What
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The coordinate system we used in chapter 7 does exist on an ideal plane, true, but one we can easily superimpose on the surfaces we encounter in the realm of our experience. We can draw sine or cosine axes vertically on, say, the bedroom wall, or scribe a pi scale on a roll of toilet paper. If we equate sine values to something such as lumens of moonlight and place 29 1/2-day intervals between each 2pi on our horizontal axis, we can plot the phases of the moon. Alternatively, we could put stock-market quotations on the ordinate (sine or cosine axis) and years on the abscissa (our pi scale), and get rich or go broke applying Fourier analysis and synthesis to the cycles of finance. Ideal though they were, our theoretical waves existed in the space of our intuitive reality. I shall call this space "perceptual space" whether it's "real" or "ideal."
In the last chapter, I mentioned that in analyzing the compound wave (as a Fourier series of components regular waves, remember) the analyst calculates Fourier coefficients--the values required to make each component's frequency an integral part of a continuous, serial progression of frequencies. I also mentioned that the analyst uses coefficients to construct a graph, or write an equation. Recall that such an equation is known as a Fourier transform and that from Fourier transforms the analyst can calculate phase, amplitude and frequency spectra.
In everyday usage, "transform" is verb; it is sometimes a verb in mathematics,
too. Usually, though, the mathematician employs "transform" as a noun, as the
name for a figure or equation resulting from a transformation. Mathematical
dictionaries define transformation as the passage from one figure or expression
to another.[1] Although
"transform" has specialized implications, its source, transformation, coincides
with our general usage. In fact, a few mathematical transformations and their
resulting transforms are part of our everyday experience. A good example is
the Mercator projection of the earth, in which the apparent size of the United
States, relative to Greenland, has mystified more than one school child and
where Russia, split down the middle, ends up on opposite edges of the flat
transform of the globe. We made use of transformation ourselves when we moved
from circles to waves and back again. In executing a Fourier transformation,
in creating the Fourier transform of components, the analyst shifts the values
from perceptual space to an idealized domain known as
But my reason for introducing transform space has to do with the hologram. Transform space is where the hologramic message abides. The Fourier transform is a link to transform space.
We can't directly experience transform space. Is it a construct of pure
reason? Alternatively, is it a "place" in the same sense as the glove
compartment of a car? I really can't say, one way or the other. But although
we cannot