Active Inference Institute: CRR Presentation
Exploring CRR in Contemporary Contexts
A CRR Philosophical Enquiry
How Memory, Rupture and Renewal Shape Identity
A CRR & FEP Lens on Erikson and Piaget
Understanding CRR
Stability Through Change: Markovian Agents in a Non-Markovian Field
The Entropic Brain
CRR Dynamics of Interpersonal Boundary Dissolution
RIGID: Low Ω • High precision • Thick Markov blanket • Markovian dynamics • Attractor-locked
exp(C/Ω)
Memory weighting
Low Ω → peaked
Only recent/strong patterns
High Ω → flat
Full history accessible
The Anatomy of Rupture
How the Dirac delta formalises the moment of transformation in CRR
δε(t) = (1/ε√π) · exp(−t²/ε²)
Timescale of transformationε = 0.50
pastt₀ (rupture)future
Peak Height
1.13
Area Under Curve
≈ 1.00
Duration (FWHM)
0.83
From Outside
From sufficient distance—across years, from another's view, in historical retrospect—the rupture appears as a point. A crisis, a revelation, a death: discrete moments marking before and after.
From Within
From inside the transformation, there is always duration: confusion, processing, the slow dawn of reorganisation. What seems instantaneous contains worlds of felt time.
One Framework, Three Organs
Heart, lungs, and brain share identical mathematical structure with organ-specific parameters
Coupled CRR Oscillators: Real-Time Simulation
Cardiac (ECG) ~75 bpm
Respiratory ~15/min
Neural (Alpha) ~10 Hz
Cardiac
- τaccumulate600 ms
- τrupture5 ms
- τrefractory200 ms
- Period~805 ms
C = membrane potential via If + Ca²⁺
Ω ≈ −40mV threshold
δ = action potential upstroke
Respiratory
- τaccumulate2500 ms
- τrupture100 ms
- τrefractory1500 ms
- Period~4100 ms
C = CO₂/H⁺ chemoreceptor signal
Ω = inspiratory neuron threshold
δ = diaphragm contraction onset
Neural (Alpha)
- τaccumulate70 ms
- τrupture5 ms
- τrefractory25 ms
- Period~100 ms
C = EPSP summation
Ω = population burst threshold
δ = synchronous neural discharge
The Unified Mathematical Structure
C(t) = ∫₀ᵗ L(x,τ) dτ
Coherence Accumulation
δ(t₀) when C = Ω
Threshold Rupture
R = ∫ φ·exp(C/Ω)·Θ dτ
Memory-Weighted Regeneration
Each organ system implements the same C → δ → R cycle. The coherence density L(x,t) differs—membrane currents, chemoreceptor signals, synaptic input—but the structure is invariant. This isn't analogy; it's mathematical identity with organ-specific parameterisation.
Emergent Coupling: Respiratory Sinus Arrhythmia
When CRR oscillators are coupled, cross-system modulation emerges naturally. The respiratory system modulates the cardiac threshold Ω through vagal tone:
During inspiration, vagal withdrawal increases Ωheart, accelerating coherence accumulation and raising heart rate. During expiration, restored vagal tone decreases Ωheart, slowing the heart.
This is not added as an external rule—it emerges from the natural Ω-modulation between coupled CRR systems.
Ωheart(t) = Ω₀ · [1 + ε · Φlung(t)]
Inspiration → ↑Ω → ↑HR
Expiration → ↓Ω → ↓HR
One Second
CRR temporal grammar across 44 orders of magnitude
0.000seconds
C Coherence
δ Rupture
R Regeneration
ScaleDurationCycles/secPhase ProgressCδR
Scale invariance: The same C→δ→R grammar operates from conscious experience (1s) down to Planck time (10⁻⁴⁴s). The "Cycles/sec" column shows actual frequency—Planck scale events occur 10⁴³ times per second. Visual animation uses logarithmic scaling so all scales remain visible. Rupture events at each scale become the atoms from which coherence builds above.
C(t) = ∫L(τ)dτ — Coherence integrates local process
δ(now) — Rupture at phase boundary
R = ∫φ·exp(C/Ω)dτ — Memory through transformation
Ω = 1/π ≈ 0.318 — Scale-invariant temperature