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

as being tokens of a particular type, symbols do not have definitive properties.
Symbols are arbitrary, in the sense that anything can serve as a symbol.
The arbitrary nature of symbols is another example of the property of multiple
realization that was discussed in Chapter 2.
What we had no right to expect is the immense variety of physical ways to realize
any fixed symbol system. What the generations of digital technology have demonstrated
is that an indefinitely wide array of physical phenomena can be used to
develop a digital technology to produce a logical level of essentially identical character.
(Newell, 1980, p. 174)
This is why universal machines can be built out of gears (Swade, 1993), LEGO
(Agulló et al., 2003), electric train sets (Stewart, 1994), hydraulic valves, or silicon
chips (Hillis, 1998).
The arbitrariness of symbols, and the multiple realization of universal machines,
is rooted in the relative notion of universal machine. By definition, a machine is
universal if it can simulate any other universal machine (Newell, 1980). Indeed,
this is the basic idea that justifies the use of computer simulations to investigate
cognitive and neural functioning (Dutton & Starbuck, 1971; Gluck & Myers, 2001;
Lewandowsky, 1993; Newell & Simon, 1961; O’Reilly & Munakata, 2000).
For any class of machines, defined by some way of describing its operational
structure, a machine of that class is defined to be universal if it can behave
like any machine of the class. This puts simulation at the center of the stage.
(Newell, 1980, p. 149)
If a universal machine can be simulated by any other, and if cognition is the product
of a universal machine, then why should we be concerned about the specific details
of the information processing architecture for cognition? The reason for this concern
is that the internal aspects of an architecture—the relations between a particular
structure-process pairing—are not arbitrary. The nature of a particular structure
is such that it permits some, but not all, processes to be easily applied. Therefore
some input-output functions will be easier to compute than others because of the
relationship between structure and process. Newell and Simon (1972, p. 803) called
these second-order effects.
Consider, for example, one kind of representation: a table of numbers, such
as Table 3-1, which provides the distances in kilometres between pairs of cities
in Alberta (Dawson, Boechler, & Valsangkar-Smyth, 2000). One operation that can
easily be applied to symbols that are organized in such a fashion is table lookup.
For instance, perhaps I was interested in knowing the distance that I would travel
if I drove from Edmonton to Fort McMurray. Applying table lookup to Table 3-1,
by looking for the number at the intersection between the Edmonton row and the
Fort McMurray column, quickly informs me that the distance is 439 kilometres.
86 Chapter 3