Natural laws and the qualitative residual. Examples of processes that are not indifferent to size are so abundant in natural sciences that one can only wonder how their existence may ever be ignored by other disciplines. At the microscale, organic chemistry offers innumerable examples where new qualities erneige after polymerization, i.e., after a certain scale is reached. For a topical illustration one may also mention the critical mass of atomic explosion. At the macroscale, in the theory of structures it is almost impossible to find a linear relation between homogeneous and perfectly divisible materials (iron, cement, insulation, etc.) and variables expressing measures of some quality (resistance to strain, elasticity, radiation, and so on). The qualitative residual of which we have spoken earlier is reflected in the non-linearity of laws such as these, which relate to two distinct categories of variables: one essentially quantitative, the other pertaining to quantified qualities.
The illustration recalls Herbert Spencer’s splendid analysis of the optimum size of a bird. As he explained, area enclosing volume grows faster than the it, and the latter, faster than its average diameter. To store energy efficiently the bird’s size must be large. But a large bird is heavy and beyond a certain weight the wing bones would have to be so long that they will break under the strain of lifting the body into the air. All individual processes whether in biology or technology follow exactly the same pattern: beyond a certain scale some collapse, others explode, or melt, or freeze. In a word, they ceased to work at all. Below another scale, they do not even exit.
(“Measure, Quality and Optimum Scale”, Indian J. of Stat., 1965, emph. added)