Dimension

A dimension is the type, kind, or category that a factor belongs to—length, weight, time, money, color, cuteness. Quantities within one dimension share an underlying nature: 3 miles plus 5 miles makes 8 miles. Different units can share a dimension (meters and feet are both length), in which case a unit conversion lets you add them. But grams cannot be converted to dollars, inches, or cuteness, because those are different things entirely.

CF uses this to expose a flaw in standard scoring methods. In CF’s algebra of decisions, factors in the same dimension are like terms (quantitatively different, same variable part); factors in different dimensions are unlike terms (qualitatively different). You cannot add unlike terms into a single ranked score—just as you cannot add acres, hours, and grams. This is why weighted-factor sums and pro/con lists fail: they smuggle in arbitrary conversions of every factor into one made-up “goodness” dimension, with conversion factors invented rather than discovered. Multiplying dimensions is logically valid but usually yields meaningless multi-dimensional units (what is an acre-hour-gram?); only special cases like miles-per-hour mean anything.

General-purpose conversion between dimensions does not exist. Temple’s resolution is contextual: relative to a specific goal, most factors carry excess capacity, so differences below a breakpoint do not matter and a narrow, approximate conversion becomes legitimate. The narrower the goal-context, the more reliably distinct dimensions collapse into a single pass/fail evaluation.