It is here important to note a generally neglected situation: for centuries the form of living beings has been an object of study by biologists, while the morphology of inert matter seems only accidentally to have excited the interest of physicochemists. There are many disciplines of obvious practical use (e.g. meterology and the forms of clouds, structural geology and the geomorphology of the forms of terrestrial relief) for which there is a valuable body of experimental observation and occasionally some satisfactory local dynamical explanations, but scarcely any attempt at global integration beyond a purely verbal description. A similar situation exists in astronomy in the study of the morphology of stellar objects (and, in particular, spiral nebulae, which we shall consider in Chapter 6), as well as in the study of dislocations in crystalline lattices, a research inspired by the needs of practical metallurgy. However, the central problem of the study of the geometrical partition of a substance into two phases has never been systematically attacked; for example, there is no model to explain the dendritic growth of crystals.
The reason for this neglect by physicochemists is clear (note): these phenomena are highly unstable, difficult to repeat, and hard to fit into a mathematical theory, because the characteristic of all form, all morphogenesis, is to display itself through discontinuities of the environment, and nothing disturbs a mathematician more than discontinuity, since all applicable quantitative models depend on the use of analytic and therefore continuous functions. Hence the phenomenon of breakers in hydrodynamics is little understood, although it plays an important role in morphogenesis in three-dimensional space. D'Arcy Thompson, in some pages of rare insight, compared the form of a jellyfish to that of the diffusion of a drop of ink in water; it may happen that biological morphogenesis, which is better known, which takes place slowly, and which is controlled strictly, may help us to understand the more rapid and fleeting phenomena of inert morphogenesis.