11 thoughts on “Which is Darker, the A or B Square?”

  1. What is illiminance? That didn’t seem to cause a protest while I was keyboarding. Keystroke errors are not the same as misunderstood concepts…

  2. There is another aspect of the neurology involved in the Adelson checkerboard; one that was part of the bioengineering study that was set up in a research lab at Rush Presbyterian St. Lukes Hospital as part of a cooperative environment while the University of Illinois at Chicago Circle was far from completing its campus.

    This, again, was integral to my undergraduate bioengineering studies. What the Adelson checkerboard does is a form of separation of brain functions, so that declarative brain function is surprised by finding that the luminance of both squares are effectively the same, while the procedural brain function automatically corrects for the reduced illumination within the shadow and correctly (no illusion) categorizes all the darker squares as having very nearly the same reflectivity and correctly categorizes all the lighter squares as having very nearly the same reflectivity; thereby accurately informing a person moving through the person’s physical three-dimensional (leaving out time as a dimension because the top picture does not change) of the nature of the object, instead of the nature of the object as altered by its varying incident illumination.

    The cognitive dissonance of learning that the luminance from the lighter square, B, is the same as the luminance from the darker square, A, results from cognition not being set up to process procedural experience.

    This distinction, very clear to me for more than 50 years, is partly made in neurologist Robert Scaer’s book, The Trauma Spectrum, W. W. Norton, 2005. Scaer’s focus is directed toward declarative memory and procedural memory issues; my work includes those memory issues and even more the neurological processes which deal with processes and their categorization.

    At work is a subtle cognitive equivocation, as to the meaning of the shade of gray. I shall make use of alternative spellings of grey, to illustrate that one thing may have to names which are both different and the same, and I shall separate the meanings so that is, in this illustration, no longer so.

    I shall use “gray” as a word for surface reflectivity, which is the proportion of incident illumination which becomes the observed luminance from a particular uniform surface area. In this sense of gray, the gray scale ranges from 0 (all incident light absorbed) to 1 (all incident light reflected)

    I shall use “grey” as a word for the observed luminance or incident illumination, whether incident or reflected. In this sense of grey, using the General Electric Model 80W40Y16 light meter from my engineering laboratory, the measurable grey scale ranges from 0.5 footcandles to 1000 footcandles.

    Methinks the narrator on the video clip makes an equivocation error, for I hear his talking of shade of gray and shade of grey as though they were the same thing, whereas, using my definitions, shade of gray cannot be the same as shade of grey because the dimension of gray is a fraction (reflected divided my incident, constrained to be not less than 0 nor more than 1′ where as the dimension of grey is footcandles if one is using my GE light meter, and is constrained to be not less than 0 and not more than all the light in the universe at a distance of 0 from the light meter (what light meter?) illumination intensity would perhaps tear apart any string-theory strings of which the light meter might be made?

    Equivocating a physical property of a surface (reflectivity)” with an external factor not a property of the surface (incident illumination) befuddles the scientific significance of Adelson’s checkerboard.

    Observable total reflected luminance is the total luminance incident to the surface multiplied by the surface reflectivity.

    That is a simplification. First, note that I am using luminance in the photometric sense, which is not the same as illuminance or illumination. The luminance of a point source of light diminishes as the square of the distance of the photometry from the source. The luminance of an infinite line radiator source falls of as the distance of the photometry from the source. The luminance of an infinite plane radiator source is independent of the distance of the photometry from the source. For a time, I was a member of the Society of Photo-Optical Instrumentation Engineers. That was over twenty years ago. Hurtrer-Driffield? Familiar with that, Lambert-Beer, likewise. I never drink Lambert Beer, though, and not because I imagine it would be tasteless.

    While the reflected light (shade of grey) will be proportional to reflectivity (shade of gray), and incident illiminance (shade of grey), grey and gray (as above defined) ain’t nohow the same.

    Perhaps the narrator is as unfamiliar with the distinction between shades of grey and shades of gray (as above defined; I just wrote them thar definitions, how could he be familiar with them?) as he is unfamiliar with the neurological distinction between the procedural brain process of making sense of objects through the mechanisms of human eyesight and declarative models of said process.

    In the manner that reflected light is not the same as reflectivity, so I deem being told about something is not the same as having actually done the something. The last time I thought I might have a tad bit of success sharing this tidbit of neurological wisdom, the resulting brouhaha here rather astonished me. Perhaps this Adelson checkerboard thing will help doubters realize there may be something useful in understanding the constrast between declarative and procedural brain functions and structures and how they interact in ways that help us construct our working models of our lives in the context of living.

  3. I enjoy that illusion very much but until I read the explanation I didn’t understand the science of it. I visit the below site now and then and it has all manner of optical illusions.


    Brian, I have read that the science behind feature extraction is a growth field. Computers are going to have to be taught to do it in order to process the enormous amount of visual data our satellites produce for government purposes. At last reading on the subject (Discover Magazine I think)the computers do/would not take the place of humans but determine which images have potential to be referred to humans, much like the language bases searching done for various electronic communications that are monitored.

    “In somewhat similar sorts of ways, perchance errors of interpretation are what lead people to accept as reality what sometimes may actually be of delusion.”

    That is a deep error indeed and one we see in operation all around us. On any given day you can find that in the postings on any thread of even this blawg, I know this because some/many of those errors are mine 🙂

  4. There is no illusion; simply normal visual image processing using the biology of feature extraction which is essential for moving about in the 3-space + time world wherein we live. An actual three dimensional object with alternating (checkerboard) squares having only two reflectivity (aka, reflection coefficients), one less reflective than the other, would, on a photograph, appear as in the Adelson image, given the apparent shadow.

    The human visual system is elegant, and rather well optimized for the routine activities of everyday living. What is perceived, with remarkable accuracy, would be, for a real three dimensional object partly shaded by an object which reduces the incident illumination of part of the larger object is of the properties of such an object, namely reflectivity spatial variation over the surface of the object.

    The mental model of the object in the simulated photograph remarkably affirms the properties of such a real object as would, if photographed well, result in such an image. There is no illusion of lighter and darker are of the reflectivity of the surface represented in the simulated photograph. The brain models shade of gray as reflectivity (a property of the object) and not as the reflected light as a combination of incident light intensity and reflectivity.

    Understanding this stuff was part of my undergraduate bioengineering education in the late 1960s. There is no illusion, and no serious error of perception. The error regarding the image is to be found in the interpretation made of what is perceived.

    In somewhat similar sorts of ways, perchance errors of interpretation are what lead people to accept as reality what sometimes may actually be of delusion.

  5. I love this illusion. It’s a great illustration of how fallible our perceptions can be.

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