Scientism and Values.pdf - Ludwig von Mises Institute

184 Scientism and Values
To illustrate this discussion it is convenient to consider the array of
points resulting from plotting the weight of an organism against its
age; the principles will apply to any other measure of size while the
extremely difficult problem of shape (Medawar, 1945) will not be
considered. In general, this array of points will lie scattered about
some line which is a picture of the general trend of growth of the
animal, and our first problem is the description of this line. Such a
line can give no information about fine details, but is rather like the
line depicting the track of a railway on a continental map; the general
direction of the railway is shown, but small variations do not
appear.
There was a time when many workers thought it possible to find the
fonnulation of such a line by a priori methods, by thinking of chemical
metabolism, surface absorption, and similar notions. There have
been numerous examples of this kind, and perhaps the best known is
Robertson's autocatalytic theory and the resulting curve. We are now
more fully aware of our inability to specify the many factors that may
be responsible for growth in terms of a few parameters, let alone
finding a mathematical statement about their relationships; in any
case, such a relationship would be of such a complexity that it would
not be expressible in terms of simple mathematical functions. Further
it must be remembered that if any such function were fitted to the
data, no demonstration of closeness of fit can ever prove the curve to
be that one which is in any sense the unique "true" curve.
At the other methodological extreme we should be tempted to use
the purely mathematical approach and use a polynomial of such a
degree that the fit was adequate. This would be statistically highly
satisfactory, but it would be very difficult to interpret the resulting
curve and to assign a biological interpretation to the parameters involved.
Consequently, we must consider a more empirical approach, and the
two criteria for choosing a curve would seem to be that it must
provide a good statistical fit and also have a reasonably simple functional
expression involving the number of interpretable parameters.
. . . Naturally, we shall draw on our biological experience where
possible and choose curves whose parameters have a biological significance.
. . . As is often the case in the application of mathematics to biology,
we see that we are well advised to combine our intuitive approach
with suitable mathematical methods....