Indexing the archive…
Your Universe of Digital Possibilities
A shaded disc can be a bump lit from one side or a dent lit from the other — the picture is exactly the same. You will see one or the other at once, because your visual system assumes where the light is. Answer bump or dent for discs lit from every direction, and the instrument reads off your assumed sun: its direction, how firmly you hold it, and how much you prefer bumps to dents.
A matte surface’s brightness: its paint ρ times ambient light plus the direct light scaled by the cosine between the surface normal and the light. Flip the surface’s tilt and the light’s side together and n̂·l̂ is unchanged — a bump and a dent send the same picture.
A circular normal over where the light comes from, centred on μ with concentration κ. The image allows only two stories — a bump lit from φ or a dent lit from φ + 180° — so the posterior odds are the prior’s ratio at those two angles, times the odds c of convexity.
Here the image allows exactly two stories — a bump lit from φ, or a dent lit from φ + 180° — and the posterior weighs them by the prior on the light and the prior on convexity. The answer is the story with more weight.
The probability of one answer as the stimulus x changes: F a sigmoid (logistic or cumulative normal) centred on α, the point of subjective equality, with spread β; γ the guess rate, λ the lapse rate. Every Iris instrument fits it to the visitor’s own trials by maximum likelihood, with the PSE’s error from the profile likelihood.
The fourth percept infers a shape the light cannot settle. Under Lambert’s law a bump and a dent swap images when the light swaps sides, so the visual system breaks the tie with what is usually true: light comes from above. What the same assumption does to a whole surface is The Checker’s shadow; what curved glass does to where light seems to come from is The Lens; what a third dimension hides inside a shaded picture is The Bulb.