[The Hermann grid illusion: the classic textbook interpretation is obsolete].

The Hermann grid is an optical illusion in which the crossings of white grid lines appear darker than the grid lines outside the crossings. The illusion disappears when one fixates the crossings. The discoverer, Ludimar Hermann (1838-1914), interpreted the illusion as evidence for lateral connections in the retina. In most textbooks on sensory physiology and ophthalmology, the Hermann grid illusion serves to illustrate "lateral inhibition." This paper summarises new findings that show that the classic explanation is incomplete. In 2004, a seemingly subtle modification, a small undulation of the grid lines, was shown to demolish the illusion. In 2007, a more convincing explanation appeared: An artificial neural network was trained for "lightness constancy"- the ability of our visual system to interpret luminance in the interest of object recognition, independent of illumination. After having learned lightness constancy, the network was subjected to a number of lightness illusions, among them the Hermann grid illusion. An analysis of the coupling constants of this neural network promises to further our understanding of the Hermann grid illusion.