Believe only half of what you see, and nothing of what you hear
Dinah Craik 1858
Introduction
In this activity you will learn that an honest report of what someone sees is not necessarily the "truth." A pencil is used to obscure the boundary between two gray areas. When the pencil is in place, you see one uniform gray area. When the pencil is removed you see two gray areas with different darknesses. But you never see the truth: both gray regions are identical to each other and grade from light gray at the left edge to dark gray at the right. In general your eyes and brain ignore slight gradations in gray.
Material
2 Exploratorium Gray step Postcards.
Or print out the gray step images at the end of this snack.
Assembly
Cut one of the gray steps in half down the middle, trim the black regions off the edges.
To Do and Notice
With a pencil over the junction between the gray regions ask another person, "What do you see?"
Most often they will say they see a pencil covering a gray rectangle.
Then I say,"You look like an honest person," and remove the pencil revealing the gray step.
Then I ask again, "what do you see?"
People now report that they see the page divided into two gray halves one lighter than the other.
I say "You look like an honest person."
Then move the two halves of the optional gray step so that one is lined up with its bottom above the top of the first to show that both halves are identical.
Then move the right gray area to the left.
The bright one now becomes the dark one.
What's Going On?
A photometer would show that the gray regions change darkness by four percent from one side to the other, your eye does not see this change.
The eye is sensitive to changes in gray level if they are great enough or if they occur over a short distance. After all, you can tell the difference between white and black which are extreme shades of gray.
When one portion of your retina is illuminated by brighter light the sensitivity of the retina in nearby surrounding areas is turned down, this is called lateral inhibition. Conversely if one region is in the dark the sensitivity of surrounding regions is increased. This means that a dark region next to a bright one looks darker and a light region next to a dark one looks brighter than either would look if surrounded by gray. As a result your visual system is most sensitive to changes in brightness imaged over a small region of the retina.
When the pencil is in place the two different grays are spread apart on the retina so that the grays are not in adjacent regions and lateral inhibition does not function. When the pencil is removed the two shades of gray fall on adjacent regions of the retina and lateral inhibition enhances the visibility of the difference between the grays.
So What?
Lateral inhibition allows for the reduction in the amount of information transmitted from the optic nerve down the retina. There are on the order of 100 million receptors (rods and cones) in each retina and merely one million neurons in the optic nerve To transmit all the information to the brain, the optic nerve would have to be as wide as the entire eye, the resulting blind spot in a human eye would be as big as the eye. As a result, the eye sends only part of the information it records down the optic nerve to the brain. The brain then creates our perception of the world. The optic nerve does not convey to the brain information on gradual brightness changes it conveys and emphasizes abrupt changes. The information going to the brain is reduced by a factor of 100, and what you "see" is not necessarily the image formed on your retina.
Engineers use similar processing to reduce the amount of computer memory necessary to store a digital image. The data necessary to reproduce a 1 megapixel photograph often can be compressed to a hundred thousand bytes or so.
Further Inquiry
I also ask the observers for suggested experiments.
Examples, I have received are:
Use a fatter or thinner object than the pencil. Try a string, and a thread.
View the gray step from different distances.
Notice in both of the above experiments that it is the angular width of the object covering the edge that matters. A wide object works better at normal viewing distances. However a narrow object works well when viewed closely.
Vary the color of the object.
Notice that some colors work better than others, black pencils work best for me.
Cover only a part of the edge, e.g. the top half.
Use a photometer, a photographers spot meter, it will see the difference from one side of each gray step to the other while the human eye does not.
Work with the cut-up cards, you will discover many neat effects:
Hold cut-ups side by side rotate one.Cut the cards into square regions and rotate one square next to another. Examine all four possible orientations of the square.
Cut a gray step card in half along the center line. Cut one side into a disk, place it over the other, uncut, side. Rotate the gray step disk in front of the gray step card.
Cut out the two regions of the gray step card. Place them over a white piece of typing paper. Rotate the two gray steps so that the white edges are together in the middle, then rotate them so the dark edges are together in the middle. Note how the darkness of the cards changes against the background.
Etc
In telescope views of Mars Percival Lowel saw Canals, straight dark lines on the planet. Other observers saw a green wave spread from the north pole each northern hemisphere Martian spring. Some people interpreted these as signs of intelligent life on Mars. They were signs of intelligent life all right, the human eye-brain system. Humans will sometimes see a row of blotches as a straight line. The green wave was actually gray, but it appeared green next to the background red color of Mars.
Math Root
How finite difference derivatives can be used to model how the retina works.
The Electric Blanket model of Lateral Inhibition
Consider an electric blanket with two separate controls, one for the right side and one for the left. Place a husband and wife in the bed and give them the two controls, however give the husband the control for the wife's side and the wife the control for the husband's side. As soon as the husband begins to get cold he turns up his control, this makes his wife warm so she turns down her control making the husband colder. This result is like that for lateral inhibition. The husband gets colder and the wife gets warmer.
Further reading
Lightness Perception and Lightness Illusions, Edward H. Adelson
The scientific American Library book Eye, Brain, Vision
Seeing the Light, by David Falk, Deiter Brill, and David Stork
Eye and Brain, by Richard Gregory
Print these grey step cards on a high quality printer This next image is large and will take a long time to load and print.
The eye is so sensitive to edges that this must be printed at high resolution.
Gray Step postcard replacement Done in photoshop.
4% gradient from 84% brightness to 80% brightness.
Gray Step Images available in two different values of the amplitude of the gray step with five different resolutions.
10% Gray step 300 pixels
10% Gray step 600 pixels
10% Gray step 1200 pixels
10% Gray step 2100 pixels
4% Gray step 300 pixels
4% Gray step 600 pixels
4% Gray step 1200 pixels
4% Gray step 2100
pixels
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Scientific Explorations with Paul Doherty |
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22 May 2000 |
