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.