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From the Method of Division to the Theory of Transformations: Thompson After Aristotle, and Aristotle After Thompson

  • Thematic Issue Article: D’Arcy Thompson’s Conceptual Legacy
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Abstract

Aristotle’s influence on D’Arcy Thompson was praised by Thompson himself and has been recognized by others in various respects, including the aesthetic and normative dimensions of biology, and the multicausal explanation of living forms. This article focuses on the relatedness of organic forms, one of the core problems addressed by both Aristotle’s History of Animals (HA), and the renowned chapter of Thompson’s On Growth and Form (G&F), “On the Theory of Transformations, or the Comparison of Related Forms.” We contend that, far from being an incidental inspiration stemming from Thompson’s classicist background, his translation of HA played a pivotal role in developing his theory of transformations. Furthermore, we argue that Thompson’s interpretation of the Aristotelian method of comparison challenges the prevailing view of Aristotle as the founder of “typological essentialism,” and is a key episode in the revision of this narrative. Thompson understood that the method Aristotle used in HA to compare animal forms is better comprehended as a “method of transformations,” leading to a morphological arrangement of animal diversity, as opposed to a taxonomical classification. Finally, we examine how this approach to the relatedness of forms lay the foundation for a causal understanding of parts and their interconnections. Although Aristotle and Thompson emphasized distinct types of causes, we contend that they both differ in a fundamental sense from the one introduced by Darwin’s theory of natural selection, which was formulated as a solution to the species problem rather than the form problem. We conclude that Thompson’s interpretation of Aristotle’s approach to form comparison has not only impacted contemporary scholarship on Aristotle’s biology, but revitalized a perspective that has regained significance due to the resurgence of the problem of form in evo-devo.

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Notes

  1. These remarks of Thompson’s are admittedly speculative. Aristotle’s description is vague, and it is not clear which species he is referring to. See Thompson’s notes 5, 6 to HA 565a23-28 and note 1 to 565b6 (Thompson 1910).

  2. A related controversy Thompson didn’t comment on concerns the chronological and conceptual relationship of HA and the other biological treatises. Balme argued that, “HA was written by Aristotle during and following his stay on Lesbos, and after writing the other biological treatises” (Balme 1987a, p. 17). Lennox (1996) has noted that one needs to distinguish when and where research was done from when and where treatises were written. Moreover, even if HA was written after the Parts of Animals and Generation of Animals, the research there recorded corresponds to the preliminary stages of inquiry according to Aristotle HA 491a7-15).

  3. Moreover, in the 1960s the problem of form got dissolved in the framework of the Modern Synthesis, either by conflating it with that of adaptation, or by reducing it to the classification or the systematic description of diversity.

  4. The independence between the definition and the identification of species implies that essentialism and fixism were not intrinsically linked, as shown by the fact that Linnaeus himself speculated on the evolution of new species through hybridization among genera.

  5. As indicated above, Aristotle applies the method of the more and the less not only to parts, but also to activities. In several books of HA dealing with methods and processes associated with successful reproduction (books V, VI, and IX), Aristotle discusses reproductive organs in forms of various kinds, but much of what we find in these books, as well as books VII and VIII, is about animal behavior in relationship to their environments. These books might be interpreted as a proto-ethology and a proto-ecology more than as a proto-morphology.

  6. For example, Thompson translates 490b9-10 as follows: “There is another genus of the hard-shelled kind, which is called oyster; another of the soft-shelled kind.” In this passage, “another genus” translates ἄλλο γένος, whereas “the hard-shelled kind” translates τὸ τῶν ὀστρακοδέρµων [γένος] and “the soft-shelled kind” τὸ τῶν µαλακοστράκων [γἐνος]. In these two cases, γένος must be supplied, but it is the obvious complement for τὸ in both cases.

  7. For details, see the introduction to Peck’s (1965) translation of HA I-III, pp. v-xxxii.

  8. While the application of the method of connections led to the realization of its limits (for instance, certain elements might be fused or even be absent in certain groups as compared to others, such as digits in the horse limb), the topological method allowed transit across widely (apparently) unrelated animal forms.

  9. Aristotle does make “analogical” comparisons across kinds, such as between lung and gills, between feathers and scales, or between different kinds of wings (e.g., insect and bird wings). But these comparisons are based on function and not on shape or structure, what Owen called analogies as opposed to homologies.

  10. Aristotle writes that despite the apparently striking morphological differences in the location of their limbs (cephalopods have their feet towards the “front,” while in testacean mollusks limbs project out from the side), when looking at the disposition of internal parts, “the configuration of the body” is alike. And by this likeness he means, in modern parlance, topological sameness, since a topological deformation (bending a straight line) is used to transform one digestive tract into the other (PA IV.684b20-25) (see Lennox 2002, pp. 311–312).

  11. There is a debate among Aristotle scholars regarding whether the conceptual schema genos/eidos is applicable to animal groups, such as birds or eagles (Balme 1987b), or parts, such as beaks or wings (Pellegrin 1987).

  12. While Aristotle’s understanding of correlations is indissociable from his causal interpretation of these correlations, the identification of correlations between parts has proved to be one of the greatest tools of morphology to unravel functional and developmental correlations (Olson and Miller 1958). As Thompson puts it: “if … diverse and dissimilar fishes can be referred as a whole to identical functions of very different coordinate systems, this fact will of itself constitute a proof that variation has proceeded on definite and orderly lines, that a comprehensive ‘law of growth’ has pervaded the whole structure in its integrity, and that some more or less simple and recognisable system of forces has been at work” (Thompson 1917, p. 728).

  13. This does not mean that the comparative study of form cannot be used for phylogenetic purposes. On the contrary, the reconstruction of phylogenetic relationships makes extensive use of morphological data. But the labor of comparative biology is epistemologically prior to the establishment of genealogical relationships, given that they are inferred from the acknowledgment of similarity among parts, and not the other way around (Patterson 1982; Rieppel and Kearney 2002). In the context of evo-devo, it has also been argued that the developmental explanation of homology depends on the previous identification of structural units, based on morphological criteria (Roth 1991; Wagner 1996). In this sense, evolutionary morphologists today seek to identify homologs by means of “operational definitions,” i.e., definitions that are necessary to reach a causal explanation without being themselves explanatory (Bolker 2000).

  14. This functional approach to living beings by no means entails that Aristotle was a Panglossian, a priori teleologist. On the contrary, he explicitly objects to the idea that every difference among animal forms should be explained in teleological terms. Instead, he argues that some biological traits necessarily derive from the formal and functional properties of other parts (PA IV.677a16-19). See footnote 15 for an example.

  15. For instance, in discussing a species of octopus with only one, instead of two, rows of suckers on its “arms” he explicitly explains it as a consequence of structure—this is a small octopus with very slender arms, so there is only room for one row of suckers. He then says: “It is not, then, because it is best that they have this feature, but because it is necessary owing to the distinctive account of their substantial being” (PA IV.9 685b12ff). That is, not only does he invoke a structural feature as necessitating the attribute in question, he is claiming that that structural feature is a defining feature of the nature of this kind of octopus, and he is explicitly ruling out a teleological explanation.

  16. “[P]aradigm set up in Heaven”: Thompson is quoting Plato’s Republic IX.592b2.

  17. Both Walsh (2015) and Austin (2018) refer to the contemporary reading of genos and eidos among Aristotle’s scholars.

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Acknowledgments

LNR expresses her gratitude to Alan Love and Sahotra Sarkar for extending an invitation to the workshop “Conceptual Legacy of ‘On Growth and Form’” in St Andrews, Scotland, where she delivered an oral presentation connected to this article. The authors would also like to acknowledge Alan Love and two anonymous reviewers, for their insightful comments that contributed significantly to enhancing the content.

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LNR received financial support from the Spanish Ministry of Science and Innovation (project # PID2021-127184NB-I00).

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  1. Complutense University of Madrid, Madrid, Spain

    Laura Nuño de la Rosa

  2. University of Pittsburgh, Pittsburgh, PA, USA

    James G. Lennox

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Nuño de la Rosa, L., Lennox, J.G. From the Method of Division to the Theory of Transformations: Thompson After Aristotle, and Aristotle After Thompson. Biol Theory (2023). https://doi.org/10.1007/s13752-023-00450-4

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