Foundational psychophysical regularity
Weber's
Law
Across a useful middle range, the smallest reliably discriminable change often scales with the starting stimulus. Perception is sensitive to proportion, not one fixed increment: adding 10 grams to 100 grams is not equivalent to adding 10 grams to 1,000 grams.
Hold the ratio constant. Watch the threshold grow.
Switch sensory examples and adjust the reference and comparison. The model predicts a 75% correct point when the change equals the teaching Weber fraction.
The comparison sits at the model threshold. Across repeated two-choice trials, this is defined here as about 75% correct - not a perfectly sharp moment of conscious detection.
The threshold increment grows with its reference.
Let I be a reference stimulus and ΔI the increment required to reach a chosen discrimination criterion. Weber's Law states that the ratio ΔI/I is approximately constant, k, within an operating range for a specified stimulus, observer, task, and method.
8 / 100 = 0.08
40 / 500 = 0.08
8 / 500 = 0.016
The last comparison shows the central idea: the same absolute increment can cross threshold at one reference and remain below it at another. The useful invariant is the ratio, not the raw difference.
A JND is not a tiny brick of sensation. It is an estimate from variable responses under a defined experimental rule.
There is no perfectly sharp sensory border.
Repeat the same comparison and responses vary. Sensory noise, external noise, attention, memory, adaptation, and decision strategy all contribute. Modern psychophysics therefore describes performance with a psychometric function linking stimulus difference to response probability.[5]
In a two-alternative task, guessing alone is correct on half the trials.
A common threshold convention is halfway between chance and perfect performance.
Lapses and noise mean fitted functions may never reach literal perfection.
Detection compares stimulus with no stimulus or background.
Discrimination compares two stimulus values. Weber's Law concerns this relation.
Experiment design is part of the result.
Randomized fixed levels
Present many preselected differences in random order, then fit the full psychometric curve. Reliable but trial intensive.
Strength: reveals curve shapeAscending and descending series
Move toward the transition from both directions. Efficient, but anticipation and habituation can bias responses.
Strength: simple historical methodObserver controls comparison
The participant adjusts B until it appears equal to A or barely different. Fast and intuitive, but vulnerable to control and stopping biases.
Strength: rapid exploratory estimateTrials follow performance
Correct responses make the task harder; errors make it easier. Modern procedures concentrate observations near threshold.
Strength: efficient threshold samplingGood experiments counterbalance order, control timing and adaptation, include enough trials, and model lapses. Threshold estimates without uncertainty can imply more precision than the data support.
There is no universal human Weber fraction.
Weber-like scaling has been investigated in weight, brightness, sound intensity, time, numerosity, spatial extent, vibration, and other dimensions. The apparent fraction depends on stimulus definition, range, background, duration, observer, training, and procedure.
Lifted loads
Weber's classic work compared weights. Active lifting, passive pressure, grip, movement, and simultaneous versus successive presentation change the cues available.
Luminance and contrast
Adaptation level and background matter. Near visual threshold, proportionality often gives way to other regimes.
Intensity discrimination
Frequency, bandwidth, duration, sensation level, and hearing status alter performance. Physical intensity and decibels are not interchangeable variables.
Scalar variability
Discrimination often worsens with magnitude, but generalized models can fit better than a constant fraction, especially for brief intervals.[8]
Weber, Fechner, and Stevens answer different questions.
Weber's Law
ΔI / I = kHow a difference threshold changes with the reference intensity.
Fechner's Law
S = c log(I/I0)Integrates equal JND steps under additional assumptions to obtain a logarithmic sensation scale.
Stevens' Power Law
S = aInModels reported sensory magnitude as a modality-dependent power function.[6]
Fechner's derivation is historically foundational, but the claim that every JND is an equal unit of sensation is an assumption, not something established by Weber's discrimination data alone. Stevens later argued that direct magnitude judgments are often fit better by power functions.
The regularity does not identify one neural cause.
Many systems can generate ratio-dependent behavior. Proposed explanations involve sensory transduction, gain control, neural variability, efficient coding, normalization, memory, and the evidence accumulated during a decision. Matching Weber behavior does not by itself choose among them.
Changes in strong inputs may produce progressively smaller changes in internal response.
If uncertainty grows with magnitude, a larger physical separation is needed to maintain discriminability.
Sensory systems adjust sensitivity to the prevailing range, making judgments reference dependent.
Observers integrate noisy evidence over time before choosing. Reaction time can therefore reveal constraints hidden by accuracy alone.[7]
A bridge from physiology to experimental psychology.
Published systematic work on touch, hearing, and lifted-weight discrimination in De pulsu, resorptione, auditu et tactu.[1]
Named and generalized Weber's relation in Elements of Psychophysics, while explicitly recognizing limited external validity.[2]
Separated sensitivity from response criterion and replaced a perfectly fixed sensory threshold with probabilistic decision models.
Advanced power-function accounts of perceived magnitude, challenging a universal logarithmic sensation law.
Adaptive procedures, hierarchical models, reaction-time analysis, and neural measurement connect behavior to candidate mechanisms.
Design above threshold - then validate in context.
Visible state differences
Adjacent weights, opacity levels, chart marks, and control states must differ enough under realistic display and viewing conditions.
Do: test the actual contextPerceptual control steps
Linear physical increments do not necessarily create equal discriminability across the full range.
Do: use calibrated psychoacousticsQuantity changes
A proportional change may be less noticeable than an equal absolute change at a smaller baseline, but detection does not predict approval.
Do: separate notice from preferenceTolerance specifications
Physical tolerances and perceptual thresholds can be compared when appearance, feel, or sound matters to product consistency.
Do: include observer variationWhat the compact equation leaves out.
"People notice a 10% change."
There is no universal percentage. The fraction varies with dimension, range, task, observer, and method.
"Below the JND, nobody notices."
Thresholds are probabilistic. Some trials will be correct below the estimate and some incorrect above it.
"Weber's Law describes preference."
Discrimination measures whether a difference can be detected, not whether it matters or is liked.
"Fechner's Law is the same formula."
Weber relates threshold to reference; Fechner proposes a subjective magnitude function.
"It works from zero to infinity."
Proportionality commonly fails near absolute threshold and can fail at high intensities or after a regime change.
"One quick adjustment measures k."
A professional estimate needs repeated trials, controlled conditions, a criterion, curve fitting, and uncertainty.
Signal detection theory
Separates discriminability from a participant's willingness or criterion to say "different."
Psychometric functions
Link a physical comparison to the probability of a response across repeated trials.
Goodhart's Law
Reminds designers that optimizing one perceptual threshold can distort broader product goals.
Benford's Law
Contrasts a psychophysical ratio with a mathematical distribution of significant digits.
Sources and further reading.
Historical works, peer-reviewed methods, open scientific reviews, and primary research are prioritized.
- Ernst Heinrich Weber (1834) - De pulsu, resorptione, auditu et tactuWeber's foundational experimental work on touch, hearing, and discrimination.Google Books digitization of the 1834 volume
- Gustav Theodor Fechner (1860/1912) - Elements of Psychophysics, selectionsHistorical English translation of Fechner's measurement argument and discussion of Weber's Law.Classics in the History of Psychology, York University
- Muniak et al. (2013) - An Undergraduate Laboratory Exercise to Study Weber's LawA clear experimental account of JND measurement with vibrotactile amplitude.Journal of Undergraduate Neuroscience Education
- Green and Swets (1966) - Signal Detection Theory and PsychophysicsThe foundational framework separating sensory sensitivity from decision criterion.APA PsycNet record
- Wichmann and Hill (2001) - The Psychometric Function: Fitting, Sampling, and Goodness of FitModern methods for fitting psychometric functions and assessing uncertainty.doi.org/10.3758/BF03194544
- S. S. Stevens (1957) - On the Psychophysical LawThe classic case for power-function models of subjective magnitude.Psychological Review 64(3), 153-181
- Akrami et al. (2008) - Weber's Law in Decision MakingBehavioral and neurophysiological modeling of ratio-dependent discrimination.Journal of Neuroscience 28(37), 9150-9160
- Toso et al. (2021) - Adaptive Psychophysics in Subsecond Interval TimingAn example showing generalized Weber behavior and careful threshold estimation in time perception.Frontiers in Behavioral Neuroscience
- Johnson, Hsiao, and Yoshioka (2002) - Neural Coding and the Basic Law of PsychophysicsA review connecting Weber, Fechner, Stevens, and candidate neural codes.The Neuroscientist 8(2), 111-121
- Oberfeld (2008) - Intensity Increments: Weber's Law RevisitedAuditory evidence illustrating the distinction between threshold and clearly suprathreshold changes.Journal of the Acoustical Society of America