Excursus 015 – On Mathematical Analysis and in silico Experiments

Hossein Jorjani

First publication: 2026 – 06 – 30

Bacon’s methodological framework assumed the universal applicability of experimentation, an assumption that modern science has found only partly sustainable. In many domains— including astronomy, evolutionary biology, cosmology, and historical human development —direct experimental manipulation of phenomena is not feasible, whether for practical or ethical reasons. In such contexts, empirical inquiry proceeds through systematic observation, inference, and computational modeling, which collectively extend the experimental ideal into realms where direct intervention is impossible.

Whereas Bacon’s intellectual context relied primarily on logical analysis together with sensory engagement through observation and experiment, modern science has added a distinct epistemic resource: mathematical formalization. Mathematical modeling, largely undeveloped in Bacon’s time, now serves as a powerful mode of discovery, capable of generating testable predictions through formal abstraction. Its role extends beyond the quantitative description of observed phenomena: mathematical structures themselves often reveal consequences that become the objects of subsequent empirical investigation. Building on this foundation, contemporary research has added a further dimension: in silico simulation. Especially in fields governed by stochastic or highly complex dynamics (e.g., statistical physics, evolutionary processes, and systems biology). Modern science therefore no longer rests upon a single methodological ideal. Observation, experimentation, mathematical formalization, computer simulation, and comparative explanatory reasoning each contribute distinct forms of epistemic access to nature. Rather than replacing Bacon’s experimental method, these developments extend and complement it within a more pluralistic philosophy of scientific inquiry.

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