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What do we really mean by our stripes? They are beats, yes. But stripes are periodic patterns of light and dark, a harmonic array of alternating densities. Given this, the memory of rings shouldn't literally be confined to stripes as such. The memory is a periodicity, a wavy logic. We should be able to back-transform rings with, say, dots. Here's what we get when we carry out the experiments:

For an enlargement see footnote [8] ***

I've presented the dot experiment for an additional reason. Maybe I was just lucky with the rings? Perhaps the various dots are fortuitously spaced so as to interact with the correct arcs on the rings. If you look carefully at the back-transformed rings, you'll see that they're not all identical. In fact, those on opposite sides of either the vertical or horizontal axes, and thus on perspective arcs of the same circles, are mirror images of each other: where one ring has a dark center, the corresponding ring is light. If the "maybes" in the above speculations were correct, these rings would have been identical, which they plainly are not.

And the dots show us something I hadn't foreseen at all, but can't resist pointing out here. Let me show you a blown up set of dots at the edge where there aren't any rings. I mentioned in chapter 4 that we humans often have a hard time remembering something exactly as we originally experienced it. Have you ever fumbled around with several vivid recollections that are similar but not identical and couldn't decide on the exact one, e.g. the first name of a bygone author, actor, sweetheart? Even our simple optical patterns seem to have this difficulty. A quick peek at the notes or a fresh percept for comparison can solve the problem much more reliably than memory alone. Likewise, with our dot system we merely have to compare the various readouts with the center ring to ascertain which recollection precisely corresponds to the original scene.

In hologramic theory, reasoning, thinking, associating or any equivalent of correlating the ring is matching the newly transformed transform with the back-transform. (The technical term for such matching is autocorrelation.)

***

Let's shift our focus back to the nature of the phase code, which in our ring system is the preservation of ring information by periodic patterns. The ring memory is not limited to dots and stripes. When we react rings with too great a distance between their centers (if their center rings do not overlap), we do not produce stripes. Instead, something interesting happens. Notice that if we get the centers far enough apart, rings form in the readout:

;

Built into the higher frequency rings is a memory of rings closer to the center. Let me explain this.

First of all, as I've pointed out, the phase code isn't literally dots or stripes or dots[7] but a certain periodicity; i. e., a logic! Our rings are much like ripples on a pond; they expand from the central ring just as any wave front advances from the origin. Recall from Huygen's principle that each point in a wave contributes to the advancing front. The waves at the periphery contain a memory of their entire ancestry. When we superimpose sets of rings in the manner of the last figure, we back-transform those hidden, unsuspected "ancestral " memories from transform to perceptual space. The last picture demonstrates that no necessary relationship exists between the nature of a phase code and precisely how that phase code came into being. The "calculation" represented by the picture shows why hologramic theory fits the prescriptions of neither empirical nor rational schools of thought. In the experiments where we superimposed rings on rings the system had to "learn" the code; the two sets of rings had to "experience" each other within a certain boundary in order to transfer their phase variation into transform space. But the very same code also grew spontaneously out of the "innate" advance of the wave front. These, reader, are the reasons why I would not define memory on the basis of either learning or instinct. As trees are irreducibly wood, memory is phase codes: whether the code is "learned" or "instinctive" has no existential bearing on its mathematical--and therefore--necessary features.

***

Consider something else our stripes, dots and rings reveal about the phase code. We can't assign memory to a specific structural attribute of the system. In hologramic theory, memory is without fixed size, absolute proportions or particular architecture. Memory is stored as abstract periodicity in transform space. This abstract property is the theoretical basis for the predictions my shufflebrain experiments vindicated, and for why shuffling a salamander's brain doesn't scramble its stored mind. My instruments cannot reach into the ideal transform space where mind is stored. For hologramic mind will not reduce directly to the constituents of the brain.

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