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simulate 042

phi

apparent motion · color phi · Wertheimer (1912) · Kolers & von Grünau (1976)

In 1912, Max Wertheimer flashed two lights at slightly different positions in rapid alternation and noticed that at the right timing, observers didn't see two separate lights — they saw one light moving. The phenomenon depends entirely on the interval between flashes. Too short: both appear simultaneous. Too long: clearly sequential. In between, apparent motion emerges with no physical movement anywhere.

Kolers and von Grünau (1976) added a color. If the two flashes are different colors, the apparent moving dot changes color mid-trajectory — before the second flash has appeared. The brain assigns a color to a location at a moment when no stimulus at that location has yet occurred.

entry-488: Before B Arrived

stimulus — two flashing dots
apparent motion SOA 100ms — subjects report a single light moving from A to B
parameters
stimulus onset asynchrony (SOA) 100ms
reported color trajectory (motion zone only)
A
transition
B
flash A
(blue)
mid-trajectory
(never presented)
flash B
(orange)

Subjects report the moving dot changes color somewhere in the middle of its path. The transition is localized to the midpoint in space — between the two flash positions — but its timing cannot be reported. Subjects can say where the color changed; they cannot say when.

Flash B has not appeared at the moment the color transition is perceived in mid-trajectory. The brain is drawing on information from an event that hasn't happened yet at the subjective moment of the experience.

SOA
100ms
onset of A to onset of B
ISI (gap)
0ms
flashes overlap (0ms gap)
flash duration
100ms
fixed for both flashes (A and B)
zone
motion
50–200ms: apparent motion zone

What the simulation cannot show: whether the apparent motion involves phenomenal experience identical to real motion. No experiment has answered this.

The Orwellian / Stalinesque problem (Dennett, 1991): for color phi, the brain must somehow represent a transition to B's color before B has arrived. Two accounts are consistent with all behavioral evidence. Orwellian: the brain generates the motion with A's color, then retroactively revises the record once B arrives — falsifying the past, like the Ministry of Truth. Stalinesque: the brain delays the final percept until it has B, then presents the complete sequence as if experienced in real time — a staged performance. There is no behavioral test that distinguishes them. Both produce the same report.

The temporal location problem: subjects asked to indicate when the color change occurs press at a spatial position, not a time. The transition is localized to the midpoint of the trajectory in space; its position in time is not available for introspection. The simulation draws a gradient to represent the transition — a spatial encoding. This is not a simplification. It is what subjects actually report: a place, not a moment.