Claire Isabel Webb & Nina Miolane | The Geometry of Consciousness

Why It Matters

Demonstrating identical toroidal dynamics in brains and AI suggests universal computational laws, paving the way for unified models of intelligence that could transform both neuroscience and machine learning.

Key Takeaways

• New imaging captures up to a million neurons in real time.
• Single-neuron doctrine limited; population coding reveals geometric structures.
• Neural activity of 150 cells forms a torus in high-dimensional space.
• Both biological and artificial networks exhibit identical toroidal dynamics during navigation tasks.
• Researchers aim to derive universal equations underlying intelligence across brains and AI.

Summary

The talk by Claire Webb and Nina Miolane introduced a "mathematical theory of intelligence," arguing that both brains and machines obey common geometric principles. They highlighted how modern imaging now records hundreds of thousands to a million neurons in vivo, outpacing existing theoretical frameworks for interpreting those data.

Historically, neuroscience focused on single‑neuron coding—Edgar Adrian’s binary‑spike rate discovery, Hubel and Wiesel’s orientation cells, and the famed "Jennifer Aniston" neuron illustrate this approach. The speakers argued that cataloguing billions of neurons this way is infeasible, prompting a shift toward population coding, where the collective activity of many neurons is examined as a point in a high‑dimensional space.

When researchers plotted the activity of 150 mouse neurons involved in spatial navigation, the high‑dimensional trajectory collapsed onto a two‑dimensional torus—a donut‑shaped manifold—both in real data and in simulations. Remarkably, training an artificial neural network on the same navigation task produced an identical toroidal representation, suggesting a shared computational geometry across biological and silicon‑based systems.

If such universal manifolds can be mathematically characterized, they could provide the equations that explain intelligence, bridging neuroscience and AI. This would enable predictive models of cognition, more efficient AI architectures, and a deeper understanding of consciousness as a geometric phenomenon.

Original Description

How do the binary electronic signals of neurons give rise to subjective experience? Mathematician and machine learning researcher Nina Miolane joined science historian Claire Isabel Webb to explore this question from an unexpected direction: geometry.

​​Plotting the collective firing rate of neurons in 3D space, Miolane's Geometric Intelligence Lab at UC Santa Barbara, found it traced the shape of a torus. When they trained an artificial neural network on the same task, it converged on the same form. Miolane posits that biological and artificial intelligence may be reaching for a universal computational design.

In this fascinating conversation, Webb and Miolane discussed how geometry is the most ancient branch of physics; it is the language we use to describe the curvature of spacetime and the General Relativity of the universe. It makes sense, then, that geometry could map the universe inside us.

This talk was presented April 20, 02026 at The Interval in San Francisco.

Episode notes: https://longnow.org/talks/02026-webb-miolane/

The event livestream is here: https://youtube.com/live/w6MvOXg9fdw

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