WHY NO CAMERA CAN FOCUS

or

THE CRUCIAL MISSING LINK IN PHOTOGRAPHY AND OPTICS

           ©1983 The Anstendig Institute 

The industry that demands the greatest degree of mechanical precision, the photo-optical industry, has a crucial flaw: its focusing systems. No available camera can focus. All available focusing devices are inexact: they are incapable of focusing a subject-point onto the film plane, and they stop functioning at distances beyond approximately 10 to 20 meters. "Depth-of-focus" does not exist. "Depth-of-field" has to do with unsharpness, not with sharpness. The only possible system of achieving absolute, focal-point-exact focus without laboratory instruments, and achieving it with ease, has been known and certified as such for decades. A dependable means of achieving perfect focus has crucial implications in all fields of science and industry, and in the general public's orientation and reactions to visual impressions.

I. THE ONLY KNOWN FOCAL-POINT-EXACT FOCUSING SYSTEM IS NOT AVAILABLE

It will probably amaze most readers to learn that no camera on the market can focus exactly, that all prevalent focusing-systems are grossly inexact, and that the only focusing-system that can achieve absolutely exact focus (and achieve it with ease and simplicity) has never been offered to the public. In fact, there is strong evidence. that this system was purposely suppressed by the optical industry when the inventor introduced it, mainly because it demanded finer tolerances in their cameras and would have damaged their prestige by directing attention to the inaccuracy of the systems then in use. The name of this invention, by a German, Joseph Dahl, is “Messraster", which translates as "Measuring-Grid" (messen = to measure, and Raster = grid). In its first form it lacked compensation for the refraction index of the glass that it was made of, the necessity for which in other devices as well was still unknown to the industry. Nevertheless, it was certified by Germany's leading optical institute as "Die exakte Basis der Photographic" (the basis for exact precision in the field of photography) and as the most important invention in the field of optics since the invention of the Tessar lens. (Any type of lens could be constructed with only three glass elements, but the necessary precision in grinding and mounting the elements would be prohibitive. The Tessar, invented in 1902, relieved this problem by introducing another glass element. Essentially, all further lenses are variations of this lens.) In the late 1950's, Mr. Dahl introduced the compensation for the refraction of the glass, achieving absolute orientation of the Messraster with the film-plane, at which time new patents were granted. 

II. AVAILABLE FOCUSING SYSTEMS CANNOT FOCUS

Because it demands the greatest amount of fine mechanical precision, the photo-optical industry has traditionally been considered the most important of all industries, the one that any country has to prove itself in before its other industries will be taken seriously. Germany has always understood this, and, after the war, Japan even went so far as to set up government inspection of all optical products before they were allowed to be exported because it knew that until Japan proved itself in that industry, there was no hope of breaking into the other important world markets. The makers of the huge reflecting telescopes for the great observatories lose money, even though they charge millions and millions of dollars. Yet Carl Zeiss, Inc., the leader of the German optics industry, cannot refuse to make these custom installations if German industry is to retain its reputation for mechanical precision.

Imagine a Mercedes-Benz or a Rolls-Royce with an exceptional motor and running gear but a transmission that is not only completely inaccurate, but is installed in such a wrong way that, if it happens to engage the gears correctly, it could only have been by mistake. That has been the case in the photo industry since 1902, the year the Tessar lens was computed*. The bodies of cameras are marvels of mechanical complication and precision, and lenses have reached near-perfection. But the focusing-system is the "transmission" that links the lenses to the camera, and every currently available focusing-device is grossly inexact. Some of these devices have the additional error that they require, but do not have, compensation for the refraction of the glass or plastic that they are made of. They are also installed so that their plane-of-focus does not correspond with the film-plane. Thus, if a photo happens to be precisely focused, it is a mistake.

Everyone who owns a camera knows the experience of going through the small prints or contacts and finding one or two that are so precious one wants them enlarged. But when the large prints arrive, they are little more than unsharp blurs. Amateurs chalk this up to inexperience, lack of professional equipment, or lack of talent, and decide to leave important things, like weddings and such, to the professionals. No one thinks of blaming the expensive, watch-maker-precision cameras, but the cameras are to blame, because of their faulty focusing systems. What amateurs do not know is that, in focusing, the only difference between them and the professionals is the amount of film used: the professionals have merely learned not to save film, but rather to shoot as many rolls as possible so that, with luck, they will at least have one reasonably sharp picture that serves their purpose. Editors and other employers have come to expect miles of film from their photographers on any assignment. Once, on assignment in Berlin, I air-freighted one partly-filled roll of film to Paris Match, only to be awakened in the middle of the night by a frantic editor asking for the rest. I had used the Messraster and did not need to take more than a few pictures. The film was developed and the next day he had his photos, big, sharp and exactly the way I had conceived them, because the focusing was so easy that I could concentrate completely on getting the picture.

III. FOCUSING AND "DEPTH OF FIELD"

When one directs a lens at a given point in one's subject, the light-rays from that point enter the lens, are refracted (bent) towards each other, and cross at one particular point behind the lens. Only at this point, called the focal-point, can the point at which the lens is directed be sharp, and it is the problem of the photographer to bring the film-plane to the exact plane of this focal-point, which can be as small as 1/lOOOth of a millimeter. Because the opening of the lens is round, the rays going through the lens approach their focal-points conically. Therefore, when taking a picture, if the film is either in front or in back of a given focal-point, that point will be pictured as a circle, not as a point, and the circle becomes larger the farther away from the focal-point the film lies. These circles are the basis of the depth-of-field tables.

The designation "depth-of-field" comes from the German word "Tiefenschaerfe" which translates literally as depth-of-sharpness and is universally understood as a distance within which everything is sharp, i.e., a distance within which everything is focused, which is an impossibility because one can only focus on one distance in front of the camera. Depth-of-field is often referred to by the misnomer "depth-of-focus". It may come as a shock to learn that there is really no such thing as depth-of-focus and that depth-of-field, far from dealing with sharpness, deals with unsharpness, but that is the case. Depth-of-field tables are merely an attempt to indicate how far in front and in back of the really sharp point the unsharpness will remain tolerable enough to not obliterate the picture. But depth-of-field tables presuppose that one can focus on the most important point in the picture, which is practically never the case. Far from being any sort of physical law, as it is usually touted, depth-of-field is a matter of opinion that changes in relation to the sensitivities of the viewer (some people are more disturbed by a particular degree of unsharpness than others) and in relation to the viewing circumstances. Depth-of-field presupposes a given viewing distance, a given print size, as well as a given tolerance in the viewer. If a smaller portion of the negative is enlarged, if the print is larger than the presupposed size, if the viewing distance changes, or if the viewer is either more sensitive or needs more clarity for a particular subject, the whole criterion for calculating the depth-of-field changes. This is reflected in the fact that there are many depth-of-field tables-some assuming less depth-of-field for more exacting needs and some assuming a much greater depth-of-field for general use--which is proof in itself that there is something wrong with the whole idea. This confusion is inevitable because, as mentioned, depth-of-field tables deal only with unsharpness and are attempts to use calculations to determine how bad the unsharpness can be and still remain tolerable, a criterion which is impossible to establish because each viewer experiences the degree of unsharpness differently. In addition, since depth-of-field is calculated for distances in front of and in back of a reference point (focal-point), it is meaningless if the focusing system does not allow one to ascertain precisely that focal-point.

Even the inventor of the Tessar lens fell victim to wrong assumptions about sharpness: he spent the end of his life trying to compute lenses with a greater, more extended range of depth-of-field. At the time, there was a concept, later disproved, called the “chaerfenschlauch", that assumed that a lens focused the rays going through it in such a manner that, instead of one sharpest point, there was a certain range within which everything was pin-point sharp. This range was thought to be tubular, hence the name "schaerfenschlauch" (tube of sharpness). But all this man accomplished was to build a type of lens that is now called a "soft-focus" lens, wherein the focusing quality was degraded to such a degree that it was no longer possible to recognize where the exact focus lies, and, of course, all the details in the photo were similarly degraded and unrecognizable. Mild versions of this type of lens are still occasionally used for portraits in order to suppress wrinkles and other blemishes.

Depth-of-field originated at a time when single-lens-reflex cameras did not exist, and serious photography was dominated by the original Leica and Contax range-finder cameras. These cameras were primitive compared to the present-day Leica range-finder camera, and it was well-known that they were incapable of anything resembling precise focusing. The remaining cameras were mostly without any means of focusing: the photographer had to estimate the distance by sight and set it manually on a scale next to the lens. The concept of depth-of-field tables presupposed this lack of any sort of precision and was developed merely as an aid until an accurate means of focusing could be achieved, and not as a valid focusing method in itself, as it is misinterpreted today.

IV. AVAILABLE FOCUSING SYSTEMS AND THEIR SHORTCOMINGS

RANGE-FINDER CAMERAS

This well-known system is a separate apparatus that has nothing to do with the part of the camera that actually takes the picture. It uses a separate, part optical, part mechanical, device that is coupled to the camera lens. The best of this type of apparatus can only focus up to about 30 meters at most, with a precision that is by no means exact. Beyond 30 meters is assumed to be infinity: focusing stops and the lens remains on the infinity marking. The moon, of course, is quite a bit farther from the earth than 30 meters, and most cameras of this type completely stop focusing at much closer distances than 30 meters. This inexactness becomes intolerable with long focal-length lenses and is also unsatisfactory for shorter focal-lengths. The inadequacy of this system is obvious in that manufacturers recommend not using the range-finder with longer lenses and supply a ground-glass attachment for use with these lenses.

SPLIT-IMAGE RANGE-FINDER IN THE GROUND-GLASS OF A SINGLE-LENS-REFLEX CAMERA

First of all, this system is impractical because, in order to work best, one must focus on lines in the subject that are exactly parallel to the film-plane. If one end of the line is a different distance from the film-plane than the other end (and therefore at an angle to the film plane) the result has to be inaccurate. Few subjects contain such lines, and when they do, they are seldom in the place that one wants to focus on. For this system to work as well as it can, a new range-finder with the two halves at a different angle to each other should be constructed for each combination of focal-length and aperture-opening. When viewing with an f-stop of 4 or smaller, the circle of the range-finder can no longer be used: it blacks out and becomes an annoying obstruction in the center of the viewing field. Also, a change in the angle of the viewer's eye (the angle with which one looks into the view-finder) will cause a wrong result, and even in its particularly imprecise way, this system can seldom measure beyond 20 meters.

FINE-FOCUSING GRID IN SLR CAMERAS

This seemingly magical optical arrangement consists of many tiny obstructions that are supposed to vanish when exact focus is achieved. Actually they never completely vanish; we simply perceive them as less disturbing, to the point where they seem to have vanished. But the grid "disappears" long before focus is achieved: in a test using an F 2/50mm lens on a number of cameras, the grid "vanished" at a distance of approximately 3 meters and remained "invisible" over a depth of 60 cm. With so great a possibility of error, no one can claim the slightest bit of focusing precision.

NORMAL GROUND-GLASS

The deficiencies of the normal ground glass were the reason the industry developed the focusing systems mentioned above, but, in the hands of an experienced photographer, it remains the most accurate of available focusing devices. All that the other systems accomplish is to achieve worse results with greater ease.

The normal ground-glass brings us to the basic problem of single-lens-reflex focusing: the capacity of human sight itself. The ground-glass is based on an impossibility: the recognition of details too fine for our eyes to discern. In a view-finder (and on the film), full-sized objects are reduced to a size so small that, as explained above, important details can be as small as 1/lOOOth of a millimeter at the focal-point. It is therefore physiologically impossible for the human eye to perceive and recognize the point of absolute focus. At a normal viewing distance of 25 cm, the human eye will no longer see objects that are separated by a distance of 0.07 mm or less as separate objects, but will see them as joined together. Also, the grain of the ground-glass is itself larger than the details to be perceived. For these reasons, one can move the ground-glass an appreciable distance back and forth over the focal-point without noticing any difference in the focus. In addition, this system makes impossible demands on the photographer's memory: The focusing procedure is to move the ground-glass back and forth over the seemingly sharpest-appearing stretch in an attempt to get the sharpest point in the middle. It is well-known that our eye only possesses a subjective, vague, fluctuating, and undependable memory. If one happens to achieve absolute focus by means of a ground-glass, it is a matter of the operation of the laws of chance.

CLEAR-GLASS WITH HAIR-LINE CROSS

This system consists of a circle of clear unmatted glass with a hair-line (thin) cross marking its center that is located in the middle of a ground-glass. The cross, etched on the side facing the lens, already produces the first error: the photographer, with the aid of a magnifier, focuses the magnifier on the hair-line cross and then focuses the so-called "aerial image" at that plane. But, due to the refraction of the glass, the hair-line cross is not seen coincident with the ground-glass. It is seen behind the plane of the ground-glass. (The hair-line cross should stand out in front of the ground-glass, the distance being the equal of the refraction of the glass. Many split-image range-finders and fine-focusing grids also suffer from lack of compensation for the refraction of the glass.) But this system also suffers from the same problem that, beyond relatively nearby distances, the lens is on infinity and no more focusing is possible.

V. THE MESSRASTER

The one capacity of the eye that is dependable and exact is the perception of contrast (contrasting tones) in direct comparison, i.e., when the tones to be differentiated are directly next to each other. For example, color tones are precisely determined in direct comparison with a color-chart. When the strengths and weaknesses of the eye are understood, three prerequisites for exact focusing become clear:

1)   It must be based on the only exact capacity of the eye, the recognition of contrast by means of direct comparison;

2)   The undependable memory of the eye and its limited power of resolving detail must be eliminated;

3)   It must function on any type of object, no matter what its structure or texture.

The Messraster of Joseph Dahl fulfills these prerequisites in the simplest manner. It consists of a ground-glass that functions on two planes. Focusing is achieved by means of direct comparison of the tone-contrast and degree of sharpness in both planes. The basic system consists of a ground-glass that is divided into strips that are displaced so that they are alternately in front of and in back of the plane that corresponds to the focal-plane. The subject-point on which one wants to focus is divided with one of the hair-thin dividing lines in much the same way one would divide it with a split-image range-finder. One then focuses until both sides of the divided point appear equal in tone and in sharpness. When the two sides of the image-point, on either side of, and right next to, the hair-line are equal, the focal-point lies exactly in the middle of the two planes. The film is then exactly at the plane of the focal-point since the Messraster is precisely constructed so that the plane that corresponds to the film-plane lies exactly in the middle of the two image-planes, after refraction of the glass. Even the slightest movement of the lens away from the position of optimal focus is doubly noticeable in that one side of the hair-line becomes more contrasty (darker) and sharper, while the other side becomes more diffuse (lighter) and less sharp. Since this system exclusively uses the most precise capacity of any of our senses, the direct comparison of contrasts, the instant when the two sides match is easily and effortlessly recognized. The customary laborious attempt at guessing the right focus by moving the lens back and forth is eliminated. In the shortest possible time, one achieves a much more precise result than any other system is ever capable of, regardless of how much trouble one takes with it. Even the smallest differences in distance can be effortlessly and precisely focused over the whole range of distances until the lens truly reaches infinity. Since it is possible with the Messraster to focus on any type of object, regardless of whether or not it has lines and regardless of its texture, the Messraster fulfills the prerequisites for an exact focusing system.

VI. THE BENEFITS OF PRECISE FOCUSING

The photographic manuals quite correctly say that the most important point in the picture should be the sharpest, but nowhere do they mention how to achieve that necessary precision, except to recommend that one take great pains to do so. Since even the smallest point in the subject has its own focal-point at a given distance behind the lens, and since the film can only be at one distance behind the lens, it is impossible to have all focal-points equally sharp at the same time. In a portrait, for example, it is impossible to have the nose, eyes, and ears equally sharp at the same time. But if the optimal focus is on the most important point (in this case, the pupil of the dominant eye), the whole portrait will appear to be sharp and will have an impression of three-dimensionality (plasticity) that adds a life-like quality and vividly highlights the facial expression. But if the optimal focus is on a less important part of the face, the portrait will not have that vivid quality; the whole picture will seem flat and vaguely unsharp, to the detriment of the facial expression. In other words, when the most important point in the picture is absolutely sharp even the unsharp areas of the picture appear sharper. The gradations of tone (the half-tones) in the subject can only be exact at the focal-point (the farther in front of or in back of the focal-point the film lies, the more diffuse and lighter the tone-values become), a factor that contributes significantly to the effect of plasticity. Because a point remains a point no matter how much it is enlarged, a considerably greater amount of enlargement is possible in an optimally focused photo without blurring of the contours and the grain of the film will be considerably less noticeable. But as important as the benefits of more resolution of detail and less apparent graininess are, they seem insignificant in relation to the effect of plasticity that arises when the most important point in a picture has been precisely focused.

Plasticity is the impression of three dimensionality on a two dimensional surface. This impression can only occur at the focal-point because only there are the details and tonal values exact. When the half-tones are faithfully rendered and the picture-area is precisely focused, a particular phenomenon occurs where the picture takes on a vivid, life-like quality and one can clearly make out the depth of the planes of the subject. In the above-mentioned portrait, one would be able to see that the eye-lashes are in front of the eye-lid; one can see the curvature of the eyeball and that the iris stands out in front of the eyeball; one can see how far the eyebrows stand out beyond the eye, etc. This effect only occurs at the focal-point because of the sharp detailing and, just as importantly, because the half-tones (the gradations of the color-tones of the subject) are only exact at the focal-point. Because the tones are diffused and diluted in front of or in back of the exact point of focus, a picture only gives the impression of plasticity if the most important part of the picture is in exact focus.

It is impossible to overestimate the efficiency and usefulness of precise focusing. The sciences that need optical and photographic precision presently have to expend enormous effort to achieve merely acceptable results when they could achieve perfection easily and elegantly with the Messraster, in a fraction of their valuable time.

Photographs of everything from important events to reproductions of art are a dominant part of our lives. But these documents are, in varying degrees, falsifications due to inability to dependably reproduce accurate detail and tonal gradations with the currently available, faulty focusing systems. This is particularly the case in art-reproduction and is the reason that so many photo-reproductions of art works convey so little of the glories of the originals. But it is also the case in advertising, where elaborately intricate techniques are used to retouch the image quality in advertising photos, techniques that often amount to repainting the whole photo.

There is talk of improving the quality of television (Sony already has a better system it wants to introduce), but the film and TV industries are those most plagued by the inability to focus. In fact, it is general practice in those industries to forget about focusing altogether and use a measuring tape to set the distance between the camera and subject (an inherently flawed and stultifying procedure--a distance scale on a lens is not fine enough to set small differences in distance and also, most subjects do not remain absolutely still--but it is nonetheless considered more dependable than focusing with the cameras). A TV system can only be as good as the material it is broadcasting. With the deplorable image-quality for which films are notorious, improvements in the TV system will not be noticeable and will probably just highlight the flaws in the broadcast-material.

I have already mentioned the amateur photographer's dilemma in achieving quality in his photos with current focusing devices. To conceive of how many people would benefit from easy, precise focusing one need only consider the millions upon millions of people who already own cameras, and how many new cameras are sold each year. Probably more than a billion cameras are already in existence, and, even though some are otherwise wonders of optical and mechanical precision and complexity, none of them focuses with precision.

VII. THE PUBLIC HAS BEEN CONDITIONED TO ACCEPT IMPRECISE FOCUSING

As with all our senses, the way we see is determined by habit and conditioning. The sad result of the astonishing deficiency in focusing, which is the most important aspect of optics and photography, is that the public has become used to, and conditioned to accept as correct, poor quality visual images that seldom approach the real possibilities. In instances of sustained viewing (movies and TV, for instance), this poor quality can have a physically debilitating effect on the viewer. In all areas of photography including movies, if the image is already degraded by poor focusing, it can become impossible to detect other sources of bad image-quality such as camera shake or movement of the subject. This has resulted in a compounding of errors that we have become used to and now accept. But, as just one example, consider what an unsharp mess the film of President Kennedy's murder was, and what a difference it would have made in the evaluation of that act, if the film had been clear enough to make out most of the details. Such instances are the rule, when they should be the exception. One can rest assured that, for every good-quality photograph one sees, whether in newspapers, magazines, books, or elsewhere, an amazingly large number of photos ended up in the wastebasket. And usually those good ones are not as good as they should have been.

In photography, the public's frame of reference has been formed by pictures that are technically wrong. Complete control of the plane of sharpest focus means the ability to decide exactly what point in the subject will be the sharpest. This control is the basis for purposeful photography. It is impossible to conceive of the magnitude and significance of the difference this control makes until one has seen examples of it. The significance is overwhelming when one realizes that it should not be the slightest bit difficult for the bulk of all photos to be precisely focused. Because they have never been able to see the enormous difference between a precisely focused subject and the usual depth-of-field results that they are used to, amateurs and professionals alike have come to accept as desirable a picture quality that does not even suggest the real possibilities of photography.

Because the most basic element (accurate focusing) is missing, the systems and methods used and taught in photography are based on totally wrong concepts, ideas and values in relation to the effects that can be achieved through manipulation of the various elements at the photographer's disposal. The most important elements of photography--the determination of which part of the picture should be the sharpest, the precise reproduction of the color-tones of the subject, and the compositional use of plasticity to bring out the most important part of the photo--are not at all comprehended because the means to intentionally control those elements and thus be able to observe and study them are lacking. In point of fact, the ability to manipulate these elements purposefully changes photographic concepts. For example, one is confronted with having to decide what point of a subject should be the sharpest. Before one can make that decision, one must be familiar with the effects of precise focus. Depth of field relationships are contradicted. For example, the usual assumption that the impression of sharpness extends at a ratio of 1/3 from the front and 2/3 from the back of the focused point does not hold true: if the most important part of the picture is placed in a different relationship (3/4 from the front and 1/4 from the back, or very close to the front of the picture, for instance), the picture will still appear sharper if one focuses on that subject-point rather than according to depth-of-field calculations. Focusing on the most important subject point in a photograph always gives an impression of greater depth-of-field than simply following the so-called depth-of-field tables.

VIII. THE MESSRASTER SHOULD FINALLY BE MADE AVAILABLE

Until recently, the precision necessary to produce the Messraster presented considerable problems, which, although by no means insurmountable, would have added appreciably to the cost of a camera. Another problem was the inventor's insistence upon exposing the insufficiencies of all other systems and his insistence on a fee commensurate with the importance of his invention, which he was well aware of. The technical means of easily manufacturing the device were perfected in the 1960's, and Mr. Dahl has long-since passed away and the patent is now public domain. The only possible problem left is that, with such an exact focusing device, the cameras have to be precisely adjusted so that the film-plane exactly corresponds to the Messraster's measuring plane, if the results are to be precise. But all cameras are supposed to have film-planes that correspond exactly to the focusing plane anyway, and anything that would cause manufacturers whose products are not precise to adjust them better can hardly be faulted.

Because of the nature and limitations of our visual powers, the Messraster is the only possibility of achieving precise focusing with the naked eye. Arguably, it should thus be public property. But the ability to achieve exact focus has so many indisputably important implications in so many fields of modern life that the public has at least a right to its availability, and camera manufacturers should finally make it available. After more than a century, the world has yet to witness the full potential of photography and will not until it has a means of absolutely exact focus.

 

*    With the Tessar lens a quality of sharpness in mass- manufactured lenses became possible that has not been exceeded. The optical formula of the Tessar remains one of the most used in modern lenses.

 

Mark Anstendig, a trained orchestra conductor and professional photographer, was, for 9 years, the associate of Mr. Joseph Dahl, the inventor of the Messraster. Under Mr. Dahl's supervision, he made the photo-experiments that demonstrated the results of absolute focus in all aspects of photography. In the efforts to make known the possibility of exact focus, Mr. Anstendig was entrusted with representing Mr. Dahl in his dealings with the press, the public, and the industry. Among other things, he has exhibited the "State of the Art" of focusing optical lenses on the stand of Arnold and Richter (makers of the prestigious Arriflex movie cameras) at the Fotokina exposition in Cologne, and in the Berlin Pavilion of the New York World's Fair, for which he was commissioned to make photographs of Berlin landmarks, demonstrating the effects of focal-point-exact focus with all types of lenses, including extreme focal-lengths up to 2000 mm, which were supplied by the Astro-Gesellschaft of Berlin. Articles about exact focusing by Mr. Anstendig have appeared in newspapers and magazines, including Spiegelreflex Praxis in Germany and U.S. Camera in America. Their association was terminated by Mr. Dahl's death in 1970. Though no longer photographing professionally, Mr. Anstendig has in his possession the materials and photographs from this period that illustrate and prove all of the information in this paper. These materials are at the disposal of THE ANSTENDIG INSTITUTE and can be arranged to be seen upon request.

 

The Anstendig Institute is a non-profit, tax-exempt, research institute that was founded to investigate the vibrational influences in our lives and to pursue research in the fields of sight and sound; to provide material designed to help the public become aware of and understand vibrational influences; to instruct the public in how to improve the quality of those influences in their lives; and to provide the research and explanations that are necessary for an understanding of how we see and hear.