THE NEXT TIME YOU ARE watching a spinning propeller, rotating fan blades or anything else turning rapidly, start humming. By changing your pitch until you reach a certain frequency you can make the rotation (as you perceive it) seem to slow down, stop or move slowly in the opposite direction. Another visual illusion you can test yourself is the appearance of blue arcs when you look under certain conditions at a small light. The humming experiment can be explained but the blue-arc illusion remains something of a puzzle.

It is usually possible to perceive any regular fluctuation if its frequency does not exceed about 40 hertz (cycles per second). At higher frequencies the fluctuations blend together. Imagine a pattern of radial black and white sectors mounted on the turntable of a phonograph and rotating at 33 1/3 revolutions per minute. If the pattern moves across your field of view slowly enough because the rotation is slow or the sectors are wide, the sectors remain visible. At higher speeds the sectors blend into a uniform gray.

In 1967 W. A. H. Rushton of the University of Cambridge reported that an observer can stroboscopically "freeze" such a rotating pattern even when the motion is fast enough to fuse the sectors. All the observer has to do is to hum at the appropriate frequency. At a slightly lower frequency the strobe pattern moves slowly in the same direction as the true rotation. At a slightly higher frequency it reverses direction. The finding was made independently in 1974 by Marlin S. Werner of the Speech and Hearing Center in Oakland, Calif. The cause of the stroboscopic effect was investigated further in 1979 by H. A. K. Mastebroek and J. B. van der Kooi of the Laboratory for General Physics at Groningen in the Netherlands.

The radial pattern employed by Rushton is on a disk often supplied with home audio equipment for checking the speed of the turntable. The check is made by illuminating the disk with a

household lamp energized by alternating current. In the U.S. such current reverses direction at a frequency of 60 hertz, causing the lamp to fluctuate in brightness at a rate of 120 hertz. The black and white sectors on the disk are spaced in such a way that when the turntable rotates at the right speed, the fluctuations in the light from the lamp stroboscopically freeze the motion of the sectors.

Suppose that when the lamp is brightest, a white sector is at a certain position in your field of view. The lamp dims and then brightens again, too fast for you to perceive it. By then the motion of the disk brings the next white sector into the same position. Each time the lamp brightens, another white sector is at that position. This matching of the rotation rate of the disk and the fluctuation in the lamp's brightness creates the illusion that a single white sector remains fixed in position.

If the turntable is turning a little too fast, the pattern moves slowly in the direction of the true rotation. On one brightening you find the white sectors in a certain orientation. By the next brightening the turntable has moved them beyond that orientation. Each new brightening reveals the same advance. You misinterpret the motion as a slow rotation of the pattern in the direction of the turntable's movement. On the other hand, if the turntable is rotating a little too slowly, the successive illuminations of the pattern generate the illusion that it is turning slowly backward. In each case the speed of the migration indicates how much the turntable is off speed.

Rushton experimented with a strobe disk intended for use in Britain to check 33/3-r.p.m. turntables. Alternating current reverses at a frequency of 50 hertz in Britain, causing the lamp to fluctuate in brightness at a rate of 100 hertz. The corresponding time between bright phases of illumination is .01 second. The strobe disk was laid out with its radial sectors spaced so that the rotation of one white sector into the place previously occupied by another white sector in an observer's field of view took .01 second. When Rushton viewed the disk on a turntable running at the right speed, the pattern seemed to freeze.

As one might expect, stroboscopic effects disappear in steady illumination such as sunlight. Rushton discovered, however, that even in steady light he could freeze the pattern by humming at a frequency of about. 100 hertz. If he hummed slightly flat, the pattern migrated slowly in the true direction of rotation. If he hummed slightly sharp, the pattern migrated slowly in the opposite direction. Other sources of sound in the room had no effect.

How does the vibration of humming give rise to the stroboscopic effect? Does it perhaps shake the optic nerve in such a way that the transmission of signals to the brain is periodically diminished or delayed? Rushton devised an experiment to check this possibility. His idea was to force a delay in the transmission of an image to his brain.

For this purpose he resorted to a dark filter. When light falls on the retina, the information is sent immediately to the brain. If the light then gets dimmer, the information is delayed by as much as several milliseconds. Rushton's thought was that if the vibration from his humming was jarring nerve fibers or something else in the pathway leading from the retina to the brain, then dimming his view of the rotating pattern would make a steady stroboscopic pattern migrate because of the imposed delay. He observed no migration, thereby ascertaining that the humming does not act on the pathway leading from the retina. Instead it apparently acts on the eye as a whole. The facial bones conduct the vibrations of humming from the mouth and throat up to the eyes.

Rushton's explanation was the subject of a paper by Mastebroek and van der Kooi. Figure 2 is pertinent to their analysis. The black-and-white pattern on a rotating turntable sweeps across the observer's field of view. In the illustration the motion is shown in relation to a fixed axis in a room. The eye, which is made to oscillate vertically by humming, is in its uppermost position in part a. The frequency with which white sectors are replaced in the field of view is matched by the humming frequency and thus by the vibration of the eye.

In part a of the illustration a white sector lies on the optic axis that runs from the center of the field of view back to the retina. The sector is the central image on the retina. In parts b and c the disk pattern and the eye move downward in phase, maintaining the white sector as the central image on the retina. In parts d, e and f the disk pattern continues to move downward as vibration moves the eye upward. The white sector that was previously central on the retina shifts upward. Meanwhile a dark sector is imaged briefly on the center of the retina. In part the cycle begins again.

For most of a single vibration of the eye the center of the retina receives an image of a white sector. Other points spaced periodically along the retina are also mostly illuminated by white sectors. At all such points neither the white images nor the dark ones are perceived individually because of the rapidity of the vibration. Instead the visual system averages the brightness over a full vibration, giving the white-image points a bright average. The points on the retina that receive mostly images of the dark sectors yield a darker average. If the observer is humming at the right frequency, this pattern of averages is reinforced with every oscillation of the eye. Although the pattern is less distinct than the one on the disk (when it is stationary), it is still observable.

Many similar stroboscopic effects induced by humming can be observed. Werner has described how humming can make the image on a television screen unstable. He stood about 30 meters from a television set and hummed through his teeth at a frequency of 60 hertz. Philip C. Williams and Theodore P. Williams of Tallahassee, Fla., had previously reported how humming can alter a television image. In their observations the humming created on the sereen an illusion of horizontal dark lines. By controlling the frequency of the hum the hummer could hold a line stationary on the screen or move it up or down. Certain higher frequencies (apparently harmonics of the lowest frequency) yielded multiple lines. On both black-and-white sets and color sets the lines were gray.

Werner also described how humming can stroboscopically freeze spokes on rotating automobile hubcaps and lug bolts on rotating truck wheels. An observer driving past a picket fence can freeze the pickets by humming. I have heard of people who can ascertain the frequency of a fluorescent lamp by humming.

The most curious report of a stroboscopic effect was published by J. L. Scott-Scott of Nuneaton, Warwickshire, England. He hit on a way of determining the direction of rotation on an airplane propeller. He made his head vibrate by allowing his tongue to Hutter gently against the roof of his mouth as he exhaled. He began with a high frequency of vibration and gradually brought the frequency down until the propellers were stroboscopically frozen. He then decreased the frequency a little more. The slow migration of the strobe image of the propellers revealed their true sense of rotation.

I made a strobe disk by taping a large sheet of white paper onto one side of a long-playing record. I put a reference point on the paper at the center of the hole in the record. Then I marked off radial sectors one degree in width. (All the measurements must be completed before the record is put on the turntable because the spindle breaks through the paper and obliterates the reference point.) I filled every other sector with black ink.

When I rotate the disk at 33 1/3 r.p.m., the turntable is running at a frequency of .555 hertz. Since I had arranged 180 pairs of black-and-white sectors around the disk, the frequency at which a certain arrangement of the pattern is repeated is .555 hertz multiplied by 180 pairs, or about 100 hertz.

It was tedious to make the disk, and the result was marred by variations in the blackness of the dark sectors. When I rotated the record at 33 1/3 r.p.m., I was easily distracted by the variations in the ink. Other features of the rotation also made me follow the movement of the record instead of fixing my gaze on one area. With experience I learned to ignore most of the distractions and to concentrate on the gray blur.

When I illuminated the rotating pattern with an alternating-current house lamp, I saw only the blur. The light flickered at a rate of 120 hertz, higher than the frequency of 100 hertz needed to freeze the pattern. With the turntable in sunlight I tried to hum at approximately 100 hertz in order to freeze the pattern. Although I could sweep my humming frequency through the proper range, I failed to freeze the pattern, largely because I cannot hold a note of one pitch.

I then turned to an easier method of making my head vibrate. I attached a speaker to an audio amplifier driven by a signal generator. Setting the amplification high, I stuck my chin inside the speaker cone. My head vibrated. With one hand I slowly swept the frequency of the oscillator through a region around 100 hertz as I stared at a section of the rotating pattern. The section I chose was on the right side of the record as I faced it. There the pattern descended in my field of view.

At a frequency of about l00 hertz a faint, stationary strobe pattern was perceptible against the gray blur. As I moved to slightly higher or lower frequencies the strobe pattern migrated in the ways described by other people. Even without looking at the frequency control I could consistently freeze the strobe pattern at the same frequency. When I took my chin out of the speaker cone or moved the frequency well off 100 hertz, the strobe pattern disappeared immediately.

You might like to make your own strobe pattern and continue the experiment. You could also experiment with other vibrating or rotating objects. Can you freeze their motions with an appropriate hum?

Early in the 19th century Johannes Purkinje, one of the pioneers in physiological optics, discovered that the light from a small piece of glowing tinder created two blue arcs across his field of view. Although the arcs soon faded, he could control their brightness and duration by moving the tinder up and down, sweeping its light across different parts of his retina. If the arcs faded, he could regenerate them by readapting his eyes to darkness for a few minutes.

The cause of the blue arcs, and particularly the reason for their being blue, has been a physiological puzzle ever since. Many investigators have studied ithe relation between the place on the retina that is illuminated and the shape of the arc that is generated. Recent publications by J. D. Moreland, formerly at the Institute of Ophthalmology in London, provided me with detailed instructions on how to repeat the observations.

Moreland suggests the following procedures for viewing Purkinje's arcs. Allow one eye to adapt to darkness for at least one minute but not more than three minutes. Switch on a small light. (A yellow or red light in the range of wavelengths between 510 and 620 nanometers is best.) Depending on the location of the light in your field of view, you should see one or more arcs for about a second. For repeated displays turn on the room lights for two or three minutes every five minutes. During the dark period turn on the yellow or red light for half a second, repeating the stimulus every four seconds.

If bright, clear arcs are to be seen, both the orientation and the size of the stimulus light are important. A small rectangular source works well because it can be positioned to excite several overlapping arcs whose brightness can be summed by the visual system. If a rectangular light source is in the part of the field of view toward the nose, its long side should be vertical. If it is in the part of the field of view toward the temple, its long side should be horizontal.

The reason for the preferred orientations has to do with the amount of the retina that is illuminated and with where in the field of view the arcs appear. Every small section of a narrow rectangular source creates a uniquely shaped arc. If the composite arc is to be bright and clear, the spread of the individual arcs should be small.

Several possible arcs for the right eye are shown in Figure 3 for a light source that is a vertical slit. The width of the slit is negligible. The height of the slit occupies 15 minutes of angle in the observer's field of view. The point labeled f is the point of fixation, that is, the point in the field of view to which you direct your gaze. (The image of this point falls on the fovea, the most sensitive area of the retina.) The graph of the field of view is measured in degrees, with the point of fixation at the origin.

If the slit is at point c, the large arc passing through c is excited. (Only the center of the arc appears in the illustration; the arc is actually one degree in width.) When the light is moved to point b, an arc is excited in the upper part of the field of view. When the light is moved to point d, an arc is generated in the lower part of the field of view.

A slit longer than 15 minutes of angle can excite many arcs. What the observer sees is a composite. The visibility of the composite depends in part on how the individual arcs overlap. Suppose the slit spans the field of view from b to c. The composite is bright because the spread in individual arcs is small enough to allow the visual system to sum their intensities. Similarly, if the slit is long enough to fill the span from c to d, another bright composite arc is created.

Still longer slits diminish the visibility of the composite arc. For example, if the span of the slit is from a to c, the overlap of individual arcs yields a composite arc too wide for a complete summation of brightness. This arc is wider than the one generated by a shorter slit but is not proportionately brighter. Perception is even poorer if the slit is oriented horizontally through c. With this orientation a large number of arcs are excited to yield a wide composite arc.

Figure 4 shows three general regions in the right eye's field of view where Moreland considers placing light sources. Good arcs are generated if the light source is in, say, section C and has the curved shape depicted in the illustration. Arcs with a different position and curvature are generated by a light stimulus positioned and curved like section B. A light stimulus like section A is different. A blue spike appears if a narrow light source is inserted between the point of fixation and the blind spot (the spot where the retinal nerve fibers exit to the brain).

Moreland does the following demonstrations of the various arcs. Place a rectangular source of light in section A. The source should be about .66 degree wide and about 2.5 degrees long. The probable appearance of the blue spike is shown in part b of Figure 5. By rotating your head you can bring the spike in line with the stimulus as in part a. If the same arrangement is presented simultaneously to the left eye, you get a striking view of two blue spikes.

Next place a light source in section B. For good results the source should be about 4.5 degrees long and about .66 degree wide at its narrowest. The ends are flared. This source generates two arcs that are symmetrical if the source is approximately symmetrical about the line connecting the point of fixation and the blind spot (part c). By tilting your head you can complete or break the symmetry of the arcs.

To demonstrate that the shape and the positioning of the arcs depend strongly on the position of the light source, set up two light sources as is shown in part d. One source occupies the upper half of section C, the other the lower half of section B. The resulting arcs are disconnected and have noticeably different curvatures. When stimulus lights are placed in all three positions, the result is two horseshoe-shaped arcs and one spike (part e).

In all these demonstrations arcs appear soon after the stimulus light is turned on. Similar but fainter arcs can be seen when a stimulus light is turned off under the right conditions. The on and off times of the room lights remain the same, but now during the dark period the stimulus light is on for 3.5 seconds and off for .5 second. You might have to repeat this sequence 10 times or so before the "off" arcs are visible.

As a light source Moreland suggests a photographic safelight with a 60-watt lamp covered with a red or yellow filter. I found that almost any small light (such as a penlight) covered with a red or yellow filter serves to generate arcs. My filters were inexpensive ones that I obtained from the Edmund Scientific Company (101 East Gloucester Pike, Barrington, N.J. 08007).

To construct sources of light in the forms suggested by Moreland attach to a lamp a sheet of sturdy cardboard with the appropriate form cut into it. Adjust your distance from the lamp until the angular size of the cutout in your field of view is right. You can use a flat lamp of the type normally employed for viewing and sorting slides.

I made most of my observations on my home computer, which has a black-and-white monitor screen. In my first experiments I had a word-processor program in the computer's memory. The blinking cursor on the monitor was the light stimulus. Since the cursor is white; I taped a red filter over the screen. To create a point of fixation I typed in period near the center of the monitor. With the cursor positioned to the left of the period I fixed the gaze of my right eye by concentrating on the period. After I had determined the best distance between my head and the monitor I held my head in position with books and other objects.

For other shapes and orientations of a stimulus light I wrote a program (in BASIC) that could light various parts of the monitor. The lighted pattern turned on and off at a rate set by FOR-NEXT loops in the program. For example, with a statement of FOR K = I to 500: NEXT the pattern remained on the screen until the computer counted to 500. Another loop kept the screen dark (except for the fixation point) for as long as I wanted. (I still operated the room lights by hand.)

Many causes have been proposed for the blue arcs. Purkinje and others thought they result from the scattering of light inside the eye. Other investigators suggested bioluminescence. Their hypothesis was that the excitation of nerve fibers by the stimulus light leads to the emission of ultraviolet radiation, which in turn excites light receptor cells in the arc regions.

These two hypotheses have been replaced by the hypothesis that the excitation of nerve fibers by the stimulus light gives rise to activity in adjacent nerve pathways. One's interpretation of the additional activity is the perception of blue arcs. The regions that appear to be covered with arcs are actually not illuminated.

The first step in the creation of the s perception of the arcs is to have a stimulus light illuminate a small section of the retina, exciting the cone cells there. The nerve fibers connected to the cones are then electrically active. Apparently the same fibers also electrically excite adjacent fibers connected to rod cells elsewhere on the retina. Thus the observer receives messages from cones that are excited by light and from the nerve fibers connected to rods that are not illuminated. The brain is misled into thinking the rods are excited by light too. The rods happen to be laid out on the retina in the shape of an arc.

Although this explanation of the arcs is promising, the source of the blueness of the arcs remains unidentified. The rods are thought to be achromatic. How then could the illusion of their excitation deceive the observer into thinking that he is seeing blue? Moreover, the arcs are blue only when the eye is still partially adapted to light. As the eye adjusts fully to darkness the arcs fade to a dull white.

In 1977 Carl R. Ingling, Jr., and Bruce A. Drum of Ohio State University presented an explanation of the color of the arcs that appears to solve the problem. To follow their demonstration you need to arrange a visual field that is dark on one side and illuminated on the other. Adapt your eyes to total darkness for about 10 minutes and then stare at the field. (The illustration in Figure 6 suggests a setup that is appropriate for the right eye.) After several minutes replace this field with one that is totally dark except for a small, faint point of fixation and a slowly flashing red light needed to stimulate the arcs. The illustration indicates one type of arc that can be seen.

The part of the arc lying in the side previously adapted to illumination is blue. The part lying in the side that was dark-adapted is dull white. The border between the two colors can be sharp if the eye has been kept steady on the point of fixation.

To repeat this demonstration on my computer I included in the BASIC program some commands that lighted the right half of the screen long enough for that side of my right eye's field of view to become adapted. The fixation point was in the left part of the screen. In the next step of the program the screen went completely dark except for a slowly flashing pattern and the same fixation point. As before, I had taped a red filter over the place where the stimulus pattern appeared.

Ingling and Drum's explanation of the colors of the arcs is based on a previously published model of retinal response called the silent surround. In this model a group of retinal photoreceptors is considered to consist of central cells that respond to light and surrounding cells that can sometimes modify the rate at which the center directs signals to the brain. A silent surround means that when the center is unexcited, excitation of the surround does not alter its firing rate. When the center is excited more than the surround, the surround inhibits the center's signals to the brain.

The silent surround might apply to the generation of Purkinje's arcs if the center includes cone cells that are responsible for the information on yellow and blue sent to the brain. The surround consists of rod cells. Rods do not respond to color, and so it would be impossible for them to directly color the arcs. According to the hypothesis of Ingling and Drum, however, the rods supply the blueness indirectly when they inhibit yellow signals from the yellow-blue cones in the center.

In modern color theory the perception of color is thought to result from two kinds of competition among cones. The cones are specialized in their color response. One type of cone responds to red another to green and a third to blue. Apparently the visual system sorts the three responses into two pairs of opponent colors: red and green as one pair, blue and yellow as the other.

Purkinje's arcs might arise as follows. The stimulus light illuminates a small section of the retina, exciting cones in it. The cones have nerve fibers running alongside fibers from other parts of the retina, so that the electrical excitation of the first group of fibers excites the second group. Presumably some of the nerve fibers in the second group are connected to rods that are among the silent-surround cells.

When the second group of fibers is excited, what signal do the fibers transmit to the brain? First, they signal the illusion that the retina is illuminated wherever they are connected to rods in the surround. Second. the fibers might also provide an illusion of blue. depending on the state of the centers of which they are a part. If the eye is fully adapted to darkness, the centers are not excited and transmit no co]or information. Therefore the excitation of the rod fibers sends a colorless signal to the brain. The result is that the observer sees arcs of dull white.

If the eye is not fully adapted to darkness, the cones of the centers are still sending color information to the brain. In particular some of them are sending the signal of yellow. The excitation of the fibers connected to the rods surrounding such cones then inhibits the yellow signal; the effect is the transmission of a blue signal to the brain. Thus the observer is misled into thinking certain regions of the retina are illuminated with blue light.

Bibliography

WHY THE BLUE ARCS OF THE RETINA ARE BLUE. Carl R. Ingling, Jr., and Bruce A. Drum in Vision Research, Vol. 17, I pages 498-500; 1977.

THE EFFECT OF HUMMING ON VISON. H. A. K. Mastebroek and J. B. van der Kooi in Physics Educator, Vol. 14, pages 253-254; 1979.

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