The Floor

Every theory the sciences and mathematics actually run on, joined by what it rests on, what limits it, and what shares its form. One body, so you can walk from any theory to the ones holding it up. Drawn rather than listed, because a list cannot show you what is missing — you would have to already know.

The same floor, read the other way, is The Floor of Discovery — Scripture and the created order as one design. That page is for seeing it; this one is for walking it.

Where the floor is missing

A lattice, because a lattice has sites that can be empty. Eight dimensions down, the catalogue's sections across; each site asks what a section contributes to a dimension, and a dashed red cell is that question with nothing on the shelf to answer it. An empty site is a question, not automatically a gap — some combinations need not exist — but a whole row of them is a thin place worth walking to.

Mathematics Physics Chemistry Life sciences Earth Applied Humanities Applied and social Physical sciences encoding 7 1 11 2 11 7 metabolism 10 12 27 6 9 2 reasoning 45 28 13 8 3 18 10 2 8 physical_substance 8 29 13 27 11 14 1 1 8 authority_trust 6 18 16 6 2 time_sequence 10 9 21 10 28 4 3 3 conservation_balance 14 30 12 16 9 24 1 2 8 discreteness 19 16 12 11 4 6 5 THE COMB 72 sites · 59 filled · 13 empty — a dashed cell is a question with no answer on the shelf. A theory appears in every dimension its domain touches, so counts exceed 178.

How well each theory is joined

The same 178, arranged by how many relations each holds — most aligned at the centre, spiralling out at the golden angle. Distance from the middle is how peripheral a theory is to the assembled floor. Zoom in, turn it to another angle, and click any cell for its card. Changing the angle changes the question the picture is answering: by depth the centre is what we actually know most about, by calibration the sealable core separates from the map-only rim.

most aligned least aligned Kolmogorov probability axioms Second law of thermodynamics (entropy) Conservation of energy (1st law of thermodynamics) Game theory (Nash equilibrium) Hermeneutics (the theory of interpretation) Maxwell's equations / classical electromagnetism Quantum mechanics (Schrödinger equation) Shannon information theory (entropy, channel capacity) The electromagnetic spectrum & modulation (radio to gamma, one axis) Acoustic wave theory (harmonics, Doppler) Chemical kinetics & equilibrium (Arrhenius, Le Chatelier) Euclidean geometry & the parallel postulate Fourier analysis & signal processing General relativity Bohr / quantum model of the atom Cell theory Chemical bonding (valence-bond / molecular-orbital) Cryptographic security (hashing, checksums, PKI) Differential equations (the language every physical law is written in) Linear programming & duality Newton's law of universal gravitation Newton's three laws of motion Spectroscopy (how we know what a distant thing is made of) Wave optics (Huygens, Snell's law, diffraction) Aperiodic tiling (Penrose, and the 2023 monotile) Central limit theorem Church–Turing thesis / computability Control theory & cybernetics (feedback, stability) Darwinian evolution by natural selection Fundamental theorem of calculus Homeostasis & physiological regulation Kinetic theory of gases Special relativity Statistical mechanics (Boltzmann — why the second law is a counting argument) Bayes' theorem Celestial mechanics / ephemeris prediction Central dogma of molecular biology (DNA→RNA→protein) Conservation of linear & angular momentum Crop rotation & biological nitrogen fixation (the low-input path) Fluid mechanics (Bernoulli, Reynolds, Navier–Stokes) Formal logic & epistemology (validity, inference) Germ theory of disease Graph theory (Euler, connectivity) Group theory & symmetry (the mathematics of what stays the same) Gödel's incompleteness theorems Haber–Bosch nitrogen fixation (bread from air) Linear algebra (vector spaces, eigenvalues) Mendelian inheritance Noether's theorem (symmetry and conservation) Nuclear decay & binding energy Nutrient cycling & agronomy (NPK, evapotranspiration) Standard Model / quantum field theory Structural & generative linguistics (Saussure, Chomsky) Zermelo–Fraenkel set theory (ZFC) Biochemistry & enzymes (catalysis at body temperature) Chemical engineering (unit operations, balances, and scale-up) Compartmental epidemiology (SIR models and R₀) Condensed matter & semiconductors (band theory and the transistor) Dalton's atomic theory Differential geometry (curvature measured from inside) Digital versus analog (why discreteness survives copying) Discrete units in living things (codon, gene, species, phoneme) Discrete versus continuous (the oldest dividing line) Dynamical systems & deterministic chaos Elasticity (Hooke's law, stress–strain) Electrochemistry & the battery (Volta, Faraday, and stored charge) Error-correcting codes (Hamming, Reed–Solomon) Evolutionary game theory (evolutionarily stable strategies) Hardy–Weinberg equilibrium Heat transfer (conduction, convection, radiation) Heisenberg uncertainty principle Heliocentrism & Kepler's laws Law of conservation of mass (Lavoisier) Measure theory (Lebesgue integration) Non-Euclidean (hyperbolic / elliptic) geometry Null-hypothesis significance testing (Fisher / Neyman–Pearson) Optimization & gradient descent (following the slope) Pauli exclusion principle Peano arithmetic axioms Phase theory (phase diagrams, Clausius–Clapeyron) Plasma physics (the fourth state, and most of the universe) Population ecology (Lotka–Volterra, carrying capacity) Quantum information & entanglement (von Neumann entropy) Quasicrystals (forbidden symmetry in real matter) Reliability & tolerance stack-up (RSS) Semiotics (sign, signified, interpretant) Simple machines & buoyancy (Archimedes) Spacetime & the quantum-gravity problem (where physics ends) Statistical learning theory (bias-variance, generalization) Stellar nucleosynthesis & the HR diagram Stoichiometry & the mole concept Structural statics (load, moment, floor-area ratio) Topology (what survives stretching) Vaccination & immune memory (Jenner to eradication) AC & the polyphase system (Tesla, and why the grid is alternating) Agricultural science (yield, soil-pH suitability) Algebraic geometry (solution sets as shapes) Antibiotics & antimicrobial resistance (Fleming's own warning) Antisepsis & handwashing (Semmelweis, Lister) Aristotelian rhetoric & fallacy taxonomy Ashby's law of requisite variety (the humility theorem) Atmospheric thermodynamics (dew point, lapse rate) Atomism (the idea that matter is not infinitely divisible) Big Bang cosmology & expansion (Hubble's law) Bioenergetics / energy balance (calorimetry, 4-9-4) Boolean algebra / propositional logic Brønsted–Lowry acid–base theory & pH Calendar theory (Gregorian reform, leap rules) Category theory (the mathematics of structure-preserving maps) Circulation of the blood (Harvey's quantitative argument) Combinatorial enumeration (permutations, combinations, binomial) Comparative advantage Computational complexity (P, NP, reductions) Contract theory & rule of law Counting & the integers (the first abstraction) Double-entry accounting identity (A = L + E) Electromagnetic induction (Faraday's law — how all electricity is made) Emergence & self-organization (more is different) Exercise physiology (VO₂max, HR zones) Fixed-point theorems (Brouwer, Kakutani) Fracture mechanics (Griffith, and why things really break) Fundamental theorem of algebra Fundamental theorem of arithmetic (unique factorization) Girih tiles — quasi-periodic design in medieval Islamic architecture Hydrologic cycle & open-channel flow (Manning, Darcy) Ideal gas law (PV = nRT) Landauer's principle (erasing information costs heat) Law of large numbers Liebig's law of the minimum (what actually limits growth) Mechanism design & auction theory Modern portfolio theory (Markowitz) Music theory (harmonic series, equal temperament) Network science (small-world, scale-free, robustness) Network theory (routing, addressing / CIDR) Neurons & the action potential (how a nerve carries a signal) Numerical analysis (why the computer's answer is not the answer) Ohm's law & circuit theory (Kirchhoff) Optimal packing & the honeycomb conjecture (Hales) Organic chemistry & functional groups (why life is built on carbon) Percolation & critical thresholds Periodic law (Mendeleev) Pharmacokinetics (dosing, clearance, half-life) Physical oceanography (hydrostatics, tides) Plate tectonics Power laws & heavy tails (Zipf, Pareto) Public choice / decision theory Quantization (why nature comes in whole units) Sanitation, clean water & oral rehydration (Snow's pump handle) Scaling laws & allometry (Kleiber's law, the square-cube) Signal detection theory (sensitivity, criterion, ROC) Supply & demand / market equilibrium Symbiosis & endosymbiosis (cooperation as a major transition) Systems engineering (requirements, interfaces, and emergent failure) Textual criticism (establishing what the text says) The Green Revolution (Borlaug, semi-dwarf breeding) The double helix (structure that explains its own copying) The immune system (innate and adaptive, and self versus not-self) Time value of money & discounting Translation theory (formal vs dynamic equivalence) Dimensional analysis & similarity (Buckingham Π) Explore versus exploit (the multi-armed bandit) Fractals & self-similarity (Mandelbrot) Hess's law / thermochemistry Historical chronology (era reckoning, elapsed years) Labor economics (minimum wage, overtime law) Map projections (why no flat map is honest) Normative ethics (consequentialism / deontology / virtue) Photographic exposure theory (exposure value, reciprocity) Prospect theory & bounded rationality (Kahneman, Simon) Pythagorean theorem Queueing theory (Little's law) Radiometric dating & uniformitarianism Real-estate valuation (cap rate, DCF) Sabermetrics / sports analytics (Pythagorean expectation, Elo) Seismology & earthquake magnitude (Richter / moment) The Carnot limit (the ceiling on every engine ever built) Third law of thermodynamics VSEPR theory (molecular geometry) Kolmogorov probability axioms Second law of thermodynamics Conservation of energy Game theory Hermeneutics Maxwell's equations / classica Quantum mechanics Shannon information theory The electromagnetic spectrum & Acoustic wave theory Chemical kinetics & equilibriu Euclidean geometry & the paral Fourier analysis & signal proc General relativity Bohr / quantum model of the at Cell theory Chemical bonding Cryptographic security Differential equations Linear programming & duality Newton's law of universal grav Newton's three laws of motion Mathematics (45) Physics (30) Chemistry (13) Life sciences (27) Earth (11) Applied (30) Humanities (11) Applied and social sciences (3) Physical sciences (8) THE FLOOR 178 theories · 285 relations · one body · most aligned at the centre
angle drag to pan · scroll to zoom · click a cell for its card
rests on limits shares a form node size = relations held · brightness = depth of the card · red ring = resting on almost nothing

What the drawing is telling you

theories178
relations285 · every one carrying its evidence
cross-domain pairs151
median relations per theory3
cards with real depth178 of 178 — the rest carry only the assay template, which is why the map is dim

Thin — a beam resting on almost nothing

These hold one relation or none. Not wrong; underbuilt. Each is a place to look for what it actually stands on.

Lone in its domain

One theory covering a whole field is a field we have barely entered.

Found and checked, never generated. Every relation carries the reason it exists; a relation without one is not written.