The Mathematical Components of Engineering



use. There is a qualitative, epistemological and cognitive restructuring of the
mathematics used by engineers as it becomes 'embedded' in engineering
expertise.

Division of mathematical labour and mathematical interfaces

The fact that the majority of design engineers can work without having to do advanced
mathematics is due to the sophisticated distribution of expertise in engineering practice.
We have identified and studied three main areas of divided mathematical labour:

4. Ubiquitous computer programs as design tools

The company uses a suite of standard programs for structural analysis, backed up by
some more specialist in-house packages. There is an issue of automation: the suite
could be made more integrated and automated, but the feeling of the user community
was to resist this1. In terms of sheer volume of mathematical calculations, computers
are the dominant labour force. The perceived relationship that the engineers had with
the computers is ambiguous: most said that they did not entirely know what the
computer was doing, but they understood (entirely adequately) what was required to
provide it with input and to make sense of its output. The ability to judge the
reasonableness of a result was considered a key component of this understanding.

5. Codes of Practice which distil knowledge and expertise into a form usable for design

For structural engineers, the various UK and international Codes of Practice represent
the baseline knowledge for practice2. They provide recommendations for the practical
design of, for example, steel and concrete structures, based on a combination of
accepted construction practice, experimental work on structures, and analytical
knowledge. The somewhat marginal role of mathematics to design can be seen in
these code documents: there is very little explicit mathematics or engineering theory
present. Guidance comes mostly in the form of ‘if-then’ rules and (underived)
algebraic formulae, which allow the engineer to substitute values of different
parameters to calculate quantities required for the design.

6. Analytical specialists acting as consultants to design practice

In the company observed, a small number of full-time specialists provide the
analytical expertise necessary for the design work of the majority: just 2% of the
professional workforce are regarded as analytical specialists. Specialists serve as a
‘line of defence’ for non-standard problems which do not fit the guidance provided by
Codes. In such cases, designers cannot simply draw on the ‘distilled’ analysis in the
Codes, and this distillation has to be undertaken by analysts, using some combination
of ‘first principles’ analytical calculations and advanced computational techniques.

A design engineer at work on a project must interact with the first two of these areas, and
in some cases, the third. As we collected more focused data, and progressed with the
analyses, we began to recognise the
mathematical interfaces that exist between specialist

1 Another example of that feeling, curious in the context of so much computer use, was to do with writing-
up design calculations: this is still very often done by hand, because it is dangerous to trust a machine to do
details, even the act of cut-and-paste in a word processor.

2 Other engineering disciplines are less tightly bound by such official, nationally-regulated Codes, but
‘codified knowledge’ is crucial to all engineers whether it is prescribed and controlled (inter)nationally or
locally to a particular specialist area, or particular company.

11



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