Notes on an Epistemology for Living Things - Understanding Understanding: Essays on Cybernetics and Cognition - page 255

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◊ ◊ ◊ ◊ ◊ ◊ ....

Since this is one of many possible definitions of p (3.14159 . . .), and p is a number,
we may take p as a (numerical) representation of this computation.
6.2 Call representations of computations of relations “second order representa-
tions.” This is clear when such a representation is written out fully:

R = Cmp ( Rel R ( , S ) ) , ij kl

where R ij and S kl are, of course, “first order representations” as before (3.3).
6.21 From this notation it is clear that first order representations can be inter-
preted as zero-order relations (note the double indices on S and R).
6.22 From this notation it is also clear that higher order (n-th order) representa-
tions and relations can be formulated.
6.3 Call a physical mechanism that computes an n-th order representation (or an
n-th order relation) an “n-th order representor” RP (n) (or “n-th order relator” RL (n) )
respectively.
6.4 Call the externalized physical manifestation of the result of a computation a
“terminal representation” or a “description.”
6.5 One possible mechanical metaphor for relator, relation, objects, and descrip-
tions, is a mechanical desk calculator (the relator) whose internal structure (the
arrangement of wheels and pegs) is a representation of a relation commonly called
“addition:” Add (a, b; c). Given two objects, a = 5, b = 7, it computes a terminal rep-
resentation (a description), c, of the relation between these two objects in digital,
decadic, form:

Add 5 7 12

(

,;

)

6.51 Of course, a machine with a different internal representation (structure) of
the same relation Add (a, b; c), may have produced a different terminal represen-
tation (description), say, in the form of prime products, of this relation between the
same objects:

( )

Add 5 7 2

,;

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6.6 Another possible mechanical metaphor for taking a computation of a rela-
tion as a representation of this relation is an electronic computer and its program.
The program stands for the particular relation, and it assembles the parts of the
machine such that the terminal representation (print-out) of the problem under con-
sideration complies with the desired form.
6.61 A program that computes programs is called a “meta-program.” In this ter-
minology a machine accepting meta-programs is a second-order relator.
6.7 These metaphors stress a point made earlier (5.3), namely, that the compu-
tations of representations of objects and events is not unique.
6.8 These metaphors also suggest that my nervous tissue which, for instance, com-
putes a terminal representation in the form of the following utterance: “These are
my grandmother's spectacles” neither resembles my grandmother nor her specta-
cles; nor is there a “trace” to be found of either (as little as there are traces of “12”
in the wheels and pegs of a desk calculator, or of numbers in a program). More-
over, my utterance “These are my grandmother's spectacles” should neither be con-