Mind, Body, World- Foundations of Cognitive Science, 2013a

mentioned in the current section are considered to be calculators for this reason.
In spite of the many-levelled differences between the abacus, electronic calculator,
difference engine, THROBACK, and slide rule, at a very abstract level—the level
concerned with input-output mappings—these devices are equivalent.
To summarize the discussion to this point, how might one explain calculating
devices? There are at least four different approaches that could be taken, and each
approach involves answering a different question about a device. What is its physical
nature? What is its architecture? What procedures does it use to calculate? What
input-output mapping does it compute?
Importantly, answering each question involves using very different vocabularies
and methods. The next few pages explore the diversity of these vocabularies.
This diversity, in turn, accounts for the interdisciplinary nature of cognitive science.
2.7 Formal Accounts of Input-Output Mappings
For a cyberneticist, a machine was simply a device for converting some input into
some output—and nothing more (Ashby, 1956, 1960; Wiener, 1948, 1964). A cyberneticist
would be concerned primarily with describing a machine such as a calculating
device in terms of its input-output mapping. However, underlying this simple
definition was a great deal of complexity.
First, cybernetics was not interested in the relation between a particular input
and output, but instead was interested in a general account of a machine’s possible
behaviour “by asking not ‘what individual act will it produce here and now?’ but
‘what are all the possible behaviours that it can produce?’” (Ashby, 1956, p. 3).
Second, cybernetics wanted not only to specify what possible input-outputs
could be generated by a device, but also to specify what behaviours could not be
generated, and why: “Cybernetics envisages a set of possibilities much wider than
the actual, and then asks why the particular case should conform to its usual particular
restriction” (Ashby, 1956, p. 3).
Third, cybernetics was particularly concerned about machines that were nonlinear,
dynamic, and adaptive, which would result in very complex relations between
input and output. The nonlinear relationships between four simple machines that
interact with each other in a network are so complex that they are mathematically
intractable (Ashby, 1960).
Fourth, cybernetics viewed machines in a general way that not only ignored
their physical nature, but was not even concerned with whether a particular
machine had been (or could be) constructed or not. “What cybernetics offers is the
framework on which all individual machines may be ordered, related and understood”
(Ashby, 1956, p. 2).
How could cybernetics study machines in such a way that these four different
40 Chapter 2