Bissell, C. C.
(2006).
Math? What math? How mid 20th century information engineers subverted mathematical formalism.
In: *Annual conference of the Canadian Society for the History and Philosophy of Mathematics*, 28-30 May 2006, Toronto, Canada.

## Abstract

During the first half of the twentieth century information engineers developed the fundamental theory of electronic circuit and filter design, telecommunications, signal processing, and control engineering. Much of this theory was rooted in linear differential equations, complex variable theory, and Fourier and Laplace transforms. Yet when it came to practical design, engineers developed a range of techniques that enabled them to exploit the power of the mathematical models underpinning their technological devices and systems without recourse to the classic formalism of the mathematics. Many of these techniques were graphical in nature, such as: the normalised time and frequency response curves of linear systems; the Bode Plots, Nichols Charts and pole-zero plots used in circuit and control system design; the Smith Chart and signal constellation diagrams used in telecommunications; and so on. These methods led to engineers talking a new language based on the characteristics of the graphical representations. Rather surprisingly, the humble decibel, originally a simple logarithmic expression of sound intensity, proved a particularly useful measure in this new graphical world.

This paper will demonstrate how these quintessentially engineering tools freed designers in the information engineering field from having to solve differential equations or deal with the niceties of complex variable theory. Perhaps rather surprisingly, most of these techniques have recently achieved a new lease of life as part of the interface between modern computer-aided design tools and designers themselves.

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