Shufflebrain

Brouwer's theorem guarantees (no less) that in a continuous distortion of a system--as in stretching without tearing a rubber sheet, or stirring without splashing a bowl of clam chowder--at least one point must be in the same position at the end of the transformation as at the beginning. The point in question is the fixed point. Shinbrot describes how variants of the theorem have actually been used to predict contours of the ocean's floor from features on the water's surface. The absence of a fixed point is sufficient to deny a truly continuous relationship between two entities.

What is an object wave? In terms of frequency, it is the reference wave plus the changes imposed on it by the object. Before the object wave arrives at the scene, its frequency is identical to that of the reference wave. The object imposes a spectrum of new frequencies on the object wave., as we've in effect already said. But, invoking Brouwer's fixed-point theorem, we note that at least one point in the object wave comes out of the collision unchanged. In other words, the frequencies in the object wave will vary, but they'll vary relative to the invariant frequency at the fixed point. Because the reference and object waves once had identical frequencies, the fixed point in the object wave must have a counterpart in the reference wave. Through the fixed point, the frequency spectrum in the object waves varies--but relative to the frequency of the reference.

We must take note of an important difference between object and reference waves, namely the phase variation resulting from their different paths to the hologram plate. Let's call this phase variation D. D will vary for each object component vis-à-vis the reference. But because of the fixed point, one of those Ds will have the same value before and after the interference of reference and object waves; and all the other waves will vary relative to the invariant D. Variation relative to some invariant quantity is the general meaning of "well-defined," including "well-defined" phase relationships in interference phenomena. And a well-defined spectrum of Ds in transform space is the minimum condition of the hologram. The minimum requirement is a fixed-point relationship between object and reference waves. Minimally then, a specific hologram is a particular spectrum of well-defined Ds in transform space.

Reconstruction of the image from the hologram involves transforming the transform, synthesizing the original compound wave and transferring the visible features of the scene back to perceptual space. This statement is a veritable reiteration of how the object originally communicated its image. In theory, the hologram regenerates what the object generates. In order for a wave to serve reconstruction, it must interact with all the components and must satisfy the fixed-point requirement.

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What is memory, then? If we transfer the principles we've developed to hologramic theory, we can define a specific memory as a particular spectrum of Ds in transform space. Again, what are Ds? They are phase differences --relative values, relationships between and among constituents of the storage medium--of the brain! Thus in hologramic theory, the brain stores mind not as cells, chemicals, electrical currents or any other entity of perceptual space, but as relationships at least as abstract as any information housed in the transform space of a physical hologram. The parts and mechanisms of the brain do count; but the Ds they establish in transform space are what make memory what it is. If we try to visualize stored mind by literal comparisons with experience, we surrender any chance of forming a valid concept of the hologramic mind, and quite possibly we yield all hope of ever establishing the existence of the noumenon where the human brain stores the human mind.

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In hologramic theory, the utilization of a series of Ds during overt or covert behavior, in recall--or thoughts or feelings or whatever--is transforming the transform into perceptual space.

A percept, the dictionary tells us, is what we're aware of through our senses or by apprehension and understanding with the mind. In hologramic theory, a percept is a phase spectrum, a series of Ds in perceptual space. An active or conscious memory, a reminiscence, is a back-transformed series of Ds that have moved from transform to perceptual space. In terms of the phase code, then, perception and reminiscence involve the same basic information, the difference being the source of the Ds: the percept is analogous to image generation by an object, while the activated memory is analogous to the reconstruction from the hologram. Both synthesize the message in the same theoretical way. As Karl Pribram asserted in a lecture some years ago, memory regenerates what perception generates.