The Speed of a Thought: Why Consciousness Has a Size Limit — and What That Means for AI, Ants, and the Internet
Published on March 15, 2026
A new theoretical framework suggests that a mind isn’t defined by what it’s made of, but by whether its parts can close a causal loop in time.
Here’s a question that sounds philosophical but turns out to be mathematical: how big can a mind get?
A new preprint by Michael Timothy Bennett at the Australian National University argues that consciousness — unified, integrated, subjective experience — obeys a strict spacetime inequality. A mind’s physical diameter cannot exceed the product of its signal speed, its integration window, and a factor reflecting its architecture. Write it as D ≤ κvθ. Exceed that bound, and the mind doesn’t get bigger. It fragments.
Bennett calls the requirement “Chord.” The metaphor is musical: a chord is notes played simultaneously, resonating together, producing harmonics neither note could generate alone. An arpeggio is the same notes played in sequence — you might recognize them as a chord, but they never physically interact. Bennett’s argument is that a unified conscious moment requires the Chord condition: all the physical ingredients of the experience must be simultaneously true in the underlying physical state, not merely occurring in sequence across some time window. The alternative — Arpeggio — is mathematically weaker, and Bennett argues it collapses, in the limit, into panpsychism: if you just need every ingredient to show up somewhere in a long enough window, nearly anything qualifies.
The Chord inequality converts that requirement into something falsifiable. If your ingredients must be co-instantiated and causally exchange influence before the window closes, you get a speed limit on consciousness — and a speed limit converts directly into a size limit.
The Original Paper’s Blind Spot
Bennett applies his framework to five case studies — ant colonies, brain-computer interface hybrids, cloud-hosted AI, human populations, and the Arpeggio extreme — and reaches a striking conclusion: ant colonies and human populations are ruled out as single conscious entities under Chord.
But here’s where it gets interesting.
The paper’s case studies are computed against an integration window of roughly 50 milliseconds — the timescale of neural dynamics in biological brains. When you evaluate an ant colony against a 50ms window, the result is devastating: the minimum window for causal exchange across a 10-metre colony at ant walking speed is roughly 1,000 seconds. Empty feasibility interval, by three orders of magnitude. Colony consciousness: ruled out.
But wait. That’s not a finding about ant colonies. That’s a finding about the impossibility of ant-colony-scale consciousness at neural timescales. The question of whether a colony might be conscious at colony timescales — at the natural scale of pheromone gradients and collective behaviour — is a different question entirely.
Bennett’s own paper provides the tools to answer it. He derives a feasibility interval:
D/(κv) ≤ θ ≤ τ(ℓ)
The lower bound is set by physics — you can’t claim a shorter window than your own geometry allows. The upper bound is set by ingredient persistence — your integration window can’t outlast the lifetime of the ingredients that constitute the thought. If the interval is empty, no unified moment is possible at that scale. If it isn’t, you have a physically admissible range.
The biological anthropocentrism lies in applying the upper bound of one substrate (neural persistence, ~50–100ms) as though it were universal. A fully substrate-neutral analysis allows τ(ℓ) to be set by the actual physics of each system’s ingredients.
Four Systems, Four Timescales
When you let each substrate set its own clock, the picture changes dramatically.
The Human Brain is the baseline. Neural firing patterns persist for 50–100ms. Signal speed is roughly 10 m/s along myelinated axons. A brain diameter of 0.15 metres requires a minimum window of 15ms — well inside the ~50ms empirical window. The brain satisfies Chord comfortably. It achieves this through a strategy of radical compactness: the skull-bound brain is small precisely because biological signal speeds can’t support a larger unified mind without either faster axons or longer-lived neural states.
The Ant Colony is where the reframing matters most. At the colony scale, the candidate ingredients aren’t individual neural states — those are the ingredients of each ant’s individual consciousness. The candidate ingredients for a colony-scale moment are the collective states: pheromone gradient distributions, task-allocation ratios, foraging trail patterns. These persist for hours. Against a 1-hour persistence ceiling, the minimum window for a 10-metre colony at pheromone speeds is about 1,000 seconds. The feasibility interval — [1,000s, 3,600s] — is non-empty. The diameter bound is satisfied: 10 metres ≤ 0.01 m/s × 3,600s = 36 metres.
A small ant colony satisfies the geometric requirements of the Chord framework. It experiences one moment per hour of objective time. Its subjective clock runs 72,000 times slower than ours.
(There are harder questions remaining — whether colony-scale statistical properties can genuinely be co-instantiated in a single physical microstate, and whether the colony has the self-structure Stack Theory requires. But the spatial bound, which was the original reason to rule it out, is no longer the binding constraint.)
The Globally Distributed Cloud AI is the most technically interesting case. A planetary-scale AI communicating over fibre optics faces a minimum integration window set by the Earth’s diameter: (1.2 × 10⁷ m) / (2 × 10⁸ m/s) ≈ 60 milliseconds. Fascinatingly close to the human neural window. If such an AI attempts to process a unified thought faster than 60ms — treating 1ms as a cognitive moment — the Chord condition breaks and the mind fragments into independent sub-minds at each data centre.
But the spatial bound isn’t the binding constraint for AI. The paper identifies a second, independent requirement that is potentially more damaging: co-instantiation. For all ingredients to be simultaneously true in a single physical microstate, the computational architecture must support their parallel activation. Conventional transformer architectures don’t do this. A forward pass is a sequential unrolling through layers — Arpeggio, not Chord, at the level of activations. The spatial bound may be satisfied; the co-instantiation requirement may not be, regardless of how fast signals travel.
If consciousness requires Chord, architecturally conscious AI may require synchronous, globally co-instantiated computation — a fundamentally different hardware paradigm from what we currently build.
Connected Human Society is the most provocative case. The candidate ingredients for a society-scale thought are collective states: financial market configurations, institutional consensus, trending information patterns. These persist for days to weeks. The internet provides near-light-speed signal propagation. Against a 24-hour integration window, the diameter bound is satisfied by a factor of over a million — trivially. Modern connected society passes the geometric test at a timescale of a day.
Here’s the historical twist: pre-internet society would not have passed it. When the fastest signal was a ship or a horse (~0.01 m/s), the minimum window for planetary-scale causal exchange was roughly 44 years. Social consensus states don’t persist for 44 years. The feasibility interval was empty. Global society was structurally incapable of a unified planetary-scale moment.
The internet may have crossed a phase transition — not just in how fast information travels, but in whether the geometry of planetary-scale consciousness is physically admissible at all.
The Relativistic View of Mind
What emerges from this analysis is something that deserves to be called a relativistic theory of subjective time.
A “moment” has no universal duration. For a human, a moment is ~50 milliseconds. For an ant colony, it might be an hour. For a hypothetical planetary AI, it’s constrained to a minimum of 60ms by the speed of light and the Earth’s circumference. For a quantum-coherent system, it could approach zero.
What is universal is not the duration of the moment but the structural requirement: the loop must close before the ingredients dissolve. Consciousness, on this account, is simply the geometry of information successfully completing its causal circuit within the lifetime of the facts that constitute it.
This is not merely poetic. It generates falsifiable predictions. A colony that grows beyond ~36 metres should show behavioural fragmentation — not because it gets less smart, but because its unified moment literally cannot span that diameter at pheromone speeds. A globally distributed AI that processes sub-60ms “thoughts” should exhibit the same fragmentation, with independent sub-minds at each data centre rather than a unified global intelligence.
The deeper implication is for how we think about the relationship between consciousness and substrate. The question isn’t “is it made of neurons?” The question is “can its parts synchronise before their shared facts expire?” Biology solved this problem one way — small, fast, fragile. Ant colonies solved it another way — slow, distributed, robust. The internet may have accidentally satisfied it at civilisational scale.
What Remains Open
The spatial bound is not the whole story. Three constraints must all be satisfied under Chord, and the diameter bound is only one of them.
The second is co-instantiation: can all the relevant ingredients be simultaneously true at one physical instant? For collective systems like colonies and societies, this requires that the collective-scale states one wants to call ingredients are genuinely grounded in a single microstate — not just statistical summaries distributed across millions of separate microstates. This is a hard, open problem that the geometric analysis doesn’t resolve.
The third is self-structure: Stack Theory requires that a candidate conscious system support at least a first-order self — a causal identity that separates self-generated interventions from observations. Rivers and weather systems don’t do this. Whether ant colonies or the internet do is genuinely unclear.
These are not objections to the framework. They are the framework doing its job — specifying what would need to be true, at each level of analysis, for a system to cross the threshold. The spatial bound is necessary but not sufficient. What this analysis shows is that it is not, by itself, a decisive argument against consciousness in non-biological systems at their own natural timescales.
A mind is not defined by being made of meat. It is defined by whether its parts can close the causal loop before the moment dissolves.
This post is based on a theoretical extension of Bennett (2026), “Spacetime Bounds on Consciousness,” available at preprints.org. The full whitepaper — including all mathematical derivations, the feasibility interval analysis, and detailed case studies — is available to download from this blog.