THE MATHEMATICAL PROBLEM IN COMPARATIVE MATERIA MEDICA


Almost every extensive proving in Herings Guiding Symptoms points the way in periodicity, some remedies showing marked relationship to the time of day, as Spigelia, increasing and decreasing in aggravation as the sun rises and declines. “Lunacy” was not an idle term for periodic mental aggravations, and the homoeopathic physician is particularly fitted to meet such conditions.


The study of materia medica presents a problem for every student, so much so that he is at first almost bewildered by the multiplicity and the similarity of symptom pictures. It is only when he can grasp the whole picture and can differentiate one remedy picture from another, and evaluate the individual symptom of one remedy from a similar symptom of another remedy and the value and importance of one symptom over against another, and its value in one remedy over against its value in another remedy, that his capacity for applying the materia medica as an art becomes easy.

This capacity for differential diagnosis of one remedy above many similars represents the acme of the homoeopathic physicians skill. Some physicians are artists in this particular, and develop naturally the art of depicting symptom pictures. For others, the differential diagnoses and differentiations must depend upon the mathematical basis.

Mathematics, which is the mother of sciences, becomes of inestimable value in our consideration of the whole subject of materia medica. Mathematics is defined as “the science that treats of the measuring of quantities and the ascertainment of their properties and relations”; therefore therapeutics should be a subject where the measuring and ascertainment of properties and relations should be well considered. Therein lies the science of therapeutics; the art of therapeutics has to do with instinctively seeing the true reflection of the symptom picture in the remedy.

Each remedy in the materia medica reflects in its proving a distinct personality; but each remedy bears a strong resemblance to numerous other remedies. We may assume that the differences in personality are greater than the resemblances, but even so, many times we get groups of symptoms, symptom pictures, which reflect idiosyncrasies of several remedies. Repertorizing the case, with its mathematical precision, will often bring out a number of remedies which may be useful in the given case; the seeming adaptability of a number of remedies to a given group of symptoms is often dissipated by repertorizing the case.

It becomes more and more apparent that the evaluation should be obtained from a greater number of remedies. Nowhere has the process of evaluation been so perfected as in Boenninghausens repertories, and he was the first to work out the system of evaluation. Jahr, in his repertory (fourth edition), gives Boenninghausen the credit for pointing the way in evaluating symptoms, and copies it in his work. Kent used three numerical evaluations, while Boenninghausen used five, which divided the symptom-values more finely still.

Boenninghausen based his evaluation of symptoms on noting the number of provings in which a given symptom appeared. If this symptom appeared in practically every proving of the remedy, it was given the fifth, or highest, rating, and it was set in the corresponding type. If the symptom appeared in a large percentage of the provings, it was given the fourth rating; and so on down according to the number of times it appeared in the provings. If this symptom had been lessened demonstrably under the application of the remedy, these clinical findings were noted and had a bearing on the rating.

If, however, the symptom had not been found in the proving, but had been observed clinically only, that remedy would appear in the first degree, in ordinary type in parenthesis. For this reason, and because this degree appears much less frequently than the other ratings, many people consider that Boenninghausen uses but four grades of evaluation.

The work of perfecting and balancing these relative ratios of symptoms depends equally upon art and upon mathematical science.

There is possible a great variety of reflections of any remedy, just as one can stand at various angles before a mirror and get many varied reflections of their own features. The remedy most often reflected, because of its wide application to miasmatic conditions and its very thorough proving, is Sulphur. One might well say that it is not necessary to know when to prescribe Sulphur; the art of therapeutics lies in knowing when not to prescribe Sulphur. Its symptom picture reflects an image that is seen on a large percentage of the faces we meet; yet on mathematical consideration we often find other remedies which are more truly mirrored than Sulphur. To a marked degree this is true of all the polychrests.

One might consider a number of cases. For instance, prescribing pathologically, one would never consider. Rhus tox. as a remedy for an asthma case. However, as a case in point the following serves as a good illustration:.

A man came to me with a severe case of asthma, and I could elicit no symptoms save those pertaining to this complaint. As far as I could find out, he seemed to experience no symptoms save in these attacks. These usually came on in the fall; they were> after winter sets in; < change of temperature, especially on going out into the cold air; < cold air in general (in the fall); < evenings; < after midnight.

Working these out with Allens Boenninghausen, and taking the rubrics “Suffocative Attacks”, and “Symptoms Accompanying Respiration”, together with the aforementioned aggravations (seven symptoms in all), sixteen remedies were found to have six of the seven symptoms, those sixteen remedies being: Acon., Ars., Aur., Bry., Carbo veg., Caust., Chin., Graph., Lyc., Merc., Phos., Puls., Ran. bulb., Spong., Sulph., Verat. alb. Each one of them lacked, however, one vital symptom, and some of them had a low numerical totality. Arsenicum, on the other hand, had a high numerical totality of 30, but it lacked the autumn aggravation, which was the marked feature of the case.

Two remedies came through having every symptom, Nux vomica and Rhus tox., standing 7/25 and 7/28 respectively. My judgment would have been to choose the Nux vomica. The man was dark, and had seemed to me the few times I had seen him that he would be irascible in disposition, although he had never actually been so. Upon careful inquiry of his wife, I found that he was of an unusually even disposition, both in his work and at home; and other inquiries also ruling out Nux vomica, I turned to Rhus tox., which did excellent work.

Now we usually think of Rhus tox. in connection with rheumatic or eruptive conditions, yet here it fits with mathematical precision into an entirely different picture. While we as followers of Hahnemann lay considerable stress on prescribing for the symptoms rather than the disease condition, yet from experience we are very apt to associate certain conditions with certain remedies; it is therefore wise at times to regard the mathematical evaluation of the symptoms to check our tendency to give undue weight to the disease conditions in prescribing.

Here is another excellent illustration of the value of mathematical comparative materia medica:.

I was called in consultation to see a woman 86 years of age, who had been confined to her bed for some days. She had a thirstless fever, with dry mouth; she was mildly delirious, that is, she lay talking to herself of events that had occurred in her early life, but she could be roused to intelligent conversation by addressing her directly and clearly. Laboratory analysis had shown much albumin in the urine and many large casts.

As for her symptoms, she had a boring pain under the left shoulder blade, also in the right hypochondria; turning in bed < very much, but change of position >; > lying on back; < by touch but > by steady pressure; < evening; complained of a sore pain in the leg below the knee, and this also was greatly < on touch. Because of the pain in the right hypochondria, the < on motion and the desire to lie on her back she had been given Bryonia in varying potencies without relief; Lycopodium had also been given without satisfactory results; and her condition grew daily worse.

The physician in charge of the case was much interested in the diagnosis as he expected the woman would die very shortly and he had been unable to come to any satisfactory conclusion as to her trouble. The pathological diagnosis did not interest me greatly, but I was deeply interested in the remedy diagnosis, and because of my eagerness to strike the right remedy I took time to repertorize the case very thoroughly.

On the basis of fourteen symptoms as already given the results were as follows: Amm. mur., 12/29; Anac. 12/36; Ars. 12/38; Calc. carb. 12/40; Canth. 12/40; China 12/30; Conium 12/35; Kali carb. 12/40; Nat. mur. 12/41; Nit. ac. 12/39; Nux vom. 12/40; Phos. ac. 12/43; Plb. 12/39; Rhus 12/44; Sabad. 12/34; Sil. 12/48; Sulph. 12/46; Acon. 13/46; Merc. 13/45; Phos. 13/46; Puls. 13/59.

All of the remedies having thirteen out of the fourteen symptoms had albumin in the urine with the single exception of Pulsatilla; yet Pulsatilla covered every single symptom beside the one defined by laboratory diagnosis. Because it fitted so perfectly the other symptoms I gave Pulsatilla 200, after giving my decision to the attending physician. He confirmed my decision by mentioning that she had been very tearful at times. The result was all that could be desired. The temperature fell to nearly normal; the albumin and casts markedly fell until they all but disappeared; the patient was in a much more comfortable condition.

The attending physician talked the case over with me about a week later, and said the patient was showing less reaction, the improvement slowing up considerably, and the delirium, if such it could be called, still continued somewhat, I suggested his plussing the remedy, which carried her along for some time longer. At that time he expected to call me in for another consultation because he had no idea (as he had had no idea in the first place) that improvement for any length of time would be possible. The consultation was not called for and at the last report the patient was still progressing. Considering the age of the patient, we did not expect a cure; but the fact that her condition was so palliated was a matter of pleasure to the family and to the physicians.

At my confreres insistence, I repertorized the diagnosis from Symptoms and Disease Applied: A Differential and Mathematical Diagnosis, by W. A. Kitchens, M.D. (reviewed in The Homoeopathic Recorder, May 31, 1931, page 380) and came to the conclusion that it was a case of chronic parenchymatous nephritis.

Upon mathematical analysis of the case, it was seen that Bryonia had failed to help the case because it lacked the type of pain described as boring, and the > from change of position, which was strongly marked. It also lacked the albuminous urine which I did not take into consideration to any degree. Lycopodium had a few of the symptoms very prominently, but did not cover enough of the symptoms to appear in the final analysis.

In other words, neither of these remedies were the similimum, and one of them was only partially similar. Pulsatilla did not occur to me from my first consideration of the case, for did not see the typical Pulsatilla symptom-picture, and had it not been for the mathematical procedure I question my reaching that conclusion, at least until I had seen the patient and studied the reflections more thoroughly.

The evaluation of a given symptom is sometimes a surprise to us. We associate certain symptoms instinctively with certain remedies, and regard them as classical indications for the remedy; yet upon investigation we often find the given symptom present in equal degree in remedies we had not considered. For instance, the symptom < on waking immediately brings to mind such remedies as Lachesis, Nux vomica and Pulsatilla. We often fail to realize however, that under this rubric Boenninghausen gives fifteen remedies as of the highest rank, as well as numerous remedies of lesser rank. Besides the remedies that immediately occurred to us in this connection, we find Ambr., Amm. mur., Ars., Calc. carb., Caust., Hep., Hyos., Nit. ac., Onos., Phos., Sep., Sulph. and Valer. in the same numerical evaluation.

Again, in the symptom > in open air we think of Pulsatilla and a few other remedies, forgetting for the time that there are eight other remedies in the repertory having equal numerical strength in this one symptom, and many remedies having this symptom in lesser degree.

Such comparisons might be carried on almost indefinitely; and it is only when we refer to the numerical evaluations that we can make a deep study of comparative symptomatology. The danger of key-note prescribing lies in the failure to evaluate symptoms and to compare remedies.

Another phase of the mathematical side of homoeopathic therapeutics is the attention which should be given to astrological and solar influences. Many of us have not evinced interest in these phenomena to any degree, yet we must all take into consideration the times of aggravation and amelioration, and upon analysis we find that these bear a strong relative value to the action of the solar system; the time of day; periodicity (daily, every seven, fourteen, twenty-one or twenty-eight days); seasonal influences; the waxing and waning of the moon; all these show themselves in our patients and in the remedies as well.

Almost every extensive proving in Herings Guiding Symptoms points the way in periodicity, some remedies showing marked relationship to the time of day, as Spigelia, increasing and decreasing in aggravation as the sun rises and declines. “Lunacy” was not an idle term for periodic mental aggravations, and the homoeopathic physician is particularly fitted to meet such conditions.

Hering gives in his Guiding Symptoms considerable attention to the aggravations in relation to the moon, to illustrate: Bufones, attacks appear with change of moon (epilepsy); Calcarea ostrearum, worse toward new moon (gangrene oris); worse during solstice (epilepsy); worse about new moon (crusta lacta); worse during full moon (epilepsy); Causticum, new moon (epileptic attacks). (It is to be remembered that two of these remedies were proven by Hahnemann, the master observer). These are but a few of the remedies mentioned as having lunar aggravations that have been recorded, as appertaining to definite miasmatic conditions.

The periodicity of aggravations as they pertain to the hours of the day are without number, and the seven, fourteen, twenty-one, twenty-eight day, etc., are also numerous.

Boenninghausens Repertory gives considerable space to the aggravations relative to phases of the moon, under the rubrics New Moon, Full Moon, Waning Moon, Moonlight, and lists twenty-one remedies. Kent neglects this classification almost entirely, giving but three remedies under the rubric Moonlight.

Again we find much consideration in homoeopathic literature devoted to the divisions of the seasons, spring, summer, autumn and winter, as having a direct action on the remedies. The metals are tremendously affected by the solar and lunar cycles; plants are hardly less so, and they respond particularly to the seasonal cycles. Therefore we find that the remedies obtained from these sources could hardly fail to reflect periodicity to a marked degree. In the animal kingdom it is not so easy to trace the influence of the astrological cycles; yet we find this reflected in the provings.

The most elaborate presentation of astrological influence is by Dr. M. Duz, a Hahnemannian physician and astrologer, in his Astrological Medicine and Therapeutics. You may find the reference to this work on page 771 of the October 1931 Recorder.

Thus we see how intimately the homoeopathic materia medica is related to the fundamental science of mathematics, which is the mother of all sciences. Therapeutics, the homoeopathic therapeutics, is an art; but the artistry has as a basis the science which is founded on mathematics.

DERBY, CONN.

DISCUSSION.

DR. IRVING LORD FARR: The doctor has given us a most excellent as well as a very unique paper. I have gotten much knowledge out of this paper relative to the use of the repertory, especially along the line of values, and since both repertories are based upon the plan of a valuation for each remedy, from one to five in Boenninghausen and from one to three in Kent, it strikes me that the doctors plan of adding valuations is one of the most unique things one can follow in distinguishing between a series of remedies.

I was very much interested in what the doctor said relative to astrology. Since Evangeline Adams went on the air to promulgate astrology, I am finding that the laity come to us and ask us about astrology: Does it mean anything or does it have any weight, etc.? The doctor has shown in his paper that the old masters certainly placed some value on astrology and worked it into the repertories and I think we homoeopathic physicians might heed this. I think there is value in it.

DR. C. M. BOGER: I wish to say something about these moon phases. As you remember, I published a paper, a couple of years ago, of observations along that line, and since then the observations have increased to over 1,500. I keep a record of tabulation of strongly marked results from remedies, when these results took place, when the remedy was given, and exactly at what phase of the moon it occurred.

This dose away with all kinds of theories and is based on the fact that these things happen just that way. There have been some very surprising things developed from that paper. The first table which was published showed that of all the remedies having aggravation at full moon, Phosphorus was by far in the lead. Continued observations, almost doubling the number of former observations, show that Phosphorus still maintains the same proportionate lead, not only in my own prescribing but in the prescribing of some others who are helping me fill up this table.

It is a strange thing that the time of the greatest aggravation of Arsenic just precedes the Phosphorus aggravation on the increase of the moon, and has about the same relative strength as Phosphorus does at the full moon.

In making this study I am trying to build upon a substantial foundation. It is a great deal too long to go into extemporaneously, especially as I do not have the exact figures in my hands at this minute, but I have noticed another thing, which is that often the very first observation in these remedies serves as a guide and maintains its lead through all the succeeding observations.

That is a strange thing and that brings us right back to the observations made by Boenninghausen in the early days. His observations, as well as those of others at that time, were based on a small number of cases. My observations are based on a very large number of cases and I do not intend to stop making these observations under at least three or four thousand. I believe then they will have same value.

Another thing it has also demonstrated which is that some remedies do not favor any particular phase of the moon. Sulphur is one of those Sulphur shows very little preference. Some of our friends who are very theoretical speak of Sulphur as being a fiery remedy and that sort of thing. It is a sun remedy, and so forth, but when it comes down to the bald, hard, rock bottom facts, Sulphur doesnt act any better one time than it does another. I hope at some future meeting to bring still more conclusive evidence of what I am doing, before you.

DR. EUGENE UNDERHILL, JR.: Have you made any observation relative to Cina?.

DR. C. M. BOGER: Very much so.

DR. C. L. OLDS: Wouldnt Sulphur be classed by itself? It is rather al inclusive. Wouldnt it be explained by itself?.

DR. C. M. BOGER: Calcarea doesnt show much variation.

DR. CLIFFORD: What about Pulsatilla?.

DR. C. M. BOGER: Maybe it is on the increase of the moon.

DR. H. A. ROBERTS: Boenninghausen has an increase.

DR. EUGENE UNDERHILL, JR.: I have observed that nearly all convulsions occur either around the new moon or at full moon.

DR. A. H. GRIMMER: This paper is without question the best I have ever listened to. It has more meaning and carries more meaning from so many different angles that it is rather a difficult one to discuss.

The doctor has wisely stressed the difference between the mathematical and the artistic side of our prescribing in the use of the repertory. I think that it is a splendid one for us all to remember. Both have their value. The mathematical is, of course, the scientific method. It appeals to those who are scientifically inclined because of its exactness, at least from a material sense, but science has not yet gotten into the higher realms where the artistic will come in. Science will serve as a balance for those who are apt to act too much on impulse and so-called intuition.

Both methods have their values, no question about it. Intuition is nothing more than stored up knowledge, after all, and from long study and practice we develop intuitional powers of prescribing, but, on the other hand, we need this material, this mathematical part, because of the stupendousness of the materia medica. Without the mathematical part to hold us down and lead us, we are apt to go into confusion, and the paper has brought those points out forcibly.

The astrological part has been of great interest to me personally for a great many years. I have not said much about it, but I have studied astrology deeply and profoundly over a long period of years; even before I took up homoeopathy, I was interested in astrology and notwithstanding that some of our fine people. Dr. Kent himself was radically opposed to it I believe that it is still based on truth. Astrology comes down from ancient times, from the ancient philosophers who had wisdom in a higher degree than we have today, and that wisdom is wrapped up and comes through the science of astrology.

H.A. Roberts
Dr. H.A.Roberts (1868-1950) attended New York Homoeopathic Medical College and set up practrice in Brattleboro of Vermont (U.S.). He eventually moved to Connecticut where he practiced almost 50 years. Elected president of the Connecticut Homoeopathic Medical Society and subsequently President of The International Hahnemannian Association. His writings include Sensation As If and The Principles and Art of Cure by Homoeopathy.