Abstractions, in turn, are what theories really deal in: when we compare six apples with six oranges, we divide or square or multiply the numbers, the abstractions-- not the pits or rinds. The old cliché about not comparing apples and oranges is (to tweak if not mix a metaphor) a lot boloney if we're talking about numbers. "How many apples will you give me for two or oranges?" A good test of a valid abstraction is to ask: does it survive if we shift it to a new set of parochial conditions? The ninety-degree angle-- the abstraction-- made by the edges of a table top does not depend on oak or maple; it can be formed of brass, or asphalt, or two streaks of chalk.
The analogy has its intellectual justification in the first axiom of geometry: things equal to the same things are equal to each other. Things dependent upon the same abstractions are analogs of each other!
Analogy can show us what a theory does , but not what a theory is . Nor does analogy provide a rigorous test of a theory's applicability to a problem. Analogy can't serve as substitutes for the experiment, in other words. Nonetheless, analogies often reveal a theory's implications. They also help connect abstractions to some concrete reality; they often put us in a position to grasp the main idea of a theory with our intuition. The analogy can also expose a subject and show important consequences of a theory, even to those who do not know the strange language of the theory. The analogy can put the theory to work on a human being's familiar ground-- experience. It is by way of the analogy that I shall introduce the reader to hologramic theory.
***
The hologram is not a phenomenon of light, per se, but of waves; in theory, any waves or wavelike events. I've already mentioned acoustical holograms. X-ray holograms, microwave holograms, and electron holograms also exist, as do "computer" holograms, which are holograms constructed from mathematical equations and reconstructed by the computer; holograms, in other words, of objects comprised of pure thought.
The same kinds of equations can describe holograms of all sorts. And the very same phase code can exist simultaneously in several different media. Take acoustical holograms, for instance. The acoustical holographer produces his hologram by transmitting sound waves through an object. (Solids transmit sound as shock vibrations, as, for example, knocks on a door.) He records the interference patterns with a microphone and displays his hologram on a television tube. Sound waves cannot stimulate the light receptors in our retinas. Thus we would not be able to "see" what a sonic wave would reconstruct. But the acoustical holographer can still present the scene to us by making a photograph of the hologram on the TV tube. Then, by shining a laser through the photograph, he reconstructs optically-- and therefore visibly-- the images he originally holographed by sound.
Sound is not light, nor is it the electronic signals in the television set. But information carried in the phase and amplitude of sound or electronic waves can be an analog of the same message or image in a light beam, and vice versa. It is the code-- the abstract logic--that the different media must share, not the chemistry. For holograms are encoded, stored information. They are memories in the most exacting sense of the word--the mathematical sense. They are abstractable relationships between the constituents of the medium, not the constituents themselves. And abstract information is what hologramic theory is about.
As I said in the preceding chapter, the inherent logic in waves shows up in many activities, motions, and geometric patterns. For example, the equations of waves can describe a swinging pendulum; a vibrating drum head; flapping butterfly wings; cycling hands of a clock; beating hearts; planets orbiting the sun, or electrons circling an atom's nucleus; the thrust and return of an auto engine's pistons; the spacing of atoms in a crystal; the rise and fall of the tide; the recurrence of the seasons. The terms harmonic motion, periodic motion, and wave motion are interchangeable. The to-and-fro activity of an oscillating crystal, the pulsation in an artery, and the rhythm in a song are analogs of the rise and fall of waves. Under the electron microscope, the fibers of our connective tissues (collagen fibers) show what anatomists call periodicity, meaning a banded, repeated pattern occurring along the fiber's length. The pattern is also an analog of waves.
Of course, a periodically patterned connective-tissue fiber is not literally a wave. It is a piece of protein. A pendulum is not a wave, either, but brass or wood or ivory. And the vibrating head of a tom-tom isn't the stormy sea, but the erstwhile hide of an unlucky jackass. Motions, activities, patterns, and waves all obey a common set of abstract rules. And any wavy wave or wavelike event can be defined, described, or, given the engineering wherewithal, reproduced if one knows amplitude and phase. A crystallographer who calculates the phase and amplitude spectra of a crystal's x-ray diffraction pattern knows the internal anatomy of that crystal in minute detail. An astronomer who knows the phase and amplitude of a planet's moon knows precisely where and when he can take its picture. But let me repeat: the theorist's emphasis is not on the nominalistic fact: It is on logic, which is the basis of the hologram.
Nor, in theory, does the hologram necessarily depend on the literal interference of wavy waves. In the acoustical hologram, for example, where is the information? Is it in the interferences of the sonic wave fronts? In the microphone? In the voltage fluctuations initiated by the vibrating microphone? In oscillations among particles within the electronic components of the television set? On the television screen? In the photograph? The answer is that the code-- the relationships-- and therefore the hologram itself, exists-- or once existed-- in all these places, sometimes in a form we can readily appreciate as wavy information, and in other instances as motion or activity, in forms that don't even remotely resemble what we usually think of as waves.
***
Lashley's experiments can be applied to diffuse holograms, as I have pointed out. His results depended not on where he injured the brain but on how much . Likewise, cropping a corner from a diffuse hologram does not amputate parts from the regenerated scene. Nor does cutting a hole in the center or anywhere else. The remaining hologram still produces an entire scene. In fact, even the amputated pieces reconstruct a whole scene-- the same whole scene. What Lashley had inferred about the memory trace is true for the diffuse hologram as well: the code in a diffuse hologram is equipotentially represented throughout the diffuse hologram.
***
The loss of detail that occurs when we decode a small piece of diffuse hologram is not a property of the code itself. Blurring is a result mainly of noise, not the signal. How seriously noise affects the quality of an incoming message depends on the ratio of noise to signal. If the signal is powerful, we may dampen noise by reducing volume or brightness. But with very weak signals, as short-wave radio buffs can testify, a small amount of noise (static) severely impedes reception. In optical holograms, the relative level of noise increases as the size of the hologram decreases. And in a small enough piece of hologram, noise can disperse the image.
We have already made the analogy between the survival of memory in a damaged brain and the survival of image in a marred hologram. Signal-to-noise ratio is really an analog of the decline in efficiency found in Lashley's subjects. In other words, the less brain, the weaker the signal and the greater the deleterious consequence of "neural noise."
***
Loss of detail in an image produced from a small chip of hologram is a function of decoding, not of the code itself. An infinitesimally small code still exists at every point in the diffuse hologram. Like a single geometric point, the individual code is a theoretical, not a physical, entity. As with geometric points, we deal with codes physically in groups, not as individuals. But the presence of a code at every location is what accounts for the demonstrable fact that any arbitrarily chosen sector of the hologram produces the same scene as any other sector. Granted, this property may not be easy to fathom; for nothing in our everyday experience is like a diffuse hologram. Otherwise, the mind would have been the subject of scientific inquiry long before Leith and Upatnieks.
***
If a single holographic code is so very, very tiny, any physical area should be able to contain many codes-- infinitely many, in theory.[1] Nor would the codes all have to resemble each other. Leith and Upatnieks recognized these properties early in their work. Then, turning theory into practice, they went on to invent the "multiple hologram"-- several totally different holograms actually stacked together within the same film.
With several holograms in the same film, how could reconstruction proceed without producing utter chaos? How might individual scenes be reconstructed, one at a time? Leith and Upatnieks extended the basic operating rules of holography they themselves had developed. During reconstruction, the beam must pass through the film at a critical angle-- an angle approximating the one at which the construction beam originally met the film. During multiple constructions, Leith and Upatnieks set up each hologram at a different angle. Then, during reconstruction, a tilt of the film in the beam was sufficient for one scene instantly to be forgotten and the other remembered.
One of Leith and Upatnieks' most famous multiple holograms is of a little toy chick on wheels. The toy dips over to peck the surface when it's dragged along. Leith and Upatnieks holographed the toy in various positions, tilting the film at each step. Then, during reconstruction, by rotating the film at the correct tempo, they produced images of the little chick, in motion, pecking away at the surface as though going after cracked corn. Some variant of their basic idea could become the cinema and TV or tomorrow.
***
Multiple holograms let us conceptualize something neither Lashley nor anyone else had ever satisfactorily explained: how one brain can house more than one memory. If the engram is reduplicated and also equally represented throughout the brain, how can enough room remain for the next thing the animal learns--and the next...and the next? Multiple holograms illustrate the fact that many codes can be packed together in the same space.
Just as important, multiple holograms mimic the actual recalling and forgetting processes: tilt the film in the reconstruction beam, and, instantly, off goes one scene and on comes the next. A few years ago, I met a young man named John Kilpatrick who suggested that a person trying to recollect something may be searching for the equivalent of the correct reconstruction angle.
But suppose that instead of using a single reconstruction beam, we use several beams. And suppose we pass the beams through the multiple hologram at different angles. We may, in this manner, synthesize a composite scene. And the objects in the composite scene may never have been together in objective reality. When the human mind synthesizes memories into unprecedented subjective scenes, we apply terms such as thinking, reasoning, imagining; or (depending on the circumstances) even hallucinating. In other words, built right into the hologramic model are analogs of much human mental activity.
***
Holography does not require lenses. But lenses may be employed to produce certain special effects. Leith and Upatnieks showed in one of their earliest experiments that when the holographer uses a lens during construction, he must use an identical lens for reconstruction. This fact should (and probably does) interest spies. For not even Gabor or Leith and Upatnieks can read a holographic message directly. It is a code in the most cloak-and-dagger sense of the word. A hologram must be decoded by the appropriate reconstruction beam, under specific conditions. And a lens with an unusual crack in it would create an uncrackable code for all who do not possess that same cracked lens.
We might even come to use a combination of different construction angles and flawed lenses to simulate malfunctions of the mind. Suppose, for instance, a holographer makes a hologram of, say, a bedroom wall, and onto the same film also encodes the image of an elephant, using a lens at this stage. Given the appropriate conditions, he could synthesize the bizarre scene of a pink elephant emerging from the bedroom wall. Humans hallucinate similar scenes during delirium tremens.
***
Leith and Upatnieks also made color a part of holography. Physically, a particular hue is the result of a specific energy or wavelength. What we usually think of as light is a range of energies lying in the region of the electromagnetic spectrum visible to humans (and accordingly called the visible spectrum). Specific molecules in our rods and cones make the visible region visible. Red light lies on the weaker end of the spectrum, while violet is on the stronger end. Thus, infra red waves have energies just below red and ultra violet waves are stronger than violet. Physicists often deal with color in conjunction with the subject known as dispersion. For when white light, say a sun ray, passes through a prism, the beam disperses into red, yellow, green, and blue light. (Dispersion also accounts for rainbows.) White light, remember, is a so-called spectral mixture. And full-color illumination of a multicolored scene requires white light.
It is possible to produce white light by mixing red, green, and blue lights. Thus the latter are called the additive primary colors. Not only will they produce white light but varying combinations of them can yield the half-million or more hues we humans can discriminate.
The colors we see depend on which wavelengths reach our retina. The pigment in a swath or red paint looks red in white light because the molecules absorb the other wavelengths and reflect red back to our eyes. The sky looks blue on a clear day because the atmosphere absorbs all but the energetic blue violets. The sea looks black on a moonless night because nearly all the visible wavelengths have been absorbed. Light is energy. Thus tar on a roof heats much more in the sunlight than does a white straw Panama hat; the tar has absorbed more energy than the hat and has therefore reflected less.
Photometrists use the word additive to describe red, green, and blue lights because subtractive primaries also exist: magenta, yellow, and green-blue. When magenta, yellow, and green-blue filters are placed in the path of a beam of white light, no visible light can pass through. The result is sometimes called black light. Black light is a potential product of even the three additive primary colors. For red and blue can produce magenta; green and blue can produce yellow, and, if the algebraic mix is right, some green-blue as well. And a beam of white light--a mixture of the primaries, red, green, and blue--can color a scene white, black, or anything in between, depending on the relative amounts of each primary color.
Leith and Upatnieks described how they would "illuminate a scene with coherent light in each of three primary colors, and the hologram would receive reflected light of each color." Now the hologram plate itself was black and white. For the hologram remembered not color itself but a code for color. Yet when Leith and Upatnieks passed a red-green-blue beam through the hologram, they produced, in their own words: "the object in full color."[2]
Offhand, it might seem as though the reconstruction beam would have to be the same color as the original light source. But Leith's equations said something different: the reconstruction beam's wavelength must be equal to or shorter than that of the original. He and Upatnieks tested the hypothesis. And it worked: they could change the scene from one color to another, if the decoding beam's wavelength did not exceed that of the original beam.
Let's put this property to use in our analogies.
***
Color manipulations also let us mimic human mental activities. For example, suppose we construct a hologram with green light. During reconstruction, suppose we use light with wavelengths longer than green-- red, for instance. The rule for "remembering" the scene, recall, is to use a wavelength equal to or shorter than the original. Thus the red light cannot regenerate the scene. But the hologram still has a memory of the scene, doesn't it? We simply can't decode it with red. As is the case with construction angles in the multiple hologram, displaying the information means satisfying certain conditions-- wavelengths, in the case of color.
Kilpatrick's scanning model might employ wavelength as well as angle of tilt to simulate the act of recalling a memory. (Indeed, the use of both would make a more versatile model.) Suppose we use a blue reconstruction beam, which has a shorter wavelength than green. Then we would produce a scene from a hologram that had been constructed with green light, although the color of the reconstructed scene would be blue instead of green. Suppose we don't know the original color. If we began scanning from the red end, we would pass through a considerable portion of the visible spectrum before any scene at all appeared. But once into and beyond the green zone, we would reconstruct the scene through a vast range of greens, blues, and violets and never know just what wavelengths had been used during construction.
Think of our own recollection process. How often have you scanned your memory to recall a past experience and, having recalled it, seen it in your mind's eye with different details from those of the experience itself? We almost never remember things perfectly. What would happen if we used red-green-blue in our model? We could vary the reconstruction wavelengths over a vast range indeed. We might contrive a wavelength mixture where, suddenly, everything seems to go blank (if we hit the counterparts of subtractive primary wavelengths). These properties give the hologram many features that Freud and his followers envisaged for the human mind.
Can we actually simulate the subconscious mind with holograms? A model is implicit in what I have already described. To illustrate it further, let's return to our green hologram. Suppose that during scanning we move off into ultraviolet wavelengths, beyond the visible region of the spectrum. There the wavelengths are shorter than green, and thus fully able to regenerate an image. But beyond the visible spectrum, the image would be invisible; and we would have to use special film or meters in order to detect it. Invisible or not, the image would burn itself into our retinas if we were foolish enough to look in its direction long enough, for the same reasons that we can suffer severe sunburns on cloudy days. Likewise, our physiology can come under incredible stress from thoughts, feelings, and so forth that do not surface in the conscious mind.
***
Acoustical holographers also do very interesting things with color. In an excellent Scientific American article in 1969, Alexander Metherell (the same person who showed that holograms are about phase) reported his methods for making full-color holograms. He used sonic waves of three different frequencies, but frequencies whose ratios corresponded with red-green-blue . He then used mixtures of light to reconstruct multicolored scenes. Sound is not light, of course. Nor are sonic frequencies colors. Metherell's experiments dramatize the truly abstract nature of the hologram's code. He encoded color information not with wavelengths but with ratios of wavelengths.
Metherell's experiments suggest many features of mind we have already discussed. In addition, they hint at a physical model of language.
Modern theoretical linguists believe that languages do not evolve pell-mell from the raw sound-producing capabilities of our voice boxes, tongues, cheeks, teeth, and so on. All languages, they believe, follow certain general rules of syntax. Still, no matter how convincing the linguists' arguments are, German is not Korean. In Metherell's experiments, ratio was the rule. But to reconstruct a specific color, Metherell did have to pay attention to specific wavelengths. Wavelength ratio can serve as an analog of the general rules of syntax, and specific wavelengths can be models of the particular features of a specific language.
But Metherell's experiments let us go beyond the spoken word. They contain the elements of translation: translation from sound to light. Built into his system is a whole scene-shifting, from one medium to the other, with an abstract code to do the remembering. We are constantly shifting our language modalities-- writing notes at a lecture, dictating words destined for print. Consider the many forms English may take: script, sound, shorthand, print. Braille, Morse code, American Sign Language, Pig Latin. We need abstract codes-- like those in Metherell's holograms-- to move among the analogs on a whole-message basis.
***
Color holography and multiple holograms also supply models for the results of split-brain research. Recall that persons who underwent the split-brain operation behaved as though their right and left cerebral hemispheres knew different things. Yet the operation did not derange them; they remained, as Gazzaniga said, "just folks." A hemisphere knew whole messages.
Suppose we decide to construct two holograms of an elephant, on the same piece of film, using two different construction angles, with, say, red at one angle and blue at the other. Remember that the reconstruction beam must contain wavelengths equal to or shorter than the original. During the reconstruction with blue light, either angle will reproduce our elephant's image; but red will work at only one angle. Still, whenever we do reconstruct the elephant's image, it is a whole image, not a tusk here, a trunk there. Wavelength manipulations, in other words, allow us to simulate the observations reported by split-brain researchers.
We can envisage another model for split-brain. Suppose we shade the left side of the film during one step of construction. Obviously, we would be able to reconstruct scenes from the right side that we would not get from the left. Gazzinga's observations hint at the possibility that humans learn to direct certain information to only one hemisphere. Active inhibition occurs on a grand scale in the nervous system, and at levels from individual cells to whole lobes. Shading in our experiment can serve as an analog of inhibition.
***
A toddler I once knew went into a gleeful prance whenever her young father entered the room. Around the perimeter of her playpen she would march, damp diaper at half-mast, singing "Dadadada!" until the man rested his chin on the rail next to her little face to receive a moist kiss. One day he came home wearing new eyeglasses. The toddler began her routine but then broke off, frowning, on the first "Da," as she apprehended the change. When he bent down, she placed a wet finger on one of the curious lenses, and, maintaining the frown, continued, "dadadada!" at a puzzled pace.
No physical hologram, multiple or otherwise, matches the complexity of that toddler in action. But holograms used in the materials-testing industry suggest one feature of her behavior, namely, the instantaneous-- and simultaneous-- recognition of both the familiar and unfamiliar attributes in a scene. The technique is known as interference holography and involves looking at an object through a hologram of the object. The light waves coming from the object and from the hologram superimpose interference fringes on the object's image. Any locus where the object has changed since its hologram was made will reflect light differently than before. And in that area the interference patterns converge toward the point of change. The method is extremely sensitive. Even the pressure of a finger on a block of granite shows up immediately. The observer is immediately aware of the change but can also recognize the object in the background.
***
In a splendid article in Scientific American in 1965, Leith and Upatnieks made an interesting comparison between holograms and FM signals. FM is, of course, the abbreviation for frequency modulation, and it is the form in which TV and FM radio stations broadcast. Frequency, remember, refers to the number of cycles occurring in a given period of time. In FM, the amplitudes of the radio waves stay constant while their frequencies vary, or modulate, to carry the message. As waves contract or expand, their peaks, or amplitudes, shift. Phase, remember, specifies the location of amplitudes. As many engineers describe it, and as Leith and Upatnieks point out, FM is in effect phase modulation, the generic feature of all holograms.
Physiologists have known for some time that neural signals involve frequency modulation (see Brinley), and therefore variations in phase. The reason for this has to do with the nature of the main neural signal carrier, the nerve impulse.
A nerve impulse shows up on the physiologist's oscilloscope as a traveling electronic wavelet. What is on the scope represents a wavelike voltage flux on the exterior of the neuron's membrane, and is often called a "spike." Now the impulse obeys what is called the all-or-none law. This means, first of all, that the cell must absorb stimulation at or above a particular threshold, or else it won't fire an impulse, per se; second, that the impulse travels at a constant rate and maintains uniform amplitude throughout its passage along the membrane; third, that increasing the stimulus above threshold will not make the impulse move faster or become stronger. Also, immediately after the appearance of the spike, and for a brief duration as the cell recocks itself, the membrane won't carry an impulse. This interval is called the absolute refractory period. The refractory period prevents impulse additions. With threshold in the van and the refractory period in the wake, the impulse becomes a wave of constant amplitude. What's left to turn impulses into signals? The answer is the number of impulses per unit of time--the frequency. FM or phase modulation, which is the fundamental principle in hologramic theory.
Groups of neurons, some firing (ON), others inhibited (OFF), can produce arrays of ON-OFF in the nervous system. This is very conspicuous on the retina and in the LGB. Some time ago, Karl Pribram, going counter to conventional thinking, analogized such ON-OFF arrays to interference patterns--implicating phase modulation, and, of course, the hologram. In more recent years, physiologists have been finding what Pribram suggested. Today, phase has become a major topic in sensory physiology, especially in vision research.[3]
Thus we do not have to search very far or long to make analogies between the generic principle of the hologram, wave phase, and the physiology of the brain.
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My purpose is not to oversimplify the mind. The pivotal question is: Do we find nonliving analogs of ourselves out there? The answer is yes.
But analogy is too causal and conjectural a process to suit scientific verification. To an empirical scientist, which I am, theory must justify itself in experiments. And this is where shufflebrain enters the story.
Internet contact:pietsch@indiana.edu