Shufflebrain

We could have grown additional dimensions off virtually any point on our original curve. And the sizes might vary greatly. Nor are we really compelled to remain on a flat surface. Our system might have budded like warts. And we can vary the sizes of any added dimensions. Or if we work in the abstract (as Riemann did) we can make a many-dimensional "figure" of enormous complexity. The point is that we can evolve incredible variety from a very simple rule (curvature).

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Now let's connect hologramic theory to our discussion in this chapter.

First, we conceive of mind as information, phase information.

We put that information into an ideal, Riemann-like universe--into a continuum of unspecified dimensions whose fundamental rule is curvature.

A relative phase value--a "piece of mind"--is a ratio of curvatures.

We gave our phase ratios expression as tensors.

The modalities and operations of mind then become tensor transformations of the same relative values between and among all coordinates within the mental continuum.

We dispose of our need to distinguish perceptual space from Fourier transform and kindred transform space because we do not set forth a coordinate system in advance, as we did earlier. Coordinates of the mind come after, not before the transformations.

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If you're still struggling, don't feel bad. Instead, consider hologramic mind as analogous to operations of a pocket calculator. The buttons, display, battery and circuits--counterparts of the brain--can produce the result, say, of taking the square root of 9. The calculator and its components are very much a part of the real world. But the operations--the energy relationships within it belong to the ideal world. Of all the possible coordinates that can exist in an ideal world, one coincides with experience.

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Believe me, I appreciate the demands Riemann's ideas can place on you, reader, especially at the outset. Therefore, allow me to offer another metaphor of hologramic mind.

Imagine a system whose rules apparently violate Riemann's curvature, a system that seems to be governed by straight lines, sharp corners and apparent discontinuities everywhere. What could epitomize this better than a checkerboard. Let's make that a giant red-black checkerboard.

Now imagine that one arbitrarily chosen square is subdivided into smaller red-black checkerboard squares. Randomly select one of the latter sub-squares and repeat the sub-squaring operation; do it again...and then again. Appreciate that "checkerboardness" repeats itself again and again, at every level. The various levels can be thought of as the equivalents of dimensions within our curved continuum. We can subdivide any square as many times as we please. Because we can pick any square for further sub-squaring--and subdivide as often as we wish--we can make any sub-checkerboards, --or sub-sub-checkerboards--carry vastly different specific checkerboard patterns.

Okay, to complete our metaphor of hologramic mind, all we have to do is say that our red-black sets, subsets, sub-subset represent spectra of phase variations at different levels.

Now that we've created imagery, let's get rid of the checkerboard metaphor. But let's reason it out of the picture, instead of issuing a fiat.

We said that the red and black squares are infinitely divisible. Assume that we subdivide until we approach the size of a single point (as we did with the hypotenuse and our pearly e 's). If the system is infinitely divisible, then there ought to be a single unreachable point-sized square at infinity. If there are really two separate squares down there, then our system is not infinitely divisible; and if it's not infinitely divisible, where did we get the license to divide it at all? Thus we must place a single indivisible square at infinity so that we can keep on subdividing to create our metaphor. But what color is the infinite and indivisible square? Red or black? The answer is both red and black. At infinity our apparently discontinuous system becomes continuous: red and black squares superimpose and, as in Riemann's universe, the one becomes part of the other. A hidden continuity underlies the true nature of the continously repetitive pattern, and it is the reason we can systematically deal with the pattern at all. Our checkerboard metaphor of hologramic mind turns out to be a disguised version of Riemann's universe. It is, therefore, an analog not a metaphor.

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Now let's use our general theory to answer a few questions.