*Illustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]*

Laurence Hewes’s and Herbert Seward’s manual on the design of nomographs, published in 1923, is an unintentional masterpiece of analogue calculation aesthetics. The topologies and contours of these charts echo the systems they encapsulate. Fluid lines plot the parameters of hydrodynamic flow. Arcing parabolas delineate ballistic trajectories. Most lead double lives as (unperformed) musical scores.

Invented in 1884 by the French engineer Philbert Maurice d’Ocagne, nomographs are graphical analogue calculating devices that allow the computation of linear or non-linear functions. Now superseded by computers and electronic calculators, these diagrams were once the preferred method for calculating solutions to practical problems when a few variables were already defined within a complex system. Ron Doerfler’s The Lost Art of Nomography is a good essay on the history of these charts, it also explains exactly how they work.

The musician/performer David Tudor used the term nomograph to describe a notation he created for the performance of John Cage’s Variations II – we might wonder if Cage ever used the term himself ? Cage created scores that not only bare an uncanny resemblance to nomography but also use a nomographic process to generate musical events within his partially deterministic musical space-time. The projection of lines into two and three-dimensional space, and their resulting intersections with other lines and points, were used to define musical events in his works of the 1950’s such as Concert for Piano and Orchestra [1958].

*Illustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]*

*Illustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]*

In the visual arts Agnes Denes used nomographs for the basis of some of her philosophical drawings which she argued represented the metaphysical aspect of mathematics conveyed through aesthetics. She wrote, “I love mathematics because I could humanize it, and in turn it gave me perfection and beauty”. In her work The System [1970], she embellished the well known Smith Chart – a nomograph designed for solving radio frequency problems with transmission lines and matching circuits in radio frequency engineering.

*Score Page from Concert for Piano and Orchestra – John Cage [1958]*

*Score for Fontana Mix – John Cage [1958]*

*Smith Chart – Phillip H. Smith *

Further Viewing/Reading:

The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

The Lost Art of Nomography – Ron Doerfler [PDF]

David Tudor’s Realization of John Cage’s Variations II – James Pritchett

48 seconds on Mathematics – John Cage

Manifesto Mathematics – Agnes Denes [PDF]

Agnes Denes: Early Philosophical Drawings, Monoprints, and Sculptures

No. 1 — September 16th, 2015 at 6:18 pm

Another excellent post. Congratulations on your wonderful website. Keep up the job work!

No. 2 — September 20th, 2015 at 10:42 pm

I’m in love with nomographs. Excellent post!

No. 3 — November 19th, 2015 at 8:58 am

thanx Paul, since a long time im looking at your blog again, and it gives me a very nourishing feeling, as if coming home:)