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Subtitle: The role of differential equations
In this article, I explain some of the mathematical context for differential equations to programmers who have not worked on scientific applications. This should help to orient them as we approach the next programming goal, which is to write an Euler-method simulator for the dynamics of a reaction network.
I picture a reader who is technically advanced, is capable of abstraction, and is motivated to learn, but has only been exposed to the typical applications which involve limited use of mathematics. They will have skills in discrete mathematics, in the analysis of process logic, in making complex deductions about the behavior of complex mechanisms, in data and process abstraction, and in the practical application of the scientific method to the experiments involved in fault diagnosis. But their work will not have led to topics in, for example, calculus or abstract algebra. Yet there is no impermeable membrane here. For instance, data abstraction falls under the heading of abstract algebra, and algorithms are both objects and vehicles of mathematical study.
Any reader with these credentials can be considered to be a virtual apprentice to science. And there are lots of them! Here it is estimated that there are 40 million programmers in the world; elsewhere, I saw an estimate of 2 million scientists. Further, they are human and so we can assume that the bulk of them are concerned about the planet.
These considerations must have strategic implications, both for the Azimuth project and for science itself.
The world's problems, as presented to science, are accumulating far faster than they are being solved. Our ship is in danger -- all hands on deck! We need more scientists, and we need broader public participation at the interface between science and society. This calls for an outreach effort from science to the broader public. To my mind, this either already is, or deserves to be, one of the core planks of the Azimuth strategy, because it is a vital way for scientists to contribute to the saving the planet. Whatever form they take, as programmers or otherwise, the virtual apprentices to science represent a potential base for the influx of people, energy and ideas into the Azimuth project. It is plausible that this kind of positive feedback could lead to an acceleration in the growth of planetary scientific awareness.
This blog article is an item of scientific outreach literature. Within the confines of a short and informal presentation, I attempt a rough explanation from the ground up of a fundamental mathematical idea. I try to keep it implicitly accurate, in the sense that with more space it could be elaborated to a rigorous presentation. I also aim to convey some of the "cultural flavor" of the subject, especially towards the end.
The article is ready for review. Thanks.