“Memory of Water” Experiments Explained with No Role Assigned to Water:
Pattern Expectation after Classical Conditioning of the Experimenter
Francis Beauvais 1, *
1 Scientific and Medical Writing, 91 Grande Rue, 92310 Sèvres, France
* Correspondence: firstname.lastname@example.org; Tel.: +33 6 68 36 58 36
The “memory of water” experiments suggested the existence of molecular-like effects without
molecules. Although no convincing evidence of modifications of water – specific of biologically-
active molecules – has been reported up to now, consistent changes of biological systems were
nevertheless recorded. We propose an alternate explanation based on classical conditioning of the
Using a probabilistic model, we describe not only the biological system, but also the experimenter
engaged in an elementary dose-response experiment. We assume that during conventional
experiments involving genuine biologically-active molecules, the experimenter is involuntarily
conditioned to expect a pattern, namely a relationship between descriptions (or “labels”) of
experimental conditions and corresponding biological system states.
The model predicts that the conditioned experimenter could continue to record the learned pattern
even in the absence of the initial cause, namely the biologically-active molecules. The phenomenon
is self-sustained because the observation of the expected pattern reinforces the initial conditioning.
A necessary requirement is the use of a system submitted to random fluctuations with
autocorrelated successive states (no forced return to the initial position). The relationship recorded
by the conditioned experimenter is, however, not causal in this model because blind experiments
with an “outside” supervisor lead to a loss of correlations (i.e., system states randomly associated
In conclusion, this psychophysical model allows explaining the results of “memory of water”
experiments without referring to water or another local cause. It could be extended to other
scientific fields in biology, medicine and psychology when suspecting an experimenter effect.
Keywords: Experimenter effect; “Memory of water”; Classical conditioning.
The controversy over the “memory of water” that burst in 1988 continues to maintain in the
shadow the whole story of Benveniste’s experiments that extended over 20 years from 1984 to
2004.1 Admittedly these claims were anything but insignificant: the experiments presented in Nature
suggested the existence of molecular-like effects in the absence of molecules.2 The authors of this
article stated that dilutions of biologically-active molecules beyond the limit defined by the
Avogadro number had nevertheless a biological effect.
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 February 2020 doi:10.20944/preprints201810.0060.v2
© 2020 by the author(s). Distributed under a Creative Commons CC BY license.
The violence of the controversy had most probably its roots in the “two centuries of observation
and rationalization” that these results were supposed to reconsider.3 Because the idea that a
“structuration” of water could mimic the effects of biologically-active molecules was considered
impossible, the inevitable conclusion was that the experiments were flawed. As a consequence,
there was no place for an alternate theoretical framework that would consider these results, without
involving water and its alleged “memory”. The fact that this study could support homeopathy, also
highly controversial, was another reason for this strong opposition. It is out of the scope of this
article to describe this controversy; details on the debate and disputed experiments can be found
elsewhere.1, 4, 5
According to the judgement of many scientists, there was nothing to explain in these experiments
as there was no scientific facts, only poor science. Therefore, the report of Nature’s investigation in
Benveniste’s laboratory has been generally considered to put the last word to the public debate.6, 7
Nevertheless, some authors reported modifications of physical parameters of highly-diluted
solutions or proposed different theoretical frameworks.8-13 How the specificity of the initial
molecule could be conveyed through the successive dilutions remained however unanswered in
these various theoretical frameworks. Moreover, correlations of changes of water parameters and
corresponding changes of a biological model have not been described up to now.
My purpose in this introduction is not to fuel this debate again but simply to structure the
arguments from both sides to explain why Benveniste failed to convince his peers. Indeed, after
the basophil model described in 1988 in Nature’s article, other experimental models, mainly isolated
rodent heart and plasma coagulation, were developed by Benveniste’s team. Experimental data
accumulated seemingly in favor of a role of water for storing information on molecules in
solution.14-20 During this period, Benveniste made a step further by stating that molecular
information could be “imprinted” in water through electromagnetic fields (1992) as in a magnetic
tape 15 and could be even digitized (1995).20 At this occasion, he coined the expression “digital
In Table 1, arguments from Benveniste’s experiments in favor of or against “memory of water”
are summarized. The arguments in favor of “memory of water” are mainly the observation of
“activated” states of the biological systems associated to test samples “imprinted” with different
methods and the apparent specificity of the biological effects. The arguments against “memory of
water” are mostly difficulties to reproduce the results by other teams and the absence of a
compelling theoretical framework. There is also another reason – less known – that prevented
Benveniste to go further in his quest of the perfect experiment that would be totally convincing.
This reason was a stumbling block that was more particularly highlighted during public
demonstrations where colleagues from other teams were invited to supervise proof-of-concept
experiments. The role of these outside supervisors was to produce “inactive” and “active” test
samples (water samples with high dilutions or “imprinted” water; computer files for digital biology)
and to mask them under a code number. After the outside supervisors had left, the coded samples
were tested by Benveniste’s team. When all measurements were completed, the results were sent
to the supervisors who assessed the rate of success by comparing for each run the measured system
state and the corresponding “label” (unbeknown of the experimenter who did the test). These
proof-of-concept experiments systematically failed in the sense that “activated” states were always
randomly distributed between test samples with “inactive” and “active” labels.1, 22, 23
To explain these troublesome failures, Benveniste proposed many post hoc explanations (e.g., water
contaminations, interferences with external electromagnetic fields, “jumps of activity” from one
test sample to another, human errors for sample allocation).1 Despite further improvements in
devices and procedures to prevent these disturbances, the weirdness persisted. The important
point, however, is that these possible external disturbances did not account for “successful” results
with open-label test samples even in blind conditions with an “inside” supervisor or an automatic
device (more precise definitions of “inside” and “outside” supervisors are given later).
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In this article, I propose to simultaneously take into consideration Benveniste’s experiments and
to abandon the “memory of water” hypothesis. A theoretical framework is constructed where these
experiments are related to an experimenter effect, which is the consequence of a previous classical
conditioning of the experimenter. In this setting, all test samples are nothing more than controls
(or placebos) and the different procedures to “imprint” water samples are nothing more than
rituals. The proposed model describes all features of Benveniste’s experiments: emergence of an
“activated state” of a biological system without local cause, correlations between “labels” and
system states, and mismatches of outcomes in blind experiments with an outside supervisor. No
role is attributed to water or another local cause but now the attention shifts to the experimenter.
The proposed experimenter effect is original and could have consequences beyond the “memory
of water” controversy. Therefore, considering Benveniste’s experiments only as an example of
specious science misses the point and prevents from seeing what these experiments could teach us.
The price that the proponents of “memory of water” have to pay is abandoning the initial
hypothesis (i.e., a molecular-like effect without molecules). For the opponents, the price to pay is
to accept that these weird experiments – admittedly misinterpreted by their authors – had
nevertheless a scientific interest.
Table 1. The arguments for and against molecular-like effects without molecules in Benveniste’s
• Emergence of an “activated” state of biological
models mimicking the effect of biologically-active
• Emergence of a relationship between
experimental conditions and states of system
• Specificity of the molecular-like effects b
• Consistency of the results with different
experimenters, biological systems and procedures
• Successful tests in blind experiments with
local/inside supervisor or automated devices. c
• Not compatible with current scientific knowledge
on water (e.g., very short half-lives of chemical
bonds between water molecules)
• Not compatible with current scientific knowledge
on biochemical interactions (e.g., law of mass
• No compelling theoretical framework
• Difficulties to reproduce the results by other
• Proximity with homeopathy
• Loss of correlations in blind experiments with an
outside supervisor. c
a In “memory of water” experiments, water samples are supposed to induce a biological activity although
the biologically-active molecules have been removed via extensive serial dilutions (“high dilutions”) or
after water samples have been “imprinted” through electromagnetic fields using different devices
(“electronic transmission” or “digital biology”).
b Water samples supposed to have been “imprinted” apparently retained the specificity exhibited by the
original molecules (“imprints” of biologically-inactive molecules were inactive even if their structure was
close to biologically-active molecules).
c See definitions of “inside” or “outside” supervisors in section “Consequences of blind experiments on
2. Classical conditioning during ordinary dose-response experiments
Classical conditioning (or Pavlovian conditioning) is a well-known associative learning process.24
We briefly describe classical conditioning with a typical example before making a parallel with an
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 February 2020 doi:10.20944/preprints201810.0060.v2
experimenter who handles an experimental system. Classical conditioning supposes first an
“unconditioned stimulus” that produces an “unconditioned response” in an organism. In the well-
known example of Pavlov’s dog, smelling or tasting food (unconditioned stimulus) induces
salivation (unconditioned response). The purpose of the learning is to pair a “neutral stimulus” to
the unconditioned stimulus. In this case, a bell (neutral stimulus) systematically rings just before
food (unconditioned stimulus) is presented to the dog. Thus, the dog learns to associate the ring
of the bell and the coming of food. During this learning process, the former neutral stimulus
becomes a “conditioned stimulus”. Indeed, salivation (conditioned response) is now induced when
the bell rings. To be complete, we must add that no food is expected (no salivation) by the dog
when the bell does not ring. Thus, a relationship is established between the conditioned stimulus
(ring vs. no ring) and the conditioned response (salivation vs. no salivation).
The purpose of most in vitro or physiology experiments is to study the effect of a biologically-active
compound on a biological system. A dose-response is performed, meaning that the effect of the
compound at different concentrations (0, x, 2x, 3x, etc.) is evaluated. For simplifying, we suppose
that only one “active” condition versus one “inactive” condition (or control) is assessed during the
experiments. We suppose also that the biological system has only two states: “resting” state (not
different from background noise) and “activated” state (different from background noise).
In such experiments, one usually forgets that the biologically-active compound has not only a direct
effect on the biological system but also an indirect effect on another “biological system”, namely
the experimenter. Even with automated systems, there is always an experimenter who prepares the
experiment, records the outcomes and interprets them. Therefore, it is easy to take a step further
and to consider that during the repetitions of experiments, the experimenter unintentionally learns
to combine the experimental conditions with the states of the biological system. Thus, the
“inactive” condition (control) is associated to the “resting” state and the “active” condition
(biologically-active molecules at pharmacological concentrations) is associated to the “activated”
After this classical conditioning process, the cognitive structures of the experimenter are changed.
The “labels” of the experimental conditions are associated to the respective system states: “inactive”
label is associated to “resting” state and “active” label is associated to “activated” state.
In the model that we construct, we posit that all samples to be tested are identical and are all
biologically inactive in the sense that they do not induce a local causal biological effect. Even if the
test samples are subjectively named “inactive” or “active” by the experimenter, it would be
impossible to distinguish one test sample from another one on physical bases; only their
identification with “labels” – in other words their meaning for the experimenter – is different. “Labels”
are nothing more than a short description for the experimenter about the expected state of the
experimental system. In Figure 1, the “labels” have the nonspecific names L1 or L2 that do not
presuppose to which experimental condition (“inactive” or “active”) they are respectively
associated by the experimenter.
It is important to underline that a relationship (direct or reverse) has a higher degree of abstraction
than its components (“labels” and system states). A relationship is similar to a pattern (or a shape)
that is thought in its wholeness, not as the simple sum of its individual components. In other words,
after conditioning, the experimenter expects an “image” (a continuous entity), not “pixels” (discrete
As the primary purpose of this article is to propose an explanation of Benveniste’s experiments,
we must underscore that the members of Benveniste’s laboratory routinely performed “classical”
experiments with genuine molecules. Therefore, classical conditioning can be easily assumed in this
Figure 1. Expectation of patterns by the experimenter after classical conditioning. The two
“labels” (L1 vs. L2) and the two possible system states (“resting” vs. “activated”) define four
couples of outcomes (A). The “labels” have the nonspecific names L1 or L2 which do not
presuppose to which of the two experimental conditions (“inactive” or “active”) they are
respectively associated by the experimenter. After classical conditioning (i.e., Pavlovian
conditioning) with “conventional” experiments involving biologically-active molecules at
pharmacological concentrations, the two possible relationships expected by the experimenter are
named “direct” or “reverse” relationships with probabilities p and q, respectively (B). A
relationship has a higher degree of abstraction than its components and is similar to a pattern that
is thought in its wholeness, not as the simple sum of its individual components.
3. Consequences of the classical conditioning of the experimenter for future outcomes
In this section, we explore the probabilistic consequences of the classical conditioning of an
experimenter named F who records the state of the experimental system S (Figure 2). These
probabilistic consequences are described in three sequential steps:
Step 1: F-S taken as a whole. The state of the system S (“resting” or “activated” state) at the end of
the experiment is obviously a property of S. However, as previously said, F has been conditioned
and expects a pattern (direct/reverse relationship). The future outcome to be recorded by F is
therefore the combination of an abstract construct (pattern) and a physical variable (state of S).
This abstract construct is composed of “labels” which are arbitrarily chosen and do not correspond
to physical properties of test samples. As a consequence, the future outcome to be recorded by F
is neither an individual property of F nor an individual property of S but is a property of F and S
taken as a whole. It is important to underline that this future outcome is not the simple juxtaposition
of a first subevent that is a property of F and a second subevent that is a property of S. Indeed, F
and S constitute a new “entity” denoted F-S that cannot be dissociated.
Figure 2. Description of the experimental situation. An elementary dose-response experiment is
performed by an experimenter F who has been conditioned to expect a pattern. This pattern is the
relationship between the descriptions X, Y (“labels”) of different experimental conditions and the
corresponding system states (0, 1). An observer F’ records the outcomes and, at the end of the
experiment, F and F’ share their records.
Note that F’ does not need to be conditioned. Furthermore, F’ does not need to be human and can
be replaced by any recording device. In this case, F takes note of the outcome of the experiment
that has been recorded by F’ after the experiment is finished. The observer F’ is nothing more than
an instance of the environment that keeps track of the outcomes.
Step 2: The outcome does not preexist. As the future outcome to be recorded by F is a property of F-S
taken as a whole (not the simple addition of properties of F and S), it means that the outcome
(direct or reverse relationship) is created when F and S join together to form F-S (i.e., when F records
the state of S). In other words, the outcome does not preexist its record by F.
A probability can
nevertheless be attributed before the experiment to each possible future outcome (direct or reverse
relationship) to be recorded by F.
In classical physics, a property of an object (e.g., its mass) is already there before its measurement. In contrast, a
property of a quantum “object” does not preexist its measurement by a macroscopic apparatus (e.g., transmission or
reflection of a photon by a semi-transparent mirror). What preexists the measurement in this latter case is not the
outcome itself, but the propensity (or probabilistic disposition) of the quantum system to produce different outcomes
with defined probabilities. In the present model, the state of S preexists even in the absence of a measurement. In
contrast, the relationship (direct/reverse) expected by F is a concept – not a physical property – and therefore the
experimental outcome, which is an actualization of the potentialities, does not preexist the measurement of S by F.
The classical conditioning of the experimenter F induces modifications of the propensity of F-S to yield defined
Step 3: Independence of the future outcome. We have now to translate into mathematical terms an outcome
that does not preexist its record.
We introduce an observer named F’ who records the state of F (correlated to the state of S). We
describe the states of F, S and F’ from a point of view outside the laboratory (observer W). The
interest of this outside point of view will appear later.
The future outcome A to be recorded by F and the future outcome B to be recorded by F’ are
independent events. Indeed, suppose that the outcomes A and B are perfectly correlated. If F’ is the
first to record the outcome of the experiment (direct or reverse relationship), then the value of A
is fixed and preexists the interaction of F with S. Therefore, if we want to describe the outcome A
not preexisting its record by F, it must be independent from the outcome B.
By definition, the two events A and B are independent if their joint probability – i.e., the probability
to be observed together – is the product of their respective probabilities:
Prob (A B) = Prob (A) × Prob (B)
4. Probability of a direct relationship with a conditioned experimenter
The different combinations of the future independent outcomes A and B to be recorded by F and F’
from a point of view outside the laboratory (observer W) are described in Figure 3.
Figure 3. Description of the possible future independent outcomes to be recorded by F and F’.
The states of F, S and F’ are described from a point of view outside the laboratory. Each possible
event to be recorded by the participants is composed of a label (L1 or L2) and a state of S, either
“resting” (↓) or “activated” (↑). These future events are independent but only some of them are shared
by F and F’ (see Figure 4).
This experimental situation is reminiscent of “Wigner’s friend”, which is a thought experiment in theoretical quantum
physics proposed by the physicist E. Wigner. In this setting, Wigner (W) is outside the laboratory where his friend (F)
performs a measurement on a quantum system.
The probability for each observer to record a direct relationship is denoted p and the probability
to record a reverse relationship is denoted q (with p + q = 1). Based on the independence of the
future outcomes to be recorded by F and F’, Figure 4 can be built using Eq. 1. For a given
participant, the probability p is the sum of p2 (probability that both F and F’ record “direct”) and
pq (probability that this participant records “direct” and the other one records “reverse”).
Figure 4. Future outcomes to be recorded and shared records. The independence of the future
outcomes to be recorded by the observers F and F’ has probabilistic consequences that are depicted
in this figure. The left panel describes the probabilities of the possible future independent outcomes
(direct or reverse relationship) to be recorded by the observers F and F’ before the experiment. The
two events A and B are independent (see section “Consequences of the classical conditioning of the
experimenter for future outcomes”). The right panel describes the actual records shared by F and
F’. Example of records that are not shared: record of a “resting” state of S by F (direct relationship)
and record of an “activated” state of S by F’ (reverse relationship) for the same label L1.
After the experiment is completed, F and F’ share their records of all elementary outcomes
(association of the “label” of each test sample with the corresponding system state). Only the
records where F and F’ agree on the concordance of their records are shared.
with a probability equal to pq are not included in the list of the actual outcomes shared by F and F’
Note that F’ does not need to be human and can be any recording device. In this latter case, after
the experiment is finished, F records each elementary outcome (outcome A with probability p) and
the recording device F’ does the same for F-S (outcome B, independent from outcome A, with
probability p). Then F takes note of the concordance of all recorded outcomes A and B (i.e., A = B
for each association of a “label” and the corresponding system state). The observer F’ is nothing
more than an instance of the environment that keeps track of the outcomes.
Because the total probability of the outcomes shared by F and F’ must remain equal to one, a
renormalization is necessary for probability calculation. For this purpose, the probability of each
shared record is divided by the sum of the probabilities of all records possibly shared by F and F’
(Figure 4). The probability that F and F’ share a record of a direct relationship is:
The agreement of F and F’ on their records plays the same role as a conservative law. The “paradoxical” future events
with probability pq (e.g., F records a direct relationship and F’ records a reverse relationship) have a comparable
mathematical status as the dead and alive Schrödinger’s cat.
)( Prob qp p
We now write Eq. 2 to obtain only p as a variable by dividing both numerator and denominator by
p2 and by considering that q = 1 – p:
This equation can be generalized from 2 to N observers by supposing that the future outcomes to
be observed by the N observers are independent (i.e., at least N – 1 observers are conditioned) and
are shared by the N observers. In Eq. 2, the square exponents are replaced by N and we finally
This generalized equation allows calculating the special case N = 0, which is the experimental
situation in the absence of any observer:
Starting from this situation without observer, we introduce again the observers F and F’ in the
model by using Eq. 3 and by replacing p with p0 = 1/2. We obtain again Prob (direct) = 1/2.
At first sight, the introduction of an experimenter – conditioned or not – in the model has no
advantage over the classical approach. Indeed, considering that the outcome preexists to its record
(classical approach) or does not preexist (present model) leads to the same result; direct and reverse
relationship are evenly observed (only the “resting state” of S is observed). This is consistent with
common sense: two control situations (or two placebos) are both associated to the “resting state”,
regardless of the presence or not of an observer.
The advantage of the present model is seen in the next section after considering the fluctuations
inherent to any measurement with a macroscopic system.
5. Emergence of correlations between “labels” and system states
Any macroscopic system is associated with random fluctuations. We note εn (with | εn | << 1)
a small fluctuation of Prob (direct) at time tn.
We have seen that before the observation of the system, Prob (direct) = p0 = 1/2. At time t1, after
the first fluctuation ε1, the new value of Prob (direct) is p1 that is calculated by replacing p0 with p0 ε1
in Eq. 3. Note that a fluctuation of Prob (direct) different of zero means that the “activated” state
of S can be possibly recorded by F even though with a tiny probability.
For the next fluctuation, we are faced with two possibilities. Either the system comes back to its
previous position or its new position is the starting point for the next state. We consider these two
possibilities separately for the addition of random fluctuations in Eq. 3:
• In the first case where the system comes back to its initial position after each fluctuation, pn+1 is
calculated with pn = p0 = 1/2:
11n 2/1)( Prob ++ = n
(with p0 = 1/2)
• In the second case, each state n is the starting point of the state n+1. A mathematical sequence
is obtained where each pn is used for the calculation of pn+1:
(with p0 = 1/2)
The distinction between return to initial position and new position as a starting point for the next
state allows specifying systems that have different behaviors confronted with small random
fluctuations. Thus, in Eq. 6, no specific relationship is established between “labels” and system
states. Such systems can be qualified as “rigid” because small fluctuations do not move the system
state away from the initial position. For example, internal thermal agitation induces small vibrations
of a coin, but the inertia is sufficiently high that an immobile coin has practically no chance of
jumping from head to tail within a reasonable timeframe. Similarly, after tossing, the trajectory of
the coin can be considered as not influenced by internal thermal agitation. These systems that are
“set to zero” after each tiny fluctuation have no interest for the present issue. Nevertheless, they
allow underscoring that any experimental system submitted to random fluctuations is not
necessarily suitable to observe significant correlations between “labels” and system states.
In the second case described by Eq. 7, the experimental system may move away from its initial
position due to random fluctuations (no forced return). Each new state is dependent on the
previous one (autocorrelation). A classical example is a pollen grain on water surface. In this case,
the grain is sufficiently small and with sufficient degrees of freedom to move away from its initial
position because of the thermal agitation of water molecules. Biological systems are more complex
but some of them have sufficient degrees of freedom to move from a “resting” state to an
“activated” state after a series of random fluctuations (e.g., coronary dilatation of isolated rodent
heart in Benveniste’s experiments). Biological system must be understood in an extended sense;
thus, biochemical systems can also be suitable (e.g., in vitro coagulation with fibrinogen and
thrombin in Benveniste’s experiments).
The mathematical sequence described by Eq. 7 is computed in Figure 5. After a series of tiny
fluctuations, there is always a dramatic transition of Prob (direct) from 1/2 to 0 or 1, at random for
each run. This transition reveals an instability of the initial situation (p0 = 1/2) after the introduction
of fluctuations in the renormalized equation of Prob (direct). In both cases, Prob (direct) tends to
achieve stable positions equal to 0 or 1. As a consequence of the breaking of the initial symmetry,
a relationship (direct or reverse) emerges between “labels” and system states.
Figure 5. Computer calculation of the model. The mathematical sequence of Eq. 7 was calculated
and eight computer calculations are showed. Each probability fluctuation εn+1 during an elementary
time interval was randomly obtained in the interval from –0.5 × 10-15 to +0.5 × 10-15. Panel A
describes the probability of observing a direct relationship. There is a dramatic transition from 1/2
to 0 or 1 at random after a series of fluctuations due to the breaking of the initial symmetry. The tiny
random fluctuations reveal the instability of the mathematical sequence for calculating Prob (direct).
The consequence is the establishment of a relationship between “labels” (L1 vs. L2) and system states
(resting state vs. activated state). The probability to observe an “activated” state increases from ε to
1/2; indeed, each test with “active” label is associated to an “activated” state (Panel B). In contrast,
in the absence of conditioning, Prob (direct) is equal to 1/2 ± εn and there is no emergence of an
“activated state” for each test with “active” label (Panels A and B).
In a real experimental situation, before testing any sample (with “inactive” or “active” label), the
system is prepared in a “resting” state (control condition) that is implicitly associated to the
“inactive” label. In stable position #1, the label L1 is the “inactive” label and therefore the label
L2 is the “active” label; conversely, in stable position #2, the labels L1 and L2 are the “active” and
“inactive” labels, respectively.
Therefore, the mathematical sequence described in Eq. 7 allows explaining simultaneously two
major features of Benveniste’s experiments, namely the emergence of an “activated” state from
background noise and the significant correlations between “labels” and system states (Figure 5).
No hypothesis on the physical properties of test samples or another local cause has been necessary.
Application to “memory of water” experiments. Perhaps the strongest argument in favor of a “memory”
related to water was the emergence of an “activated” state of the biological system. This was
particularly striking in Benveniste’s experiments with an isolated rodent heart that allowed “live”
demonstrations of the coronary flow variations. Moreover, from 1992 to 1996, the experiments
with the isolated rodent heart were performed using two systems that worked in parallel.1 These
parallel experiments were used to confirm the measurement of each test sample, particularly in
experiments designed as proof of concept. In a previous publication, I reanalyzed the duplicate
outcomes of a series of experiments performed with this double system.22 These results were
pooled regardless of the method used to “inform” water. The high correlation of the duplicate
measurements (changes of coronary flow) was a very strong argument indicating that these
experiments had an internal consistency and deserved to be considered through a scientific
There were, however, some features that should have drawn the attention of Benveniste’s team.
Indeed, many devices, settings, protocols, procedures or molecules were used in Benveniste’s
experiments involving very different physical principles. Despite these diverse approaches, the
response of the biological system was generally in the same range: for example, 20–30% of coronary
flow variation for the isolated heart for “active” conditions (the same remark applies to basophil
degranulation or plasma coagulation).22 Yet, the physical mechanisms involved in the different
methods of “water imprinting” were quite different (high dilutions, “electromagnetic transfer” of
a molecule in a solution, “electromagnetic transfer” from a computer file, solubilization of
homeopathic granules). The molecules that were diluted or “electronically transmitted” had various
characteristics, from small pharmacological molecules to large proteins (e.g., acetylcholine,
ionophore, ovalbumin). In other words, what seemed to be important was the a priori “inactive”
or “active” status of the test sample and not the physical process supposed to “inform” water. It
was as if a unique “cause” was at work and that the different methods used to “imprint” water
were only meaningless rituals, perhaps helping the experimenters to focus on the experiment.
At first sight, the apparent specificity of the active test samples was also a strong argument in favor
of “memory of water”. Thus, it was reported that water “imprinted” with an antigen induced a
biological change in the isolated heart, only if the animals were immunized to the same antigen.1, 17,
18 Similar arguments have been reported for high dilutions in basophil degranulation (e.g., active
histamine vs. inactive histidine; active anti-IgE vs. inactive anti-IgG).2 In fact, this argument is not
valid if one considers that specificity is always indirectly “demonstrated” through an intellectual
construct. These assessments of specificity were nothing more than comparisons of “active” versus
6. Consequences of blind experiments on correlations
In this section, we see how the model predicts the vanishing of the correlations between “labels”
and system states in blind experiments with an outside supervisor.
We suppose that the observer W provides F with test samples under a coded name (the “inactive”
and “active” labels are masked). When the experiments are ongoing, W is outside the laboratory
and does not interact with F-S. After all states of S associated to the series of test samples have
been recorded by F, these results are sent to W. The two lists, namely “labels” (unknown to F) and
the states of the system recorded during the experiments, are compared by the supervisor W to
assess the rates of direct/reverse relationships.
In this setting, there is a transfer of the information about labels from the inside to the outside: there is
a loss of information for F-S and a gain for W. The experimenter F continues to expect a pattern,
but no information is available on the label of each sample. Therefore, the “activated” state is evenly
distributed among samples with “L1” and “L2” labels: Prob (direct L2) = Prob (reverse L1) = 1/2;
consequently, Prob (direct) = Prob (reverse) = 1/2 (see Figure 1). This means that there is no
relationship between “labels” and system states although the “activated” state is still observed (but
associated indifferently to “L1” or “L2” labels). With an outside supervisor, the states of the entity
F-S (direct and reverse relationships) are dissociated into their different components, namely labels
on the one hand and states of S on the other hand. This experimental situation with an outside
supervisor can be summarized as follows:
Prob (direct) = Prob (L1) × Prob (directL1) + Prob (L2) × Prob (directL2)
= 1/2 × 1/2 + 1/2 × 1/2 = 1/2
Blind experiments can also be performed with a local/inside supervisor (F’ for example) or with
an automatic device for the blind random choice of “labels”. In this setting, all participants and
devices are inside the laboratory. From the point of view of W, the local supervisor or the automatic
device is nothing more than a part of the system S and the outcome is a property of F-S taken as a
whole as previously described for open-label experiments. In this situation, the emergence of a
significant relationship between “labels” and system states is predicted as previously seen with
Prob (direct) = 0 or Prob (direct) = 1
Blind experiments with or without an outside supervisor have therefore different consequences on
the experimental outcomes. These differences cannot be described within a classical framework
that considers that in all cases the “whole” (pattern) is the simple sum of its parts (labels plus states
Application to “memory of water” experiments. The vanishing of the apparent relationship in proof-of-
concept demonstrations with an outside supervisor was a stumbling block for Benveniste’s
experiments. This weird phenomenon could be considered as the scientific fact that emerges from
Benveniste’s experiments. It is important to emphasize that despite the disappearance of
correlations, activated states persisted – as described in this model – but they were randomly
associated with “inactive” and “active” labels.1, 22 As explained in the introduction, the spreading
of “activated” states regardless of “labels” was interpreted as the consequence of external
disturbances. However, further improvements of experimental conditions and devices did not
prevent this unwanted phenomenon.25, 26
In 2013, I reanalyzed in depth a series of “digital biology” experiments with isolated rodent heart
performed by Benveniste’s team.23 The main interest of this series of experiments was that both
inside and outside supervisors operated on the same test samples. For these experiments, a wealth
of precautions had been taken and nevertheless the disturbing effect of an outside supervisor was
7. Experimenter’s conditioning as a stepwise learning process
For simplicity, we considered in a first approach that the classical conditioning of the experimenter
was 100% efficient. However, as in every learning process, conditioning can be only partial. In this
section, we complete the model for situations between no conditioning and perfect conditioning.
These considerations also allow deepening the understanding of the probabilistic consequences of
the conditioning of the experimenter.
In a first step, we vary the degree of independence of the future events A and B to be recorded by
F and F’, respectively. We generalize Eq. 1 by adding a parameter named d:
Prob (A B) = Prob (A) × Prob (B) + d (with 0 ≤ d ≤ 1)
The future events A and B are independent if d = 0; their degree of correlation increases when d
increases (d can be understood as the abbreviation of “dependence”). In a second step, the
generalization of Eq. 3 follows (Figure 6):
)( Prob 22
(with 0 ≤ d ≤ pq)
If d = 0, Eq. 11 is equal to Eq. 2 and after introduction of probability fluctuations there is a
dramatic shift from 1/2 toward 1 or 0 as previously shown with Eq. 7. In contrast, the future events
A and B are perfectly correlated with d = pq and we find again the classical situation:
Probability fluctuations can be introduced in Eq. 12:
pn+1 = pn ± εn+1 (with p0 = 1/2)
We easily see with Eq. 13 that there is no dramatic transition from p0 = 1/2 toward 0 or 1 and
therefore no emergence of the “activated” state of S; there are only tiny fluctuations of Prob (direct)
around 1/2. It is as if there was only one future event (A and B are perfectly correlated) that existed
before its record. Therefore, varying the value of d from pq to 0 allows describing the progressive
shift from no conditioning (no pattern expectation) to optimal experimenter’s conditioning
(pattern expectation) (Figure 7). Even with a slight conditioning (value of d near 1/4), Prob (direct)
is > 1/2. In this case, provided that the statistical power is sufficient, significant correlations
between “labels” and system states could be evidenced.
We can also calculate when the classical approach (preexistence of outcome to measurement) and
the original approach of the present model (creation of outcome by measurement) are not
discernible. This situation is achieved when p = p2 / (p2 + q2). We easily calculate that the two
members of the equation are equal in only three situations: p = 0, p = 1 and p = 1/2. We have seen
that the situation with p = 1/2 is unstable and evolves toward either p = 0 or p = 1. When these
stable states are achieved, the future outcomes A and B to be recorded by F and F’, respectively,
are perfectly correlated (A = B). However, the relationship between labels and states of S is causal
only apparently since the relationship disappears with an outside supervisor.
Figure 6. Shift from no conditioning to conditioning of the experimenter. The conditioning process
is more or less complete; this is mathematically translated by varying the degree of independence of
the future outcomes to be observed by F and F’. The change of the parameter d from pq to 0 is
therefore an assessment of the experimenter’s conditioning to expect a pattern (a relationship). When
d = pq, the experimental outcome is a property of S alone (no conditioning) and, when d = 0, the
experimental outcome is a property of F-S taken as whole (optimal conditioning of experimenter).
Application to “memory of water” experiments. The consequences of the degree of conditioning of the
experimenter described in this section find particular resonance in “memory of water” experiments
through the reproducibility issue, which was a major concern. Needless to insist on the difficulties
to reproduce the experiments by other teams but – even in Benveniste’s laboratory – it was a
common lore that some experimenters were more “gifted” than others.1, 27, 28 Thus, in a series of
blind experiments with basophils published in 1991 by Benveniste’s team, a statistically significant
difference in favor of a biological effect of high dilutions was reported. However, this conclusion
rested on the results from only one of the two experimenters who participated to the study.1, 29
Interestingly, the experimenter who obtained significant results was the more experienced.
Figure 7. Experimenter’s conditioning as a stepwise learning process. The probabilities of
Prob (direct) achieved with different value of d from 1/4 to 0 are calculated in panel A. The maximal
value (stable position) achieved by Prob (direct) as a function of the value of d is depicted in panel B.
In the absence of probability fluctuations (ε = 0) or if d = p0q0 = 1/4, Prob (direct) = 1/2, meaning,
that there is no relationship between “labels” and system states. Only with probability fluctuations
(± ε) and with values of d ≠ 0, correlations between “labels” and system states emerge as a function
of d value. For simplicity, only data corresponding for L1 as “inactive” label are shown. For this
figure, each probability fluctuation εn+1 during an elementary time interval was randomly obtained in
the interval from –0.5 × 10-5 to +0.5 × 10-5.
Another example is the robot analyzer built by Benveniste’s team to perform automatically
experiments based on plasma coagulation. In these experiments that provided clear-cut results, the
“molecular signature” of an anticoagulant drug recorded on the hard disk of a computer was
supposed to be “transmitted” by an electromagnetic field to water samples. Then, “informed”
water was added to plasma to inhibit the coagulation process.1 This robot was precisely built to
minimize a possible interference of the experimenter with the ongoing experiment. Thus,
“inactive” and “active” files were randomly chosen by the computer and were masked to the
experimenter until the experiment was completed. The intervention of the experimenter was
limited to the supply of consumables and the start button. In 2001, the robot analyzer was evaluated
by a multidisciplinary team mandated on behalf of the United States Defense Advanced Research
Projects Agency (DARPA). These experts concluded that they observed some effects supporting
the concepts of “digital biology” when the scientist from Benveniste’s team who was dedicated to
this research was present. However, the experts were unable to reproduce these results after the
team left.27 Of interest, the experts suggested that an experimenter effect could be the cause of
these curious results, but in the absence of a theoretical framework, they stated that they could not
Model and Benveniste’s experiments. The strong point of this model is that all features of Benveniste’s
experiments are described: 1) emergence of an “activated state” from the background noise of a
biological system without local cause; 2) correlations between “labels” and system states;
3) mismatches in outcomes from blind experiments with an outside supervisor. It is important to
insist that these characteristics emerge from the formalism and are not ad hoc hypotheses. The
model rests on reasonable assumptions about the measurement process of a biological experiment
aimed to establish an elementary dose-response. Classical conditioning is also a plausible
hypothesis. Moreover, the conditioning is self-sustained because the observation of the expected
pattern reinforces it. Indeed, the more significant correlations are recorded by the experimenter,
the more these correlations have a chance to be recorded in the next experiments.
This hypothetical model suggests that some cognitive processes (namely classical conditioning)
might extend to systems spatially separated from the experimenter. It is important to underscore
that there is no action at a distance, but coordination of events according to a structuring pattern.
Thanks to their plasticity and degrees of freedom, biological systems appear the most suitable
among the possible experimental models to evidence such non-classical relationships between
observers and systems.
The model needs to be built from a point of view outside the laboratory. Indeed, from an “inside”
point of view, the states of F, S and F’ are strictly correlated at any time. In contrast, only an outside
point of view allows describing the independence of the future outcomes to be recorded by F and
F’. This is in line with the demonstrations of Breuer who established that an observer (or a
measurement apparatus) contained in a system cannot distinguish all the states of this system.30
The description of all states of the first observer (or apparatus) needs a second external observer
Consequences of blinding. With this model, the consequences of “external” blinding that disturbed
Benveniste’s team so much are easily explained. It is important to underscore that the relationship
between “labels” and system states in this setting is not a local causal relationship (“labels” and
states of S that participate to the observed relationship can be considered as coincident events).
Indeed, if these correlations are forced into a causal relationship (e.g., to send a message or to give
an order), the correlations vanish and the outcomes become evenly distributed among labels. This
is precisely what happened with Benveniste’s proof-of-concept experiments with outside
supervisors when the results seemed to become crazy. These apparent “jumps of activity” among
test samples were not because of external disturbances but were intrinsic to the phenomenon at
Note that an outside supervisor is not immune of conditioning. To avoid the consequences of
conditioning, the outside supervisor should not be accustomed to the experimental system and
systematically replaced between series of experiments.
Gestalt psychology. The model has some common points with Gestalt psychology.31 This theory states
that the human mind perceives objects as a whole or a form (Gestalt) and not as the simple sum
of their constitutive parts. The whole has its own independent existence. Necker cube is an example
of the perception of a two-dimension design as a three-dimension Gestalt (Figure 8). Of interest,
this three-dimension configuration “exists” only for an observer. Therefore, the “cube” is not a
property of the two-dimension sheet alone where a picture has been drawn, but is a property of
the sheet and the observer taken as a whole. The three-dimension “cube” does not preexist its
observation, but is created at the very moment of its observation.
Application of the model to other situations. The model constructed to describe Benveniste’s experiments
and more generally experiments related to “memory of water” could be extended to other
experimental situations in medicine, biology or psychology where repetitions of experiments by the
experimenters could possibly lead to their conditioning. Alternative medicines such as homeopathy
or placebo effect are examples where this model could be applied.32 As depicted in this article, the
structuration of the observer’s mind by classical conditioning could organize the observations and
measurements. In such a situation, the experimenters are trapped into a circular process: they
describe what they contribute to construct and they construct what contributes to their description.
Moreover, the observation of the expected pattern reinforces the experimenter’s conditioning.
Although many other classical explanations are possible, such processes could also be at work in
the reproducibility crisis reported in experimental biology, medicine and psychology.33 As we have
seen, there is nevertheless a possibility of detecting and avoiding these unintended interferences of
the experimenters with the experimental system that they describe. Generalizing the use of an
outside supervisor in blind experiments is a method to confirm that an observed relationship is
This psychophysical model allows explaining the results of “memory of water” experiments
without referring to water or another local cause. It could be extended to other scientific fields in
biology, medicine and psychology when suspecting an experimenter effect.
Figure 8. Necker cube as an example of pattern expectation after learning. Necker cube is a 2-
dimensional drawing that we perceive as a 3-dimensional volume as a consequence of learning at an
early age. Because of the ambiguous drawing, perceptions from top and bottom alternate (only one
of the two patterns can be “seen” at one time). The 2-dimensional drawing is a property of the paper
sheet alone, whereas the interaction of the observer with the 2-dimensional drawing literally “creates”
the 3-dimension cube that does not preexist its observation. Similar to Necker cube with top/bottom
configurations, direct/reverse relationships are perceived as patterns after learning (through classical
conditioning). Both 3-dimensional Necker cube and relationships (between “labels” and system
states) are constructs of observer’s mind that considers them in their wholeness and not as the simple
sum of their individual components. Mixtures of the two relationships are possible (e.g., half
outcomes with direct relationship and half outcomes with reverse relationships) but, for each
outcome, the relationship is always expected and perceived in its wholeness by the conditioned
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