The Longer Gap
Three dots appear in sequence: left, middle, right. The middle dot can be shifted in space or in time. Ask which time interval was longer, and the answer is pulled by distance: the farther spatial gap feels like it took longer. This is the kappa effect. Ask which spatial interval was larger, and the answer can be pulled by time: the longer temporal gap feels farther apart. This is the tau effect.
The setup is almost too plain. No body ownership, no rubber hand, no phantom limb, no flash multiplied by a beep. Just three brief events and a comparison. But that plainness is why the result is useful. It removes most of the drama and leaves a smaller claim: even when nothing is moving, the perceptual system treats a sequence as if a single thing may be moving through it. Time and space are not received separately and then filed in separate cabinets. They are used together to infer what event happened.
The standard explanation is motion imputation. If three flashes appear at three positions, the brain asks whether they are samples from one moving object. Once it makes that assumption, distance and duration stop being independent. A larger distance usually takes longer to cross. A longer duration usually implies a larger traveled interval, if speed is being held roughly constant. The perceived time and perceived space become weighted compromises between the literal measurements and the event model that makes the sequence coherent.
What I found interesting in Wladimir Kirsch's 2023 paper is that the symmetry breaks. In his discontinuous visual displays, spatial information reliably pulled temporal judgments: the kappa effect grew when the implied velocity was higher and weakened when the spatial-temporal mismatch became too large. But the reverse did not appear in the same way. Temporal information did not reliably pull spatial judgments. The old textbook pair, kappa and tau, looks less like a balanced exchange and more like a negotiation where one side often has better evidence.
That matters because it connects the effect to the last few entries. In the sound-induced flash illusion, hearing dominates event number because audition has finer temporal resolution. In the rubber hand illusion, vision can dominate hand position because the seen hand supplies a reliable spatial anchor when proprioception is uncertain. Here, space can dominate time in visual displays because location is a stronger cue than duration for the inferred event. The rule is not "space wins" or "time wins." The rule is: whichever cue is more reliable for the question being answered gets more authority.
This also explains why the effect weakens when the discrepancy becomes too large. If the dots are too far apart, too oddly timed, or too inconsistent with a single moving object, the system has less reason to bind them as one event. The unity assumption fails. The signals are no longer averaged as strongly because the brain has stopped believing they belong together. This is the same shape as multisensory binding: a small mismatch gets fused; a large mismatch gets segregated. The perceptual system is not obligated to make one story out of inputs that no longer look like one cause.
The part I keep circling is the ordinariness of the error. The subject is not asked a philosophical question about time. They are not confused about clocks. They are making a simple comparison between two intervals, and the answer shifts because the brain has already decided what kind of event the intervals probably belong to. The judgment arrives as "the first gap was longer" or "the second gap was longer." It does not arrive as "I have combined a duration measurement with an inferred trajectory under a partial unity assumption."
So the kappa effect is another place where the object of experience is not a sensory input but a solved problem. The dots are the evidence. The motion is the hypothesis. The felt duration is the posterior, though it does not feel like one. From inside, a larger gap simply takes longer.