Or asked about the torsional vibration of a galvanometer suspension, he studies a fiber loaded with any number of mirrors at arbitrary points along its length. The boundaries of the profession are perhaps not made sharper by this definition, but is has the merit of being based upon type of mind, which is an attribute of the man himself, and not upon such superficial and frequently accidental matters as the courses he took in college or the sort of job he holds. It is, moreover, a more fundamental distinction than can be drawn between, say, physicist, chemist, and astronomer. Next, we have a list of categories of usefulness for mathematics in service for industry, taken from 'Applications of Undergraduate Mathematics in Engineering' by Ben Noble, pp. If data can be interpreted in terms of a preconceived theory, it is possible to draw deductions from the data regarding things that could not be observed conveniently, if at all, without a great deal of additional experimental work.
Mathematics often provides a quantitative check on a preconceived theory.
If the data are incompatible with the theory, further mathematical study frequently aids in perfecting the theory. It is frequently necessary in practice to extrapolate experimental data from one set of dimensions to a widely different set, and in such cases some sort of mathematical background is almost essential. Mathematics frequently aids in promoting economy, either by reducing the amount of experimentation involved or by replacing it entirely. Sometime experiments are virtually impossible, and mathematics must fill the breach. Mathematics is frequently useful in devising experiments to check whether a theory is correct.