Quantitative Relationships & Scaling

Primes about fundamental ways of relating quantities to each other, including ratios, gradients, exponentiation's repeated scaling, half-life's decay timescale, discrete-versus-continuous representation, and partitioning one quantity across exclusive channels.

6 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

• Discrete vs. Continuous (Quantization) — Step vs continuous evolution.
• Exponentiation — Repeated multiplication scaling.
• Gradient — Distribution and change over space/time.
• Half-Life — Time to halve quantity.
• Input Partition — One incident quantity is split among mutually exclusive output channels whose amounts or fractions exhaust the input, so changing one share necessarily changes at least one other under a closure constraint.
• Ratio — Compare one quantity with a nonzero reference quantity by division, so the quotient states how much numerator obtains per unit of denominator and stays interpretable only while both quantities, their units, and their scope are named.