried and tested, those that will give us immediate returns in the short run?
Why should scaling up be important? After all, people argue, research is not a commercial enterprise where we want to attract a huge number of customers and sell out to all of them. How does scaling up affect the few people who are currently doing a great job of it? Will it “dilute” the quality of research?
First, scaling up within a particular sub-discipline of mathematics may simply mean letting people from other sub-disciplines access the results of that sub-discipline with greater ease. It may help clear up the “confusions” and “misunderstandings” and “intellectual barriers” between sub-disciplines of mathematics. Thus, when the differential geometer wants to understand that little bit of algebraic geometry, he/she can use a free and easy-to-access algebraic geometry resource along with a couple of standard texts in algebraic geometry rather than hunting around for algebraic geometers, fixing appointments with them, and trying to attend conferences/seminars in the subject (of course, he/she could do these later — but is not forced to do it for a minor point).
In other words, people come to use the bigger and more precious resources (like personal discussions, conferences, lectures etc.) only after exhausting the smaller ones — which also means they come better prepared to gain value from the bigger resources.
Second, there are people in other professions/disciplines who need to use and understand mathematics, and not all of them may be interested in taking mathematics courses to get clear on a couple of definitions. Even those who are keen may not be fortunate enough to take formal courses or have personal sessions with people who can clarify their doubts. For such people, a bok can be a great help. An online resource designed for all people along with a book can be an
even greater help.
For instance, a physics student in my institute wrote in his blog that mathematics teachers urging him to understand the whole thing mathematically, was a principal factor in putting him off mathematics in the beginning.
Third, mathematics is not done only by people in the best of institutes who can meet each other. True, these may be the only people “producing new mathematics” but there are many others who are studying mathematics, either professionally or as a hobby pursuit. There are young student who are thinking of pursuing mathematics. There are people who could not pursue their dreams of research in mathematics and are stuck in more mundane careers, but would like to stay in touch
with the subject.