The SCIENCE of engineering is the mathematics, physics, and scientific experimentation used to size the parameters and predict the performance of circuits, fields, mechanisms, and structures. Much of design engineering is the application of mathematics and physics to engineering problems. The ART of design is the knowledge of everything else that's useful and the skill to use that knowledge. Art backed by science produces good designs.
The science is quantitative; the art is qualitative. But the science also crosses over the boundary by teaching insight on the behavior of matter and energy. This insight enables design engineers to imagine and understand the behavior of devices to a degree that those untutored in mathematics and physics can't match.
Most of our academic engineering study was on the science. Mathematical physics and engineering require disciplined study in sequential order. One can't pick up a little calculus here and a little vector analysis there and accumulate understanding or utility. The only sure thing about using cookbook formulas is that they will be used incorrectly. (But I think it would be easier to learn the science of an engineering problem if a nonmathematical description of the corresponding art introduced it.)
Some people keep trying to make the art of design into a science. They employ the phrase "Theory of Design" in trying to write computer programs that will design. I once attended a convention of such program writers. They treated me with great respect as a "practitioner," because they had never actually designed anything. They seek "a unified theory for the synthesis process"—but don't hold your breath.
Most design books consist of parameter calculations. Voltage, impedance, power, stress, strength, deflection, frequency and amplitude, and other parameters are the subjects for mathematical analysis. Engineers learn these calculations in academ-ic courses, and nondegreed designers take calculation problems to engineers.
Computers have enormous value as mathematical instruments in the science of design. Computer-aided drafting is particularly helpful in the art of mechanical and electromechanical design. In the design of fields, like magnetic, heat flow, and mechanical stress distribution, finite element analysis by computer has no competition in accuracy from any other method.
Our study of the art of design began in childhood with toys, tools, and devices of life, and it shouldn't stop unless senility turns off our minds. This isn't poetic exaggeration. Any bit of knowledge may be useful when least expected.
For example, for the U.S. Post Office's first automatic mail sorter, my boss told me to design a code carrier to escort each moving letter, and a code detector for each stationary sorting bin. Both had to be all-mechanical because the Post Office had no electronic technicians then. There would be 10,000 code bit sensings per second, so he told me to design the action impact-free to minimize noise and wear. I argued, "It can't be done, and I can prove it mathematically!" He said, "Okay, it can't be done. But if you could, how would you do it?" I looked up at the ceiling and mentally saw an image of a recent Bob Hope movie. I sketched it, and my boss demanded, "If it was so easy, why did you give me such a hard time?" (Millions of these elements served until electronics took over 20 years later.)
The moral: all knowledge is grist for your mill. Also, be very careful about what you say can't be done. That way, you won't have to eat your words. Many aspects of design aren't subject to calculation at all. Consider "robustness," "aesthetics," and "customers' and managers' tastes and prejudices."