CF Dictionary · Decision Making
Dimension
The unit of a factor. CF treats different-dimension factors as incommensurable — you can't directly add them.
A dimension is the unit or kind of a factor. "Dollars" is a dimension. "Cuteness" is a dimension. "Miles per gallon" is a dimension.
Why dimensions matter in CF
You cannot directly combine factors of different dimensions. "$20 + 5 cuteness" is not a meaningful quantity — there's no rule for adding dollars and cuteness.
"you cannot add -20d + 5c. there's literally no way to combine them."
This is the central insight of CF's multi-factor-decision analysis.
Same-dimension factors combine easily
- $20 + $30 = $50. (Same dimension: dollars.)
- 5 miles + 3 miles = 8 miles. (Same dimension: length.)
- 1 kg + 2 kg = 3 kg. (Same dimension: mass.)
Different-dimension factors don't combine naturally:
- $20 + 5 cuteness = ??? (Different dimensions.)
- 1 kg + 2 meters = ??? (Different dimensions.)
The multi-dimensional unit exception
Some multi-dimensional units are useful — when they correspond to a real-world concept:
- Miles / hour = speed. Real, useful.
- Dollars / pound = price per pound. Real, useful.
CF calls these "useful multi-dimensional units." Most combinations aren't useful.
CF's rule
- Same dimension. Combine freely.
- Different dimension. Convert via a real relationship (rare), or evaluate separately via pass-fail.
"whether you view them as units in different dimensions or variables, that is maximally simplified. the only way to simplify further is if you have another equation, such as a conversion factor, like 5d=1c that tells you how many dollars are worth a cuteness." — criticalfallibilism.com