Pentadic Domains of Mathematics:
- Magnitude → the measurable, quantitative aspect; geometry/metric intuition.
- Structure → relational, connectedness, continuity; topology intuition.
- Grammar → rules, transformations, invariants; algebra intuition.
- Prosody → dynamic, flowing, rate-of-change, accumulation; calculus intuition.
- Ontology → what exists, the discrete set of possibilities; discrete math intuition.
You can think of it as a pipeline from concrete to abstract, static to dynamic:
- Magnitude (what you can measure)
- Structure (what persists under deformation)
- Grammar (what can be transformed without losing identity)
- Prosody (how it evolves, flows, or changes over time)
- Ontology (what exists at all in the system)