Perception demos

How long does it look? The Müller-Lyer illusion, measured three ways

Which horizontal line is longer? Most people see the line between the outward fins as longer than an identical plain line. That is the Müller-Lyer illusion. But how much longer does it look? To put a number on an impression, psychophysics has three classical methods. Try all three on yourself and compare what each one tells you.

Müller-Lyer, F. C. (1889). Optische Urteilstäuschungen. Archiv für Physiologie, Supplement-Band, 263–270. · Fechner, G. T. (1860). Elemente der Psychophysik. Breitkopf & Härtel.

How it works. The line between the fins is always the same length; only the plain line changes. Which figure is on top is random, and both are shifted sideways by a random amount, so you cannot simply line up their ends.
  • Adjustment: you set the plain line yourself. Fast, and it feels natural, but you control the stimulus, so your strategy enters the measurement. Half of the settings start too short, half too long.
  • Limits: the plain line grows (ascending series) or shrinks (descending series) by 4 % per display, and a series ends when your answer changes. The threshold of a series is the midpoint of its last two lengths. The order is predictable: if you keep giving the same answer too long (habituation), ascending series end higher than descending ones; if you switch too early (expectation), lower.
  • Constant stimuli: seven fixed lengths, ten times each, in random order. Nothing is predictable, and you get the whole psychometric function: the PSE is where it crosses 50 %, and its steepness tells you how precisely you judge length (the JND). The price is the largest number of trials.
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