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Last Updated on May 10, 2015, by eNotes Editorial. Word Count: 1472

Instruction and Learning
Thompson’s text is instructional by its very nature. From the outset of the work, his purpose is solely as he himself describes it:

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To correlate with mathematical statement and physical law certain of the simpler outward phenomena of organic growth and structure or form, while all the while regarding the fabric of the organism, ex hypothesi, as a material and mechanical configuration.

The entire text is then divided by topic, each one an important aspect pertaining to the study of morphology. Chapter 9, for example, is a discussion ‘‘on the theory of transformations, or the comparison of related forms,’’ as indicated by its title. As in previous chapters, Thompson establishes first the context or frame of reference for the discussion. He repeats the path his work has so far taken, mentioning his consideration first of ‘‘the inter-relations of growth and form, and the part which physical forces play in this complex interaction’’ in the beginning of the book. Thompson then moves to another aspect of the same enquiry, which he calls ‘‘comparatively simple cases’’ in which he has tried ‘‘to use mathematical methods and mathematical terminology to describe and define the forms of organisms.’’ The text moves from Thompson’s attempts to assert the relation between mathematics and biology to his recognition that the laws and methods of mathematics can not only be used to enhance explanation of an organism’s growth and form but ‘‘are bound to underlie all aspects of physical science.’’

In the use of such review, Thompson demonstrates that he is not only a thoughtful scholar on a mission to prove a rather innovative thesis but also a thoughtful teacher, careful to take certain steps to make sure that even the least scientifically adroit individual can follow the discussion. His painstaking efforts to consider such an audience are also apparent in his continual address of such an audience, as he engages in the practice of reiterating points, repeatedly using specific language, such as ‘‘we begin’’ or ‘‘we have learned’’ or ‘‘we are apt to think.’’ Such statements, by their very nature, are statements of inclusion, demonstrating that the author considers his audience to be an important influence on the message he is trying to convey in the text.

Finally, the ideas of a particular chapter are supported by the careful use of example and illustration. In chapter 5, an analogy with snow crystals is used to apply ‘‘biological meaning’’ to illuminate the highly detailed nature of spicules or spicular skeletons and, by extension, the very beauty and nature of growth and form. For example, Thompson makes a statement on snow crystals: ‘‘the beauty of a snow-crystal depends on its mathematical regularity and symmetry; but somehow the association of many variants of a single type, all related but no two the same, vastly increases our pleasure and admiration.’’ He discusses the geometric nature of such snow crystals, or snow flowers, but he also offers illustrations to demonstrate some of the shapes a snow crystal may take. In this way, Thompson’s work reads more like a scientific textbook than a thesis on morphology (the study of growth and form).

Intellectuals and Intellectualism
Thompson undoubtedly takes great pains to bring his audience along with him in a consideration of the concepts of growth and form. At no time, however, does he suggest the topic is easily simpli- fied. His very mode of explanation is proof positive of the level of intellectual engagement necessary to figure out biological mysteries such as the study of morphology presents. He supports his assertions by quoting classic philosophers and scientists as well as more contemporary intellectuals, references suggesting an engagement of rational, intelligent thought.

On the theory of transformations, or the comparison of related forms, in chapter 9, Thompson draws on the principle of Aristotelian ‘‘excess and defect’’ in a discussion of the comparison of related forms. The reference is timely and reiterates the same ideas present throughout the text. On Aristotle’s definition of genus, or class of forms, the author states

he showed that (apart from those superficial characters, such as colour, which he called ‘accidents’) the essential differences between one ‘species’ and another are merely differences of proportion, of relative magnitude, or (as he phrased it) of ‘excess and defect.’

Another impressive aspect of such references is the endless variety they represent. Such variety demonstrates not only the level of intellectual engagement morphology demands, but it underscores the literal genius behind the work, namely Thompson. Throughout the work, he draws on the wisdom of philosophers Descartes, Goethe, and Hegel, astronomer Galileo, literary giant Herbert Spencer, and physicist Albert Einstein, with a decided authority, indicating Thompson’s varied background and great intellect.

Logical and Illogical
Thompson employs a hierarchy in the text to organize his discussion of morphology. The resulting movement of the text is very precise and logical in its construction, successfully demonstrating the author’s valid reasoning. Thompson very carefully guides his readers through the discussion. First, he states his thesis, working from a very general argument, namely, that

My sole purpose is to correlate with mathematical statement and physical law certain of the simpler outward phenomena of organic growth and structure or form, while all the while regarding the fabric of the organism, ex hypothesi, as a material and mechanical configuration.

The text then moves, chapter by chapter, in the same fashion, Thompson continuing to act as guide, but moving from the specific to a much broader context. The text moves, as stated by the author in chapter 4, from the subject of the single cell to the interaction between two cells to the activities of groups of cells and finally on to the study of the complex tissues to which cells contribute.

Great consideration is also given to the study of an individual topic within the scope of the chapter. Each topic is edified or strengthened by a matheO matical premise or formula. Accordingly, each mathematical formula is followed by an example, an instance in nature that puts the formula into a sharper, more practical perspective for the reader. For further clarity, each topic is also enhanced by the presence of detailed illustrations. Unexplainable phenomena are classified as being a function of the divine, the unexplainable; therefore, the illogical is made logical by default.

Nature and Its Meaning
Central to Thompson’s work is the investigation of morphology in relation to nature. Also central to the work is the author’s intense admiration for and fascination with natural forms of various kinds. His careful examination and consideration of such forms is apparent in the scope of knowledge that the author draws upon to explain the shape of a honeycomb or the crystals of a snow- flake. Thompson is apt to explain the smallest of physical aspects, taking care to account for growth and form in great detail, such as the form a splash of liquid takes. The appearance of a breaking wave of a splash, an observation based on what the author characterizes as ‘‘beautiful experiments on splashes’’ is described as

the smooth edge becomes notched or sinuous, and the surface near by becomes ribbed or fluted, owing to the internal flow being helped here and hindered there by a viscous shear; then all of a sudden the uneven edge shoots out an array of tiny jets, which break up into the countless droplets which constitute spray.

Employing such thorough description demonstrates the effort Thompson takes to consider his biological subjects thoughtfully. It is this methodology, a system of great care reflecting a serious consideration of the subject, that the author employs, which seems to support his respect for natural form.

Thompson does indeed demonstrate his love affair with nature in several ways. For example, the text often engages in nature worship, specifically in its references to various experts in various disciplines (i.e., philosophers, scientists, and physicists). It is not uncommon to find references to intellectuals like Pappus the Alexandrine, a Greek mathematician who spoke in admiration of the bee’s architectural skills, ‘‘that bees were endowed with a certain geometrical forethought.’’ In another instance, he mentions a ‘‘beautiful discovery,’’ a specific ‘‘Gestaltungskraft,’’ or molecular force.

Most fitting, perhaps, to convey the deep wonder and appreciation Thompson has for nature is found in his comments concerning ‘‘many a beautiful protozoan form’’ difficult to account for mathematically. His reaction to this challenge he thus states: ‘‘That Nature keeps some of her secrets longer than others—that she tells the secret of the rainbow and hides that of the northern lights—is a lesson taught me when I was a boy.’’ Nature is described as a great spectacle of mystery, wonder, and awe, personified, named, and, by implication in conjunction with Thompson’s gender reference, truly named the mother of all, or the final determinate in the study of morphology.

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