In Modern Mathematics

Chaos, fractals in Mandelbrot’s Equation

And the unexplained too….

Crop circles…….

In the stock market

and even in your pocketbooks, purses and handbags

Golden Ratio in the credit card

This Law has received public exposure in this book

And was discovered by this man

Leonardo Fibonacci

1170 -1250

As shown, you will find the Fibonacci series and the Golden Ratio everywhere you look, from microcosm to macrocosm, so why not use it in Homeopathy?

The Fibonacci Series.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,….is constructed by adding one number to the previous one, which forms the next in the series:

0 + 1 = 1

1 + 1 = 2

2 + 1 = 3

3 + 2 = 5

5 + 3 = 8

8 + 5 =13 and so on, giving the famous Fibonacci Spiral

The Golden Ratio which can be seen in the rectangular picture leading to the Fibonacci Spiral is the most harmonious proportion between width and length, always equivalent to the ratio 1:1.618

In the Fibonacci series, every number divided by the preceding one “vibrates” (is approximately equivalent) around this ratio.

How does that relate to potencies?

0 is the crude material, which we do not use

1 would be the Mother Tincture, which is in fact a 1:10 dilution, therefore a 1C is in reality not a one hundredth dilution but a one thousandth, just to make things more complicated

2 = 2C

3 = 3C

5 = 5C

8 = 8C

13 = 13C and so on.

Although costly and time consuming, it is easy to prepare those potencies by hand as described by Hahnemann up to 144C or 233C; those are real Centesimal Hahnemanian potencies although the number of succussions is a variable (Simillimum 10 succussions, Helios 40 succussions, some others 100 succussions or anything inbetween), meaning that you should use the same provider and decide about a fixed number of succussions so cases can be compared; later on we can start comparing the relevance (or lack thereof) of different number of succussions.

For higher potencies, we would resort either to Korsakovian ones or any of the machine-made ones, but as I tried to demonstrate, we would not know what potency we give as a matter of fact. I will come back to that in a moment and you will see it is not relevant at all.

Using that mathematical progression, I postulated that I could achieve an exponential action of one dose after the other.

I was worried though that I would remain in the realm of low and medium potencies, unable to achieve the deep action we want from the 10M, 50M, CM, MM or higher LM/Q potencies. But looking at the Nautilus

and after a short trial with a few patients, I soon realized the fact that the potencies were boosting each other, not by addition but in a real exponential progression, by multiplication.

If the first potency used is a 3C

3 = 3C

5C is 3×5 = 15C equivalent

8C is 15×8 = 120C equivalent

13C is 120×13 = 1560C or 1.5M equivalent

21C is 1560×21 = 32760C or 33M equivalent

34C is 32760x 34 = 1113840C or MM equivalent

55C is 1113840x 55 = 61216200C or 61MM equivalent

If the first potency used is a 5C (3C not being available or not recommended for toxic substances)

5 = 5C

8C is 5×8 = 40C equivalent

13C is 40×13 = 520C equivalent

21C is 520×21 = 10920C or 11M equivalent

34C is 10920×34 = 371280C or 370M equivalent

55C is 371280×55 = 20420400C or 20MM equivalent

Of course to obtain that progression, you must follow the order of one potency after the other. You cannot skip any potency, they have to be taken one after another in the proper order.

Are those jumps logical and not haphazard? Look at the graph when those numbers are converted in logarithms.

Those are almost straight lines, showing that the progression is regular and mathematically logical. The small irregularities are explained by the fact that, as written earlier, the numbers of the Fibonacci series are not exactly within the Golden Ratio, but slightly different in the lower decimals (5:3=1.666; 8:5=1.60).

But doesn’t the use of potencies that build upon each other to reach activities akin to extremely high potencies contradict my previous question about the jumps between 30C to 200C then 1M and 10M as being too big and exaggerated?

Let’s have a look at those potencies in logarithmic form:

and it appears that not only are they sufficiently close to each other, but the logarithmic progression is itself slowly exponential, which makes it mathematically sound.

It appears that used in that manner, those are not static potencies, but like in the Fibonacci spiral every potency builds its action upon the previous one, filling a full “time-space” volume (continuum) progressively before the next one is to be introduced.

By itself, each and every potency is low or medium; the combination with the previous one produces a depth of action equivalent to the value of the multiplication.

Compare it to the launch of a space shuttle; the first rocket lifts it somewhat from the ground, the next one puts it in the atmosphere then the boosters come in and propel it into the stratosphere and the empty space.

Theoretical and practical questions and management of a treatment.

I must admit that I hesitated for some time before starting offering this system to my patients.

I assumed that:

- the first potency (3C or 5C) would do very little

- the higher we go, the more time we would need between potencies, more time/space to fill

- there would be a precise time to give the next potency, not too early that would interfere but not too late when the action would have started to dissipate (I was still full of the image of the shuttle falling back if the boosters do not ignite at the proper time)

I had some anxieties:

- would there be horrible aggravations?

- would there be intense provings?

- would there be permanent grafting?

- what would happen if the remedy is not correct?

The patients.

All patients were informed that this was an experimental methodology, but that the remedy was decided upon according to the usual methods of repertorisation and selection through Materia Medica reading.

The prices were quoted and they agreed on the expenses. Email or phone contact was to be made with me after each dose, describing what was happening and not taking the next dose without consulting me. They all gave verbal consent to use their progress for this work, although I will not describe the full cases.

Each dose was provided by the Simillimum pharmacy in Wellington as an individual powder. Each powder was to be either dissolved in a teaspoon of water and taken on a clean mouth or dissolved in a 250 mls glass of water and repeated aliquots taken as indicated.

The test of reality.

First and foremost, I have again to repeat that finding the right remedy is the most important part of the treatment; without it, no matter how you administer it, if it is not the correct one, it will not work. We all know that but it is better to reaffirm it clearly.

Statistics.

As of July 2008, 32 patients were included totalizing 45 prescriptions and 28 different remedies; 3 patients disappeared and could not be contacted, 6 patients just started the treatment and about half of the remaining patients are still currently under treatment to fine-tune the results.

Remedies.

Amethyst 1, Arnica 2, Argentum Nitricum 1, Arsenicum Album 2, Aurum Arsenicosum 1, Aurum Muriaticum Natronatum 2, Bromium 1, Calcarea Arsenicosa 1, Calcarea Phosphorica 4, Calcarea Silicata 1, Causticum 1, Coriander 1, Ignatia 1, Lac Humanum 2, Lachesis 1, Lycopodium 1, Natrum Muriaticum 3, Natrum Silicata 1, Phosphoric Acid 1, Phosphorus 1, Platina 1, Pulsatilla 3, Sanguinaria 1, Sepia 3, Silica 3, Stramonium 2, Tarentula Hispanica 2, Thuja 1.

Safety.

No patient experienced any proving of any remedy, yet the number of patients is too small to have any statistical significance.

There were few aggravations and not serious ones, of the same kind we can expect from any other method of prescription, dry dose, liquid dose or LM/Q. Here are the major ones, with their presenting complaint:

- T.D. multiple allergies and skin problems. Coriander aggravated with mucosal inflammation, puffiness of the face and some diarrhoea, nothing dramatic; this was a detoxification reaction, did not lead to a cure, but the patient said the allergies improved greatly.

- T.H. headaches, vomiting, diarrhoea, chronic and recurrent with tiredness all the time. Phosphoric Acid, the 8C was followed with a large amount of phlegm, a weird, unusual headache, then it settled and there was no more aggravation on the following potencies; this case is still in progress.

- A.P. abandonment issues with loads of fears. After taking Stramonium 5C, RIF pain started that was eventually diagnosed as an ovarian cyst and endometriosis; not sure whether the remedy was a triggering factor in this case.

What would happen if the wrong, incorrect, not simillimum remedy is taken?

- T.D. Coriander 3C to 89C was a “focal remedy”, not a simillimum, it did what it had to do and nothing else.

- O.P. benign prostatic hypertrophy (BPH), received Thuja 5C to 144C; the patient did not describe any change although there might be a slight diminution of the volume of the prostate (PR, subjective); nothing else happened despite the very high calculated potency.

- K.W. dysmenorrhea, polymenorrhea, migraines and eczema, received Sepia, Silica, Calcarea Silicata and Calcarea Phosphorica all in 5C to 55C; all but the last one were partial, layer remedies that opened the way for the next one (my interpretation), with no side effects.

What would happen if the doses were taken too close to each other? Remember the hypothesis that each dose needs to develop it’s whole action before giving the next one, the shuttle analogy.

- J.S. migraines for 11 years, complicated by the pill and Provera injections. She received Sepia 5C to 55C and decided to take one powder every day over 6 days; results: no more migraines at all except for 3 food-induced ones (finished with Carcinosin). Even when not waiting for the full action of each dose, the final result is there……..mind you, you could say that one single dose of a high potency would have done the same….

- G.O. infertility, side effects of the pill and Provera, heavy periods, ovulation aggravates; received Phosphorus 5C to 89C and decide to take one dose at regular interval of 4-5 days: periods became normal, an old rash reappeared we are waiting to see what will happen with next ovulation.

After all, we might not need to be too strict about the question of timing; what happened then when the doses were taken too far apart? Quite a few patients emailed me “Ooops, I forgot to take the next dose, should I take it now?” and then resumed treatment, some of them to forget again, and nothing happened even though I thought they would “fall back” or revert to previous symptoms; apparently, with that system, you can “remain in orbit” at the level of the last dose taken for some time. If symptoms recur at the end of a series, you might need to continue with a high LM (D.E. Amethyst 5C to 89C, was OK while on the remedy, recurrence after the 89C is now on a LM7) or more probably you need to prescribe another remedy (I.E. skin and behavioural problems, Stramonium 5C to 55C, OK while on it, recurred 2 weeks after the 55C, Tarentula picture appeared clearly).

Speed of action.

- J.S. Sepia 5C to 55C, 6 days to cure

- P.S. ulcerative colitis, Pulsatilla 5C to 55C, days are in brackets: 5C (1) 8C (3) 13C (3) 21C (5) 34C (7) 55C: 19 days to cure

- V.R. broken family, molested, emotional blackmail, forced marriage. Natrum Muriaticum 5C to 89C, finished the series in 50 days with the removal of a lifetime of emotions and psychological trauma (more about her later).

- I.E. and W.E. both are children with behavioural problems, hyperactivity, jealousy and more; the mothers reported their amazement at the speed of change and the increased depth of change with each dose. I.E. went through the Stramonium 5C to 55C in 15 days which then exposed the layer of Tarentula Hispanica; W.E. needed 40 days for Calcarea Phosphorica 5C to 55C to cure.

- S.B. headache, hay fever, “sore gut” received Silica 3C to 55C and achieved cure in 2 weeks.

- J.H. main complaint of a sour smell from the body; other remedies took care of other complaints but this one remained along with a very tense and stressful personality; received Natrum Muriaticum 3C to 55C; within 2 months not a single symptom remained, smell completely gone.

When the remedy is correct the speed of action is remarkable, there is no need to wait for months especially in deep mental/emotional situations; if by the end of the series there has been no result, the remedy was obviously wrong…but nothing happened and not too much time was wasted.

When I write “cure” at this stage of the development of the technique, it means that there were no more complaints whatsoever, no recurrences, no need for further treatment for the time being, less than a year at most and a few months in general.

Depth of action.

At the Physical level the treatments removed the effects of physical events many years back and are a clear indication for NBWS situations where the past has to be cleared before treating the present:

- P.S. tinnitus and loss of hearing with a very heavy emotional background of anger, betrayal, abuse, very sensitive and multiple allopathic treatments; after a series of different remedies with mixed results, he finally acknowledges an exposure to noises (firearms) since early childhood, then in the industry and music without wearing any protection, sound trauma; treatment with Arnica 3C to 89C resulted in the disappearance of noise intolerance (which was very serious) and the next remedies could work = removal of obstacles to cure.

- J.P. breast cyst of sudden appearance, very painful. Bromium 5C to 55C removed the pain and the sensitivity, slightly shrunk the cyst before it was eventually aspirated; could it have worked better given time?

- M.W. generalized breast cancer; as part of a full treatment, received Lac Humanum 3C to 89C; she described only a few dreams and old memories emerging, but in my opinion, this has opened the way and allowed the rest of the treatment to work by removing the deep-rooted origin of her cancer (see Geerd Hamer, New German Medicine theory); her tumour and the metastases are disappearing; a short course of chemotherapy has been added at the oncologist’s insistence, is well tolerated and is synergistic with the natural treatment.

- J.H. see above, complaint of sour smell of the body, completely gone along with the emotional problems.

At the emotional level the results are even more apparent:

- V.R. broken family, molested, emotional blackmail, forced marriage and more; prescribed Natrum Muriaticum 5C to 89C: at 5C, reappearance of old memories; at 13C, urge to cry, old memories but a feeling of healing; at 21C reappearance of a very old backache; then a sort of regression therapy started: at 34C went back to teenager’s emotions and memories; at 55C back to 10 -13 years old; at 89C back to 2 – 8 years old; all this with “hurt and soul soreness” (her words) but a sense of “purging the emotions”; her actual memory has now increased, her body feels lighter and she has been able to loose weight. Isn’t that the Law of Hering in all its splendour?

- P.S. tinnitus and loss of hearing; the Arnica we spoke about earlier opened the way to Causticum 3C to 89C that brought a flood of emotions and presented me with a “raw” patient who received Aurum Arsenicosum; 1 teaspoon of the 5C in 250 mls of water had him regress to the age of 18, with flashbacks, anger, morbid impulses, etc,….who said low potencies cannot act deep or on the mind? Just strip all the other layers first…

- K.P. breathing problems, claustrophobia, sense of inadequacy, low elf esteem; received Aurum Muriaticum Natronatum 5C to 55C; after the 8C dose he reported having become “neutral”, the depression lifted but he is not yet happy…case in progress.

Increased efficiency as “case openers” or “obstacle to cure removers”.

- P.S. again: the Arnica paved the way to the Causticum that stripped every obstacle to the deepest remedy Aurum Arsenicosum, as demonstrated by his reaction to 1 teaspoon of diluted 5C

- M.W. the generalised breast cancer patient: Lac Humanum opened the way for the rest of the treatment to work flawlessly as it removed the root of the disease.

- A.L. breast cancer treated with lumpectomy and radiotherapy; is asking for prevention of recurrences, is emotionally down and pessimistic and has a few physical symptoms; history of early promiscuity, rebellion, feels unheard and unseen, alone, abandoned; familial history of depression and mental illness. Lac Humanum 5C to 55C and everything is gone, she has become the clown at work; all the emotions of the past have been dealt with allowing her to heal fully.

Use with the so-called constitutional remedies.

There is no theoretical reason not to use this series when dealing with constitution, whatever that term means to each practitioner. The following patients received the remedy that was most appropriate for their actual situation and was at the same time deemed to be their constitutional, with the exception of the first one, where the remedy was prescribed without taking the clinical status into account. – I.V. suffers from a very complex endocrine problem; most of the treatment was “running after the symptoms” over the last few years, without getting to the bottom of the issue; we decided together to look at stabilising and rebalancing her constitution so that the picture becomes clearer and hopefully a cure can be achieved with further treatment. Platina 5C to 89C was prescribed and taken diluted in water (250 mls) because of her medical condition; liquid doses in teaspoons were repeated as needed and during that time there was less muscular pain, the breathing is better, the mind is quieter, there is a diminution of buzzing in the ears, of burning sensation (GERD) and of fears and anxiety as well as helping to keep recurrent infections under control or make them easier to treat. Although this amelioration is maintained, the physical, endocrine, pathology has not been touched and is clearly a one sided disease, but it has made the whole picture clearer and less confused and has allowed the selection of a little known remedy that seems now very well indicated…results are pending.

- J.S. migraines and the pill, Sepia 5C to 55C, cured

- P.S. ulcerative colitis, Pulsatilla 5C to 55C, cured

- S.B. headaches, hay fever, Silica 3C to 55C, cured

I need to write again that “cured” must be completed by “until now” as the time frame is at best one year, and often less.

Administration of the remedies.

My way with powders is according to the Organon 4.5: not a strictly dry dose as in the Organon 4, not in a glass of water and repeated doses as in the Organon 5, but dissolved in a teaspoon of water as a single dose. For sensitive patients in general when I do not use LMs, and specifically with this series, I followed the Organon 5, dissolve in a glass of water and repeated doses as needed with succussions.

- I.V. Platina; the first teaspoon of 5C was unremarkable but the second one had an immediate effect lasting for a few days; when it had to be repeated regularly at 24 hours interval, moved to 8C that had an immediate effect and was repeated until needed more frequently; 13C and 21C followed the same pattern; 34C was used every third day until it stopped working; 55C just maintained the situation and we are now at 89C taken when needed to keep the clinical picture stable or help bring it back to stability.

- P.S. Aurum Arsenicosum was prescribed when the patient felt he had been stripped of all layers of defence (see earlier presentation); the 5C powder was given in 250 mls of water, one teaspoon; it brought intense flashbacks, anger, violence and regression to 18 years old, with an aggravation of the tinnitus and hearing problem; against my advice, the patient repeated the dose a few days later as he was worried about his hearing: the memories and surges of emotions were even more intense, but, fortunately, the hearing came back (although not totally) and the tinnitus diminished; the patient wrote “I have a renewed respect for your powder, I could not imagine that they could bring back such intense feelings that I managed to bury over the years”.

Water potencies are recommended for sensitive patients who would otherwise be using LM potencies, but are ready to try to go faster and have enough energy and courage to sustain possible aggravations. Better be on the safe side, as I wonder if P.S. could have gone onto a destructive rampage in his office if I had given him a single full dose….gladly, I will never know.

Provisional conclusions.

It works well.

It works fast.

It works deep.

It is not as “aggressive” as I thought it could be despite the speed and depth: proper timing is still needed in my opinion for optimal action but does not seem to be too big a problem; the Simillimum stays in “orbit” and there is no falling back; if it is a Simile or “goodenoughicum”, it will fall back but then we let it do its full job and move on to the Simillimum.

It can be used as per Organon 4, dry dose (untested)

It can be used as per Organon 4.5, in one teaspoon of water (well tested)

It can be used as per Organon 5, in one (or more) glass of water, giving more adaptability and plasticity to dosing, if need be, being still faster than LM potencies

It can be used for presenting complaints, for constitution, for the removal of past diseases, obstacles to cures, NBWS situations.

Advantages.

- no racking the mind about which potency to start with

- all potencies are purely Hahnemanian, we know exactly what we give

- fast, deep and safe

Disadvantages.

- cost for the time being, not all remedies being available and have to be made on demand

- very close monitoring in theory, although it does not seem to be more demanding or necessary than what we would do ordinarily when using LM potencies

- still better be careful with sensitive patients or weak ones, rather stick to LMs when in doubt but time and experience might show that this is not true Just imagine what we could do in emergency situations by using this series within a few hours with trauma, head injuries or epidemics like Ebola…the sky is the limit, dream on.

Nomenclature.

I would like to suggest the following shorthand when using this method: if we take for example the remedy Silica, we would write Silica 5-89FiCHs meaning the remedy Silica from 5C up to 89C (without the need to write the intermediate potencies) in a Fibonacci Centesimal Hahnemanian series.

For more precision we could add D for a dry dose, W for a dose in a teaspoon of water, L for liquid dose in a glass of water, xS for the number of succussion used for the preparation of the remedy so that we can compare the action of same potencies of the same remedy prepared with a different amount of succussions.

If you do not like patronyms in your prescriptions and do no want to use the name of Fibonacci, Centesimal Hahnemanian in Progressive Series could be used instead so you would write Silica 5-89CHiPS.

And YES, I am aware of the impending joke that I am treating my patients with FiCHs and CHiPS…

A final word.

Just try it out. Maybe this will be the next step forward since the LM/Q potencies. Maybe this will be a wet petard, a nice idea but not working out for most of the practitioners. Or maybe you can improve it. Only experience will tell.

Let me know.

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Dr. J. Rozencwajg, NMD.

New Plymouth.

New Zealand.

Copyright Dr. J. Rozencwajg, NMD.