Engineering - Molecular Theory of the Living Cell - page 140

generalization known as the synthesizer theorem (Herbert 1987, pp. 82-84) can be
used to decompose any wave, either physical or nonphysical, into a sum of finite set
of component waveforms. The difference between the “physical wave” such as
water waves and “nonphysical wave” such as quantum wave is this: The square of
the amplitude of a physical wave is proportional to energy, whereas the square of
the amplitude of nonphysical wave is proportional to the probability of the occur-
rence of some event.
Herbert (1987, pp. 87-89) provides an example of the spectral area code in
action, namely, the complementary abilities of analog and digital synthesis
techniques. An analog synthesizer can construct a sound wave X out of a range of
sine waves with different frequencies k. Each wave X, depending on its shape,
requires a certain spectral width D k of sine waveforms for its analog synthesis. The
sine wave's conjugate waveform is the impulse wave, which is the basis of digital
music synthesis. A digital synthesizer forms a wave X out of a range of impulse
waves with different values of position x. Each wave requires a certain spectral
width D x of impulse waves for its digital synthesis. According to the spectral area
code, Eq. 5.46 , the product of the spectral bandwidth of sine waves ant that of
impulse waves must satisfy the spectral area code , leading to:

D k D x > 1 (5.47)

Short musical sounds (such as from a triangle or a woodblock) have a narrow
impulse spectrum. According to Inequality 5.47 , to analog-synthesize such crisp
sounds (i.e., with small D x) requires a large range of sine waves (i.e., with large
D k). To synthesize an infinitely short sound, that is, the impulse wave itself,
requires all possible since waveforms. In contrast, musical sounds that are nearly
pure tones such as from a flute, an organ, or a tuning fork have a narrow sine
spectrum. To digitally synthesize such pure tones, the spectral area code requires a
large range of impulse waves. The spectral area code informs us that analog and
digital music synthesizers are complementary : One is good for synthesizing long
waveshapes, the other for short ones. Analogously, it may be stated that the
photoelectric effect devices and optical interference devices are complementary
to each other: One is good for measuring the particle nature of light, the other is
good for measuring the wave nature of light. Thus, it may be concluded that the
complementarity principle of Bohr is a natural consequence of the spectral area
code , Inequality 5.46 .
These considerations based on the synthesizer theorem and the spectral area
code provide theoretical support for the notion that there are at least three kinds
of uncertainty principles in nature - (1) the Heisenberg Uncertainty Principle
in physics (see Inequalities 2.38 and 2.39 ), (2) the Cellular Uncertainty Principle
in cell biology formulated in the late 1990s based on the molecular model of the cell
known as the Bhopalator (Ji 1985a, b, 1990, 1991, pp. 119-122) as explained in
Fig. 5.10 below, and (3) the Knowledge Uncertainty Principle in philosophy (see
Sect. 5.2.7 ). One question that naturally arises is “What, if any, is the connection
among these three uncertainty principles?” Is the HUP perhaps ultimately