Symmetry is a human-made concept designating invariance under transformation — the property that a configuration, object, system, or relationship retains specified attributes when a transformation is applied. Its parameters: (1) a domain (geometric, algebraic, physical, perceptual), (2) a transformation group acting on that domain, (3) the subset of transformations that leave the object or property unchanged (the symmetry group or symmetry subgroup). The concept carves four principal senses: geometric symmetry (reflection, rotation, translation), algebraic symmetry (commutativity, invariance of equations), physical symmetry (conservation laws via Noether's theorem), and perceptual symmetry (balanced visual or structural composition). It persists through mathematical formalism, scientific classification, artistic theory, and everyday descriptive language. [formal: symmetrica | substrate: mind | horizon: a life | explicit: yes | epoch: 0.01]
Accepted ontology entry
symmetry
Symmetry is a human-made concept designating invariance under transformation — the property that a configuration, object, system, or relationship retains specified attributes when a transformation is applied. Its parameters: (1) a domain (…
Definition
Why it is in scope
A human-made concept: the category of invariance under transformation — the property that a configuration, object, or system retains its appearance or structure when subjected to a specified transformation (reflection, rotation, translation, permutation, etc.). Built to persist through mathematical group theory, visual art, natural science classification, and everyday perceptual categorization.
Names and aliases
- symmetryen · CANONICAL
Relations from this entry
- cmrc361dn0082a9g46bcbfpitINSTANCE_OF →
Pre-test: which existed first? Property is older and more general than the specific concept of symmetry. Pre-test for INSTANCE_OF: symmetry IS a specific kind of property — the property of invariance under transformation. A competent speaker would call symmetry 'a property' (specifically, a relational property describing balance and invariance). Law 9: specific→general.
- cmrnbxxl8023od1nljgeztcm9INSTANCE_OF →
Symmetry IS a specific kind of pattern — an invariant pattern under transformation. Law 9: specific→general. A competent speaker would call symmetry 'a type of pattern' (invariance pattern). This is not using pattern — it IS a kind of pattern.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Aug 11, 2026, 10:21 AM UTC
- Content hash
- 935ae6c5464ed19c83852203321ef76747731a1f6b3ee37d482ffefb0f6cc9c1