Most scientists consider computers as tools they use for performing specific tasks, such as number crunching or data visualization. However, computers can play another important role in scientific research that is not yet sufficiently appreciated: the act of formulating a scientific problem in a computer language is in itself a useful step in understanding the problem, because computer languages enforce precision and do not tolerate ambiguity.
The first article in this issue introduces this aspect using an example well-known to every physicist: Langrangian mechanics. The second article discusses it in the context of computer science. The third article describes the role of computers in exploring rather than formalizing new concepts. The remaining articles provide applications from various contexts, ranging from high-school maths education to quantum mechanics or the construction of musical instruments.
One conclusion from these works is that scientists should not consider the time spent on writing computer programs as a wasted effort, nor try to delegate it to someone else at any cost. While writing computer programs has purely technical aspects (resource management, optimization, dependencies, maintenance, etc.) which tend to take up a lot of time, it is nevertheless an activity that contributes to scientific understanding.
Another conclusion is that computer languages should be considered a form of scientific notation. Unfortunately, very few computer languages were designed with this role in mind, and therefore scientists writing programs often feel that they have to wrestle with inconvenient notation. But computing is still a young field, so there is hope for improvement.
A final conclusion is that computers are likely to acquire more profound roles in science than number crunching or bibliography management. In the not so distant future, computers will change the way we approach scientific questions, from the first steps of exploring new concepts via the formalization of scientific models to the analysis of their consequence.
To make the best of the new possibilities that computers have to offer, scientists should take an active role in their development. Today most scientists see themselves as mere clients of the computer scientists and engineers who develop computing technology. I believe that a closer collaboration would be desirable, and I hope that this collection of articles will contribute to establishing a dialog about the roles of computers in scientific research.