CHAPTER 14
MEASURING THE INVISIBLE RAINBOW
Suppose that we are asked to arrange the following into two categories: distance, mass, electric force, entropy, beauty, melody. I think there are the strongest grounds for placing the entropy alongside beauty and melody. . . . Entropy is only found when the parts are viewed in association, and it is by viewing or hearing the parts in association that beauty and melody are associated. . . . It is a pregnant thought that one of these association should be able to figure as a commonplace quantity of sciences.
—ARTHUR STANLEY EDDINGTON, The Nature of the Physical World
The British astronomer Arthur Eddington is credited with several important discoveries, including the relationship between the mass and luminosity of stars. He was an early advocate and popularizer for the general theory of relativity, a contentious hypothesis at the time, and provided the first experimental results that supported its predictions.
Figure 14.1. Arthur Stanley Eddington (1882–1944).
Eddington’s profound insight, presented at the start of this chapter, reveal an early scientific consideration of a shared quantity related to entropy, beauty, and melody. More specifically, he discusses a shared quantity related to the association of parts. The calculation of coherence, outlined in the preceding chapter, relates to this idea.
Modern science has naturally developed from the study of simple systems to the study of more complex systems. The solar system, thoroughly studied and described by Copernicus, Galileo, Kepler, Newton, and many others, is a simple system. Similarly, an atom, which in many ways is like a miniature solar system, is also simple in structure. The human body is a considerably more complicated system.
To summarize the earlier discussion, traditional reductionist approaches to studying such a complex system involved portioning it into progressively simpler systems. While highly successful in meeting crucial medical challenges of the past, the progressively closer focus on individual components came at the expense of our understanding of the interactions among them. In the face of the chronic degenerative diseases stemming from functional disorders that currently challenge health care systems, the reductionist approach is of limited use. Consequently, holistic medical systems have enjoyed a dramatic increase in demand in recent times.
In order to move forward with treating and preventing chronic degenerative conditions, we have to refocus our research on the interactions of the components of living systems. Analyzing coherence is key to progressing this research. While quantitatively assessing and evaluating the degree of coherence once posed a daunting, some believed insurmountable, challenge, scientists have devised methods to achieve this goal.
The preceding chapter introduced coherence theoretically and mathematically. The next step is practically measuring the coherence of a body-mind system. The process of discovering the invisible dissipative structure of electromagnetic fields in living systems provides an insight into how analysis of coherence can be performed. This analysis not only enables insight into a new aspect of the human body but also provides a practical new method to instantly evaluate the condition of a person, holistically and quantitatively. This is achieved by measuring the energy distribution of the invisible electromagnetic structure in individuals.
Coupling Oscillators and Energy Movement
The dissipative structure of electromagnetic fields in living systems is composed of chaotic standing waves. To explore how coherence operates in this situation, let us first investigate a simplified example of how the degree of coherence can be measured from the study of the coupling of waves. Coupling refers to the degree to which two oscillating bodies are constrained to move cooperatively.
In terms of coherence, the lungs, considered as a single organ, and the heart can be regarded as something akin to two dancers, because they are permanently pulsating with their independent rhythms but still require a degree of coordination. This will enable their degree of coherence to be evaluated.
Figure 14.2. Coupling relationships of two pendulums.
Given their differing functions, a situation where they were acting identically, in a highly ordered state, would obviously be detrimental to the living system. Similarly, working completely independently, as in the chaotic state, would also be far from ideal. For example, when someone is running, both the heart and the lungs need to work harder than usual, even though they do so at different frequencies. This means that there must be some coupling between the heart and the lungs that is neither too strong nor too weak. Flexible coupling enables coherence.
From the viewpoint of physics, the heart and the lungs can be modelled as a pair of oscillators, for example as a pair of pendulums. Figure 14.2 depicts three important coupling relationships that can exist between two pendulums. The first relationship, at left, shows no coupling, which can be referred to as zero coupling. The two pendulums move completely independently. Their oscillations emit two independent waves with differing frequencies. This represents an ideal chaotic state.
In the middle image, the two pendulums are connected by an inflexible connector. This results in very strong coupling between them. The two pendulums oscillate as a single body and emit waves of only one frequency. This represents the ideal crystal state, like the soldiers marching in an honor guard.
The image on the right depicts flexible coupling, provided by an elastic cord with a weight suspended from it. The two pendulums are neither rigidly connected not completely independent, and are in a coherent state.
In figure 14.3, y1 and y2 show examples of two waves of different frequencies that could be emitted by each of the pendulums oscillating either independently or with flexible coupling. If the two pendulums are flexibly coupled, constructive and destructive interference leads to the development of a third frequency, labeled y1 + y2. This is referred to in physics as the “beat” frequency. As with the two dancers in a ballet, the unusual formula 1 + 1 = 3 applies.
Figure 14.3. A beat frequency occurs when two pendulums are flexibly coupled.
Figure 14.4. Amplitude of the frequencies.
Figure 14.4 expresses the frequencies of the waves in figure 14.3 in a frequency spectrum. The beat frequency (f1 − f2) is in fact equal to the difference between frequencies 1 and 2. The vertical axis shows each of the waves’ amplitude, which is proportional to the energy level. In sound waves, higher amplitude means a louder sound. The higher amplitude of the beat frequency shows that flexible coupling has transferred energy from the higher original frequencies to the lower beat frequency. This is one of the important phenomena in coherence.
So far, we have considered only a limited case of coherence, between two oscillators or waves. When an infinite number of oscillators emitting an infinite number of waves is considered, the frequency spectrum no longer shows separate discrete frequencies like those in figure 14.4. It instead shows a continuous frequency distribution (fig. 14.5), which is a combination of countless waves.
Figure 14.5 shows the spectra of two typical combinations of a nearly infinite number of waves. On the left is the outcome of acoustic waves combining in an ideal chaotic state. The amplitudes of all frequencies are almost the same. In technology, this ideal chaotic combination of acoustic waves is called white noise. On the right are acoustic waves combining in an ideal coherent state. In technology, this combination was called “1/f noise” but was later also commonly referred to as pink noise. In comparison to white noise, the energy in pink noise has moved from the higher frequencies to the lower frequencies. This is consistent with the simple two-oscillator example in figure 14.3. This leads to the conclusion that in pink noise, there are many flexible couplings among the oscillators emitting these acoustic waves.
Pink noise was first detected emanating from an electronic circuit in 1926. It took physicists more than fifty years to determine that the underlying mechanism emerges from the grouping movement of electrons in a circuit. Interestingly, scientists working with music found that the frequency distribution of most classical and folk music was consistent with pink noise, while the frequency distributions of some modern forms of music are similar to white noise.
Modern technology makes it straightforward to analyze the frequency spectrum of acoustic waves; all that is required is a digital recording device and a computer to apply a mathematical technique known as the Fourier transformation, invented by the French mathematician Joseph Fourier (1768–1830). However, studying the frequency spectrum of electromagnetic waves in human bodies and in other living systems is significantly more challenging. The frequency range of electromagnetic waves in living systems is very broad, ranging from extremely low-frequency (ELF), on the order of 0.5 hertz, to the ultraviolet, at 1017 hertz. In comparison, audible acoustic waves occur in the relatively limited range of 20 to 20,000 hertz. This range is within the recording ability of acoustic samplers and the processing capacity of modern computers. Conversely, the range of electromagnetic frequencies present in living systems, from 0.5 to 1017 hertz, is so broad as to be virtually infinite. As such, it is beyond the ability of present technology to comprehensively detect or process.
Figure 14.6. Energy distribution changes when the test subject listens to sad music (left) and happy music (right).
Fortunately, physicists have found that skin conductivity, which is relatively easy to measure on the surface of the body, is proportional to the strength of the electric field. Thus measuring skin conductivity allows us to observe the distribution of electromagnetic fields in the body. This is determined by the dissipative structure of electromagnetic fields generated by the superposition of chaotic standing waves inside the body.
In other words, it is not necessary to measure the individual frequencies of electromagnetic waves to produce a frequency distribution, as is done for acoustic waves. Instead, the cumulative result of the superposition of the countless, even infinite, electromagnetic waves within a living system can be measured and analyzed.
Through history, mathematicians have developed statistical methods for studying the final result of the combination of infinite factors. These methods only require a finite test sample and around one hundred sample measurements to obtain meaningful results. The method, called probability distribution, makes it possible to observe changes in the energy distribution within the human body. Probability distributions generated from body conductivity measurements, depicted in figure 14.6, show that the dissipative structure of electromagnetic fields inside a body is very sensitive to changes in the music being listened to. In fact, it is quite sensitive to many psychological and physiological disturbances.
To understand the implications of these results, a couple of questions have to be addressed. First, what is the meaning of a probability distribution? Second, what is the relationship between probability distribution and coherence?
Idealized Energy Distribution
Interestingly, long before the scientific study of coherence, mathematicians developed methods to describe its three ideal states—the chaotic state, the crystal state, and the coherent state.
1 + 1 = 2: Gaussian Distribution in an Ideal Chaotic System
Prior to the introduction of the euro, the old ten-mark German note (fig. 14.7) bore a portrait of Carl Friedrich Gauss (1777–1855). He was born into a poor family but was noticed as a prodigious talent in his early years; a wealthy aristocrat financed his education. Gauss started making profound contributions to mathematics from his student days and became an influential and famous professor at the University of Göttingen. He is widely regarded as one of the greatest mathematicians of all time.
The banknote also depicts one of Gauss’s greatest contributions to mathematics, shown as a small curve with a mathematical formula (lower left in fig. 14.7) adjacent to his portrait. The curve portrays Gaussian distribution (fig. 14.8), a symmetric curve that is widely used for statistics in scientific research, industry, and other areas. It is such a standard everyday tool in statistics that it is referred to as “normal distribution.”
It was not until recently that people became aware that Gaussian distribution also describes a perfectly chaotic state. The basic hypothesis behind Gaussian distribution is that measurement data is influenced by an infinite number of factors, and that all of these factors are independent of one another. As such, the underlying hypothesis describes the state of those children in a nursery without supervision described in chapter 13. In other words, Gaussian distribution describes an ideal chaotic system.
Figure 14.8. Gaussian distribution, from a system in the ideal chaotic state.
Figure 14.9. Delta distribution, from a system in the ideal crystal state.
Practically, this means that if a collection of measurement data conforms to a Gaussian distribution, as in figure 14.8, the data comes from a system composed of infinite independent elements, and is thus an ideal chaotic system. While no real system exists in a perfectly ideal chaotic state, Gaussian distribution is approximately applicable to many nonliving systems and is widely applied in this context.
1 + 1 = 1: Delta Distribution in an Ideal Crystal System
In addition to Gaussian distribution, there are various other probability distributions in mathematics, and one that is relevant to this discussion is delta distribution, perhaps the simplest probability distribution in mathematics. It resembles a narrow pillar or an upside-down T (fig. 14.9), which means that all the measurements are identical.
If the data conforms to a delta distribution, all the system’s elements act with the highest degree of order—all acting as one. A system described by a delta distribution is like the soldiers in the honor guard, exhibiting a crystal state. Clearly no living system would function like this, but this probability distribution provides a point of comparison for the real state of an individual.
1 + 1 = 3: Log-Normal Distribution in an Ideal Coherent System
In terms of living systems and the concept of coherence, the most important probability distribution of measurement data is the log-normal distribution (fig. 14.10). Log-normal distribution presents a nonsymmetric curve. Compared to the symmetrical Gaussian distribution shown in figure 14.8, the peak of the curve is shifted to the left. Log-normal distribution was considered unimportant until 1969, when the German mathematician Lothar Sachs found that the measurement data from many physiological systems was inconsistent with Gaussian distribution and instead conformed to log-normal distribution. This revealed that there is some relationship between log-normal distribution and living systems.
In 1994 I proved mathematically that log-normal distribution comes from an infinite-elements system in which each element has the ability to function independently, and at the same time, is also able to cooperate with other elements. In other words, if the measurement data from a system conforms to log-normal distribution, this demonstrates coherence among the elements. This means that the unusual arithmetic that describes a ballet, 1 + 1 = 3, applies. Consequently, the beauty and coherence present in music, ballet, and living systems is no longer limited to eloquent poetic description; it now exists in the realm of rigorous mathematical formulas, practical measurement, and quantitative calculation.
Infinite Dimensional Space and the Coherence Pyramid
This book has looked at three ideal states: the ideal chaotic state, like children in a nursery; the ideal crystal state, like soldiers in an honor guard; the ideal coherent state, like dancers in a ballet. We have also discussed the three types of probability distributions that correspond to these ideal states: Gaussian distribution, delta distribution, and log-normal distribution, respectively.
All three states represent ideal states. In fact, no real system is so chaotic as to be perfectly described by Gaussian distribution, nor so highly ordered as to perfectly conform to delta distribution, nor so perfectly coherent that it is perfectly consistently with log-normal distribution. A real system always exist somewhere between these three. Consequently, the probability distribution of its measured data is also somewhere between the three typical probability distributions.
The frequency distribution on the right in figure 14.6 shows a real distribution of data that is quite close to log-normal distribution, but not exactly the same. This means that the person being tested was in a very coherent state when listening to happy music, but not a perfectly coherent one. This raises the practical challenge of quantifying how far the state of a person is from a perfectly coherent one. While quantifying distance from coherence seems counterintuitive, much like doing so for beauty would be, this is the challenge at hand.
The techniques required to tackle the contemporary challenge of determining a coherence distance have again been provided by a great German mathematician, David Hilbert (1862–1943), shown in figure 14.11. He developed the mathematical tools to calculate the distance between two states that are composed of infinite elements.
Figure 14.11. David Hilbert, who theorized infinite dimensional space.
Like Gauss, Hilbert was also a professor at the University of Göttingen, and in many ways he can be considered Gauss’s successor as one of the most influential mathematicians of the era. At the beginning of the twentieth century, he presented a talk at a conference about the development of mathematics in which he predicted the main focus for mathematicians. This talk ultimately served as a navigation chart for mathematicians worldwide in exploring the unknown areas of mathematics.
Hilbert’s most important discovery is the concept of infinite dimensional space, which mathematicians call Hilbert space or space of functions. In Hilbert space, there is generalized distance that makes it possible to measure the “distance” between two mathematical functions that are both composed of infinite elements.
In everyday language, distance refers to a measurement between two points, like on the surface of a piece of paper or across a room. Hilbert generalized the concept of distance from real-world two- and three-dimensional spaces to an imagined four-dimensional space, five-dimensional space, and so on, extending it to n-dimensional space, which could even be infinite dimensional space. The calculation of distance in all these spaces is the same.
This infinite dimensional space allows for the distance between the real state of a patient and the ideal coherent state to be calculated. In other words, with Hilbert’s help, it is possible to quantitatively state how far away a patient is from a state of perfect coherence. In addition to calculating the distance, it is also necessary to have some kind of coordinate system to stipulate the precise position of the state of a patient relative to the three ideal states.
The three ideal states are described by three rigorous mathematical formulas and a practical method of measurement. Hilbert space allows a mathematical formula or function to be condensed into a mathematical point. By condensing the three probability distributions, and thereby the three ideal states, into three mathematical points, a special coordinate system can be established (plate 16 in the color plate section). This allows the location of the real state of a person to be perceived.
As shown in plate 16, the special coordinate system in Hilbert space that allows us to evaluate the degree of coherence resembles a pyramid. Consequently it is referred to as a coherence pyramid. At the top of the pyramid is a green dot, the coordinate of the ideal coherent state as expressed by log-normal distribution. A black dot, marking the ideal chaotic state as expressed by Gaussian distribution, is at the left corner. The right corner of the coherence pyramid has a red dot, marking the ideal crystal state expressed by delta distribution.
To explain the choice of colors, black is the color of anarchy. Physiologically and psychologically, anarchy possesses both positive and negative aspects. The positive aspect is that anarchy provides relaxation to the system after hard work or conflict, and as such it is beneficial to health. On the negative side, anarchy sometimes steers a system into chaos or depression, the accumulation of which can be dangerous to the body-mind system. It can be argued that many cancers stem from the accumulation of chaos and depression.
Red is the color of revolution or dictatorship. Physiologically and psychologically, dictatorship also has two sides. On the positive side, it brings a system into very high order, which is important for conflict or for highly focused work. However, this focus comes at the expense of increased stress. Accumulated stress can lead directly to hypertension. It can also lead to a breakdown in the system, leading to chaos and its associated health risks.
Green is generally associated with ecological balance or a positive state, and has therefore been applied to denote an idealized state without negative implications.