Two lights flash in sequence. Your task: report which came first. At long intervals the answer is obvious. Below a threshold — around 20–30ms for visual stimuli — order becomes ambiguous or invisible. Events closer together than this are experienced as simultaneous even when they are not.
The psychometric function maps this transition. At each stimulus onset asynchrony (SOA), the proportion of "B first" responses traces an S-curve. Where it crosses 50% is the point of subjective simultaneity (PSS) — the SOA at which you report each order equally often. The PSS is often not at zero: there are systematic biases in how quickly different signals reach awareness.
The simulation samples 11 SOA levels symmetrically: −300, −200, −100, −50, −30, 0, +30, +50, +100, +200, +300 ms. Positive SOA means A appeared first; negative means B appeared first. Each level is sampled roughly equally (the algorithm picks whichever level has the fewest responses so far). Each flash lasts 80ms. At short SOAs there is temporal overlap: both circles are on simultaneously for part of the flash. This is normal — it is the onset-to-onset interval that matters for temporal order perception, not whether they overlap.
Typical visual-visual threshold is 20–30ms. Below this, order is invisible. The PSS — where the psychometric function crosses 50% — should be near zero if both circles are processed equivalently. If it deviates, one stimulus is being processed faster: possibly due to eccentricity, brightness, or attentional asymmetry. In real experiments, the visual-auditory PSS is often offset by ~40ms: a sound must precede a light by that much to feel simultaneous, because visual cortex processing takes longer. This simulation is visual-visual, so the bias should be small.
The JND (just noticeable difference) is estimated as the half-width of the transition zone between 25% and 75% on the curve. A smaller JND means finer temporal resolution.
What the simulation can show: your own psychometric S-curve, the location of your PSS, the width of your temporal grain. What it cannot show: the neural mechanism of temporal binding; what events feel like below threshold (ambiguous? absent order? fully simultaneous?); whether the S-curve slope reflects a single threshold or a distribution of thresholds across trials.
This simulation relates to entry-489 (No Knife-Edge) on the specious present, but it measures something different. The TOJ threshold (~30ms) is the grain: the resolution of temporal experience, the smallest detectable interval. The specious present (~3000ms) is the window: how far back "now" extends. A 3-second specious present contains roughly 100 temporal grains of 30ms each. Both are measured behaviorally. Neither is accessible from inside.
temporal order psychophysics specious present grain vs window psychometric function