Models and Analogues in Biology

By J. W. L. BEAMENT Agricultural Research Council Unit of Insect Physiology; Department of Zoology, University of Cambridge

According to those elementary text-books which are the usual reference sources of biologists, physics is the science of measurement from which it might follow that bio-physics is the science of measuring the properties of life. Measurement is indeed a starting point in all physical experimenting but the core of physics is the formulation from measurement of relationships: the relationships between matter and energy. The eventual aim of the science is the reduction, or analysis, of formulated relationships into the terms of a number of statements or propositions which we call the 'laws' of physics and which we have come to regard as fundamental properties of the materials and energies comprising our universe. When a biologist looks at a text-book of physics and considers these 'laws'--the behaviour of heat or light or electricity in relation to matter and the exact way in which energy is transduced from one form to another--he cannot but be greatly impressed by their simplicity. The behaviours of physical systems are expressed by simple mathematical relationships: linear, integer geometric and first-order exponential equations. What he is inclined to overlook is that these expressions represent the behaviour of simple systems composed of very few inter-related variables. We must however distinguish very carefully between these statements of physical systems and 'theoretical' relationships, for it is supposed that matter and energy obey these 'laws' implicitly and exactly. It may be that these relationships are virtually undemonstratable in the exactness of their simplicity in practice, because all natural systems are systems of many inter-related variables--complex systems--and the great success of physics (some may say, the art of physics) is its ability to dissect complex systems, to control or to discount for all other variables in a practical system of complexity, while assessing a particular relationship between a small number of variables in it.

Although examples do not prove generalizations, it is expedient to remove apparent superficial objection to the general statement that the properties of matter and energy obey simple mathematical laws. Thus the original crude optical experiments led to the formulation of a simple equation representing the refraction of light by a spherical lens:

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If one takes a real thick lens and a beam of white light, the image is complex and one might suggest that the simple law does not hold. But if one considers

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