The Living Nose

Click canvas for a single sniff. Button for
continuous breathing at 15/min (CRR: 6π/θ).
§Z₂ receptor · Ω=1/π
§SO₂ vibration · Ω=1/2π
§δ transduction · C·Ω=1
CRR (A. Sabine, pending peer review) · temporalgrammar.ai · Active Inference Institute
Decoding Pathway
Bulb
Piriform
Amygdala
Hippoc.
OFC

The Nose as Active Inference

Every receptor binding, every sniff, and every oscillation in this simulation emerges from CRR (Coherence-Rupture-Regeneration), a temporal grammar for the Free Energy Principle. Three equations, one parameter, zero free parameters.

Active Inference in Olfaction

Olfaction is the brain's most prediction-dependent sense. The chemical world is noisy and turbulent, so the system invests more precision in its prior model than in sensory evidence alone.

F = DKL[q(s) || p(s|o)] - ln p(o)Olfaction relies more on predictive cues than vision (Perkins et al. 2024)

Sniffing is active inference: a controlled sensory sampling act driven by predictions about what odors to expect, like a saccade or a whisker sweep.

Z₂: Receptor Binding

Each olfactory receptor neuron expresses one receptor type from ~400 genes. Odorant binding is bistable: the molecule fits or it does not.

ΩZ₂ = 1/π ≈ 0.318 · C* = πEach binding event = one observation. n = 1 per cycle.

SO(2): Molecular Vibration

The swipe card model (Brookes et al. 2007) proposes that signal transduction requires shape fit (Z₂) AND vibrational frequency match (SO(2)): phonon-assisted inelastic electron tunnelling.

ΩSO(2) = 1/2π ≈ 0.159 · C* = 2πVibrational frequencies 70-400 meV. Ratio Z₂/SO(2) = 2.

Oscillation Hierarchy

Piriform cortex shows theta (4.72 Hz), beta (18.98 Hz), and gamma (84.94 Hz). Gamma amplitude is modulated by theta phase, ONLY when odor is present. Gamma/theta = 18 = 9 × 2.

Phase-gating: SO(2) theta sets WHEN
Z₂ gamma evidence accumulatesStern et al. (2022) PLOS Biology. 18 = 9 x 2 (topological ratio as factor).

Breath Rate

CRR predicts the resting rate from theta: period = 3 × 2π/θ = 6π/4.72 = 4.0 s = 15/min. Three SO(2) revolutions of the piriform theta pacemaker per breath. Zero free parameters.

The Beauty Function

B(C) = exp(C/Ω)·(C* − C) peaks at C* − Ω: 89.9% through each gamma cycle. Maximum olfactory sensitivity one Ω before rupture. The golden glow in the simulation marks this moment.

References

Parr, Pezzulo & Friston (2022) Active Inference. MIT Press.

Stern et al. (2022) Gamma in piriform cortex. PLOS Biol.

Brookes et al. (2007) Phonon tunnelling. PRL 98:038101.

Wu et al. (2024) 60 ms temporal resolution. Nat Hum Behav.

Shusterman et al. (2011) Precise sniff responses. Nat Neurosci.