Calculation

On August 29, 1907, the Quebec Bridge collapsed into the St. Lawrence River. This collapse can be traced to a failure to calculate.

Modern engineering practice is highly quantitative, and it is this quantitative practice that distinguishes engineering from the trial and error practice of earlier artistry.  When faced with a problem engineers most start with the tools of creative design: brainstorming, sketching, dreaming, editing,.. it's fun, exciting and produces many sketches on napkins or whiteboards.  But in engineering such ideation must be followed by analysis: are there quantitative specifications that define the need being addressed? Does the proposed system perform within this specification? Without building the system (trial), this question of fitness to purpose can be answered only by mathematical modeling, prototyping, and testing.  All too often failure to analyze leads to a system that fails (error).

Only naive approaches to engineering emphasize design without analysis. It is all too common to see students building a prototype system without any quantitative analysis of the system. This is medieval at best (although even early cathedral builders did some quantitative analysis).  Our ability to model the physical world using mathematics allows us to "test" a design before it is built.  Our ability to do this is not perfect, but it is very good and improving rapidly, especially as computational power increased.  In developing new ideas for radiation shield design my student and I have tested over 100,000 different designs using mathematical techniques.  Of course this is all done algorithmically, and we never personally look at most of these designs: they are generated and rated automatically using our ability to model reality.

The Quebec Bridge collapsed because the design was not sufficiently strong to hold the weight of the bridge; the steel members were not the correct size.  When the steel for the bridge weighed more than expected, there was no recalculation of the stresses in the members.  When the bridge span was lengthened from 488 m to 550 m there was no recalculation. The failure to calculate was a retreat to a naive process of trial and error.  And over 80 men died.