>[!warning] >This content has not been peer reviewed. # Solomonoff induction & Kolmogorov complexity — RST application **Total ontology pillar:** *Information theory (Shannon/Solomonoff) — the logic of selection.* Solomonoff induction says the shortest description is the most probable reality; Kolmogorov complexity $K(x)$ is the length of that description. In RST the substrate has a **finite bit budget** (Landauer, A2): maintaining a state costs at least $k_B T \ln 2$ per bit. So the substrate **naturally favours compressed states** — high signal-to-noise $\eta = \Omega/N$, high fidelity $\mu$ — because they cost less to maintain. **Occam's Razor is derived from the ledger**: the universe prefers simple laws because they are cheaper to sustain. --- ## I. Mapping to RST | Solomonoff / Kolmogorov | RST reading | |:---|:---| | Shortest description $K(x)$ | Fewer bits to maintain → lower Landauer cost; substrate favours low $K$. | | Prior $\propto 2^{-K(x)}$ | Probability of a state scales with **fidelity** $\mu$: high $\mu$ = high $\eta$ = compressible = favoured. | | "Law" = compact encoding | **Substrate macro**: a law is a shortcut that reduces the work of maintaining a pattern; $W^n = \Omega^n + N^n$ with high $\Omega/W$ = low effective $K$. | | Occam's Razor | Selection by **maintenance cost**: ordered relations (high $\eta$) are cheaper than random noise (low $\eta$). | **Identity:** The RST fidelity $\mu(\eta, n) = \eta/(1+\eta^n)^{1/n}$ is the **substrate's selection curve**: as $\eta$ (signal-to-noise) increases, $\mu$ increases; the substrate "chooses" states that maximise $\mu$ for a given budget $W$, i.e. **compressed** (lawful) states. --- ## II. Script: fidelity as selection (Occam from the ledger) The script **[[Solomonoff Induction - Code]]** (`rst_solomonoff_fidelity_selection.py`) plots $\mu(\eta, n)$ over a range of $\eta$ and annotates: - **Low $\eta$** (noise-dominated, incompressible) → low $\mu$ → high relative maintenance cost → disfavoured. - **High $\eta$** (signal-dominated, compressible) → high $\mu$ → low relative cost → favoured. So the **same curve** that gives the Newton–MOND transition (gravity) and the Resource Triangle is the **logic of selection**: the substrate allocates budget so that compressible (lawful) configurations win. Run via **`run_all_further_scripts.py`** or from this folder. --- ## III. Total ontology tie - **Thermodynamics (Landauer):** Cost of existence → defines the ledger. - **Information (Shannon/Solomonoff):** Logic of selection → **this application**: $\mu(\eta,n)$ as the curve that favours compressed states; Occam from the ledger. - **Fractal geometry (percolation/Bejan):** Shape of the wires → $n$ as backbone dimension. - **Dynamics (MOND/Navier–Stokes):** Flow of the render → $\eta = g_N/a_0$, etc. - **Intelligence (Friston):** Optimisation of the signal → life as active noise suppression. --- ## Links - **Knowledge note (established result):** [[expanded theory/knowledge/The shortest description is the most probable reality]] - **Code:** [[Solomonoff Induction - Code]] - **Resource Triangle:** [[expanded theory/Resource Triangle]] - **Roadmap:** [[../../Applications Roadmap]]