Consilient Analogies: Colometry, Euler's Method, and Generative AI for Computational Metrics

This article develops a structural analogy among philological colometry, Euler's iterative numerical method, and generative AI, with particular attention to recurrent neural networks. It identifies shared principles of sequential iteration, hierarchical discretization, and analytical reconstruction. Colometry segments poetic texts into rhythmic units, Euler's method approximates continuous dynamics through discrete steps, and generative models process sequences through recursive state updates. Drawing on Greek, Latin, and Sanskrit materials, examples from Homer, Tacitus, Cicero, the Rigveda, and the Bhagavad Gita illustrate the convergence, the article argues that these domains share a common local-to-global logic with potential applications in digital humanities and natural language processing, including the reconstruction of fragmentary texts and the development of rhythm-aware language models.