PHYSICO MATHEMATICAL INTERPRETATION
OF THE PHARMACOLOGICAL EFFECT OF HIGH DILUTIONS : REMANENT WAVE, CONTONIAN APPEARANCE (conton) 
Henri BERLIOCCHI, Rolland CONTE 7° Symposium du GIRI, Montpellier 2021 Novembre 1993 
For the interpretation of the
hormesis curves we are introducing a new statistics:
the contonian statistics.
The underlying mathematical theory of this statistic is the theory of Ethers. This theory is not probabilistic but introduces a problematic of indecidability. The physical frame concerned is related to the quantum theory of fields, the central problem of which lies in the construction of a field that is solved by using the theory of Ethers. 
From this approach, we have a
complete mathematical frame for the analysis of this remanent wave and for the
examination of the possible irradiations effects it can produce to the
surrounding remaining matter (for example the substrate of a homeopathic drug).
Of course, at this stage, it is only a model (we take into consideration only the "mass" character of the particle when other characters exist as well). However, a possibility to enjoin the experimental approach exists throughout contonian statistics and the conceptual frame in which the remanent wave is represented in the form of contons is therefore well founded. 
For the definition of the
contonian appearances (contons) the following method is used. From the remanent
wave, products called chronological are built and then "read" via the
help of a character (contonian appearance). By doing so, the contons are
obtained.
In practice, a conton is defined as an appearance of a dynamic system, general mathematical notion that summarizes the approach of any type of evolutionary system. When using this modeling, the principle consists in considering the space of the" states" of the system, that means all possible values of the parameters of the system, and in defining a dynamic system as a way to pass from one state to another one. More information on the general definition of the conton are given in the book : "Nouvelle Economie Théorique" (Conte and al., 1993) (1). 
We will now describe the
practical methods that allow to "read" a contonian phenomenon and, for
doing so, we will consider hormesis curves.
Let v be the parameter we will call Hahnemannian parameter whose usual units are CH or DH. We observe a quantitative character x(u) that can be very various (optical density, death rate of a batch of mice,...) and by using the method of the trapezes we calculate the integral that is expressed as follows: 
Int (v_{o}, v) x(u)du = L(v) 
This integral will be the
contonian lagrangian, so called because its typology is the same as the optic path in physics.
The aspect of the curves L(v) will be linear. We can calculate the contonian frequency H, since the conton is defined by the relation: 
exp(i H Int (v_{o}, v) x(u)du 
and represents the point of the circle that varies as a function of the Hahnemannian parameter according to a circular movement: 
Teta= H Int (v_{o}, v) x(u)du 
Teta being the polar angle of
a point of value equal to the v
parameters.
The Euler’s relation allowing the expression of an exponential in the complex plane is illustrated in Figure 3. The second step of the practical construction of a conton consists in adjusting the constant H in order to get, in the complex plane, a continuous trajectory. The H value so determined is called the contonian frequency. A dedicated software, used for the analysis of the experimental results and that will do the operations described in the above methodology, is under development (*). By using this methodology and/or this software it is then possible to verify the action of the infinitesimal dilutions. 

To illustrate the results gotten with this new statistics, we chose contons deriving from other fields such as rainfall, geodesy, economy, physics in nuclear magnetic resonance and infrared absorption. 
Figure 4 presents the
sum of the rainfall data of 66 ONM French stations
(ONM = National Meteorological Office ) as well as the related lagrangian values. We draw the reader's attention to the almost linear aspect of this lagrangian, aspect that is characteristic of the contonian processes. 

(*) Software: Analyse Activité Pharmacologique Dilutions Infinitésimales  
In spite of this, we
definitively observe the linear shape of the contonian lagrangian as shown in
Figure
7.

We can imagine some
interactions between the remanent wave and the variation of the phase in a
given point of the earth. In the chosen examples the contons were temporal, that means that the time was taken as reference of the phenomenon. In the following examples we will take the hahnemanian parameter (CH or DH) as basis of the conton. The setting in evidence of the remanent wave (Figure 11) appears very clearly on Nuclear Magnetic Resonance (NMR) measures. The example that illustrates the contonian behavior of the relaxation time T2 according to the hahnemanian parameter is relative to the nitric acid (Lasne, 1993) (2). 

This Figure shows the
characteristic aspect of the NMR signals that fluctuate according to the
Hahnemanian parameter that varies from 1 to 60 CH. The integral of this signal
is remarkably linear with a coefficient of determination R^{2}=
0,999974.
The lagrangian of the nitric acid is higher than the one of the water (non succussed). The respective contonian frequencies are: H_{1} = 8,384 * 10^{5} for the nitric acid and H_{2} = 1,0667*10^{4} for the non succussed water. The ratio of the contonian frequencies gives the coupling between the succussed nitric acid and the water. This ratio is of 0,786. 
The gap between these two
values of H is about 2% and within the margin of error for this type of
measures.
This confirms the interpretation by the remanent wave of the activity of the high dilutions. Indeed, the theory foresees that the parameter "contonian frequency" is a data that only depends on the substance put in solution, here the nitric acid, so long as the same source of water is used for dilutions in order to eliminate the effects due to the residual impurities of this water or that one makes sure, for every source of water, that the parameter measured for the first source of water remains unchanged. The observed phenomenon is really due to the remanent wave, that is to say to the radiation of a " white hole" left by the disappearance of the matter in solution. This phenomenon is located at the level of the nucleons of the solution as shown by Y. Lasne who measured the T2 parameters of the ion H^{+} become " super proton" by the action of the remanent wave and of the ion O^{17}H^{ } also modified by the remanent wave. A phenomenon of remanence exists effectively when matter disappears, that means a certain form of "memory", but this concerns the memory of the emptiness, if one must take a vivid expression, and we are going to see that this same phenomenon of remanence is observed for nonaqueous solutions. We will simply point out that the theory due to J. Benveniste and his team, theory that the polemic translated by the setting in evidence of the" water memory”, doesn't permit to interpret the remanence correctly. According to this theory, the "memory", would be due to a modification of the water dipole by the substance in solution. This theory is based on the physicomathematical calculation developed by Del Guidice (Del Guidice and al, 1988)(3) that supposes that at least a molecule of the initial substance still remains, what is not the case when we passe the 12 CH. Besides, this physicomathematical interpretation has the inconvenience to make appear the same type of field before and after the succussion, what is not verified by the experiences achieved by Y. Lasne in NMR. 
This phenomenon of remanence
of the nonaqueous solutions has also been observed by Samuel Hahnemann who
showed that, if gold or silver in their natural state have no action on man,
their infinitesimal dilutions in another solid invest them with other
properties: "... from the grinding continued during one hour of a gold
grain with hundred grains of lactose in powder, results a preparation that
already has a lot of medicinal virtues.
If one continues to act until every grain of the ultimate preparation contains a quadrillionth (10^{24}) of gold grain, then we will have a medicine, in which the medicinal virtue of gold will be so developed that it will be sufficient to take one grain, to store it in a small bottle and to give it for breathing during some instants to a melancholic, to whom the disgust of life is pushed up to the point to lead him to the suicide, so that, one hour after, this poor wretch is delivered of its bad demon and recovers the charm to life. (4). 
The last illustration of the
contonian behavior is relative to an older publication from Heintz (Heintz,
1941)
(5) on the infrared absorption by solutions diluted n tenfold
and succussed.
In this article, we have selected the solutions studied with the same wavelength of 7,1 microns and having the same initial concentration of D1 = 0,1. The selected products are sodium nitrate, hydrazine and acetic acid. 

Figure 13 shows the variations of the raw signal measured by Heintz according to the Hahnemanian parameter expressed in D H. The graph obtained shows a certain analogy between the signals of the three compounds studied. One notes that, qualitatively, when the non succussed water corresponds to the lowest value of the signal, intensities are increasing from hydrazine to sodium nitrate via acetic acid. 
Starting from these raw data, that were not very usable, contonian statistics allows to put in evidence the fundamental parameter that drives the phenomenon. 
Their statistics
is interpreted in the Theory of Ethers and is not a probabilistic statistics as
already said while beginning this
presentation.
A typical example of random phenomena, the white noise or Brownian movement, is not contonian. A contonian process has an"informational" content that the white noise, that " forgets" its past, doesn't have, and its" memory" has the same nature that the one of light (electromagnetic waves): the light from the stars keeps, after millions, or even billions light years away, the information of the matter of the periphery of the star. 
The illustration of the
contonian behavior of the high dilutions effect has been tackled by M.
Bastide and col. on a model of Candida
albicans pretreated with the 5FC at different CH.
Other experimentations are in progress in the toxicological field that should allow us to generalize this mathematical interpretation to other contonian characters such as mortality for example. The illustration of the contonian behavior of the high dilutions effect brings us to recall two major ideas of Hahnemann. In page 275 of the book already quoted, Hahnemann expresses as follows his 2nd natural law "A stronger dynamic disease extincts, in a lasting manner, another less strong dynamic disease in the living organism, when the first looks like the second as for the species." 
These are in fact the white
holes that, while combining with the
black holes (the" toxic") lead to a resultant specter that goes from
the disappearance of the black holes (Pi phase displacement) to super
black holes (nil phase displacement )
while going through the formation of holes having all nuances of gray.
It is this resultant that will interact with the organism and will produce the observed effects. Let's recall that, in astronomy, one calls "black hole" a region of the spacetime having an infinite density of matter. The region where are localized the nucleons behaving locally in this way, we used this terminology. We also recall that, for Hahnemann "the medicinal substances are not dead matters; their real nature is dynamic: it is a pure strength". 
This mechanism, that has
been illustrated by Yves Lasne by the interaction between a hahnemanian
dilution and peroxydases, has to be brough closer to another idea already
expressed in these terms by Hahnemann in page 276 of the quoted work:"the organism, as a living unit,
cannot admit two similar dynamic diseases at the same time without the weakest
being oblige to give way to the
strongest.
However, since it tends to be affected more strongly by a medicine than by an analogous illness, this one must necessarily leave it, and he is then cured". In fact, it is the "Nature" and no the organism that cannot admit the coexistence of two " similar dynamic disease". There is an interaction between the phases of the white and black holes. When these phases are opposed, their interaction leads to a nil resultant and the patient is cured. 
Acknowledgments: 
We are pleased to thank the
personalities who helped us in this survey and more particularly
Mr. P. Dorfman of the Dolisos Laboratory, Mrs. Professor Madeleine Bastide, Mr. Professor J. Cambar and Mr. Y. Lasne for their attitude and the enthusiasm they testified to undertake some experiences or "to search" in their laboratory notebooks in order to extract some experimental results. 
Bibliography  
1. 
CONTE (R.R), BERLIOCCHI (H), ANDRAS (H.G.) :
Nouvelle Economie Théorique.
Editions Economica, Paris, 1993 
2.  LASNE (Y.) : L'homéopathie de/par l'information De Natura Rerum, 1993,7,pp 95168 
3.  DEL GUIDICE (E), PREPARATA (G.), VITTELLO (G.) : Water as a free electric dipole laser. Phy. Rev. lett., 1988, 61, pp 10851088. 
4. 
HAHNEMANN (S.) : Etude de Médecine Homéopathique, première série.
Editions J.B Baillière, Paris, 1855, p.579. 
5.  HEINTZ (E.) : Physikalische Wirkungen Hochwerdünnter potenzierter Substanzen Die Naturwissenschaften, 1941, 29, pp.713725. 