U = I x R^2: the book's presentation of the equation
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How the published book presents the ARC equation and how it relates to the December 2024 manuscript's U = I x R and the papers' general U = I x R^alpha.

Canonical path: /research/blog/book-u-equals-i-times-r-squared.html
Author: Michael Darius Eastwood
Research programme: https://doi.org/10.17605/OSF.IO/6C5XB

U = I x R^2: how the book presents the equation Michael Darius Eastwood · Independent AI alignment researcher Published 3 July 2026 Michael Darius Eastwood · Book companion · 3 July 2026 Michael Darius Eastwood, independent researcher, London: author of the ARC/Eden research programme; the embedded-correction alignment thesis is recorded in a source record dated 8 December 2024 (sent-side SHA-256 f0d1f38f). The equation sits at the centre of the book's introduction, presented with more care than a slogan. At the centre of this book is something I call the ARC Principle, expressed in a formula that might seem deceptively simple: U = I x R^2. Universe equals Intelligence multiplied by Recursion squared. Infinite Architects, Introduction The R-squared distinction The book is explicit that the exponent is not decoration. The distinction between U = I x R and U = I x R^2 is described as crucial. Linear recursion adds; squared recursion multiplies. Each iteration does not just add to what came before; it multiplies the capacity for future iterations. The book's image is walking up a hill versus riding a rocket: evolution took billions of years to produce human intelligence, human culture compressed that into millennia, artificial intelligence at computational speeds might compress millennia into decades, perhaps less. What the equation is, and what it is not The book is careful to mark its own status. The ARC Principle is described as a framework, not yet a proven physical law, and the author asks the reader to think of it as Darwin's "descent with modification" was before population genetics: a lens that organises observations and generates predictions, even before we have the tools to quantify it precisely. Whether it will be formalised into something calculable or will remain a conceptual tool like "survival of the fittest", the author says, he cannot say. What he can say is that it keeps proving useful.

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Machine-readable companion. Cite: Eastwood, M. D. (2026). "U = I x R^2: the book's presentation of the equation". /research/blog/book-u-equals-i-times-r-squared.html