20)

PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - -§

the two prices will, in general, again diverge unless A=o0 is
changed back to A=1.

Thus the purpose of the black box is to ensure that the
model stays in touch with reality. As I have said, the example
is a formal one, but there is no necessity in practice to restrict
the device marked B to a single, instantaneous decision.

d) Computability. With a large model, computability presents
 a problem at every stage: in the preliminary processing
of data, in estimating the parameters and in reaching solutions
for the system of equations. I have already emphasised the
importance of making a start and later modifying and extending
 the initial model; if to this is added the need to reach solutions
 for a wide range of initial assumptions, it is clear that
some special steps will have to be taken if the computing
problems are to be kept under control. As explained in greater
detail in [7] [44], a number of straightforward techniques are
useful for this purpose.
First, the extensive use of matrix algebra, in addition to
its notational convenience, has the advantage that in the numerical
 manipulation of matrices a fundamentally simple set
of operations is repeated a fixed number of times. This number
depends on the order of the matrices and can be regarded as
a parameter of the programme. Accordingly, if the number of
categories in some classification has to be increased, it is only
necessary to change a parameter and continue with the old
programme.
Second, great convenience lies in the computer’s facility
for handling iterative or relaxation processes. By requiring a
sequence of operations to be repeated until some numerical
condition is satisfied, the same master programme can be retained
 when linear relationships, which would themselves admit of
direct analytical solution, are replaced by more complex relationships
 which would not. To do this, a general method of
solution must be adopted at the outset.

‘1] Stone - pag. 18