Collective Knowledge

At the moment, I have a few drafts I am writing but they are not progressing very fast and I am offering this short reflection. Looking around and reading different kinds of research, I can't help but feel that there exists a hierarchy of collective knowledge. Science is part of that hierarchy but it is not the whole story. As somebody who is strongly mathematically inclined, I have a tendency to view formal mathematics as the only means for expressing one's understanding but this position does not hold water. Since I am also very interested in methodology, namely, how we program and how we do mathematics, I have to have considerations for human activities and those are particularly hard to formalize and one might wonder what need we have of formalizing them. It must be honestly revealed that the activity of formalization demands tremendous efforts which are not carried out merely for the beauty of formal theories (although, many don't need much more motivation for doing it). The point is that, at any time before embarking on a formalization project, it is worth it to wonder if it is worth embarking on. On one hand, there is a class of programming languages, of which C++ and PL/I are nice representative, for which the formalization is not worth the effort because they are so complex and there documentation is so ambiguous that the formalization amount to reinventing them. Also, while reinventing them for the sake of formalization, for survival's sake, one should have the reflex of questioning every design decision before deciding to adopt them and, doing so, one would not end up with C++ or PL/I but with a language à la Wirth. If we carried that judgment to a further conclusion, it can also mean that they are not worth using either. On the other hand, there are subjects which are worth studying but the gain of a formalization is not immediately obvious. We have other tools than formalization to be rigorous and precise in our discourse and should not neglect them (to name only one: we have our natural language for which an exceptional mastery can do wonders). Once the benefit of formalization is seen, though, one should not hesitate. At the moment of writing, I am thinking about the general literature about programming methodology (aka software engineering). I have the feeling that although some publications concentrate on giving examples of the use of a particular method, some succeed at being very rigorous by being modest and accepting that they are merely working with one example. Also, their rigor seem to rely on the analysis of their example, of what helped and what did not. On the hand, some very disappointing papers on the topic try to be more rigorous by building a tool, having a handful of programmers use them, measure (in some vague sense) the improvement in their productivity and publish the statistic. Without a theory to compare those numbers to, they are meaningless and I can't help but see it as another instance of the general hype around statistic which I would summarize with "a number is better than no numbers at all". Simon Hudon Zürich, September 5th 2009