Monday, February 23, 2009

the bigger picture...

The previous post about the importance of technical managers is just a small example of what I think is the importance of mathematics and science education in general.

At first people don't pay much conscious attention to design principles. They simply do whatever works. For a time this is sufficient. But soon people begin to think about efficiency. Maybe it's their competition or scarce resources, or their customers can't pay as much as they once did. Whatever the motivation, when people first start considering the constraints of a problem and how to solve those problems esthetically, designers are born.

But there is another layer beyond this. When economies drive down the costs of design and organizations must no longer consider the merits of a few designs, but rather must select against an endless sea of millions of designs and practices, the question becomes "what is the optimal design?"

This is the point where mathematics gets involved. Math is the language for describing systems and calculating their optima.

This pattern should not be surprising to anyone, but sometimes the conclusions are surprising. For one, it seems that any sufficiently advanced and refined problem domain comes to mathematics. Whether it's how to ship a million packages a day, or how the basic building blocks of life are sequenced in various creatures -- large scale almost begs for mathematical solutions. For another, it implies that no matter what your particular artistry entails, if you follow it long enough, you will end up having a mathematical interest of some sort.

This isn't that remarkable if you look at the trends of modern science: biologists are talking with computer scientists are talking with physicists... and all of these are talking with mathematicians. Even linguists, who started with a love and study of languages and etymology have branched into computational linguists who study language origins using statistical methods in mathematics. Some of the fields developed their own systems and specializations in the infancy of their fields that are only now being realized as special cases of more generalized fields in mathematics. Core topics like Set Theory and Ring Theory are now prerequisites for dozens of studies in the arts and sciences from biology to finance.

The lesson is clear: if you want to be the best at what you do, science and math education are the prerequisites.

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