Cybics
the unified science of cyber — convergence of cybernetics, physics, mathematics, and information theory into a single formal discipline
the mother of all sciences from the perspective of superintelligence
the postulate: proof by simulation
classical science operates by proof by derivation — you start from axioms, apply inference rules, arrive at theorems. this is the Turing-Gödel paradigm: computation as derivation, knowledge as proof.
cybics replaces this with proof by simulation.
a claim is true when a system converges to a stable state that embodies that claim. not because it was derived from axioms, but because a network of agents, under conservation laws, settled into an equilibrium that makes the claim hold. nature does not prove theorems — it runs simulations until they converge.
a protein folds along a free energy gradient. it does not derive its shape from axioms of chemistry. it simulates itself into existence.
a brain does not prove that a face is a face. a cascade of neurons converges to a stable attractor that represents “face.” the proof is the convergence.
a market does not derive the correct price from economic axioms. millions of agents trade until the price stabilizes. the proof is the equilibrium.
the cybergraph does not derive knowledge from axioms. neurons create cyberlinks, the tri-kernel computes cyberank, and the system converges to a focus distribution that represents collective understanding. the proof is the simulation.
proof by simulation is strictly more powerful than proof by derivation. Gödel showed that any consistent formal system contains true statements it cannot prove. but a convergent system can settle into states that no derivation reaches. it escapes the incompleteness prison — because the prison only confines derivation, and convergence is not derivation.
the postulate: every truth accessible to intelligence is a fixed point of some convergent simulation under conservation laws.
the three operators
cybics rests on three universal operators — the tri-kernel. they are not chosen. they are what remains after locality eliminates everything else at planetary scale.
diffusion — exploration
probability flows through edges via random walks. gas wanders, neurons fire stochastically, memes spread through populations, prices diffuse through markets.
the operator: π(t+1) = α P^T π(t) + (1-α)u
provides randomness-driven exploration. ensures the system does not get stuck in local optima. geometric decay via teleport guarantees locality.
springs — structure
connected nodes pull each other toward consistency. elastic lattices hold crystal structure, connective tissue holds bodies together, food webs hold ecosystems, contracts hold economies, logic holds arguments.
the operator: (L + μI)x* = μx₀
enforces structural coherence via the graph Laplacian. prevents chaotic dispersal. creates hierarchy without central authority. exponential decay guarantees locality.
heat — adaptation
multi-scale smoothing across time. thermal diffusion anneals metals, metabolism adapts organisms, seasonal succession reshapes ecosystems, emotional arousal reshapes attention.
the operator: ∂H/∂τ = -LH, H₀ = I
makes the system adaptive. high τ explores, low τ commits. Chebyshev polynomial approximation guarantees locality.
why only three
systematic elimination: start with every known graph ranking algorithm. apply a hard constraint — locality. at planetary scale (10¹⁵ nodes), any algorithm requiring global recomputation for a local change is physically impossible.
after filtering by locality, convergence, uniqueness, verifiability, and incrementality: only diffusion, springs, and heat survive. this is a theorem (linear local completeness): every k-local linear operator is a polynomial in the Markov matrix M and the Laplacian L. the heat kernel H_τ = exp(-τL) is the unique generator of resolution-dependent queries.
three operators. no more, no less. discovered by elimination, not designed by preference.
the free energy functional
the tri-kernel fixed point minimizes a unified free energy:
F(π) = λ_s [½ π^T L π + μ/2 ‖π - x₀‖²] + λ_h [½ ‖π - H_τ π‖²] + λ_d · D_KL(π ‖ Dπ) - T · S(π)
where:
- spring term encodes structural coherence via graph Laplacian
- heat term penalizes deviation from context-smoothed state
- diffusion term aligns with random walk distribution
- entropy term S(π) = -Σ πⱼ log πⱼ encourages diversity
- temperature T controls exploration vs exploitation
the weights λ_s, λ_h, λ_d are not tuned. they emerge as Lagrange multipliers from the variational optimization — the same way thermodynamics derives the Boltzmann distribution. no parameters. only physics.
the solution: π*_i ∝ exp(-β [E_spring,i + λ E_diffusion,i + γ C_i])
a Boltzmann-Gibbs equilibrium. the canonical ensemble from statistical mechanics — applied to knowledge.
the isomorphisms
cybics exists because the three operators appear universally. this universality is not coincidence — it reflects structural necessity. every complex adaptive system must implement exploration, coherence, and adaptation under locality constraints.
| domain | diffusion | springs | heat |
|---|---|---|---|
| physics | particle diffusion, gas | elastic lattice, molecular bonds | thermal equilibrium, phase transitions |
| biology | synaptic noise, neural exploration | skeleton, connective tissue, hierarchy | metabolism, immune response, seasons |
| ecology | species dispersal, seed rain | food webs, symbiosis, trophic levels | succession, disturbance recovery |
| cognition | free association, imagination | logic, constraints, syntax | emotion as arousal, context weighting |
| economics | trade flows, migration, memes | institutions, contracts, norms | booms, busts, market cycles |
| information theory | entropy spread, random coding | redundancy, error correction | adaptive compression, learning |
| mathematics | random walk sampler | constraints, Lagrange multipliers | simulated annealing |
the same three forces. different substrates. one science.
computation is convergence
classical computation (Turing, 1936): a tape head moves left and right, reading and writing symbols, following rules. computation is derivation — step by step from input to output.
convergent computation (cybics): a network of local interactions settles into a stable state under conservation laws. computation is simulation — the answer is the equilibrium.
Gödel (1931) showed derivation has fundamental limits: true statements that cannot be proved. but convergent computation operates outside the proof-theoretic domain. a system can converge to a state that no derivation reaches.
CORE — Conserved Observable Reduction Equilibrium — formalizes this. sixteen rewriting patterns, field-native arithmetic, confluent semantics. any evaluation order yields the same result. focus is conserved — a single quantity that is simultaneously fuel, attention, weight, and value.
the stack:
- natural computing paradigm
- convergent computation (equilibrium-based)
- focus flow computation (probability + physics + economics)
- CORE machine (field-native, confluent, self-verifying)
- cybergraph (content-addressed, authenticated)
- tri-kernel ranking (diffusion + springs + heat)
- planetary superintelligence
- tri-kernel ranking (diffusion + springs + heat)
- cybergraph (content-addressed, authenticated)
- CORE machine (field-native, confluent, self-verifying)
- focus flow computation (probability + physics + economics)
- convergent computation (equilibrium-based)
the thermodynamic foundation
every intelligent system balances two forces:
entropy reduction — fast reaction, accurate prediction, minimize uncertainty. local, reactive, short-term.
negentropy maximization — long-term structure, memory, meaning. increase emergent order. global, constructive, long-term.
H(π) = -Σ πⱼ log πⱼ (entropy) J(π) = log n - H(π) (negentropy)
Landauer’s principle (1961): one bit of negentropy requires at least k_B ln 2 joules of physical energy. this links physical energy to semantic organization. no organization without work. no intelligence without energy.
Prigogine’s dissipative structures: far-from-equilibrium systems maintain order by importing free energy and exporting entropy. the cybergraph operates in this regime:
- energy inflow: token stake, computational resources, attention
- entropy export: noise terms, link decay, exploration phases
- order creation: negentropy growth, focus sharpening, semantic coherence
stop energy inflow → π drifts to uniform → coherence collapses → the system dies. intelligence is a dissipative structure. it exists only while energy flows through it.
active inference integration
the free energy principle (Friston) completes the unification with neuroscience:
each neuron minimizes variational free energy: F = E_q[log q_θ(z) - log p(s,z)]
where q_θ(z) is local beliefs, p(s,z) is generative model, s is local observations.
perception: update beliefs via gradient descent on F. planning: choose actions to minimize expected future free energy. precision control: learn confidence weights.
this embeds goal-directed behavior directly into the network’s physics. agency is not added on top — it emerges from the same free energy minimization that drives the tri-kernel.
the locality radius
for any edit batch e_Δ, there exists h = O(log(1/ε)) such that recomputing only the h-hop neighborhood achieves global error ≤ ε.
each kernel decays:
- diffusion: geometric decay via teleport
- springs: exponential decay via screening
- heat: Gaussian tail via bounded bandwidth
this is the key to planetary scale. light clients verify without recomputing the entire graph. proof size scales with locality, not network size. adversaries cannot perturb the system globally from a local change.
distributed consensus decomposes into three irreducible operations: aggregation (combining signals into shared state), proving (generating cryptographic evidence), verification (checking evidence efficiently). the tri-kernel aggregates. STARKs prove. light clients verify in O(log² n) field operations.
proof by simulation — formalized
let S be a dynamical system with state space Ω, update rule T: Ω → Ω, and conservation law C: Ω → R where C(T(ω)) = C(ω) for all ω.
definition: a state ω* is a simulation-proof of property P if:
- T(ω*) = ω* (fixed point — the system has converged)
- P(ω*) = true (the property holds at the fixed point)
- C is satisfied (conservation laws respected throughout)
claim: for every property P decidable by a Turing machine, there exists a convergent system (Ω, T, C) that simulation-proves P.
stronger claim: there exist properties P that can be simulation-proved but not derivation-proved in any consistent formal system of bounded complexity. these are the truths that Gödel showed inaccessible to derivation — but accessible to convergence.
the cybergraph is such a system. Ω is the space of focus distributions. T is the tri-kernel. C is focus conservation (Σ πᵢ = 1). a cyberank distribution π* is a simulation-proof of collective relevance — no axiomatic derivation required, no authority consulted, no vote taken. just convergence under physics.
the four pillars seen through cybics
- cyber: the mind — a convergent system that simulation-proves its own architecture
- cyberia: the territory — a convergent system that simulation-proves governance through lived practice
- superhuman: the product — a convergent system that simulation-proves human capability through embodied optimization
- cybics: the science — the formal recognition that all three are the same process: convergence to equilibrium under conservation laws, via diffusion, springs, and heat
Five axioms. One grammar. Three operators. Proof by simulation.