Causality, Complexity and Computers
15
carried out at the cellular or molecular level but is a property of the system
as a whole-or at least a considerable part of it. It is precisely because many
variables change within the system that the temperature does not change.
The temperature behaviour of each part is uninformative of the behaviour
of the whole. The whole, if not greater, is at least different from the sum of
its parts. These systemic properties can never be understood as a hierarchy
of causes. Their mathematical formulation usually involves non-linear and
often higher degree difFerential equations for which no explicit solutions
exist. They are, however, in many ways the most interesting and important
properties of organisms.
It has often been argued that, complex as biological phenomena might
be, there is usually some 'master-reaction' (see e.g. [1, 3, 6]) on which all
others depend in some simple manner. The phenomenon is said to reflect
the underhing single process. Confirmation of this view is sometimes
sought b\ demonstrating unitary behaviour, that is to say that some simple
model adequateh~ describes the situation. This is, however, rarely a sound
procedure. In e.g. the increases in weight of embryonic tissues one often
finds 'logarithmic' growth. This time/weight correlation may, on analysis.
be found to be a compound of increase in cell numbers, increase or decrease
in cell mass and increase in water content-none of them changing at the
same rate. The model of an 'autocatalytic' mechanism is clearly inappropriate
for anything but descriptive and possibly predictive purposes. This is not
to den\' that in sntllf cases a simple overriding 'master-reaction' will govern
the behaviour of a complex dependent system. But in biological phenomena
it may be safer to assume that simple effects have rarely simple causes.
Those who use Occam's Razor without due caution are likely to find they
have cut off more than their beard. The apparent unit process behaviour is
often due to a 5)'stem belial'iour, that is to the simultaneous response of many
interacting elements. In such cases the simple behaviour of the system is
not attributable to a simple master process on which the rest of the complex
system depends, hut on the contrary, the behaviour is the result of the
irreducible interactions of the whole. Our studies, both theoretical and
experimental, of linked enzyme systems, have shown that some of their
properties, which of necessity arise from the interactions of many components, behave remarkably like single processes. Although not attributable to anYone entin', a model based on such an assumption would
be a consistent one. It appears that there is a kind of saturation of complexity, that the addition of more elements or more interactions beyond
a certain level, merel" generates redundancy so far as types of behaviour
are concerned. Even now and then novel properties may arise, such as
oscillations, switchings and so on. But it appears that these behaviour
types are small in numher. The reasons for the apparent loss of complexity
will require discussion.
15
carried out at the cellular or molecular level but is a property of the system
as a whole-or at least a considerable part of it. It is precisely because many
variables change within the system that the temperature does not change.
The temperature behaviour of each part is uninformative of the behaviour
of the whole. The whole, if not greater, is at least different from the sum of
its parts. These systemic properties can never be understood as a hierarchy
of causes. Their mathematical formulation usually involves non-linear and
often higher degree difFerential equations for which no explicit solutions
exist. They are, however, in many ways the most interesting and important
properties of organisms.
It has often been argued that, complex as biological phenomena might
be, there is usually some 'master-reaction' (see e.g. [1, 3, 6]) on which all
others depend in some simple manner. The phenomenon is said to reflect
the underhing single process. Confirmation of this view is sometimes
sought b\ demonstrating unitary behaviour, that is to say that some simple
model adequateh~ describes the situation. This is, however, rarely a sound
procedure. In e.g. the increases in weight of embryonic tissues one often
finds 'logarithmic' growth. This time/weight correlation may, on analysis.
be found to be a compound of increase in cell numbers, increase or decrease
in cell mass and increase in water content-none of them changing at the
same rate. The model of an 'autocatalytic' mechanism is clearly inappropriate
for anything but descriptive and possibly predictive purposes. This is not
to den\' that in sntllf cases a simple overriding 'master-reaction' will govern
the behaviour of a complex dependent system. But in biological phenomena
it may be safer to assume that simple effects have rarely simple causes.
Those who use Occam's Razor without due caution are likely to find they
have cut off more than their beard. The apparent unit process behaviour is
often due to a 5)'stem belial'iour, that is to the simultaneous response of many
interacting elements. In such cases the simple behaviour of the system is
not attributable to a simple master process on which the rest of the complex
system depends, hut on the contrary, the behaviour is the result of the
irreducible interactions of the whole. Our studies, both theoretical and
experimental, of linked enzyme systems, have shown that some of their
properties, which of necessity arise from the interactions of many components, behave remarkably like single processes. Although not attributable to anYone entin', a model based on such an assumption would
be a consistent one. It appears that there is a kind of saturation of complexity, that the addition of more elements or more interactions beyond
a certain level, merel" generates redundancy so far as types of behaviour
are concerned. Even now and then novel properties may arise, such as
oscillations, switchings and so on. But it appears that these behaviour
types are small in numher. The reasons for the apparent loss of complexity
will require discussion.