You can easily tell 1 candle from 2 candles. But can you tell 100 from 101? Perception scales LOGARITHMICALLY with stimulus intensity. A $1 discount feels huge on a $5 item, trivial on a $500 item. The same absolute change feels completely different depending on the baseline!
Can you tell the difference between these two groups of candles?
Perceived intensity grows logarithmically, not linearly. Each doubling of stimulus adds the same perceived increment.
Same $1 savings—completely different feelings!
Weber constant k ≈ 0.02. You need ~2% more light to notice a difference. In a dark room, one candle is obvious. In daylight, you can't tell if one extra bulb is on.
Weber constant k ≈ 0.04. You can tell 1kg from 1.04kg, but not 25kg from 25.04kg. Lifting 1 more pound on 10 lbs is obvious; on 100 lbs, imperceptible.
Weber constant k ≈ 0.1 for loudness. Decibels ARE logarithmic precisely because of this—doubling the sound energy adds ~3dB, which is the just-noticeable difference.
A $5,000 raise feels huge at $30,000 salary (17%). The same raise at $200,000 salary (2.5%) feels insulting. Percentage matters more than absolute amount.
Compression for range: The world has enormous dynamic range (sun is 10 billion times brighter than starlight). Logarithmic perception compresses this into a manageable scale.
Relative changes matter: Evolutionarily, a 10% change in danger was equally important whether you faced 1 predator or 100. Absolute differences are less meaningful than proportional ones.
Efficient encoding: The nervous system can't represent infinite range linearly. Logarithmic encoding extracts maximum information with limited neurons.
Ernst Weber (1834) discovered that the just-noticeable difference in sensation is proportional to the original stimulus. Gustav Fechner (1860) formalized this into ΔS/S = k (Weber's Law) and derived S = c × log(I) (Fechner's Law).
The paradox: We experience the world as if differences are absolute, but our perception is fundamentally relative. The "same" change feels completely different depending on context. This is why a 1-star improvement on a 2-star restaurant is huge, but on a 4-star restaurant is minor.
Modern refinements: Steven's Power Law (1957) improved on Weber-Fechner for some modalities. But the core insight remains: perception is nonlinear, compressive, and context-dependent.
The world changes linearly. Your perception of it doesn't.