Information Technology Reference
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The mathematician, given the purpose of the model, will select the right combina-
tion of calculations. This understanding of how to use the model to make appropriate
predictions will be called 'heuristic knowledge'. Heuristic knowledge may be con-
sidered to be the result of another form of inference since it requires a similar kind of
insight observed in abduction; the perception of the significance of certain particulars.
The design of this slide (the artifact) currently uses two models: the model of
forces represented in mathematical terms, and the model of spatial relationships that
uses a scaled projection of the slide on to two dimensions. The two models are two
different abstractions from experience and two different abductions from theory.
The two models are related in that there is a clear mapping between points of
contact. In this case, the points of contact are the angle of the slope and the direction
of the forces acting on the Body 1 . Other design tasks, such as the construction of VLSI
chips, will use nine or ten different models to represent different abstractions of the
same object. Each of the models is related to some theory that uses a generalization
of the characteristics to be controlled and formed in the design. A theory is only
useful if it provides this control. The control is incorporated in the constraints (lawful
behavior) and in the procedures for deriving the consequences of any design decision
within the domain of the theory. Hence, the laws of electronics (e.g. Ohm's Law)
provide a means through which particular circuits (electronic models) may have
predictable performance.
Related to each model type are one or more preferred representations and a means
of deducing measurable features of the artifact. Before the invention of Cartesian
Projection as a method of depicting a normalized view of objects, the only means
of representing spatial relationships was through sketches. Sketches (or perspective
drafts or drawings) do not allow the possibility of extracting measurements or making
detailed predictions of the distance between any two points on the object. Sketches
do show certain ordinal relationships such as next, above, below, inside and meshing.
However, the Cartesian projections, with the aid of a ruler and in some cases a little
geometry, will provide not only this ordinal information but will also give a prediction
of the distance between any two points.
Figure 10.6 shows details of the elements involved for one of the models in de-
signing the slide. The theory involves both the representation scheme (mathematics)
and the generalization of a particular aspect of the world (dynamics). The theory is
made explicit by the model in the form of equations (case). Both the theory and the
artifact influence the model. A mathematician interrogates the model using calcu-
lations. This person is usually the same person as the designer and who may use a
calculator or lookup tables. The engineer must be able to interface with the artifact
(the construct) through measurements (e.g. the angle of slope and the acceleration)
in order to provide observations that can be compared with the predictions of the de-
signer; the artifact must engage the model. The mathematician, engineer and designer
indicate the skills (tacit knowledge) required to progress a simple design.
1
The triangle of forces is not shown.
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