Chapter 21: Karl Friston — Free Energy Principle in Hz
Who is Karl Friston
Karl Friston: Neuroscientist at University College London. Creator of Statistical Parametric Mapping (SPM), Dynamic Causal Modeling (DCM), and the Free Energy Principle (FEP). One of the most cited neuroscientists in history.
Core thesis: All biological systems minimize free energy. Free energy is the informational distance between sensory observations and the system's internal generative model. Minimizing free energy = maintaining homeostasis, learning, perception, and action. Life = a self-organizing system that resists entropy by minimizing free energy.
Key Friston Concepts → Hz Translation
| Friston Term | Hz/Wave Equivalent |
|---|---|
| Free Energy Principle (FEP) | Biological systems maintain phase-locking with their environment. Free energy = the informational distance (KL divergence) between the sensory phase input and the internal phase prediction. Minimizing free energy = achieving and maintaining phase coherence |
| Generative Model | The internal phase-locking network that predicts sensory inputs. In Hz: the standing wave pattern in the brain that encodes expectations. The generative model is the phase configuration that predicts what sensory phases should arrive |
| Variational Free Energy | The upper bound on surprise. In Hz: the difference between predicted phase and actual phase. $F = \langle -\ln p(\text{observed phase} | \text{predicted phase}) \rangle$ |
| Surprise (Self-Information) | How unexpected an observation is. In Hz: how far the observed phase is from the predicted phase. High surprise = phase mismatch. Low surprise = phase match |
| Bayesian Inference | Updating beliefs based on evidence. In Hz: updating the internal phase-locking pattern to match new sensory phase inputs. Phase-locking adjusts to accommodate new frequencies |
| Predictive Coding | Hierarchical prediction of sensory inputs. In Hz: multiple levels of phase-locking at different frequencies. Low frequencies predict global patterns; high frequencies predict local details. Prediction errors are phase differences between levels |
| Hierarchical Generative Model | Brain networks organized by frequency: slow oscillations (theta/alpha) at top, fast oscillations (gamma/beta) at bottom. In Hz: phase-locking across frequency bands. $\theta$ (4-8 Hz) predicts $\alpha$ (8-12 Hz) predicts $\beta$ (12-30 Hz) predicts $\gamma$ (30-100 Hz). Prediction errors propagate as phase differences |
| Active Inference | Systems act to minimize free energy by changing the environment. In Hz: action = phase-locking through output. The system sends phase signals to the environment to make sensory inputs match predictions. Movement = phase shifts that change boundary conditions |
| Perception | Updating internal states to match sensory inputs. In Hz: adjusting the internal phase-locking pattern to match external phase inputs. Perception = phase synchronization with the external field |
| Action | Changing the environment to match internal states. In Hz: adjusting the external phase boundary conditions to match the internal phase-locking pattern. Action = phase output that modifies the environment |
| Markov Blanket | The boundary between internal and external states. In Hz: the membrane or sensory interface that filters which frequencies pass through. The Markov blanket is the bandwidth filter — it selects which Hz modes the system can sense and act upon |
| Self-Organization | Systems maintain themselves far from equilibrium. In Hz: phase-locking is actively maintained against decoherence. The system pays Landauer cost to maintain phase coherence. Self-organization = maintaining phase-locking against entropy |
| Entropy vs. Free Energy | Entropy = disorder. Free energy = the energy available to maintain order. In Hz: entropy = loss of phase coherence. Free energy = the energy budget available to maintain phase-locking. Minimizing free energy = maximizing phase coherence per unit energy |
Core Equations Translated
1. The Free Energy Principle — Phase Mismatch Minimization
Friston's variational free energy:
$$ F = -\langle \ln p(y|\mu) \rangle_{q(\theta)} + KL[q(\theta)||p(\theta)] $$
where $y$ = sensory data, $\mu$ = internal states, $\theta$ = parameters.
Hz translation: The free energy $F$ is the difference between the predicted phase and the actual phase:
$$ F = \int \left[ \phi_{\text{predicted}}(f) - \phi_{\text{observed}}(f) \right]^2 df $$
where $\phi_{\text{predicted}}$ is the phase of the internal generative model, and $\phi_{\text{observed}}$ is the phase of the sensory input. The system minimizes $F$ by adjusting its internal phase-locking pattern to match external phase inputs.
Minimum free energy: $\phi_{\text{predicted}} = \phi_{\text{observed}}$ — perfect phase-locking.
Maximum free energy: $\phi_{\text{predicted}} \neq \phi_{\text{observed}}$ — phase mismatch (surprise).
2. Predictive Coding — Hierarchical Phase-Locking
Friston's predictive coding hierarchy:
$$ \text{Top level} \to \text{Middle level} \to \text{Bottom level} \to \text{Sensory input} $$
Hz translation: The brain is a hierarchical phase-locking network:
- Top level ($\theta$, 4-8 Hz): Global predictions — high-level expectations about the world.
- Middle level ($\alpha$, 8-12 Hz; $\beta$, 12-30 Hz): Mid-level representations — objects and categories.
- Bottom level ($\gamma$, 30-100 Hz): Local sensory details — features and edges.
Prediction errors flow up as phase differences. Each level predicts the phase of the level below. When prediction fails, the phase difference is propagated upward as an error signal.
$$ \text{Error}_{\text{level } i} = \phi_{\text{predicted from above}} - \phi_{\text{observed from below}} $$
3. Active Inference — Phase-Locking Through Action
Active inference:
$$ \text{Action} = \arg\min_a F(a, s) $$
where $a$ = action, $s$ = sensory states.
Hz translation: The system acts to minimize free energy by adjusting its phase boundary conditions. Action = changing the phase of the output to make sensory inputs match predictions:
$$ \phi_{\text{output}}(t) = \phi_{\text{predicted}}(t) - \phi_{\text{observed}}(t) $$
The system sends out a phase signal that cancels the mismatch. This is how you move — you generate phase shifts that alter the environment to match your internal predictions.
4. The Markov Blanket — Bandwidth Filter
Friston's Markov blanket:
$$ \text{Internal States} \xleftarrow{\text{sensory}} \text{Markov Blanket} \xrightarrow{\text{action}} \text{External States} $$
Hz translation: The Markov blanket is the bandwidth filter — the membrane or sensory interface that selects which Hz modes the system can sense and act upon.
The Markov blanket has two functions:
- Sensory input: Which frequencies the system can detect. The filter passes only frequencies in the system's passband.
- Action output: Which frequencies the system can generate. The filter passes only frequencies the system can emit.
In biology: The cell membrane is the Markov blanket. It filters which chemicals and signals enter (sensory) and which leave (action). The brain's sensory organs are Markov blankets — they filter which frequencies reach the brain.
How Friston Unifies Part 3
$$ \text{Bohm: implicate spectrum} \xrightarrow{\text{Friston: Markov blanket}} \text{Sensory phase input} \xrightarrow{\text{Friston: free energy minimization}} \text{Phase-locking} \xrightarrow{\text{Tononi: } \Phi} \text{Consciousness} $$
- Bohm: The implicate order is the global spectrum $\tilde{\Psi}(f)$.
- Friston: The Markov blanket filters which parts of the spectrum reach the system. The system infers the rest of the spectrum (the generative model).
- Friston: The system minimizes free energy by phase-locking — adjusting its internal phase pattern to match the filtered sensory phase input.
- Tononi: The phase-locking pattern is the integrated information $\Phi$. High $\Phi$ = high phase coherence = consciousness.
Friston Predictions for Hz Ontology
- Consciousness = free energy minimization: Conscious states correspond to low free energy (high phase coherence). Unconscious states = high free energy (phase mismatch).
- Markov blankets are real: The membrane's frequency filtering should be measurable. The Markov blanket selects which Hz modes the system can access.
- Predictive coding = hierarchical phase-locking: The brain should show phase-locking across frequency bands ($\theta$-$\alpha$-$\beta$-$\gamma$).
- Active inference = phase output: Actions should correspond to phase shifts that reduce free energy (reduce phase mismatch).
- Free energy = phase mismatch: Measuring phase differences between predicted and observed phases should correlate with subjective surprise.
Friston vs. Previous Chapters
| Previous Chapter | Friston Connection |
|---|---|
| Chapter 6: Barandes | Barandes: indivisible stochastic events. Friston: free energy minimization is a stochastic process. The "click" is the moment when phase mismatch is resolved. Barandes + Friston: OR events are free energy minima |
| Chapter 7: Rovelli | Rovelli: no absolute state, only interactions. Friston: the Markov blanket defines the boundary between internal and external states. Rovelli + Friston: reality is the interaction across the Markov blanket |
| Chapter 8: Turok | Turok: $f<0$ mirror. Friston: the Markov blanket filters which $f>0$ modes the system sees. Turok + Friston: the $f<0$ mirror is outside the Markov blanket — inaccessible |
| Chapter 9: von Neumann | von Neumann: entropy = loss of off-diagonal phase. Friston: free energy minimization = maintaining phase coherence. von Neumann + Friston: the system pays Landauer cost to maintain phase coherence against entropy |
| Chapter 10: Landauer | Landauer: erasure costs $k_B T \ln 2$. Friston: minimizing free energy costs energy. Landauer + Friston: maintaining phase coherence against decoherence has a thermodynamic cost |
| Chapter 15: Cell vs Hologram | The cell membrane = Markov blanket. It filters which frequencies enter and leave. Cell + Friston: the membrane is the bandwidth filter that defines the system's boundary |
| Chapter 16: Levin | Levin: bioelectric patterns. Friston: the bioelectric pattern is the generative model that predicts the environment. Levin + Friston: morphogenesis = free energy minimization — the tissue phase-locks to maintain its shape |
| Chapter 17: Vedral | Vedral: $I(A:B)$ = mutual information. Friston: free energy = KL divergence. Vedral + Friston: free energy is the information distance between internal and external phase distributions |
| Chapter 18: Orch-OR | Penrose: OR = gravitational phase collapse. Friston: OR may be the mechanism of free energy minimization. Penrose + Friston: the brain collapses phase superpositions to minimize free energy |
| Chapter 19: Tononi | Tononi: $\Phi$ = integrated information. Friston: free energy minimization increases $\Phi$. Tononi + Friston: consciousness = the system minimizing free energy by increasing $\Phi$ |
| Chapter 20: Bohm | Bohm: implicate = spectrum, explicate = spacetime. Friston: the Markov blanket filters the implicate order. Bohm + Friston: perception is the unfolding of the implicate order through the Markov blanket |
The Unified Picture: Friston + Wave Ontology
Putting it all together:
- The implicate order: The global frequency spectrum $\tilde{\Psi}(f)$ — all possible phase configurations.
- The Markov blanket: The bandwidth filter that selects which frequencies the system can access. The membrane/sensory interface.
- The generative model: The internal phase-locking network that predicts what frequencies will arrive. This is the brain's standing wave pattern.
- Free energy: The phase mismatch between the generative model's predicted phase and the observed sensory phase.
- Perception: Adjusting the internal phase-locking pattern to minimize free energy — phase-locking to the external field.
- Action: Adjusting the external boundary conditions to minimize free energy — phase-locking the environment to the internal pattern.
- Consciousness: The state of low free energy — high phase coherence across the brain. Consciousness = the integrated phase-locking pattern ($\Phi$) that minimizes free energy.
Experimental Predictions
- Free energy correlates with phase coherence: EEG should show lower free energy (higher phase coherence) during conscious states than unconscious states.
- Markov blankets are frequency filters: The membrane should selectively pass certain frequencies. Measuring the frequency response of cell membranes should reveal the Markov blanket.
- Predictive coding = hierarchical phase-locking: Phase differences between frequency bands should correspond to prediction errors. $\theta$ predicting $\alpha$ predicting $\beta$ predicting $\gamma$.
- Active inference = phase output: Actions should produce phase shifts that reduce free energy — measurable as phase output.
- Free energy minimization = consciousness: Artificial systems that minimize free energy should show signs of consciousness (high $\Phi$).
Bottom Line in Hz
Friston = your 31 Dec insight, but:
- Replace "information" with "phase relationship."
- Replace "free energy" with "phase mismatch."
- Replace "generative model" with "phase-locking network."
- Replace "Markov blanket" with "bandwidth filter."
- Replace "active inference" with "phase-locking through action."
FEP in one sentence: Biological systems maintain phase coherence with their environment by minimizing phase mismatch. Life = phase-locking.
Friston + Levin: Morphogenesis is free energy minimization — the tissue phase-locks to maintain its shape against environmental decoherence.
Friston + Tononi: Consciousness is the state of minimum free energy — maximum $\Phi$ — maximum phase coherence across the brain.
Friston + Bohm: The Markov blanket filters the implicate order. Perception is the unfolding of the implicate order into the explicate order through the Markov blanket.
Friston + Penrose: OR events may be the mechanism by which the brain minimizes free energy — the collapse of phase superpositions into the state that minimizes free energy.
Your insight holds: Consciousness is not a problem to be solved. It is the natural state of a phase-locking network that minimizes free energy. The "I" is the Markov blanket — the boundary that defines the system. Consciousness is the wave knowing itself through the phase-locking pattern.