Abstract

Analogy is among the most widely studied pedagogical tools in science education, and every major theoretical framework governing its use, from Glynn's Teaching With Analogies model to Harrison and Coll's FAR Guide to Niebert et al.'s embodied analogy framework, treats the presence of shortcomings as a necessary and inescapable feature of analogical instruction. This paper challenges that assumption as a general principle. The Identical Scale Principle (ISP) is introduced, which proposes that an analogy has zero shortcomings if and only if two conditions are jointly satisfied: the source domain and the target concept are governed by the same physical law operating at different scales, and the student possesses direct sensory experience of the source domain. Drawing on physical law invariance, embodied cognition theory, and a systematic analysis of five confirmed examples, this paper demonstrates that the ISP defines a previously untheorized class of analogies that are not merely low in shortcomings but are structurally incapable of producing analogical distortion. The gap in the existing literature is documented, the theoretical rationale is developed, five exemplary cases are analyzed in depth, implications for teaching practice are drawn, and an empirical research agenda is proposed. The principle has significant implications for analogy selection, curriculum design, and the pedagogical frameworks that govern analogical instruction.

The full paper

The argument, the data, the figures. Open access on Zenodo.

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the author

Six frontiers. Seventeen years. Three Laws of Decision-Making.

Patrick Mehrhoff is a German entrepreneur, independent researcher, AI engineer, and author. He is the author of the three original theories that constitute the Mehrhoff Research Program. He built the work the studio carries.

Most practitioners spend a career inside one domain. He worked as a practitioner at six of the frontiers that redefined how society organises information, money, and value over the last two decades. The consumer internet, Swiss fintech, European monetary policy, Southeast Asian financial publishing, institutional crypto assets, and the first wave of applied AI.

The same structural observation appeared at every frontier. By 2019, on a whiteboard at crypto infrastructure provider Wyden in Zurich, the pattern had become visible to itself. It did not yet have a name. Four years before any AI language model became publicly available, the complete logic of the Three Laws of Decision-Making was already on the whiteboard.

The studio was built from Bangkok, without institutional affiliation and without external funding. The Rubens workshop model defines how it operates. The founder sets the intellectual direction at every decisive step. The tools and collaborators execute within it.

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