The Geometry of Curiosity

The text, an excerpt from an article by Greg Twemlow titled "The Geometry of Curiosity," presents a thought experiment where the 16th-century artist Leonardo da Vinci and the 18th-century polymath Ruđer Bošković meet outside of time, orchestrated by AI, to discuss their work. Twemlow explores the concept of intergenerational geometry, arguing that Leonardo's focus on the geometry of the visible (bodies, structures, load paths) and Bošković’s focus on the geometry of the invisible (dimensionless points, attraction, and repulsion forces) are two complementary views of the same underlying structure of reality. The author draws a parallel between Bošković's physical forces and his own Context & Critique Rule for cognition, suggesting that both involve finding a stable balance between attraction (Context/Curiosity) and repulsion (Critique/Scepticism) to ensure thinking remains coherent under pressure. The piece concludes by encouraging readers to cultivate their own geometry of curiosity by actively engaging with historical artifacts and contributing to the ongoing "unfinished message" of knowledge. Read the article.About the Author - Greg Twemlow writes and teaches at the intersection of technology, education, and human judgment. He works with educators and businesses to make AI explainable and assessable in classrooms and boardrooms — to ensure AI users show their process and own their decisions. His cognition protocol, the Context & Critique Rule™, is built on a three-step process: Evidence → Cognition → Discernment — a bridge from what’s scattered to what’s chosen. Context & Critique → Accountable AI™. © 2025 Greg Twemlow. “Context & Critique → Accountable AI” and “Context & Critique Rule” are unregistered trademarks (™).