Explore
Explore the map
Mettica’s first public corpus is still small. What is here already shows its shape: six domains, concepts that cross between them, and a depth model that applies to every idea.
Subjects
Domains
Each domain page lists its disciplines and the concepts it shares with other fields.
Philosophy
Being, knowledge, and value
ExploreFormal Sciences
Structure, inference, and proof
ExploreNatural Sciences
Mechanisms, models, and measurement
ExploreSocial Sciences
People, institutions, and behavior
ExploreHumanities & Arts
History, meaning, and expression
ExploreApplied Sciences
Knowledge put to work
Explore
Concept index
Concepts across disciplines
Select a concept to trace where it appears. The list carries the same connections on every screen size.
Hover over, focus, or select a concept to trace the disciplines it connects.
Symmetry
Invariance under transformation: formalized as a group, tied to conservation laws, used in structural design and artistic composition, and debated as a question about sameness.
Causation
What it means for one thing to bring about another: analyzed by philosophers, formalized in causal models, tested in experiments, and inferred from social data.
Revolution
Abrupt structural change: in political orders, in frameworks of thought, and in artistic movements.
Harmony
A fitting relationship among parts: heard in music, explained by acoustics, and expressed as numerical ratio.
Infinity
The unbounded: made rigorous in set theory, argued over in metaphysics, and evoked in art.
Feedback
Outputs that loop back to change the system producing them: control in engineering, homeostasis in biology, self-reinforcing cycles in markets and societies, and stability in dynamical systems.
Depth model
Symmetry at four depths
Every concept is designed to be approachable at four levels. Symmetry is the first fully sketched example.
Level 1
Intuitive
Orient the learner before requiring specialized vocabulary.
Symmetry: Looks the same after a change
Level 2
Conceptual
Make distinctions and relationships explicit.
Symmetry: Invariance under transformation
Level 3
Formal
Introduce the technical representation appropriate to the field.
Symmetry: The dihedral group D₄
Level 4
Advanced
Expose complexity rather than conceal it.
Symmetry: Symmetry and conservation