Classical Morphology of Plants as an Elementary Instance of Classical Invariant Theory

It has long been known that structural chemistry shows an intriguing correspondence with Classical Invariant Theory (CIT). Under this view, an algebraic binary form of the degree n corresponds to a chemical atom with valence n and each physical molecule or ion has an invariant-theoretic counterpart. This theory was developed using the Aronhold symbolical approach and the symbolical processes of convolution/transvection in CIT was characterized as a potential “accurate morphological method”. However, CIT has not been applied to the formal morphology of living organisms. Based on the morphological interpretation of binary form, as well as the process of convolution/transvection, the First and Second Fundamental Theorems of CIT and the Nullforms of CIT, we show how CIT can be applied to the structure of plants, especially when conceptualized as a series of plant metamers (phytomers). We also show that the weight of the covariant/invariant that describes a morphological structure is a criterion of simplicity and, therefore, we argue that this allows us to formulate a parsimonious method of formal morphology. We demonstrate that the “theory of axilar bud” is the simplest treatment of the grass seedling/embryo. Our interpretations also represent Troll's bauplan of the angiosperms, the principle of variable proportions, morphological misfits, the basic types of stem segmentation, and Goethe's principle of metamorphosis in terms of CIT. Binary forms of different degrees might describe any repeated module of plant organisms. As bacteria, invertebrates, and higher vertebrates are all generally shared a metameric morphology, wider implications of the proposed symmetry between CIT and formal morphology of plants are apparent.