A Hypothesis on Homeopathy, Part 2

0. Preliminaries:

From this post on, we begin to engage in the hypothesis—if not that, at least the topics prerequisite to understanding it. The hypothesis can be stated simply, but we will have to first clarify the terms being used in it. We begin to undertake such a clarification with this post. Hope the description isn’t so general as to be vague. (I will appreciate feedback.)

1. The Idea of States Applied to Living Beings:

It will help if we approach the issue by first considering the biological nature of man (or of any sufficiently complex organism such as dogs, cats, horses, etc.) Certain salient characteristics that are pertinent to homeopathy will be brought out in the ensuing discussion.

For our purposes, we first consider a healthy i.e. a normal adult who has no unusual habits of food, daily routine, etc.

Suppose that such a man is not habituated to tobacco. Suppose further that he chews tobacco for the first time in his life. What does typically happen? Immediately, he will find a different kind of a taste in his mouth. Soon thereafter, he will feel a light feeling in head, followed by giddy-ness. His pulse will become both more quick and more irregular. He may experience nausea, and may even throw up. If he has tobacco through smoking, several of these symptoms will still appear though to a somewhat lesser degree. To those smokers who have stopped smoking and then pick up a cigarette after a long gap (of, say months), it never fails surprising them that these “newbie’s” symptoms come back for a while, once they restart smoking.

One somewhat abstract way to describe such a set of observations is to say that the state of a man changes from, say “normal” (N1) to, say “tobacco-affected” (or generally, SA, short for substance-affected). The SA state is characterized by a certain group of symptoms. As the man continues having the substance, the further occurances of the SA state now become progressively less intense. A time comes when, what the man now calls his normal state (N2) is completely unaffected by his consumption of the substance. However, upon quitting, withdrawal symptoms can appear, leading him to yet another state WS (withdrawal symptoms). If he continues staying quit, the WS state gradually recedes and his state falls back to N1. Now, he again is biologically ready to experience the TA state.

Of course, you may object, tobacco (or the nicotine in it) is an addictive substance. For a non-addictive substance such as tea or the table salt, the state corresponding to withdrawal will not apply. To a certain extent, you are right. However, a more careful study shows that several finer symptoms still arise even if the substance is as benign as tea, the table salt, hot chilly (jalapano), etc. Overall, the idea of changes of states, does remain generally applicable.

Some further comments on the living states of a man, are in order. A given specific living state can be distinguished by the particular group of attributes or symptoms associated with it. If such attributes change, we may associate a change of state with the man. We are free to associate a changed state regardless of the nature of the causes underlying the change, and regardless of whether we know these causes or not. Clinical evidence ought to be considered sufficient to indicate that states do change—even if by itself it may not explain anything at all. Explanation is not the first stage of a science; observation is.

The state that a man considers as his “normal” state, itself can undergo a slow change over a period of time. In the aforementioned example, the reported normal case changed from N1 to N2 over a period of time.

Philosophically, such a change does not imply a metaphysical flux: what a man considers to be his “normal” state, at any given time, is definite. However, it is just that the attributes that distinguish an N1 state from another N2 state may be so fine, or the change may occur so slowly over time, that differences between them may fall beyond a the man’s capacity to grasp or distinguish. (The story of the frog unable to notice the dangerously increasing water temperature in a slowly heated pot, is provides an example from the animal world.) However the failure to recognize the distinction does not mean that the states themselves are identical. They are not.

Thus, in our hypothesis, we emphasize objectivity of states, and as an implication, we do not elevate the subjectively described experiences to the same level as of objective observations/existential states.

BTW, observe that a chemical substance is not necessarily a pre-requisite of a state change; also radiation, heat, pressure etc. can bring about a change of state. More on this, later, in appropriate context.

2. Life Processes: Dynamic Equilibrium, Complexity and Non-linearity

(2.a) Dynamic Equilibrium

The next idea that observations such as the above suggest is one of equilibrium, more specifically, of a dynamic equilibrium.

In the above example, N1 is a state of dynamic equilibrium and so is N2. On the other hand, the SA or WS states do not refer to equilibrium even in a dynamic sense. They refer to departures from equilibrium. (BTW, depending on the nature of the substance involved, it is possible that both N1 and N2 may refer to a state of health. We shall mostly not dwell on such cases.)

Living organisms are complex enough that the number of metastable equilibrium states that may be assumed by them can be huge. For instance, consider the change of state introduced by keeping all your food habits the same but changing the consumption pattern for only one kind of a food-item. Thus, for example, consider having or not having red chillies (jalapanos) in your diet. Each such a change impinging on your body leads to a fine but definite change in its state, and indicates a different possible state of dynamic equilibrium.

Notice that we still are considering only the more or less “healthy” variety of states that may be assumed by a man (or any sufficiently complex living organism). The states assumed during the various diseases simply add another set of states.

The concept of dynamic equilibrium is vital to both the medical science and our hypothesis. Our description here is not at all adequate. We shall come back to this topic again later on.

(2.b) Complexity:

Another observation that we wish to note here is that life-processes are not only dynamic but also complex.

The word complex, in general, does not mean either “indeterminate” or “hard” (though the word is often used by physicists in the former sense, and by computer scientists in the latter sense.) Indeed, the antonymn of “complex” is: “simple.”

The idea here is that anything of interest may be imagined to be a system, made of up certain interrelated parts. If the number of parts is great or their workings, or the interrelations too numerous, or their realistic description requires too much detail to be provided, then we say that the system is complex. The politics of a village local governing body vs. that in the UN provides one good example—the moral level often is not at all different, but the latter is more complex. The difference between the simple and the complex is brought out also by considering machines: there are simple machines like the inclined plane or a system of pulleys, and there are complex machines such as a space-shuttle.

BTW, as the example of machines indicates the word “complex” does not mean: “unmanageable.” Indeed, engineered systems are often intelligently designed so as to bring complexity (including any naturally occurring chaos) under control.

The biological processes of metabolism are both extremely complex and highly interdependent. Their complexity is the reason why the medical science is not easy to build or practice. The best way to appreciate the complexity of living beings is to trace in detail all that which happens when the organism takes a particular action. For example, suppose you are hungry and decide to have a fruit. Trace all the biological systems involved in this simple set of actions: the level of energy-producing materials (say, sugar) available at the cellular level drops below a certain limit; this triggers a certain chemical signal; it translates into a neural system signal; it reaches a certain part of the spinal rod and/or brain; this last again triggers some other process because of which the biochemical states corresponding to your becoming aware of the state of hunger, happens; your conscious thinking and decision—to eat fruit—again correlates with the electro-chemical signals and states in the brain; your decision further triggers some complex process in the command center… you can carry on…

But important point is that each of these processes again is both extremely complex in itself and extremely dependent on the other parts of the overall system….

I think the fact that biological processes are complex need not be stressed any further.

Coming back to the variety of complex states assumed by a man, due to the reason of interdependencies and complexity, it is possible that a given state may be reached via many different alternative paths. Here, a path is defined as a definite (also continuous) sequence of intermediate state changes. Due to the complexity, existence of multiple pathways between the states is not an exception but rather a norm in the biological systems. Further, the attribute of interdependence means that the dynamic equilibria (corresponding to each individual state) are also highly susceptible to both fleeting disturbances as well  restoration of the system back to some or the other state of dynamic equilibrium. A very tiny biological stimulus may be enough to make the organism slide into another nearby state; a net effect of yet another set of stimulii may take the organism back to the original equilibrium state via some other path.

(2.c) Nonlinearity:

Finally, we shall touch upon yet another feature of biological processes: namely, that often times, they also are nonlinear in nature.

The basic meaning of the term “nonlinear” is very simple; obviously, it means: not linear. Since nothing can be defined via negations, it is perfectly logical to ask: so, what’s the point?

The point has a scope large enough that we have to go step by step, taking some concrete examples alogn the way.

If you attach a weight to a spring, the spring elongates by a certain amount. If you attach a heavier weight, the elongation of the spring is proportionately greater. A smaller input leads to a smaller output; a bigger input leads to a proportionately bigger output.

This property of proportionality does not always hold true for all classes of systems.

For a certain class of systems, reducing the input below a threshold level may lead to a zero output (e.g. the photoelectric effect). For others, the threshold may be present on the higher side (e.g. the electric fuse). For still others, the relationship may be more complicated than just the binary presence/absence of the output.

For instance, consider the human ear. We are able to clearly hear not only whispers but also loud conversations, and then, also rock concerts. The emphasis is on the clarity—we are able to make out subtle nuances of speech at each of these levels. The range of input values over which the ear can function is almost impossible to emulate in the usual, linear physical systems. For example, imagine weighing a gold ring on a weigh-bridge meant for trucks up to 10 tonnes in weight. The differences in the magnitude (a few tons vs. a few grams—about 10^7 times difference) is actually smaller than the range (10^9 or more) that the ear is able to handle.  The reason is that the ear is a nonlinear sensor. For a hundred-fold increase in the acoustic input, the ear produces a signal that is only twice as strong. This allows the further brain circuitry to remain sensitive over the entire hearing range. Nonlinearity does not necessarily mean weird.

A still more complicated behaviour is displayed by some other nonlinear systems, ones in which the system changes its behaviour near certain ranges of input conditions. We shall look at it in the next post.

References for the Next Post:

We shall deal with topics of dynamic instability, catostrophe theory, nonlinearity and chaos during the next post. We shall conceptually touch upon some of those ideas which are relevant to our discussion. If your background did not have any maths beyond XII, it would be worth your while to make a list of the topics or keywords that you found to be either too bizarre or too easily believable, about the chaos theory. If your background includes, say, first two years of maths in BSc/BE courses, you may wish to note that the references that I will mostly draw on are the following (in the decreasing order of relevance):

1. Addison, Paul S. (2005) “Fractals and Chaos: An Illustrated Course,” New Delhi, India:Overseas Press (originally published in UK by Institute of Physics Publishing).

2. Baker, Gregory L. and Gollub, Jerry P. (1996) “Chaotic Dynamics: An Introduction, 2/e” Cambridge, UK:Cambridge University Press

3. Tel, Tamas and Gruiz, Marton (2006) “Chaotic Dynamics: An Introduction Based on Classical Mechanics,” translated by Katalin Kulacsky, Cambridge, UK:Cambridge University Press

4. Hirsh, Morris W. and Smale, Stephen and Devaney, Robert L. (2004) “Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2/e” San Diego, CA, USA:Academic Press

Further, I have to dig up suitable references for the catastrophe theory…. It all has become such an old thing for me by now; no touch with these topics whatsoever at all!…

Before closing: Whether you know the required maths or not, since, undoubtedly, all of you have read about chaos, here is a couple of questions—a sort of “one for the road,” that got repeated!: (i) What is (or what do you think is) the relation between resonance and chaos? (ii) Can conservative systems exhibit chaotic dynamics?

Links to my earlier posts on this topic:
A hypothesis on homeopathy, part 1 [^]
A comment on homeopathy [^]

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