Unit Conversion
also Conversion Factor · Dimensional Conversion
Translating a quantity between units of the same dimension by multiplying it by a ratio that equals one; legitimate within a dimension, generally unavailable across dimensions.
A unit conversion changes the units a quantity is expressed in without changing what it measures. You can swap meters for feet, or hours for minutes, because both units describe the same underlying dimension (length, time). The mechanism is multiplication by a conversion factor that equals one: since 1 hour = 60 minutes, the ratio 60min/1h is just a disguised 1, and multiplying by it is always permissible. This is not a matter of opinion; it is arithmetic, definitions, and fact.
CF’s specific point is about the limits of conversion. A general-purpose conversion factor exists only between units in the same dimension. There is no factor that turns grams into dollars, inches into cuteness, or one factor into another when they are qualitatively different things. Special-case conversions exist in fixed contexts (grams to liters of water at a set temperature, or a shop’s price per gram of gold), but no universal rate links unlike dimensions.
This matters for multi-factor decision making. To add factors and rank options, you must reduce them to one term, which requires converting everything to a shared dimension. Because the needed conversion factors usually do not exist, addition cannot combine factors honestly. This is the arithmetic face of CF’s like-terms vs. unlike-terms distinction: only like terms add. CF argues that weighted factor analysis hides this by inventing weights to convert everything into a generic “goodness” dimension, smuggling in pre-existing conclusions rather than deriving them.