Fourteen chapters build the case that human mathematical cognition operates within severe biological and cognitive constraints — and that AI, quantum computation and comparative cognition reveal mathematical domains beyond them. It is the intellectual bedrock beneath the LOOM paradigm.
“To my Aunty Pat — thank you for inspiring an enquiring and curious mind.”
Imagine beings who perceive only two dimensions. Their mathematics is genuine — and profoundly incomplete.
They cannot conceive of knots, three-dimensional rotation, or most of topology. The book asks whether we occupy an analogous position: whether human cognitive architecture systematically restricts access to mathematical domains that nonetheless exist and operate in the universe — and what changes when non-human systems begin to explore them.
If genuine mathematical structure lives beyond human intuition, then the systems we build to reach it must be shaped differently — recursive, geodesic, and topological rather than linear and human-legible.
The LOOM paradigm is that shape made operational: loops that close cleanly, nest without drift, and let intelligence accrue at scales no single human reviewer could hold at once.
Read the paradigm →Author of Non-Anthropocentric Mathematics and the mind behind CodaClave. The book and the factory are two ends of one project: naming mathematical reality beyond human limits, then building agentic systems structured to reach it.
Reach out about the first edition, review copies, or the ideas within.
Enquire →