Ants and Acorns:
Some Thoughts on Complexity, Chaos,
and the Therapeutic RelationshipHaving devoted much of my time over the past two years to a study of chaos and complexity, I find myself asking why the scientific community is so fascinated by these concepts, and what relevance they may have to the therapeutic encounter. I have gained important insights into the difference between determinism and the Chinese concept of ming (destiny, the "unfolding of original nature" [Rochat, 1992]) and the practical application of these concepts to our clinical work.
Chaos and complexity are aspects of systems theory. General systems theory, as first expounded by Bertalanffy in the 1930s and 40s, is based on the notion that all systems—whether physical, biological, or social—are united, not by similar contents, but by regularities of dynamic pattern. As Bertalanffy observed, "The Unity of Science is granted, not by a utopian reduction of all sciences to physics and chemistry, but by the structural uniformities of the different levels of reality" (Bertalanffy ,1968).
Bertalanffy was particularly concerned with and opposed to the attempt, on the part of reductionist/positivist science, to resolve biological phenomena into atomic entities and partial processes. He maintained that positivist science reduces living organism to cells, its activities to physiological and, ultimately, physicochemical processes, its behaviour to unconditioned and conditioned reflexes, its heredity to particulate genes, and so on. He opposed this scientific perspective with the concept of "organism," and argued compellingly that it is necessary to study not only parts and processes in isolation, but also to solve the problems found in the organizations unifying them and to explore the dynamic interaction of parts instead of viewing each part in isolation.
Early systems theorists were intrigued by the observation that, while non-living systems seem to follow the Second Law of Thermodynamics (accumulating entropy), living systems exhibit the capacity to self-organize, generating higher levels of order. How to define a living system and what distinguished "life" from "non-life" were the central issues of their investigations.
The closing of the gap between the physical and the biological realms began with the relatively recent discovery that even aspects of the "merely material" world can, under certain circumstances, propel themselves into states of higher order, higher complexity, and higher organization.
The new sciences dealing with "self-organizing systems" are known collectively as the sciences of complexity, and include general systems theory, cybernetics, nonequilibirum thermodynamics, cellular automata theory, catastrophe theory, autopoietic system theory, dynamic systems theory, and chaos theories.Chaos
Chaos is a mathematical concept applied to the modelling of complex dynamic systems. In order to understand it, we must first understand the concept of an attractor.
All stable systems exhibit patterns of behaviour, which are stable because, after any disturbance, the system is "attracted" to its usual pattern. When a complex system is first established, it may exhibit "transient" behaviour, like a car when you first start it up or the turbulence in the flow of water from a tap when you first turn it on. But most systems eventually settle down to some sort of stability, and the form of this stability (the "attractor") can be mapped mathematically: for example, an unchanging value is represented by a point, and a regular oscillation by a wavy line or a loop.
There are three types of attractors:
1) Point attractors: Imagine a marble rolling around in a bowl and eventually coming to rest at the bottom of the bowl; the bottom of the bowl is the attractor. This is the ultimate stable state: in living systems, complete stability is equivalent to death.
2) Periodic attractors: This type of behaviour repeats itself continuously without significant variation (for example, machines that perform repetitive movements or a planet in orbit). Many physiological systems display apparently periodic behaviour such as circadian thermal rhythms, the menstrual cycle, and the pulse.
3) Strange Attractors: Any structurally stable attractor that is not a point or a cycle is said to be a strange attractor. A strange attractor, when plotted mathematically, consists of orbits that never repeat exactly the same cycle, but never wander outside a limited region of space. The point moves erratically, but within certain boundaries. Because the point does not move outside these boundaries, the visual image created by such a mathematical representation has a characteristic shape.
Thus, a strange attractor is a mathematical depiction of a system that, paradoxically, has a predictable and recognizable overall form made up of unpredictable details.
Why has chaos become such a buzzword? Because it describes most of the phenomena we encounter in real life.The Mechanics of Chaotic Systems: Feedback
The occurrence of these different types of attractor can be understood in terms of feedback. There are two general types of feedback. "Negative feedback" is the "feeding back" of information so as to keep the behaviour of a system in check, like the valve on a steam engine, which opens when the engine is running too fast in order to slow it down, but closes to keep the pressure up when the engine starts to slow down . In living organisms, the classic example of negative feedback is temperature regulation: if there is a discrepancy of even1° C from the body’s set point, "thermometer neurons" in the hypothalamus alter their firing rate, which triggers an action either to warm or cool the blood. Warming is accomplished by increasing muscle tone and shivering, which increases heat production, and by curling up and constricting blood vessels in the skin to diminish heat loss. Cooling is achieved by loss of fluid through sweating and vasodilation in the arms, legs, and head. Both actions return body temperature to its thermal attractor of approximately 37° C. Through oscillations on a small scale, negative feedback calms disturbances to maintain homeostasis, which is essentially a point attractor.
"Positive feedback," by contrast, amplifies disturbances, and, if not countered by other influences, pushes systems to explode or spiral out of control. Familiar examples include the "feedback" that results when a microphone is placed too near its speaker, the careers of pop stars and artists, the popularity of children’s’ games, and fads that "catch on" and escalate, feeding on and multiplying their own impetus.
Many dynamic systems and all chaotic systems exhibit a combination of negative and positive feedback. Negative feedback prevents the system from destroying itself or changing beyond recognition, while positive feedback amplifies small changes into large results, making the system extremely sensitive to external or internal environmental inputs. Positive feedback in orderly systems can cause complex and chaotic behaviour, and negative feedback in an otherwise chaotic system can organize and stabilize it.
Combinations of these two types of feedback can be found everywhere in nature. In weather systems, for example, negative feedback works to keep the overall atmospheric temperature stable, while positive feedback can amplify a relatively small local perturbation into a major meteorological event. Because the planet’s interlocking positive and negative feedback loops make the global system fundamentally chaotic, weather prediction is notoriously difficult in the short term, and simply not possible in the long term.
Chaos in living organisms is caused, in part, by the constant feedback that occurs when highly complex organic subsystems interact with each other according to various timescales: nervous impulses have a periodicity of fractions of a second, hormonal frequencies run between minutes and hours, "circadian" rhythms are normally between 22 and 28 hours, the menstrual cycle is normally around 28 days, and so on. Time delays on different scales build up so that the internal processes of the organic system are subtly, but constantly, shifting, lending a great deal of plasticity and adaptive potential to the system as a whole.Scale
One property of chaotic systems is that their structure and behaviour on a large scale is reflected on a small scale. If you cut open a cauliflower so that its branching structure is revealed, you will see an exquisitely beautiful example of self-similarity of structure.
Self-similarity is a fundamental characteristic of all natural systems and can be seen everywhere around us—in coastlines, clouds, lightning, and rivers. Our own bodies are no exception: the vascular system, neural networks, the tracheobronchial tree, the bowel, and the brain are all "fractal" structures, displaying self-similarity on many scales.
Self-similarity breaks down at the ends of the spectrum of scale, that is, in the realms of the very large and the very small. You can measure the scaling of a coastline in greater and greater detail without significant qualitative change until you reach the molecular level. A flea can jump about a metre, but it would not be able to jump a thousand metres if it were magnified a thousand times; in fact, the poor creature’s legs would break under its own weight.
The Chinese classics abound with poetic descriptions of our self-similar world. One of my teachers, Dr. Song Ke, related a story he was told as a child: humans have four limbs because the earth has four directions; we have hair because grass grows on the earth; our blood flows in its vessels because rivers flow on the earth; and we have two eyes because the heavens are lit by the sun and the moon. But the ancient Chinese also were aware of the points where self-similarity breaks down:
A small square is of the same class as a big square. A little horse is of the same class as a big one. But little knowledge is not of the same class as great knowledge. In the State of Lu there was a man called Kungsun Cho who said he could raise the dead. When they asked him how, he replied, ‘I can heal hemiplegia (apoplexy). If I gave a double dose of the same drug, I could therefore raise the dead.’ But among things there are some which can have small-scale effects, but not large-scale ones, and other things which can perform the half but not the whole. (From the Lu Shih Chhun Chhiu, cited in Needham, 1956)Prediction and Explanation
In the philosophy of science, it has been argued that prediction and explanation are two sides of the same logical process, and differ only in the sense that predicted events have not yet happened, while explained ones already have. This would imply that every prediction counts as an explanation after the event, and every explanation counts as a prediction before the event. Neither of these two principles is true (Harre 1972).
We would not call the predictions made by nautical almanacs the explanation of the risings, settings, and conjunctions of the heavenly bodies. Characteristically, giving an explanation involves describing one or more causal mechanisms resulting in a particular event, and this may not be sufficient to allow prediction. We know at least some of the causal mechanisms of evolutionary change, but we are completely unable to predict the appearance of new forms of plants and animals. And, as Bertalanffy (1968) pointed out, professors of economics may be able to explain the mechanisms underlying economic trends (even this claim is open to debate!), but very few of them are millionaires.
On the other hand, we can predict a great many regular occurrences in our daily lives (including our clinical practice) without any explanation involving causal mechanisms, and sometimes without any explanation at all.
In chaotic systems, even when explanation is complete, prediction is not possible. If we map a chaotic system, and choose two points that appear indistinguishable (i.e., that have approximately the same value), and we follow the trajectories of these two points through time, we will find that they very quickly diverge to become two distinct trajectories. This will happen unless the two points are absolutely identical (i.e., unless their values are calculated to a precision that is infinite, which is, of course, impossible).
In a chaotic system, then, due to the combination of positive and negative feedback, even an unavoidably small discrepancy will rapidly grow, multiplying itself at an escalating rate, and making prediction all but impossible. This characteristic is known as sensitivity to initial conditions, and, in practical terms, it means that you cannot predict the exact behaviour of a chaotic system even if you understand the rules by which it functions. In other words, even when your explanation is complete and valid, not all of your predictions can lead to repeatable experiments.
You can, however, still make very accurate predictions—not of exact behaviour, but of its general qualitative nature. You can, for example, test whether a chaotic model of turbulence accurately describes the way a fluid behaves, but you cannot test whether a given fluid particle is obeying the dynamic equations.Chaos in physiology
Many aspects of physiology, once considered "homeostatic," have been revealed to exhibit chaotic characteristics when inspected at a different scale or through more refined methods of mathematical analysis. Consider the following examples:
· EEGs of healthy individuals have shown evidence of chaos in the central nervous system. By contrast, several types of pathology including epilepsy, tremors, and manic-depressive oscillations are characterized by a loss of complex variability and the appearance of a too-regular periodicity (Briggs, 1992).
· The patterns of brain activity were recorded while people performed various tasks, and it was found that the complexity of the patterns changed in response to changes in intellectual effort, with higher-dimensional, more complicated EEG patterns apparently corresponding to a more alert state (Briggs, 1992).
· It has been found that white blood cell counts in healthy individuals fluctuate chaotically from day to day. Periodic oscillations in white blood cell counts occur in certain cases of leukemia (Briggs, 1992).
· Hormone levels in healthy individuals seem to undergo chaotic fluctuations.
· Research on the chaotic dynamics of cardiac function indicates that the heart rate in healthy individuals, even those at rest, is neither constant nor strictly periodic, but displays complex irregularities, which vary on timescales from seconds to days. A number of pathologies, including heart rate patterns preceding sudden cardiac arrest, are characterized by increasingly periodic behavior and a loss of complex variability, as are heart dynamics associated with aging (Goldberger, 1991).
Chaos is the interaction of a number of different frequencies, producing a complex pattern; too much order reflects a lack of responsiveness to a variety of inputs and a lack of integration with the rest of the body. The diseased heart begins to disconnect itself from the myriad messages of the whole organism and responds to only a few stimuli (Goodwin, 1995).
Perhaps "stress" really arises from the ubiquitous psychological threats of modern life, which are, as far as the body is concerned, false alarms; still, unwinding from an alarm, even a false one, is a much slower process than jumping to alert, which takes only a second. It can take many minutes, sometimes hours, for the body to return to a state of relaxation. If we don’t have time to recover from one alarm before the next one is triggered, our bodies remain in a permanent state of emergency. This may not be dangerous in itself, but it decreases our physiological variability.
Health is a condition of responsiveness and sensitivity to a wide range of different variables, a state of adaptability and openness to change, which is, at the same time, supported by a stable core, bounded by that strange attractor which defines one’s essential nature as a member of a species, a participant in broad natural and social systems, and an individual. As therapists, we aim to help our fellow beings attain and maintain a state of dynamic balance in which they are stable and changing, bounded and responsive, yin and yang.The "Edge of Chaos"
The desirability of this state of balance is reinforced by the fact that most living systems seem to thrive best somewhere near the border between rhythmic regularity and chaos. For example, recent research with ants (Goodwin, 1994, 1996) has shown that each ant, in the absence of interaction with other ants, fluctuates between activity and rest in a random pattern. As it interacts with other ants, however, one can observe order "emerging from chaos": as the population of the colony increases, its density increases, eventually reaching a critical point where the colony as a whole starts to demonstrate a rhythmic oscillation between activity and rest.
Of particular note is that the frequency of interactions between ants is determined by the density of the colony, and the colony regulates its own density: if the walls of the nest are moved, the ants will adjust them inward or outward as necessary to ensure their ability to interact in this orderly manner. But the colony functions just on the border between order and chaos; if 8-10% of its population goes out foraging for food, the density drops and the remainder of the colony temporarily reverts to chaotic patterns of activity.
What is significant here is that the order within the colony emerges spontaneously from its own dynamics, rather than being imposed from without. It is not known why the ant colony functions in this way, but the emergence of order through interaction does seem to be a universal quality of living systems.
This strikes me as a metaphor for the way that my own life and those of my family, friends, and patients proceed. At our normal level of "density," we have a more or less comfortable level of interaction, and, all being well, order emerges in our lives. But at other times, either because our "walls" have been moved by events beyond our control or because we ourselves have gone out "foraging" for new experience, our lives become chaotic. And because, as human beings, we have (I hope) a greater capacity for creativity than ants, we can generate new types of order out of this chaos, so that we may continually "begin again."The Yin and Yang of Order and Chaos
Chaos theory is one way of attempting to map a complex reality, but, of course, all maps of reality are, in principle, flawed, incomplete, or, at best, oversimplified. The scientist aspires to map that which already exists, that which has been created, teasing out the principles behind the regularities in both structure and process. The artist and the mystic ride the wave of the always-now, flowing around and into gaps in regularity, celebrating the novel, the anomalous, and even the unlawful; in Chinese terms, they pursue the ji, the "irrational numbers"—the irregular bit that doesn’t fit, the fragment that is left over after the world has been ordered into regular divisions.
Perhaps it is the tension between these perspectives that drives creativity, which is manifest as an oscillation between two modes of meeting the world, now dreaming the impossible dream of grasping it intellectually, now colliding with the elusive yet "hard" reality of the incongruous—those things and events that don’t belong and that shouldn’t, according to our constructed systems of understanding, exist at all. This is another sense of the "edge of chaos."
As science progressively generates explanations for physical phenomena at the level of structured regularity, the horizon continues to recede. New discoveries throw spanners into the works, reminding us that it is the flux of yin and yang that powers not only the natural world but our participation in it.Seeing the Order in the Chaos
The American psychologist James Hillman (1995) describes the process of "mentoring," which, I feel, is the key to bringing all these concepts together and establishing their relevance to the therapeutic relationship. Hillman’s thesis is that "Each person comes into the world with his or her own genius . . . something that is not the result of your parents or the environment but is particularly your destiny." Perhaps we could consider individuals as unique "strange attractors," determined only by their place in the universal tao, their potential infinitely varied but bounded by their own distinctive shape.
Our distinct character will be present, in a self-similar manner, in every aspect and stage of our lives, and it is thus possible for another person to recognize the "acorn" in us, our particular genius as yet unmanifest—what we might become. When someone sees the unique aspect of another, the element that cannot be contained within categories and typologies—which is to say the "irregular" or "extraordinary"—an interpersonal space is created in which that uniqueness can blossom and come to fruition. Hillman speaks of "the necessity of being seen in order to be," and declares "Such sight blesses; it does transformative work."
Chinese philosophy has never divorced the regular from the irregular, the objective from the subjective, nor fact from meaning. This is exemplified by the belief that the quality of life and health is dependent on the development of specifically human qualities. The crucial human quality celebrated by Taoism is that of "spontaneity," which is only possible when one rejects fixed rules of conduct and intuitively grasps all the relevant aspects of one’s situation, without the clouding of consciousness that results from identifying with one’s desires and aversions. From the perception of one’s situation with perfect clarity, spontaneous inclination moves inevitably in the right direction, and the Western dichotomy between freedom and determinism dissolves in the unity of spontaneity and inevitability.
The Taoist rejection of fixed rules of conduct illustrates the Chinese focus on the complex nature of process; it highlights the uniqueness of all situations, which are, nevertheless, bounded by rules of transformation. In medicine, this translates into an emphasis on an individualistic approach to health care. Whereas in contemporary Western medicine diseases and disease agents have an ontological status, in Chinese medicine disease is traditionally viewed as an ongoing process in a unique individual. The classics tend to avoid not only the reification of disease but also the reification of health in the sense that we understand it in the West, for one person’s state of health cannot be the same as another’s.The Therapeutic Technique and the Therapeutic Relationship
Our patients, too, live their lives on the edge, and if our therapeutic work aims to restore regularity, we will proceed differently than if we aim to facilitate our patients’ creative self-transformation.
Realization of the full potential of therapeutic work requires that we maintain a tension between regularity and uniqueness, order and chaos, the predictions of scientific law and Taoist spontaneity. Diagnosis demands that we categorize; in essence, it is an activity that consists of placing the patient within a conceptual structure. The therapeutic relationship, on the other hand, demands that we see the uniqueness, the genius, within the person—and this applies equally to all systems of healing, modern or traditional.
When we diagnose, we work within a deterministic system; we can predict—at least in a general way—the course of disease and the effects of our interventions. By assisting our patients to regulate their state (as ants regulate the density of their colony), we allow them to restore their own internal order.
Truly transformational work requires us to see into the acorn "with the eye of the heart" and facilitate the emergence of creative growth and the realization of unsuspected potential.
"Patients" relate to "practitioners," "physicians," or "therapists" (whatever term you choose for the professionalized persona of the healer). "Persons" relate to "persons." If we wish to engage in transformative—as distinct from and in addition to reformative—work, we must engage with the person, and we can do so only as persons ourselves, in all our glorious and messy complexity.
Bibliography
Bertalanffy, Ludwig von (1968). General Systems Theory. Harmondsworth: Penguin.
Briggs, John (1992). Fractals: The Patterns of Chaos. London: Thames and Hudson.
Goldberger, Ary L. (1991). "Is the Normal Heartbeat Chaotic or Homeostatic?" Reprinted by The Open University.
Goodwin, Brian (1994). How the Leopard Changed Its Spots. London: Weidenfeld and Nicolson.
Goodwin, Brian (1995). Health: A Biological Attractor. Lecture series presented at the University of Exeter Centre for Complementary Health Studies.
Goodwin, Brian (1996). Qualitative Life Science. Lecture series presented at Schumacher College.
Harre, Rom (1972). The Philosophies of Science. London: Oxford University Press.
Hillman, James (1995). The Art of Mentoring. Videorecorded lecture presented at Schumacher College.
Larre, Claude, & de la Vallee, Elisabeth Rochat (1992). Heart Master Triple Heater. Cambridge: Monkey Press.
Needham, Joseph (1956). Science and Civilization in China, Vol II: 72
HOMEOPATHIC DILUTIONS
Originally published in Resonance.
Helen Cohen, ND
"Nothing will come of nothing"
Shakespeare
The most frequent allegation brought against homeopathic medicine is: "There is nothing there but water! If you take nothing—you get nothing." Such a charge casually dismisses two hundred years of research and practice by thousands of medical doctors, scientists, and lay people using homeopathic drugs. Homeopathic thinkers are accused of breaking the established laws of physics and pharmacology; they are told that medicinal substances diluted to parts per billion (ppb) and parts per trillion (ppt) concentrations have no biological action. This line of argument disregards the fact that biological processes take place on both molecular and submolecular levels. Biochemical reactions and bonding always require an exchange of electrons and protons, not just an exchange of ions! To insist that molecular biochemistry is sufficient to represent the entire physiology of a living cell or an organism is absurd.
I once discussed the common response to homeopathic dilutions with a University of Toronto electronics professor. "Do you know how diluted electronic alloys are?" he inquired. Yes, I do. But do members of the NCAHF know? I doubt it.
In this paper I will endeavour to show the striking similarities between electronic alloys and homeopathic drug dilutions, and demonstrate that bioactive substances are, in fact, semiconductors. If you bear with me, through the sometimes tedious explanations, you will be surprised at the obvious conclusions. (See How Semiconductors Work.)Water and Life
So, there is nothing in a homeopathic remedy but water? Perhaps. But what is water?
Even a superficial study of liquid water [says biophysicist Felix Franks] and to some extent of ice, must suggest that life on this planet has been conditioned by its abnormal properties, since water was present on this planet long before the evolution of life. It is well known that water forms a necessary constituent of the cells of all animal and plant tissues and that life cannot exist, even for a limited period, in the absence of water, so that we have the somewhat strange position that the naturally occurring inorganic liquid is essential for the maintenance of organic life. Bearing in mind also that natural processes are characterized by the economy with which energy (matter) is utilized, it seems permissible to conclude that in organisms which consist of up to 95% water, this liquid fulfills a function other than that of inert substrates. . . .
Nothing is yet known about the manner in which water acts in the formation of organized biological structures at the subcellular, cellular, and multicellular levels, and, at the molecular level, the role of water in the stabilization of native conformations of biopolymers has only recently been receiving some attention. The almost complete disregard of the role of the solvent in tertiary and quaternary structure phenomena is an interesting example of how established experimental findings are sometimes ignored because they cannot be reconciled with existing concepts. Thus, some time before X-ray techniques were successfully applied to establish the structure of DNA, it was well known that the polymer required some 30% of water to maintain its native conformation in the crystalline state, and that partial dehydration led to denaturation. Available X-ray techniques cannot "see" the water in biopolymers because of its relatively high mobility and therefore when the double helix structure was confirmed it was claimed that it owed its stability to intramolecular hydrogen bonds, van der Waals-type interactions between purine and pyrimidine bases, and electrostatic interactions between purine and pyrimidine bases, and electrostatic interactions between sugar phosphate groups. Clearly this cannot be the whole story, and further research will reveal the function of water in the stabilization of the double helix. (emphases added) (1)
In addition to stabilizing and holding biopolymers, water molecules are probably involved in the shaping of their three-dimensional structures.Enigmatic Liquids
Not only is it the case that "the contribution of water to life processes at a molecular level is almost completely unexplored," as Franks notes, but our knowledge of the structure of liquids in general, and not just water, is practically nonexistent. The liquid state of matter is of the least interest to engineers because our technology is based on the use of gases and solids, not liquids. Liquids are enigmatic. They exist in a very narrow range of temperatures; their molecules are packed almost as closely as those of solids, which means that all the molecules are touching their neighbors; therefore, one cannot discount the role of internal forces. Yet these same molecules have enough kinetic energy to move as rapidly as gas molecules at the same temperature. Mathematically, the liquid state of matter is described either as a poor approximation of an ideal gas (a far stretch) or a disordered solid.
Liquids are extremely difficult to examine, since their study requires not only expensive, time-consuming, sophisticated experimental techniques but also a new way of thinking about nature. The knowledge of classical thermodynamics is only sufficient to study mechanical and thermal properties of gases; it is permissible to disregard the interaction of gas molecules and to describe it in terms of "temperatures," "volumes," and "pressures". Solids, on the other hand, are so densely packed that we can consider them perfectly ordered, with a few "defects" such as dislocations or grain boundaries. Not much is known about the microscopic behavior of a liquid state; in fact, it is frequently viewed as chaotic. Liquids are too complex to be accommodated by our limited understanding of the world order, or disorder for that matter. In other words, they are not equilibrated static packs of molecules, so we need to transcend classical physics in order to try to understand their behaviour and treat them mathematically.Water as a Polymer
These comments on the complexity of liquid structures refer to the so-called "normal" liquids. Water is an "abnormal" or atypical liquid, however. This means that water is far more complex and enigmatic than a normal liquid. As Franks explains,
Even a cursory examination illustrates the anomalous position of water. The contraction which accompanies the melting of ice is well known, and while it is not unique, it is nevertheless rare. The very large liquid temperature range is an indication of long range forces in liquid water. This is confirmed by the very small latent heat of fusion which only amounts to 15 per cent of the latent heat of evaporation and suggests that liquid water retains much of the order of the solid state and that this order is only destroyed at the boiling point [italics added] (2)
Let us now consider what is known about the structure and properties of this unique substance—water. A water molecule is made out of three ions (electrically charged atoms): two hydrogens and one oxygen. The electrical charge in water molecule is not distributed evenly: at one end there are electron-deficient hydrogen atoms—a positive charge—and at the other negative end there is an electron-rich oxygen atom. A water molecule, then, is a dipole; it possesses a permanent dipole moment. In addition to this intrinsic moment, another dipole moment will be produced if a water molecule is placed inside the electrical field, which means that water is a dielectric material. Alcohols, which are also used for homeopathic dilutions, possess electrical polarity as well. The internal forces in a polar liquid are strongly directional, which accounts for the fact that they are powerful solvents. Most chemicals can be dissolved in water. Once such "uneven" electrical units come close to each other, they must change their respective electron cloud densities. According to Franks:
A large distortion of the electron clouds gives rise to a so-called delocalization energy, whereas small-scale but coordinated electron displacements give rise to the dispersion (van der Waals) energy. Finally, the Pauli exclusion principle dictated that for a full description of an interaction, a repulsive contribution must exist. It is now held that the hydrogen bond contains all the above contributions, although there is still some uncertainty about their correct relative weightings.
Once all the known data and theoretical principles are considered it becomes obvious that the polymeric nature of water is more energy efficient than the dimer structure. The covalent contribution to the interaction energy accounts for the fact that trimers and larger aggregates of water molecules are more stable than the simple dimer, that is, the interaction of a given water molecule with an already existing cluster of hydrogen bonded molecules is more favorable, and therefore more probable, than the interaction with another single molecule to form a dimer. This type of interaction, which depends on previous processes, is called cooperative interaction, and hydrogen bonding in water is believed to be highly cooperative [italics added]. (3)
All these considerations, however logical, are very difficult to ascertain mathematically due to the number of variables involved:
"One of the major shortcomings of present day theories of the liquid state is the necessity of expressing total interaction energy between the molecules by the sum of pairwise molecular interactions . . . when it is known that the characteristic behaviour of a liquid is in fact due to simultaneous interactions between many molecules. However the mathematical problems of coping with triplet and higher order interactions are so severe that such systems have to be treated in terms of summations of three (or more) pairwise interactions." (4)Solid Water
Due to the fact that the water molecule is not symmetrical, the bonds between its atoms are "bent," and the whole structure is shaped like a tetrahedron. If we assume that a liquid has a structure similar to its own solid (which still needs to be proven), then the best way to study liquids is to investigate the molecular and electronic arrangement of their respective solid states. Considerably more is known about the structure of ice than the structure of liquid water. The following investigative techniques can be used to decipher ice structures: X-ray diffraction, Raman spectroscopy, neutron diffraction, infrared studies, and dielectric measurements. In its solid state, the hydrogen bonding between positive protons (the hydrogen ion is a single proton) and negative oxygen ions gives rise to an open structure of regular tetrahedral packing where every water molecule is bound to four of its nearest neighbors.
Ice (and, therefore, water) is a polymorph—it exists in several distinct crystal forms. There are thirteen different forms of ice, and each has different densities and melting points. Perhaps the most important, as well as the most familiar, ice structure is ice I ("ice one"). It is almost perfectly tetrahedral in its coordination, and each water molecule is connected to four other molecules by means of hydrogen bonding. The nature of the bonding is an electrostatic attraction between a proton of one molecule and an unshared electron pair of another, since the orbital electron structure is the sp3 type. (Hydrogen bonding is the most important type of bonding in biomolecules.) The long-range molecular arrangement of ice I is a hexagonal, closed-packed, three-dimensional network (hcp) very much like tridymite—a mineral that is one of several distinct forms of SiO2, or silica. Another closed-packed form of ice—cubic closed-packed (ccp)—is very similar to cristobalite—a ccp form of silica. The denser polymorph of silica, quartz, does not, however, have an analogue among ices, for two major reasons. First, the bond-bending energies of H-O-H are different from the energies of the Si-O-Si arrangement. Second, atoms have to be packed differently because of their relatively different sizes. Large oxygen atoms lie at the tetrahedral centers in H2O but near the bond linkages in SiO2. Even though this structural analogy is incomplete, it serves its purpose, since we are not interested in densely packed solids, but in liquids.Water and Silica
It is important to appreciate the structural similarity that approaches an identity between silica and water. Silica, which is the most important semiconductor and electronic material, as well as a traditional ceramic material, is a major constituent of metallurgical slags, and also a constituent of volcanic magma. As such, it has been investigated very thoroughly in all three of its states: liquid, vitreous, and crystal (luckily for homeopathy). In fact, it can be argued that the two most important substances on our planet are water and silica. Both, water and silica (soil) support life, especially plant life. Silica, which derives its name from the Latin "flint," is the main component of our planet’s surface. Silica and alumina, as alumosilicates, make up what we call the inorganic matter or minerals of the Earth’s crust. Sand is silica; quartz is silica; agate is silica. Many other minerals are not pure silica but silicates—the solid-state solutions of several other oxides in silica, mostly calcium, iron, magnesium, sodium, and potassium oxides. Silicon and oxygen together constitute seventy-four per cent of the mass of the Earth’s crust. Asbestos, talc, micas, kaolin, feldspars, garnets, olivines, and serpentine are all naturally occurring silicate minerals.
Silicates have exceedingly complex molecular structures, since they are not stoichiometric compounds and, therefore, can only be approximately characterized by chemical formulae. It is equally difficult to describe them thermodynamically, in the forms of phase diagrams, because they are only feasible for binary or ternary alloys. Often, the only way it is possible to fit the natural variety and complexity of silicates into the rigidity of chemical formulae is to view the water molecules as an essential element of the silicates’ structure, or as chemically or structurally bound to them. Consider, for example, the following formulae of these naturally occurring hydrated zeolitic minerals:Natrolite Na2(Al2Si3O10) x 2H2O
Scolecite Ca(Al2Si3010) x 2H2O
Mesolite Na2Ca2(Al2Si3O10)3 x 8H2O
Gmelinite (Na2Ca)(Al2Si4O12) x 6H2OThis bonding is probably analogous to that between water and peptides in proteins, and water and nucleotides in DNA. Obviously, it is the unique and flexible electronic structure of silicone and its oxide that makes it so abundant and so polymorphous. Nature, organic or inorganic, does not waste either energy or substance. Hydrogen and silicon are the two most abundant elements in the solar system (remember, water is an oxide of hydrogen). Like water, silica is a powerful solvent. Since, due to our oxygen-rich atmosphere, most elements exist in the form of oxides, most of Earth’s minerals are solid solutions of these oxides in silica. Each mixture of oxides produces a distinct mineral with its own crystal structure.
Back to TopHomeopathic Semiconductors
For homeopathic practitioners, the most important information revealed by studies of the structure and properties of ice is the fact that, as J.B. Hasted notes, it exhibits "extensive proton semiconductor effects, especially when donor or acceptor impurities are added". (5) I would like to stress, at this point, that Dr. Hahnemann was, in fact, the first creator of electronics, because over a hundred years before the electronic age he "doped" pure dielectric water with impurities (drugs) and turned it into an extrinsic conductor capable of reacting with the biomolecular semiconductors. There is an impressive amount of literature available on semiconducting properties of biopolymers that, apparently, is unknown to doctors and pharmacists.
Semiconductors are created either by doping or annealing processes, which make their structure nonstoichiometric, creating electrical carriers of either positive (holes) or negative (electrons) types. To create a p-type or a deficit conductor, the elements from group VI of the periodic table, with a valence of four (silicon, germanium, tin, lead), have to be alloyed with the impurity atoms with a valence of three (boron, aluminum, gallium, indium—group V). To make an n-type or an excess conductor, silicon or germanium must be doped with five-valence impurities (group VII). If, subsequently, an n-conductor is connected to a p-conductor, a miniature rectifier is formed. Create a million of these transistors, add resistors (capacitors), and you have an integrated circuit of a computer memory.
Please note the following list of the most important elements from groups V, VI, and VII, which are used in impurity semiconductors. (6)
Element Symbol Electronic Structure Semiconductor Type
Aluminum Al Al2O3 Amphoteric
Antimony Sb Sb2S3 p-type
Arsenic As GaAs
Barium Bs BaTiO3 BaO n-type
Bismuth Bi Bi2Te3 p-type
Cadmium Cd CdS CdSe CdO n-type
Carbon C SiC Amphoteric
Cobalt Co Co3O4 Amphoteric
CoO p-type
Copper Cu Cu2O Cu2S p-type
Chromium Cr Cr2O3 p-type
Gallium Ga GaAs p & n-type
Indium InSb
Iodum I p-type
Iron Fe Fe3O4 n-type
Iridium Ir IrO2 Amphoteric
Lead Pd PbS PbTe PbSe Amphoteric
PbCrO4 n-type
Manganese Mn Mn3O4 Amphoteric
MnO p-type
Mercury Hg
Nickel Ni NiO p-type
Selenium Se Se p-type
Silicon Si Si SiC Amphoteric
Silver Ag Ag2S n-type
Strontium Sr SrTiO3 n-type
Sulphur S Ti2S Amphoteric
Tellurium Te Te p-type
Tin Sn SnO p-type
SnS Amphoteric
Titanium Ti TiO2 n-type
Uranium U U3O8 n-type
UO2 Amphoteric
Vanadium V V2O5 n-type
Zinc Zn ZnO n-type
The above table is a partial list of the regular homeopathic remedies that are made from inorganic sources (see Homeopathic Remedies). For people who are new to homeopathy, here is a list of some of the corresponding homeopathic medicines:Aluminum-based (Al)
Aluminium metallicum, Alumina, Alumen, Aluminium acetate, Aluminium chloridum, Alumina silicata
Antimony-based (Sb)
Antimonium arsenicosum, Antimonium crudum, Antimonium chloridum, Antimonium iodatum, Antimonium sulphuratum auratum, Antimonium tartaricum
Silver-based
Argentum metallicum, Argentum cyanatum, Argentum iodatum, Argentum nitricum, Argentum oxydatum, Argentum phosphoricum
Arsenic-based (As)
Arsenicum album, Arsenicum bromatum, Arsenicum hydrogenisatum, Arsenicum iodatum, Arsenicum metallicum, Arsenicum stibiatum, Arsenicum sulfuratum flavum
Gold-based (Au)
Aurum arsenitum, Calceria arsenica, Chininum arsenicosum, Fowler’s solution, Levico Water, Natrum arsenicum
Barium-based
Baryta acetica
Baryta carbonica, Baryta iodata, Baryta muriatica
Bismuth-based
Bismuthum
Bromide-based
Strontium bromatum, Zincum bromatum
Cadmium-based
Cadmium bromaticum, Cadmium oxide, Cadmium sulphuricum
Carbon-based
Calceria carbonica, Carbo animalis, Carbo vegetabilis, Carbolicum acidum, Carboneum hydrogenisatum, Carboneum oxygenisatum, Carboneum sulphuratum, Graphites, Kali carbonicum, Lithium carbonicum, Magnesia carbonica
Cobalt-based
Cobaltum metallicum
Copper-based
Cuprum acetum, Scheel’s green, Cuprum cyanatus, Cuprum metallicum, Cuprum oxidatum nigrum, Cuprum sulphuricum
Chromium-based
Chromicum acidum
Gallium-based
Gallicum acidum
Indium-based
Indium metallicum
Iodine-based
Iodum, Aurum iodatum, Calceria iodata, Ferrum iodatum, Mercurius iodatus flavus, Mercurius iodatus ruber, Sulphur iodatum
Iridium-based
Iridium metallicum, Irridium chloride
Iron-based
Ferrum aceticum, Ferrum arsenitum, Ferrum bromatum, Ferrum citricum, Ferrum cyanatum, Ferrum magneticum, Ferrum metallicum, Ferrum muriaticum, Ferrum phosphoricum, Ferrum picricum, Ferrum pyrophosph.
Lead-based
Plumbum metallicum, Plumbum iodatum
Manganese-based
Manganum aceticum, Kali permanganicum
Mercury-based
Mercurius hydrargyrum, Mercurius aceticum, Mercurius auratus, Mercurius bromatus, Mercurius corrosivus, Mercurius cum kali, Mercurius cyanatus, Mercurius dulcis, Mercurius nitrosus, Mercurius phosphoricus, Mercurius precipitatus ruber, Turpethum minerale, Mercurius tannicus, Cinnabaris mercuric sulphide
Nickel-based
Niccolum metallicum, Niccolum sulphuricum
Phosphor-based
Zincum phosphoricum
Selenium-based
Selenium
Silicon-based
Silicea, Calceria silicata, Kaolin, Slag Silico
Strontium-based
Strontia , strontium carbonicum, Strontium iodatum, Strontium nitricum
Sulphur-based
Sulphur, Aethiops mercurialis, Aurum sulphuricum, Chininum sulphuricum, Hepar sulph. calcerium, Calceria sulphurica, Kali sulphuricum, Magnesia sulphurica, Natrum sulphuricum, Sulphuricum acidum, Sulphurosum acidum
Tellurium-based
Tellutium metallicum
Thallium-based
Thallium
Tin-based
Stannum, Stannum iodum
Titanium-based
Titanium metallicum
Uranium-based
Uranium nitricum
Vanadium-based
Vanadium metallicum, Ammonium vanadicum
Zinc-based
Zincum metallicum, Zincum acetum, Zincum arsenatum, Zincum carbonicum, Zincum cyanatum, Zincum muriaticum, Zincum oxidatum, Zincum picricum, Zincum sulphuricum, Zincum valerianum
It is only logical to assume that the homeopathic remedies made from complex organic materials, rather than the well-known chemicals, contain the same elements from the groups V, VI, and VII of the periodic table and, thus, also possess semiconducting properties. In retrospect, the work of Hahnemann and his followers was groundbreaking! And the blind prejudice they met from the apothecaries and their comrades, the allopaths, will someday be recognized as a chapter in the continuing record of human ignorance and intolerance.Experiments to Verify Homeopathic Laws
Like water molecules, the molecules of silica form long-range polymeric structures. A vast array of different three-dimensional arrangements is possible. Every time a new ion is introduced, a different network is created. While these added ions are considered impurities by the electronic industry, in the creation of ceramics they are referred to as network-modifiers. When a network-modifier is dissolved in molten silica, the bonds between the molecules are "stretched" to accommodate the foreign ions (this is another way of looking at changes in electron densities and energies). During the production of glasses, glazes, and enamels, each modifier changes the optical, mechanical, magnetic, or electrical properties of these vitreous materials by altering their internal molecular and electronic structures. If these silicates are cooled under certain conditions, instead of crystallizing, they turn into a glass; that is, they retain their liquid structure but become solid. After these network-modifiers are dissolved, it is quite possible to calculate exactly how much the bonds were stretched. This could provide another useful model for homeopathic dilutions of drugs. During such an experiment, we would have to see if the bonds remain stretched to the same degree, and whether optical and other properties remained unchanged, after a modifier is eliminated from the silicate solution by a series of dilutions analogous to homeopathic potentizations. Will the glasses remain "modified" when the modifier’s concentration is very low? And if the diluted ceramics do retain their colour or translucency, would this undermine the laws of physics?
If such experiments are performed properly, we will take homeopathy out of the realm of "natural" and "spiritual energy" nonsense and into the world of sophisticated, modern, and truly physical medicine.
If the "quack-busters" from NCAHF had known the basics of electronics, they would have never touched a computer: according to their logic, computers cannot possibly work, because they are made of nothing but ordinary sand. One can imagine their verdict: "Semiconductors cannot possibly be real, because the amount of element they are doped with is too small to create any electricity. They are nothing but insulators. People who think they are using computers (phosphors, lasers, digital cameras, etc,) have been conned." But most lay people are very enthusiastic about electronic alloys: "Imagine, this tiny crystal can contain enough information to fill a library!"
Well, this tiny drop of water contains enough drug to cure a human being!
BIBLIOGRAPHY
1. Franks, Felix, Ed. Water: A Comprehensive Treatise, Vol.1, The Physics and Physical Chemistry of Water. New York: Plenum Press, 1975.
2. Franks, Felix. Water. London: The Royal Society of Chemistry, 1983.
3. Franks, Water.
4. Franks, Water A Comprehensive Treatise.
5. Hasted, J.B. Aqueous Dielectrics. London: Chapman and Hall, 1973.
6. Kingery, W.D., et al. Introduction to Ceramics. Second Edition. New York: John Wiley, 1976.WATER MEDICINE AND THE AGE OF SILICON
Helen Cohen, ND
According to most ancient cosmologies, the world was created by the interaction of four primordial elements: Air, Fire, Water, and Earth. Air and Fire represented the male principle and Water and Earth were their female counterparts. The surviving writings of the pre-Socratic Greek philosophers contain much speculation on which of the four entities is the most primordial and elemental, or which one gave rise to the other three. One can assume that, the prehistoric matriarchal thinkers, who preceded the philosophers, had no doubt that the female entities, Water—the primordial ocean of menstrual blood—and Earth—the universal womb—were the elements capable of giving birth to the Universe. The sexual union of Fire and Water created the Cosmos and Life in it.It is amazing to realize that the oxygen (Air) in our planet’s atmosphere was not here originally, but was formed as a direct result of a function of our biosphere—the photosynthesis of ancient blue-green algae; in other words, Water gave birth to Life, and Life, in turn, created oxygen (Air), which turned metals into oxides, which, with the help of Fire, became dissolved in silica (Earth)—whose structure is almost identical to that of Water. And the ancients knew this!
Now 3.5 billion-year-old algae have been found embedded in a silica mineral (chert). This may have been the silica gel that supported the very first life form, which, in turn, created the oxidizing atmosphere that bonded silicon with oxygen and water to give it a life-supporting colloidal form, in a typical chicken-and-egg fashion. When the first plant organisms began to emerge from the ocean and explore the solid ground, fertile, wet, and rich soil already existed. What makes soil fertile is its clay minerals. Clays are hydrated silicates (colloids) with a very large surface area, which allows them to absorb and release water and essential ions (eg, phosphorus). Thus, the union of water and silica made it possible for organic life to continue without the ocean.
The first human societies centred their social, commercial, and artistic activities on the two most important elements: the fire and the kiln. It was a hard flint, struck with another stone, that produced the fire. Flint became the first tool of art (to train the hand), a digging device, a scavenging knife, a hunting weapon, an instrument of agriculture, and a writing tool. Perhaps the Stone Age should be renamed the Silicon Age, in accordance with the terminology of later periods, such as Copper and Iron.
And look now where our evolution has led—we are back where we started: in the Silicon valley of ideas! Time and History are not merely circular or linear: they are both; they are spiral. The Stone Age was the First Silicon Age, and the Age of Information is the Second Silicon Age. As our city culture crumbles, we are turning back to Earth and the infinite possibilities of our planetary mother, who gives us the magic of Silicon again to connect via computer "chips" all over the globe. And we will use the magic of homeopathic Water to heal us on the way there.
All ancient peoples eventually discovered another exceptionally useful property of silica and water: when mixed together they form a substance that is very plastic and, if molded, will retain its shape—a clay. When fired, the clay can be used to make pottery and building materials. It is strong enough to protect us from the elements. It is dense enough to retain liquids—cold, hot, or caustic. It is hard enough to store anything. It will never deteriorate with time, because it is "entropy-resistant": it is an oxide, which is the final stage of any chemical transformation on Earth (most metals have very strong metal-oxygen bonds). One can cook with ceramic materials, store active chemicals, or build ageless temples. By varying the time and temperatures at which it is fired or by incorporating other elements, a simple mixture of sand and water can give rise to an infinite number of aesthetic and practical possibilities, not the least of which are glazes and window glass. Human art, as it has evolved through millennia, is greatly indebted to the structural properties of silicon.
Water is to life what silica is to human society; ordinary sand and ordinary water engender real things. The human mind—a recent evolutionary creation of life on this planet—is now attempting to conceive artificial intelligence using the awesome possibilities of silicon and similar semimetals.