Steven’s Power Law
While reading Principles of Neuroscience (I have a physical copy of this 1,646-page textbook and it’s awesome), I learned of a pretty cool fact. In 1953, Stanley S. Stevens demonstrated that the subjective experience of the intensity (I) of a stimulus (S) is best described as a power function. Stevens’s law states that:
$$I = K(S - S_0)^n$$where the sensory threshold \(S_0\) is the lowest stimulus strength (this reminded me of FeatureChangeSM in Monty from the Thousand Brains Project) a subject can detect, and \(K\) is a constant.
I looked up in Wikipedia for some values of \(n\) for different modalities. Just as a brief note:
\(n < 1\) means perception compresses the stimulus (diminishing returns)
\(n \approx 1\) means linear perception
\(n > 1\) means perception amplifies the stimulus (increasing returns)
While values are highly dependent on stimulus conditions, I created a table below for some sensory modalities:
| Sensory Modality | Approx. η Value | Interpretation |
|---|---|---|
| Brightness (light) | ~0.3 – 0.5 | Strong compression — large changes in intensity feel mild |
| Loudness (sound) | ~0.6 | Still compressive — doubling sound pressure doesn’t feel twice as loud |
| Weight (heaviness) | ~1.45 | Superlinear — we perceive heavier objects as more than proportionally heavier |
| Length (line size) | ~1.0 | Linear — perception matches physical length |
| Electric shock (pain) | ~3.5 | Highly expansive — small increases feel exponentially stronger |
| Taste (saltiness) | ~1.3 | Perceived intensity grows faster than physical concentration |
| Vibration | ~0.7 – 1.0 | Varies depending on frequency and amplitude |
One interesting dichotomy was discomfort from cold (1.7) vs. discomfort from warmth (0.7). I personally handle cold weather much better than warm weather, though I suppose it doesn’t mean the exponent will be significantly different. I wonder how much variation there is in the exponent values in the population? 🤔 What about the context? Or cross-modal interactions?
To any sensory neuroscientists who may be reading this, how prevalent is Stevens’s Power Law in current literature? How is it used? Have there been any more nuances or a completely different law or method to measure subjective experience of sensory modalities?