“It is easy to doubt matters which cannot be laid before our ocular vision, but in itself this doubt proves nothing at all, for according to the old rule of logic: negantis est probare”
from The Chronic Diseases (Â I:79)
Based on the 6^{th} edition of The Organon of the Medical Art and The Chronic Diseases Their Peculiar Nature and Their Homeopathic Cure ^{1, 2}, two most important books written by the founder of Homeopathy Dr. Samuel Hahnemann, I have decided to further show the links between the superior philosophical concepts regarding disease and treatment in Homeopathy on one side, and their consequences for the future, and on the other side. I have also tried to show the usefulness, actually the necessity, of mathematics as a tool when applied correctly, in describing such concepts at the level of biological sciences, with its most common application – the bio statistics.^{3}
The simple statistical model that I want to present here, through its incontestable recognized validity,^{3} has many usages and consequences, in particular on the correct understanding of the relation between health and disease, disease definition and levels, and the correct level where the treatment of chronic diseases in particular should be calibrated on objective facts, in accord with the original ideas that we can find in the founding homeopathic books.^{1, 2}
To further illustrate the above ideas, I would first of all like to present the set of concepts as they are described by Dr. Samuel Hahnemann, that would lead to the idea of making such a model, in their original presentation as they are described in The Organon of the Medical Art the 6^{th} Edition^{1} and in The Chronic Diseases Their Peculiar Nature and Their Homeopathic Cure.^{2}
1.The Organon
Aphorism 103 – ” I had to investigate the chronic wasting sickness (namely and principally Psora) much more exactly than ever before. I had to do this because of the extent of the symptoms in these chronic diseases and also because one patient carries only a part of the symptoms in himself, while a second or third patient, etc suffers from some other befallments which likewise as it were, are only a part torn off from the totality of the symptoms that make up the entire extent of one and the same disease. Therefore, the complex of all the symptoms belonging to such a miasmtic wasting sickness (in particular psora) can only be ascertained from very many such individual chronic patients. Without such a complete overview and total image, the medicines that are homeopathically curative for the whole wasting sickness (namely the antipsorics) cannot be searched out. These medicines are at the same time, the true remedies for the individual patients that are suffering from these chronic maladies“
2.Â Â Â Â Â The Chronic Diseases
“But usually, after repeated attempts to conquer the disease which appeared in a form always somewhat changed, residual complaints appeared which Homeopathic medicines hitherto proved, though not few, had to leave uneradicated, yea often undiminished”.(I:4)
“What was the reason of the thousands of unsuccessful endeavours to heal the other diseases of a chronic nature so that lasting health might result? Might this be caused, perhaps by the still too small number of Homeopathic remedial means that have so far been proved as to their pure action?, The followers of Homeopathy have hitherto thus consoled themselves; but this excuse, or so called consolation, never satisfied the founder of Homeopathy particularly because even the new additions of proved valuable medicines, increasing from year to year, have not advanced the healing of chronic (non venereal) diseases by a single step…” (I:4; emphasis added)
“…What is there to prevent this? The answer to this question which is so natural, inevitably led me to discover the nature of these chronic diseases…. The Giver of all good things permitted me within this space of time to gradually solve this sublime problem through unremitting thought, indefatigable inquiry, faithful observation and the most accurate experiments made for the welfare of Humanity”. (I:5^{)}
” These are the characteristic secondary symptoms of the long unacknowledged, thousand-headed monster, pregnant with disease, the Psora, the original miasmtic malady which now makes its manifest appearance”. (I:78; emphasis added)
And also below, one of the most peculiar and hidden paragraphs, in an explicative note:
“To prove the psoric nature of these chronic diseases without acknowledged infection, we do not even need the fact that the anti psoric remedies prove effectual therein; this serves only like the proof to a correctly solved mathematical problem” (I:79; emphasis added).
I consider the above paragraphs of greatest relevance for my demonstration as they are at its base. They indicate a statistical model which I consider to be a necessary reality, starting right from the beginning, with my lectures on homeopathic texts and in particular on The Organon of the Medical Art.
Although I make below a presentation for the theoretical model and its collateral ideas, a few years ago I used the same principle which I describe today, and the results were surprising and a real proof for the validity of the model itself that anybody can try any time. At that time, using the results only for justifying economical needs, I did not know that a wonderful science has already founded a whole system on such observations, and that this validates its usefulness and truth.
Samuel Hahnemann observed from clinical experience that in chronic diseases, although he and those that followed the homeopathic principles correctly, have applied the treatment as indicated by these principles in counting the totality of the individual signs and symptoms, there were patients with relapses and for them the disease did not stop in its progress.^{1,2}
Through careful observation, he could see at some point the cause of these failures was the impossibility of treating some patients with chronic diseases. These belong to a disease that is at another logical level than the combination of individual signs and symptoms, and is invisible to the eye in its totality. It is a collective statistical disease that makes the remedy almost impossible to find if we start at the individual level.
I will show below that the collective statistical disease does exist indeed.
Samuel Hahnemann made the connection with the ways of transmission and origins of such disease, and he showed the links of the statistical disease with certain origins and ways of transmission, in particular parasites and micro organisms. He also discovered there is not only one such collective disease. During his life, he proved three of them which have origins in infectious diseases. He called them Miasm and they were Psora, Syphilis, and Sycosis; of which Psora is the oldest and the most widespread amongst the patients with chronic diseases. To avoid their transmission, the treatment of the miasms must always be homeopathic from the start, from the moment of infection to avoid the contamination of the new subject with the disease, and to further avoid the spread of such a disease in ways that may not necessarily be via infection.
Based on the above, I would like to show that in fact miasms are statistical diseases in the common sense.
Following Samuel Hahnemann, through the work of other homeopaths, other major miasms have been discovered and connected with their ways of transmission
However, there is another homeopathic principle which states that for homeopathy it is not necessarily important which types of stressors are involved in the development of a disease. We may never have complete access to the full possible variations in the type of stressors or their strength. Combined with a logically possible internal susceptibility, and based on the above as a principle of incontestable validity, I have started in the search of mathematical functions that would best describe such an idea.
Searching for possible models, I have first realized that Homeopathy does not use any quantitative concepts in the description of the disease parameter. It operates with perceptible signs and symptoms which statistically speaking are qualitative variables, and not quantitative or numeric variables.
Inside the science of statistics, I have found a few mathematical functions or tests belonging to inductive statistics, which are used in data correlation, and when applied these will show if there is a mathematical correlation between variables. Amongst them, there is a specific statistical function, the Chi square test that can in particular be used to show and certify such correlations between variables.
This is exactly our case and I believe is a clarifying answer.
As we want to find valid correlations between signs and symptoms, as qualitative variables, and Chi square is more permeable to errors in introducing these variables, it is without doubts that this function is suitable for our purpose.^{3}
At the same time, being permeable to certain errors in introducing the qualitative data to be processed, Chi square is also indicated by the fact that it would be impossible to accept that any symptom which at any point in time is similar at the conceptual level to the same symptom in another patient, can at the same time be fully similar to the same symptom in another patient in reality, in its objective expression.
For that reason, as we are starting from homeopathic principles which indicate such a study, we need to further expand the study with the aid of and inside homeopathy. It is a necessity that in performing the study, the best description of qualitative data (symptoms and signs) will find their expression in the homeopathic Materia Medica, as the place we can find maximum degrees of expressing the perceptible signs and symptoms we see in patients with chronic diseases suitable for our study.
The Chi square function
The Chi square test is a statistical function that shows if 2 qualitative variables are independent in a random population and it has a wide range of applications in research within biological sciences.^{3}
It can only test if the two variables are independent without indicating, which is smaller of greater. It does not express quantitative differences between variables, it just express if the variables are independent or correlated.
The first step in applying the chi square test is to establish the correct hypothesis. The null hypothesis is indicating that the two variables are not correlated and they are independent.
There are many tutorials on the web for the Chi square function and its applications and is not the purpose of this communication to be a Chi square tutorial which is a clear mathematical function with well defined characteristics and very simple to use and calculate.
Our hypothesis is that in a 2×2 table, in the 2 rows present or not present are variables indicating the patients that have a specific symptom and the patients that do not have it. In the columns are the symptoms to be checked for the null hypothesis (for independence). Symptom 1 is tested against all other symptoms until we finish the testing of it with the symptom 1 with all the others we have found in the randomly chosen patients.
The Chi square shortcut function for 2×2 tables is:
A | B | A + B | |
C | D | C + D | |
A + C | B + D | A + B + C + D = N |
X^{2} =Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â N (AD – BC)^{2}
__________________________
(A + C) (B + D) (A + B) (C + D)
Theoretical examples:
Present | Not present | Total | |
Symptom 1 | 67 | 34 | 101 |
Symptom 2 | 36 | 15 | 51 |
Total | 103 | 49 | 152 |
Chi Square 0.2804
For significance at .05 level Chi Square should be >/= 3.84 which is the minimum level where we can accept or reject the null hypothesis using the Chi square function.
The distribution is not significant
Present | Not present | Total | |
Symptom 1 | 23 | 55 | 78 |
Symptom 3 | 36 | 22 | 58 |
Total | 59 | 77 | 136 |
Chi Square 14.377
P </= 0.01
The distribution is significant
The degrees of freedom for the 2×2 table are 1.
If we would have for example 30 symptoms as a total after introducing random data from individual patients, S1 to S30, then, as shown before we will test S1 with all the other 29 independent symptoms in 2×2 tables, and for example we find that S1 has a statistical correlation with S5, S6, S9, and S22; then if from the practical result we cannot reject the null hypothesis for S1 being associated with the variables mentioned, then we cannot reject that they are all associated with each other as well.
We do the same with each one of the symptoms until we have tested them all against possible correlations and we have finished all the possible combinations, and then we connect the correlative chains together. As they all are independent, they will join in an imaginary root at the source that has produced the qualitative variables.
In such a way we have built a three-dimensional inductive statistical disease, impossible to see in any of the individuals who belong to it. It is a reality that cannot be seen but it is as real as anything we can see with the open eyes.
Conditions in using Chi square function:
- The sample must be randomly drawn from the population.
- Data must be reported in raw frequencies (not percentages);
- Measured variables must be independent;
- Values/categories on independent and dependent variables must be mutually exclusive and exhaustive;
- Observed frequencies cannot be too small.
Before discussing the ideas derived from these theoretical facts and this model, which is specific within the science of homeopathy, I would like to further comment on some of the ideas at their general conceptual level, starting from the level of accepted validity of the above model.
As shown above in the mentioned texts, the model is first of all I believe, in complete concordance with the original ideas of the founder of the science of Homeopathy Dr. Samuel Hahnemann. It is first of all showing the philosophical level at which homeopathy was created. It is a complete conception about the term chronic disease and its consecutive treatment, which reaches the heights of the absolute. It is a true system of medicine derived from fine observations and their correct interpretations. ^{1,2}
First of all, as we all know that in homeopathy the correct diagnosis equals the correct treatment through the correct identification of the remedy, further search past that point is not necessary or possible.Â When we have 1 remedy being identified through the statistical model for a particular chain of associated symptoms we can say we have revealed one of the heads of the monster. This is a statistical disease, discovered in an objective way through inductive statistics, using a superior logical model indicated by homeopathy. It is a miasm in full light, without the need to find its origins or ways of transmission. It shows clearly at which level, and why and how we need to start the treatment.^{1,2}
A consequence of the above facts is also a logical necessity in accepting the movements of the “heads of the monster” in different planes, as suggested by the results. The weakness of the statistical model through its incapacity to reach 100% precision is also its strength and warning. It is a small lack of precision that is showing a variation that it cannot catch at the time of its application, which is nothing else than the movement of the living statistical disease in all possible directions. That is exactly what the inherent small level of errors of the model is showing in an objective way. A movement is a development, a dynamic movement in a certain direction, and not a fixed entity that can be expressed in definitive numbers or states.
A first possible cause of such movement can be related to the previous idea, that as we do not have total access to all the factors which can produceÂ disease in general, and such a statistical disease in particular, it is without doubt a reality that the above stressorsÂ have an important geographical variation in presence and strength, also leading to a variable geographical response in the individuals. In such a case, for many miasmatic diseases we cannot use correctly the miasmatic remedy that we find by using this model, without testing the validity of the expression for that remedy on a specific territory, and then using its objective and possibly specific certification, which is the presence of the particular miasm. This is especially so when we are at a very long distance from the territory where a remedy was calibrated on a local miasmtic tendency. Based on the above, and combined with the specific characteristics of a population, I expect that we will find different miasmtic tendencies in different geographical areas.
It is another example, which illustrates how Dr. Samuel Hahnemann had good reason to use the metaphoric image of a monster with a thousand heads. This symbol as it is shown here expresses his mathematical thinking, and also his surprise of the developments of the disease itself, an invisible living creature revealed only by statistics. And we will further see how that this also refers to the constitution as well.^{4}
If we process the data we have obtained at the statistical level and we find the main separate tendencies, it is obvious that they are all joining together as they are dynamic entities present in human populations. Without the human subjects they would not exist. It is an imaginary monster with many heads (revealed by statistics) of the same biological body.^{1,2,5}
A consequential result is that at the level of representation, the homeopathic remedy suitable for the treatment of that level has a circular shape at the individual level, (where it was first created using descriptive statistics), then travels around the body in an imaginary circle which closes at the mental level. It then becomes spherical in its full three-dimensional (via inductive statistics) shape, best described by Leonardo Da Vinci’s Vitruvian Man.^{6,7} The Vitruvian Man shows how the human body can anatomically fit at the same time in a circle in one plane, then becomes a sphere in a three-dimensional plan. Both are geometrical shapes of the absolute. At the same time it will also fit perfectly inside a square in one plane that becomes a cube in a three-dimensional plane, both being geometrical shapes of mathematics and calculus. In the original drawing we can also see how the human can touch both the circle and the square with the middle finger which is number three regardless of where we start counting the fingers of one hand. This is also a universal reality indicating the negation of duality. This is a conceptual connection beyond coincidence, lying between ideas and representation. The drawing shows a philosophy of medicine, telling the message and universal truth that Leonardo Da Vinci wanted to send from his time. It is a way of thinking as a source, and not a simple coincidental drawing as it may look at the first sight. Simple and very complex, with many meanings, an art in itself, and in the same time an inspiring way of thinking, speaking about numbers as well, whichÂ seems to transcendÂ historical time.
Following the above, a most surprising idea self-arises from this calculation and model.
Creating the statistical remedy has first of all an importance in the treatment of the total statistical disease at its dynamic functional level.
However the statistical remedy itself was created using descriptive statistics, adding together symptoms and signs of the individuals from provings on healthy people.^{1,2,8,9} For the above model we have used inductive statistics which in fact magnify the total picture in a three-dimensional plane, like accessing another dimension. It is clear that the remedy we created in such way is a perfect three-dimensional spherical image of the similar disease, and is showing and acting at the same time at the level of three-dimensional possibility in the individual patient.
The same remedy in such a way is the measure of a dynamic specific level as an incontestable proof of a constitutional functional answer ^{4 }inside a population (a group) and at the same time at the individual level in that population. It is a constitutional and functional memory at the same time. It has the characteristics of a memory as it is a calculated entity and has a definite presence and at the same time is complex functional as indicated by the lack of the total number of organic symptoms in an individual that join together only after using a statistical function. Something we can see through a simple mathematical function, but we cannot fully describe it, as that is exactly the key in mathematics, its inability to describe a functional memory that we can see as our psychological level has a start exactly at such level and has the freedom to express it.^{10,11,12}
Even if we start building the remedy only at the organic level, using organic ways of expression where the standard is more clearly defined, just like any homeopathic remedy; the calculated statistical remedy is also asking for its specific set of psychological tendencies. This time it is at a calculated expression in a population, and is a reflection of the level of its possible presence in the individual as a multidimensional (non dimensional) reality.
That has several consequences.
In such a case, the psychological level is an immeasurable dynamic function in itself, and supposedly is the result and expression of those lower levels of dynamic cumulative functional tendencies, which arise from the imperceptible organic molecular developments, and it then has imaginary layers within the same function, each one expressing a qualitative difference from the others. Based on its unique characteristics and unitary way of expression, we can safely search and most definitely find psychological particularities in the statistical disease characteristics.
These are measured by the matching remedy inside the perceptible language of this function, without even the presence of virtually any perceptible organic symptom at the body level. The perceptibly expressed psychological function is the magnified expression of a microscopically functional and non-perceptible level of smaller invisible functional combinations, which pre-exist before reaching the expressed level. Thus if the statistical tendency does exist in an individual, supposedly only at the microscopic imperceptible level, it is impossible not to be expressed in its dynamic movement by the superior perceptible levels, which are the instantly magnified image of the dynamic movement at the microscopic level. Also small movements in the layer below within the same function will lead to big movements of the above level.
Dorn, one of the followers of Paracelsus, best describes that in De Speculativa philosophia: “Sic paulatim scintillas aliquot magis ac magis indies perlucere suis oculis mentabulis percipiet, ac in tantam excrescere lucem, ut succesivo tempore quaevis innotescant, quae sibi necessaria fuerint.”Â (“That is how he will perceive with his spiritual eye as some sparkles will be more and more transparent day after day, joining together in a such bright light as after that, he will know everything is necessary for him”.)^{ 10 }
This is a functional memory in its full light, sitting above a multidimensional (non dimensional) reality that communicates between planes through the Ether, as a Sun above a Kingdom with no borders and no enemies It has the freedom to describe itself and its own creation in simple words, as being the result of an original need that has no causality.
It is an example of how words are created as spherical entities at the subliminal level of the collective subconscious from where they start being perceptible, just before being expressed at the individual level. This is at the collective level of functional memory, and then they travel through different layers of individual expression as through the Ether and reach their expressed level in an individual. This is a result of a functional need that is contained in itself as an individual functional three-dimensional memory, where “the possible” is equal with the image we see in front of out eyes.
If Psora is present in an individual, it will peculiarly deviate the formation of ideas and words in a certain dynamic direction that the practitioner must find.^{1,2,4,5,13}
He was also indicating, as Paracelsus also did, the presence of an “invisibilem solem plurimis incognitum” inside the human.^{10}
The characteristics of the psychological level as a function above another non-perceptible functional level, allow further investigations without the change in the concept of the characteristic itself. It is a function that has no other way to express itself than through the magnified answers of the same function at the lower levels. Up and down and in all directions within that function we have variations of the same level of expression without change in the ways of expression, as in the case of the body where things start from a functional level to a defined organic expression. Having an organic base as well, the psychological level has a depth that is perceptible without the requirement of any other tools. At any time we may be able to see a tendency within itself using the same concepts without switching the concepts. That is not possible at the organic level without starting to measure things which require continuous changes in the tools we use, the more we go inside the organic below the symptoms.
As the psychological level is by itself as a concept and function, independent in its way of showing perceptible symptoms, there are no doubts we need to consider that level, practically and conceptually as mentioned, as a separate function, based on its unity and unicity of self expression, in a different way compared with the all the organic ways of expression. Then we can say there is a central tendency for a remedy at that level in an individual. Even if we would consider the individual body as a unitary entity without separating the different organs in systems, the characteristics of the statistical remedy are not present at that level, as we built its presence based exactly on the lack of theÂ individual characteristics.
In that way, being a unique function where the symptoms have actually only a functional dynamic way of expression, and having its roots in lower levels of functional activities, the psychological level indicates independence in expressing some tendencies. It is a unique function that is expressing other functional levels. It does not require the presence of any of the organic symptoms to actually indicate by itself the presence of the possible dynamic statistical movement at the individual functional level which precedes the organic expressions, and which can possibly lead to perceptible organic disease symptoms in the course of time.
That is not the situation with the organic perceptible symptoms. If we have the example of a patient in which we see just one perceptible symptom and that symptom belongs to the statistical disease, we would not be able to easily and precisely identify the statistical remedy at the individual level. To do this we would need to calculate the correlations based on such a model, or we would need to reveal with great precisionÂ the peculiar psychological characteristics that belong to that remedy. This requires skills and experience, but at the same time there is no better medical device to follow a mind than another mind (the practitioner’s) looking for specific tendencies belonging to a disease. The weakness of this method is actually its validated valuable strength as well.
If we further develop the idea, if the functional level seems to mathematically indicate the presence of another level of memory, the functional memory, above and past DNA or even included at its level as an inductive and immeasurable memory as precise as the genetic model is, then any normal individual psychological tendencies that are perceptible and are also matching the characteristics of a statistical remedy in a population, must be carefully monitored in its dynamics as it is possible that when it becomes of a marked intensity measured by the patient itself in his feelings, it can be a warning of a future possible organic pathology and may indicate homeopathic treatment using the miasmtic remedy as a prevention of further such developments. Sulphur for example as one of the miasmtic remedies discovered by Samuel Hahnemann will treat the “ragged philosopher” and actually strengthen the philosopher within its own limits of happiness, a difference measured by the individual strength, a measure that the individual would perceive if things tend to become too intense.
And we have today practical models and methods, such as the one discovered and promoted by Dr. Rajan Sankaran, one of the masters of modern homeopathy. Dr. Rajan Sankaran shows in all his books, the real practical results we can get with homeopathy as a treatment, using the peculiar psychological characteristics and tendencies of the patient in finding the correct remedy.^{13}
If instead of following the organic symptoms of the individual, we simply follow a special and unique function that can express itself tri dimensionally (which we can classify for purely logical purposes as an “organ – function”) within the same function; and then we consider its qualitative specificity in expression, unicity and unity; then the “organ-function” is revealed as a superior dynamic complex function, which is independent from the body and organs at least in its level and ways of expression. Thus we find the functional level everywhere in the body in different ways of expression.
It does incorporate present and past, individual and collectively in a way that no other level of the body organic functional level itself can show, as demonstrated.