Like Terms vs Unlike Terms
also Like terms · Unlike terms · Commensurable vs incommensurable terms
An algebra analogy CF uses to show that only terms sharing the same variable part (the same dimension) can be added, while terms with different variables cannot be combined into one.
In elementary algebra, a term is a coefficient times a variable part (e.g. 4x). Terms are like when their variable parts are identical (x, 5x, 22x; or 3xyz and 17xyz) and unlike when they differ (5, 5y, 5x). Only like terms can be additively combined: 3x + 2x simplifies to 5x because you are adding different amounts of the same thing. Unlike terms such as 3x + 8y stay stubbornly separate—just as “3 pounds of bacon + 2 apples” cannot be merged into a single quantity.
CF promotes this from arithmetic trivia to a decisive argument about decision making. A factor in a decision belongs to some dimension (price, cuteness, weight, time). Factors in different dimensions are unlike terms. So summing weighted factors—the heart of weighted factor analysis and pro/con lists—is mathematically as invalid as writing 3 acres + 8 hours + 5 grams. You cannot reduce it to one term, and without one term you cannot rank options.
The only legitimate escape is unit conversion, which works within a dimension because the units measure the same underlying thing. Across dimensions there is generally no honest conversion factor (no fixed amount of cuteness equals a dollar), so converting everything to a made-up “goodness” dimension smuggles in arbitrary weights.
CF’s contrasting move is multiplication of binary factors rather than addition of analog ones: pass/fail values multiply cleanly regardless of dimension, yielding yes-or-no evaluation grounded in good enough thresholds. The like/unlike-terms point is thus the negative half of the case—diagnosing why the dominant additive methods cannot work.