Communication Compactness

June 18, 2007

Languages support communication. Hence, mathematics is a language, just as much as English is. Languages may be ordered in terms of their “compactness”, that is, how many characters/words are required to convey a single idea in the given language. In general mathematics is more compact than English. A single idea can often be transmitted in one formula, or theorem. This is very unlikely in the communication of non-mathematical ideas in English. You will no doubt point out various exceptions, and I will say that they only serve to prove my point. I am in short, being a little loose. I am speaking generally.

Compactness explains why journal articles in law and literature tend to run fifty to hundred pages, whereas those in social sciences such as economics are about 30 on average. And many in physics, mathematics and computer science run just 10. This is by no means a value judgment, all I am doing is trying to elucidate this idea of compactness. Compactification of intellectual communication does not mean its all good. When communication becomes too compact, the quality and clarity of the communication suffers, resulting in lowering the value of the communication.

On the other hand, compact communication reduces the sheer physical size of the communique, meaning that it more likely to be read fully. I suspect that fewer people read the longer journal articles properly, and more people read the short ones. One way to test this hypothesis is to do so indirectly – see whether shorter articles tend to have more citations than longer ones, after controlling for quality somehow. I suspect someone will eventually run this research idea through the data.

Should academics in the field of literature seek to make communication more compact? Should they write fewer books and more short articles? I think not. In their case, the message is the medium, and many times, longer communiques are far more aesthetic. Likewise, in mathematics, artful compactification of theorem and proof is also highly aesthetic. In the end, depending on field, one has different trade-offs of clarity, size of communique, and aesthetics.

Compactness is obviously not a new idea, it is an obvious relative of the ideas in Information Theory (Claude Shannon) and Algorithmic Information Theory (Gregory Chaitin).

In my own field of finance, the size of journal articles appears to be growing. We are generating immense bloat in many journals. So, is there some way to determine what an optimal compactness is for research communication in any field? This may be a useful question because the answer enables us to ascertain what page limits might be imposed by journals in the field. But more important, readers will be able to get the most from the journals they read, by not reading too much or too little. I am going to leave this thought out there, just in case someone does come up with some way to determine what on average, optimal compactness should be. And in the name of compactness, I will stop here.


Method Supreme

June 4, 2007

Today was the penultimate class in my new course titled “Quantitative Business Models” (QBM) which comprises a collection of topics about the use of quant models used in various business settings. We studies topics ranging from optimizing portfolios to estimating systems using neural networks. The entire course is an eclectic collection of topics that do not fit inside any other course, nor do they form a meaningful thread in this course itself, apart from the common feature that all topics required somewhat advanced quantitative work.

The course was a list of topics I really wanted to learn about, and in my own selfish way, I realized that teaching was an easy way to pre-commit to my learning. I made this clear at the outset of the course, and warned folks that they were taking a big risk here. Since no one listens to me anyway, about twenty-five students remained, and I am immensely grateful. It has been one of my best teaching experiences ever. And certainly one of the best learning ones too. I hope it was as good for my students.

I think I have learned from experience that the courses I like the most are the ones where the teacher learns as much if not more than the students. When its a 2-way street, its not more an effort. This course was really hard in terms of the new things that needed to be learned before teaching, and I am sure it was hard on the students too, since they needed to come up to speed in gaining a pretty big new skill set, mainly from using a lot of mathematics, and translating that into working code using a widely used open-source econometrics/matrix language. But with feedback going both ways, it felt like no work, and all satisfaction. Last week I was away at a conference, and I missed the class.

On a more important note, this class did something else for me. At a time when education is being dumbed down, and in particular, as business education gets really soft, this course was like the last bastion of an age in which rigorous thought trumped fluffy verbiage. As buzzwords fill up the heads of business students, the chance to teach cleaner technique and eschew jargon felt like a breath of fresh air. In contrast to teaching how to sell snake oil, it was a relief to teach pure mechanics, and show that one can optimize a business decision in the old-fashioned way, that is, by thinking hard about a problem, and then applying apposite technique. Like in all business decisions, there comes a time when one needs to make a judgment call, but taking the analysis as far as it can go is an important pre-requisite that we must not lose sight of. Teaching QBM renewed my faith in the idea that there is hope left for the idea that business in schools may become a hard science, especially when it certainly seems to be heading that way in the real world.

I usually teach derivatives, and since these are zero-sum contracts, one always ends up feeling that a good derivatives trade is a scam perpetrated by the quantitatively adept on the mathematically inept. Or, one ends up teaching where arbitrages might be detected and how to profit from them. Maybe all of finance as a discipline seems tainted with this issue. So for a change, it was nice to teach QBM, where the purity of the techniques was given most play, rather than the “free lunch” aspect. It was more about the journey (technique) than the destination (making profit). Good method is its own reward.

Of course, this is just my view. Researchers fall into two broad types, those that enjoy the story and the others that enjoy the method. I fall into the latter group. A good story is what sells papers, but a good method still needs some story to go with it. Happily, this is not the case with the teaching side of QBM – the method tells its own story through the applications we looked at, but these stories never detracted from the pure enjoyment of the creativity embedded in these models. How I envy the people who first thought them up! If it is so much fun teaching this, how much more fun it must have been to discover these creative ideas. I am sure that in this class of more than twenty students, there is some chance that one of them will develop a whale of a good idea, what in the Valley we term a “killer app”.

Teaching method has another valuable feature – it trains the mind to think rigorously. It does not teach you what to say, but what to do. Actions speak louder than words, and the models are all about action. Action that is generalizable to other domains, because a thought process knows no boundaries. Its hands-on learning, and brings the satisfaction of learning by doing. In my case, learning by teaching. Today evening, as the class presented their projects, I kept on learning. For this gift, I am immensely grateful to all in class.