The Argument
From thesis to proof to implications
The Claim
Intelligence arises from high-dimensional coherent dynamics—systems that maintain many degrees of freedom moving together, beyond what external observers can track.
This applies at every scale: neurons, immune cells, ecosystems, societies. It's not a human monopoly. It's what happens when internal complexity exceeds external bandwidth.
Why external observers can't keep up
On statistical manifolds with negative curvature (most real inference problems), the number of distinguishable states grows exponentially with uncertainty.
You can't outrun this with more probes—it's geometric. The covering numbers (how many observations you need to track a system) scale exponentially in the geodesic radius of uncertainty. This isn't implementation difficulty. It's mathematical inevitability.
Observation is dimensional collapse
When you measure a high-dimensional system, you project it into fewer dimensions. Information is lost—not gradually, but categorically.
Below 3 effective dimensions, continuous dynamics become impossible; the system snaps into discrete categories. This is a hard geometric constraint, not a design choice.
Biology operates in the gap
Living systems exploit the regime where external tracking fails:
Thermodynamics
Brains defer Landauer costs by computing reversibly until output. 100,000× more efficient than silicon—not because of clever algorithms, but because they don't pay per bit at every clock cycle.
Timing Inaccessibility →Timing
Synchronization between brain regions—not spike rates—sets the speed of thought. Visual binding takes 30–50ms because that's how long it takes visual areas to lock their oscillations.
Coherence Time →Development
Same genome, different trajectories. History matters because the system never explores its full state space. Identical twins in different environments navigate completely different dynamical landscapes.
Nonergodic Development →Emergence is real (and measurable)
When high-dimensional systems couple, new properties become statistically identifiable—properties that were not accessible in either system alone.
This isn't mysticism; it's a rank increase in the Fisher information matrix. The correlation between two oscillators is literally unmeasurable when they're independent. Couple them, and it becomes a parameter you can estimate. That's emergence: zero → nonzero Fisher rank.
What is Fisher rank?
The number of parameters you can actually distinguish from observations. Different from:
- Entropy — how many microstates exist
- Dimensionality — how many degrees of freedom move together
- Parameter count — how many numbers describe the system
Fisher rank asks: how many of those parameters actually change what you can see?
Implications
For AI
Digital substrates may have hard capability ceilings—not because of algorithms, but because of dimensional poverty. One global clock vs. 1014–1018 continuous degrees of freedom in a biological brain.
Scaling parameters doesn't add substrate dimensions. We may already be approaching the ceiling of what digital hardware can achieve.
Substrate Dimensionality →For Consciousness
Subjective experience may require volumetric field dynamics, not just graph connectivity. You can't simulate your way to qualia on a substrate that can't support the dimensionality.
The binding problem—how distributed neural activity becomes unified experience—may be a synchronization problem with measurable timescales.
For Science
Some phenomena are unfalsifiable—not because they're unreal, but because observers are low-dimensional projections of high-dimensional truth.
The appropriate response isn't relativism; it's epistemic humility calibrated to the gap. Scale-aware epistemology that acknowledges what physics places limits on.
Limits of Falsifiability →Start Here
Suggested reading order, depending on your background:
For the math/physics reader
- Minimal Embedding Dimension — the geometric constraint
- Tracking Complexity — why observers fail
- Coupling-Induced Rank Transitions — emergence formalized
For the biology/neuro reader
- Intelligence as High-Dimensional Coherence — the thesis
- Timing Inaccessibility — thermodynamic efficiency
- Coherence Time — the speed of thought
For the philosophy reader
- Limits of Falsifiability — epistemology of measurement
- Agency and Power — graded agency across scales
- Quantum Mechanics Without the Math — accessible intro
For the AI/ML reader
- Substrate Dimensionality — capability ceilings
- Tracking Complexity — interpretability limits
- Bits vs Dynamics simulation — the core distinction
See the papers page for the full list organized by role, or explore the interactive simulations.