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Are there some loopholes in experimental biosciences? The lessons from Benveniste’s experiments

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The case of the “memory of water” was an outstanding scientific controversy of the end of the twentieth century which has not been satisfactorily resolved. Although an experimenter effect has been proposed to explain Benveniste’s experiments, no evidence or convincing explanation supporting this assumption have been reported. One of the unexplained characteristics of these experiments was the different outcomes according to the conditions of blinding. In this article, an original probabilistic modeling of these experiments is described that rests on a limited set of hypotheses and takes into account measurement fluctuations. All characteristics of these disputed results can be described, including their “paradoxical” aspects; no hypothesis on changes of water structure is necessary. The results of the disputed Benveniste’s experiments appear to be a misinterpreted epiphenomenon of a more general phenomenon. Therefore, this reappraisal of Benveniste’s experiments suggests that these results deserved attention even though the hypothesis of “memory of water” was not supported. The experimenter effect remains largely unexplored in biosciences and this modeling could give a theoretical framework for some improbable, unexplained or poorly reproducible results.
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IJRRAS 27 (2) ● May 2016
Francis Beauvais
91, Grande Rue, 92310 Sèvres, France
The case of the “memory of water” was an outstanding scientific controversy of the end of the twentieth century
which has not been satisfactorily resolved. Although an experimenter effect has been proposed to explain
Benveniste’s experiments, no evidence or convincing explanation supporting this assumption have been reported.
One of the unexplained characteristics of these experiments was the different outcomes according to the conditions
of blinding. In this article, an original probabilistic modeling of these experiments is described that rests on a limited
set of hypotheses and takes into account measurement fluctuations. All characteristics of these disputed results can
be described, including their “paradoxical” aspects; no hypothesis on changes of water structure is necessary. The
results of the disputed Benveniste’s experiments appear to be a misinterpreted epiphenomenon of a more general
phenomenon. Therefore, this reappraisal of Benveniste’s experiments suggests that these results deserved attention
even though the hypothesis of “memory of water” was not supported. The experimenter effect remains largely
unexplored in biosciences and this modeling could give a theoretical framework for some improbable, unexplained
or poorly reproducible results.
Keywords: Experimenter effect; Scientific controversy; Experimental artifacts; Cognition.
Although the notion of “memory of water” did not succeed to become taught in biology and chemistry textbooks,
this scientific controversy is now a classical topic in sociological studies of science [1-4]. The early experiments
reported in 1988 in Nature by a French team and other laboratories suggested that samples of highly diluted
molecules retained the ability to activate cells [5]. Although no molecule could still be present in these high
dilutions, the authors of the article claimed that the biological effect persisted in strictly controlled blind
experiments. Of course, contamination was the first suggested cause to explain these unexpected results. It was
argued however that appropriate controls had been done and that the number of possible contaminant molecules was
too low to induce an effect of the same magnitude. Moreover, the interest of lay press – which coined the expression
“memory of water” – was aroused because these results seemed the therapeutic claims of homeopathy.
Benveniste, the lead author, was not a newcomer, but was a reputed senior director of a laboratory of INSERM (the
national French medical research organization). He was a member of the scientific establishment after his discovery
of a new inflammatory mediator in the 1970s that was the main research topic of his laboratory [6].Therefore, he
was given credit for having nothing to gain by promoting such eccentric results. The journal Nature played a key
role in this affair. Indeed, Maddox, the Editor of Nature, was first reluctant to publish the data, but then changed his
mind in part due to the insistence of Benveniste to expose and discredit what he thought to be “second rate”
science in the service of the discredited homeopathy. The Benveniste-Maddox conflict is not the subject of this
article and details can be found elsewhere [7-11].
Today, most scientists think that the controversy vanished after the affair with Nature. However, Benveniste pursued
his experimental investigations, thus confirming and extending his previous results [7]. Of course, storing in liquid
water the specific information that allow describing molecules – some of them as huge as immunoglobulins –
appears, at first sight, quite impossible. One must also admit that direct physical evidence of a change of water
structure specific of the original molecule (“ghostly imprint”) has never been reported. The evidence rested on a
circular reasoning: a modification of water structure was claimed to induce a change of a biological system and this
change was exhibited as a proof that water structure had been modified. Actually, this research continued after the
episode with Nature and extended overall from 1984 to 2004. After the basophil model, Benveniste’s team explored
other biological models. The most remarkable results were initially obtained with the isolated rodent heart model
(Langendorff’s apparatus) and some years later with an in vitro coagulation model that had the advantage of being
possibly automated.
In 1992, Benveniste hypothesized that molecules in solution emitted electromagnetic waves that could be picked up
by an electric coil, amplified and transmitted to a sample of water via another electric coil at the output of an
amplifier (“electromagnetic transmission”). After confirmatory experiments, Benveniste claimed that he was now
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Beauvais The Lessons from Benveniste’s Experiments
able to “inform” samples of water through other means than high dilution (thus escaping the criticisms about
homeopathy). In a further step in 1995, he reported that the alleged specific electromagnetic “signal” that was
emitted by molecules in solution could be digitized, stored in a computer memory and played at will to a sample of
water through an electric coil. For these last experiments, he coined the expression “digital biology”. The
experimental results obtained with “electromagnetic transmission” and “digital biology” have been mainly described
as abstracts of congresses [12-20].
These biological and electronic devices will not be detailed in this article and information on them can be found
elsewhere [7, 8]. The aim of the present paper is to expose the logic of these experiments and therefore, the
experimental devices will be schematically described as simple black boxes with input and output.
In Benveniste’s experiments, it was hypothesized that if some “memory of water” existed, then a biological change
(noted “↑”) above background noise (noted “↓”) should be more frequently observed with samples supposed to be
active (AC) compared with samples supposed to be “inactive” (IN) in biological models. Active samples were
thought to have received “biological information” through high dilutions or using devices for “electromagnetic
transmission” or “digital biology”. In mathematical terms, we can write the aim of these experiments as a test of the
following question:
Prob (xy) is the conditional probability of A given B (or the probability of x under the condition y).
If modifications of water structure whatsoever were able to change a parameter of a biological system in a
conventional causal relationship, it would not be different from a classical pharmacological effect. In this case, why
did Benveniste’s experiments fail to be fully convincing?
Benveniste often invited colleagues to witness his experiments. These “public demonstrations” were designed as
“proof of concept” to give a definitive confirmation on the reality of “electronic transmission” or “digital biology”.
A protocol was defined and after the experiments were done, a report with all raw data was sent to all particip ants
[7, 21, 22].
During these demonstrations, control samples and samples supposed to have received specific “biological
information” were prepared (in some experiments of “digital biology”, the “samples” were computer files) [7, 21,
22]. The sample preparation was performed in another laboratory under strict control by other scientists, and the
initial labels of the samples were replaced with code numbers by participants not belonging to Benveniste’s team.
Open-label samples were also prepared; they were nevertheless in-house blinded. All samples were then tested in
Benveniste’s laboratory within the next few days after the preparation. Then the outcomes obtained with each
sample were sent to the external supervisor who compared the two lists (i.e. the list of inactive/active samples vs. the
list of biological effects under a code name) and who assessed the rate of “success”. Note that the supervisor did not
assist in the testing of the samples and remained uninformed about them until the end.
Details of these public demonstrations organized from 1992 to 1997 with the rodent isolated heart model have been
given elsewhere [7, 21, 23] and one of them has been thoroughly analyzed in a recent article [22]. So what did not
work in these demonstrations?
The unexpected obstacle encountered by Benveniste can be described through an illustration. Let us imagine a stage
magician who presents four empty cages to the public. He covers each cage with a scarf and claims that he will
predict in which cage a parrot will appear. First, he announces “cage number two” and when the cage is uncovered,
a parrot is indeed present in this cage, whereas the other cages are empty. For a new trial, the cages are again
covered with scarves. The magician announces “cage number four”, but in fact, a parrot is present in cage number
one and only in this cage. After a great number of trials, it finally appears that the magician is right with a
probability which is not different from 1/4. We can conclude that the stage magician had at best a random success
rate in guessing the cage number. Nevertheless, in each case, a parrot appeared by an unknown manner in a cage that
was previously empty. Therefore, the apparition of a parrot not the guessing game is the scientific issue to be
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Beauvais The Lessons from Benveniste’s Experiments
If one replaces the parrot by the emergence of a “biological signal” from background noise, this is exactly what
happened in Benveniste’s experiments: In some experimental conditions such as blind “public demonstrations”, the
biological parameter did change, but not at the expected places.
Figure 1 is a graphical representation of the different experimental conditions encountered during Benveniste’s
experiments. Alice is the experimenter and Bob observes Alice doing the experiment; Bob can also b e a supervisor
in in-house blind experiments. Eve is an outside supervisor; when she participates to blind experiments, she sends to
Alice the samples to be tested under a code number. After all tests have been done with the biological device, she
receives the list of the observed effects (“↓” and “↑”) and she calculates the rate of success. There is an essential
difference with Bob: Eve neither observes Alice nor the experimental device and she has no information during the
testing of the samples.
Results of Benveniste’s experiments with the Langendorff apparatus are summarized in Table 1 according to
different experimental conditions: (1) Alice assessed the success rate (open-label); (2) Bob assessed the success rate
(Alice blind); (3) Eve assessed the success rate (Alice blind). One expects the respective probabilities of success
being identical with or without Eve’s assessment. Details on these experiments have been given elsewhere [7, 21-
Figure 1. Description of the different roles of the agents who participate in the experiments. Alice is the
experimenter (1) and two other observers participate (if necessary) in the blind experiments. Bob is inside the
laboratory, and for him who observes Alice in her environment, Alice and the experimental system (S with two
possible states ↓ or ↑) are in a defined state. To control Alice’s experiments, Bob can locally assess the results in
blind experiments (2). This means that he replaces the initial label of each experimental sample by a code number
before giving it to Alice for blind testing. Eve is outside the laboratory (3). Therefore, for Eve, Alice and the
experimental system are in an undefined state until all samples have been tested and results are transmitted to
Eve. When Eve participates in a blind experiment, she keeps secret the list of sample labels to be tested by Alice.
After the completion of the experiments, she receives the list of outcomes of the experimental device and she
compares the two lists to calculate the rate of success.
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Table 1. Outcomes of Benveniste’s experiments according to three experimental conditions.
Experimental situations
Number of
Observed outcomes
(Success rate, %)
Outcome “↓”
(resting state)
Outcome “↑”
(“activated” state)
Eve did not assess the success rate*:
Alice assessed the success rate
(Open-label) (1)
Bob assessed the success rate
(Alice blind) (2)
Eve assessed the success rate*:
(Alice blind) (3)
Summary of results presented in [21].
“Success” (in bold type) is defined as “Inactive” label associated with “↓” or “active” label associated with “activated” state “↑”.
Without Eve’s assessment, ProbA (success) = 0.92 (Alice’s assessment) and ProbB (success) = 0.88 (Bob’s
assessment). Then Eve tried to confirm these results by supervising blind experiments with the participation of Alice
(Figure 1). After receiving the results corresponding to each label, she assessed the “success” rates for the inactive
and active labels and she calculated the overall rate of “success”: ProbE (success) = 0.57. Therefore, the probability
of “success” was different according to the experimental conditions (assessment of “success” rates firstly by
Alice/Bob or firstly by Eve):
)(Prob)(Prob ~)(Prob EBA successsuccesssuccess
The remote assessment of “success” rate by Eve was associated with a decrease of this rate. Note however that the
biological signal was present, but not at the “expected” place (as the parrot in the above illustration). For Benveniste,
the failure of the “public experiments” did not call into question the validity of his theses on “digital biology”,
“electromagnetic transmission” or high dilutions, but showed that technical improvements were yet necessary.
Indeed, he considered that the change of a biological parameter in his experiments was not a trivial artifact, but a
proof that a discovery of great scientific value was at stake [21]. Therefore, various explanations were proposed by
Benveniste and his team to try to overcome these experimental failures: water contamination, electromagnetic
perturbations from the environment, spontaneous “jumps” of “electromagnetic activity” from one water sample to
another one, etc. However, despite improvements of the experimental devices to prevent possible external
influences, the mismatches persisted in experiments with “external” blinding [7, 22]. The impossibility to overcome
this barrier was the main reason why Benveniste did not succeed to convince his peers.
These ad hoc explanations were indeed unsatisfying. It was difficult to explain how a simple change for blinding
conditions could lead to such differences (i.e. in-house blinding vs. blinding by a supervisor located outside the
laboratory). From this point of view, the opponents of “memory of water” were right: no causal relationship between
“informed” samples and change of biological signal was convincingly established. However, in the present state of
knowledge, the consistent changes that had been repeatedly observed (including after in-house blinding) remained
puzzling. From this point of view, Benveniste and his team were right. In this article, we will see how a third
explanation based on the involvement of the participants could make a synthesis of these apparently irreconcilable
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Another weird observation during the “memory of water” story was the notion of “gifted” experimenter. Indeed, in
experimental sciences, the experimenter is assumed to be neutral with regard to the outcome of his/her observations.
If such an influence exists, the result is called an “artifact”, whatever the conditions for its production. Thus, in early
experiments on the effects of high dilutions on basophils performed by Benveniste’s team, one of the two
experimenters of a series of blind experiments obtained results in favor of an effect of high dilutions and not the
other [7, 24]. Of course, many trivial explanations were possible that could explain why one of the two
experimenters was a better “measurement device” than the other; it is well known i n all laboratories that some
people are more skillful and dexterous. Nevertheless, these results with basophils were obtained in blind conditions.
The possibility that the experimenter could disturb results, which were attributed to “memory of water” or “d igital
biology”, was repeatedly suggested during the twenty years of research that Benveniste devoted to this topic [7].
A trivial explanation is however more difficult to hold for automated experiments that record objective
measurements. Thus, in 2001, the United States Defense Advanced Research Projects Agency (DARPA) appointed
a multidisciplinary team to provide expert evaluation of an automatic biological analyzer set up by Benveniste’s
team. This robot analyzer automatically assessed the effects of “digital biology” on plasma coagulation (more
precisely fibrinogen-thrombin coagulation) with minimal human intervention. The members of the expert team
reported in an article that they were unable to obtain replicable successful experiments of digital biology with the
automatic biological analyzer [25]. Nevertheless, they witnessed that successful experiments had been obtained
during the initial phase of the expert evaluation provided that the experimenter from Benveniste’s team was present.
With this automated device, the intervention of the experimenter was very limited; even the computer files to be
“played” and transmitted to water through an electric coil were randomly chosen by the machine. When the machine
was ready with all consumables, the experimenter pushed a button and waited for one hour before details of the
results were printed. In the conclusion of their article published in 2006, the experts pointed out:
[Benveniste] stated that certain individuals consistently get digital effects and other individuals get
no effects or block those effects. While it is possible that other, unknown “experimenter” factors, such
as the influence of chemical residues, energetic emanations or intentionality from individual
experimenters could be an explanation for these findings, we did not test these hypotheses nor
developed a framework that would control for such factors[25].
In the probabilistic modeling that we propose of Benveniste’s experiments, the experimenter is not a simple neutral
“observer”, but is an essential component of the experimental system.
In this section, some terms necessary for the formal description of Benveniste’s experiments are precisely defined.
“Inactive” and “active” labels: Since we assume that there is no “memory of water” and that the structure of water
is not modified, all samples that are assessed in the experiments are physically comparable. Samples with “inactive”
and “active” labels cannot be distinguished by physical means; they only differ by their labels. As a consequence,
experiments with series of samples are like comparing repetitions of measurements associated either with the
“active” label or with the “inactive” label.
“Success” and “failure”: As previously defined, a “success” is defined as the association of the inactive label (IN)
with resting state (i.e. change not different from background noise noted “↓”) of the biological device or the
association of the “active” label (AC) with a biological signal (i.e. change above background noise noted “↑”).
“Failure” is defined as AC associated with “↓” or IN associated with “↑”. Therefore, the aim of the modeled
experiments is to establish whether the state “↑” is more frequently associated with the label AC than with the label
Macroscopic environment and measurements: The experimental situation can be summarized as the interaction of
the macroscopic environment with the mental state (perception) of the participants. The macroscopic environment
consists of the experimenters/observers considered as macroscopic objects (including brain structures, sensory
organs, etc.) and the experimental devices. The interactions between participants who are macroscopic structures are
like measurements of the perceptions of the other participants. The knowledge of the perception of an observer is an
answer to the question asked by another observer: “According to the definition, do you observe a success?” The
outcome is “yes” or “no”. Moreover, since these interactions are like measurements with macroscopic devices, they
are subjected to fluctuations.
Perception and objective reality: In this modeling, an important point is that the respective perceptions of different
observers are independent. Nevertheless, when the observers of an experiment interact, they agree on the outcomes
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(intersubjective agreement). In other words, there is a public space that is the locus of the “objective reality” and
there is a private space for each observer. Each private space (made of perceptions) independently interacts with t he
macroscopic environment, which constitutes the objective reality.
We describe the experimental situation from the point of view of a remote observer who perfectly knows the initial
conditions of the experimental situation and describes its evolution without interacting.
First, we consider the general case of the observation of an experimental relationship. One of the possible
relationships is named “success” and the other one is “failure” with Prob (success) equal to p and Prob (failure)
equal to q (with p + q = 1) (see definition above and Figure 2).
Figure 2. The different associations of labels and states of the experimental system in Benveniste’s experiments. The
two labels are “inactive” (IN) and “active” (AC). There are two possible states for the experimental system: (1)
“resting” state or background (“↓”) and (2) “activated” state or signal above background (“↑”). The purpose of
Benveniste’s experiments was to answer the question: “Is Prob (↑ AC) > (↑ IN)?” In other words, were “signal”
more frequently associated with the “inactive” label or with the “active” label? Note that in initial state, the
probability to observe “↑” is low, but is not equal to zero (dashed line).
When two observers assess the same outcome, they agree on their conclusion, namely “success” or “failure”. An
experimental situation such as “success” for one observer and “failure” for the other is not allowed. Moreover, as
previously said, the interactions of the macroscopic environment with the respective cognitive states of the two
observers are independent. Therefore, as depicted in Figure 3, the estimation of the joint probability for “success”
for these two observers is:
)( Prob qp p
This equation can be easily generalized to a number N of participants who all agree on their observations for
)( Prob
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In classical physics, the description of the world is independent of the presence of observers (n = 0). In the absence
of any observer, the above equation has a unique value:
2/1)( Prob 00
qp p
Figure 3. Consequences of the independence of perception of “success” of each observer. In this figure, we show
only two observers for simplification. Although observers’ perceptions are independent, after interaction, observers
nevertheless agree on the outcome of the experiment. We suppose that these two agents observe an experiment and
that the rate of “success” (according to defined rules) is p and the rate of failure is q (with p + q = 1). White areas
correspond to impossible situations where the outcomes are not consistent (e.g. “success” for Alice and “failure”
for Bob). The white areas are consequently excluded for probability calculations. The probability that both agents
observe “success” is thus the ratio of the central gray area (both Alice and Bob observe “success”) divided by the
probability of observing consistent outcomes (either “success” or “failure”) for both observers (all gray areas).
Prob (success) = 1/2 is the starting point of the modeling. For simplification, we first consider only two observers.
Moreover, we take into account measurement fluctuations. As for any measurement, there are fluctuations of the
interaction of the “public space” (macroscopic environment) with the “private space” (perceptions) of the observers.
As a consequence, there are fluctuations of the probability to observe “success”. The fluctuations of the probability
of “success” are noted i for one observer and εi for the other one. i and εi are independent random numbers around
zero with an absolute value << 1/2.
Since the initial probability of success is p0 = 1/2, when we assess the probability of success after a first
measurement, we can estimate that the probability to perceive “success” is 1/2 + 1 for the first observer and 1/2 + ε1
for the second observer. The introduction of measurement fluctuations implicitly means that the biological state “ ↑”
has a probability that is very small, but not equal to zero. Indeed, Prob (success) slightly higher than 1/2 means that
the probability to see an “active” label associated with “↑” increases and Prob (success) slightly lower than 1/2
means that the probability to see an “inactive” label associated with “↑” increases. In other words, the biological
state “↑” is present in the background noise.
As shown above (Figure 3), the estimation of the joint probability for the two observers after a first measurement is
given by the following equation:
)( Prob 11 εδ
   
1111 21212121Δ εδεδ
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The initial probability of success equal to 1/2 is updated with the new value, which in turn is updated after another
measurement and so on in a mathematical sequence. For the measurement n+1, the probability pn+1 is obtained by
re-entering the probability pn. The general equation of this mathematical sequence that describes Prob (success) is:
)(Prob 11
   
Δnnnnnnnn εqδqεpδp
Table 2 shows a detailed numerical example in order to make clear each calculation step of this mathematical
sequence and to show how the transition from 1/2 to 0 or 1 emerges. The random parameters and ε have been
chosen with relatively high values in order to obtain a transition within a few rows. In this example, a stable state
was randomly achieved with Prob (success) = 1, but 0 could also have occurred with even probability.
Table 2. Calculation of the mathematical sequence of Prob (success) with
and ε randomly obtained in the interval
0.5 to +0.5 × 10-3
Step n
pn + n+1
pn + εn+1
qn – εn+1
= pn+1
Figure 4 shows a computer simulation with probability fluctuations around 10-6 (calculations have been done also
with probability fluctuations as small as 10-15; see legend of Figure 4). After a number of measurements, in all cases,
a stable position is obtained in Figure 4:
Prob (success) = 1 or Prob (success) = 0
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Figure 4. Evaluation of the probability of “success” by taking into account measurement fluctuations. In this figure,
the probability is computed with the formula defined in Figure 3. The probability of success is initially equal to 1/2.
The equation
Δ/))(()(Prob 11 nnnnnn εpδppsuccess
with p0 = 1/2 (see text for the definition of
) allows
calculating the probability of success after successive measurements subjected to fluctuations. The initial 1/2
probability is replaced with the new calculated value and the joint probability obtained after each random step is
used for the next calculation of probability of success and so on. The values of
and ε at each calculation step are
randomly obtained in the interval 0.5 to +0.5 × 10-6. We observe in this computer simulation that the probability of
“success” is unstable and after a few calculation steps, one of the two stable positions is achieved: either “success”
or “failure”. The same calculations have been made with a smaller change of probability of “success”; in this case,
the transition occurs after a greater number of calculation steps: 40–50 calculation steps with ε = random [–0.5 to
+0.5] × 10-15). Moreover, with a number of observers >2, the transition towards stable positions occurs with fewer
calculation steps (not shown). The figure depicts the results obtained after eight computer simulations.
We conclude that the initial state with probability of “success” equal to 1/2 is metastable if we take into account the
measurement fluctuations. Comparable results are obtained with a number of observers > 2 (the transition of the
probability from 1/2 to 1 is achieved after fewer measurements when the number of observers increases).
Table 3 shows that the transition of Prob (success) toward 0 or 1 is possible only with a number of observers 2 and
taking into account measurements fluctuations.
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Table 3. Calculation of Prob (success) according to the number of observers..
Number of observers
Calculation of Prob (success)
qp p
qp p
qp p
Evolution of Prob (success) taking into account
measurement fluctuations*
1/2 + ɛi
0 or 1
0 or 1
0 or 1
* Starting with p0 = 1/2.
In Figure 4, only one of the two stable positions, namely the stable position #1, corresponds to the “expected”
results; indeed, in the stable position #2, an “inactive” label is always associated with “↑” and an “active” label is
always associated with “↓”. Note that in both stable positions, the probability to observe “↑” increases from ~0 to
1/2. However, an “experiment” is not limited to sample testing, but begins with the preparation of the experimental
device. Thus, we must take into account that the biological systems are prepared in an asymmetrical state since the
resting state (background noise) is always implicitly associated with the label IN. As a consequence, only the stable
position #1 is a possible state for the observers and therefore:
Prob (success) = 1
In stable position #1, Prob (success) = 1 (Figure 3). This means that “↓” is systematically observed in association
with the label IN and “↑” in association with the label AC. Therefore, the same process describes both the emergence
of “↑” from the background and the concordance of the labels with the states of the biological device. Thus, the
initial question – “Is Prob (↑AC) > (↑IN)?” – receives a positive answer.
When Bob participates in in-house blind experiments, Alice and Bob are in the same stable position. Therefore, they
both observe that the label IN is always associated with the outcome “↓” and that the label AC is always associated
with the label “↑” and therefore:
1/2)( Prob( Prob )IN
1/2)( Prob( Prob )AC
When Eve acts as an external supervisor of blind experiments, she associates each label of the list with each
outcome (↑ or ↓). We can calculate the probability of “success” and “failure” in this experimental situation:
C)| ( Prob)( Prob)| ( Prob)( Prob)( ProbEAsuccessACINsuccessINsuccess
)( Prob)( Prob)( Prob)( Prob ACIN
 
22 )( Prob)( Prob ACIN
2/1)2/1()2/1( 22
C)| ( Prob)( Prob)| ( Prob)( Prob)( ProbEAfailureACINfailureINfailure
)( Prob)( Prob)( Prob)( Prob ACIN
)( Prob)( Prob)( Prob)( Prob INACACIN
2/1)( Prob)( Prob2 ACIN
Therefore, the outcomes “↑” and “↓” are associated at random with the labels IN and AC. This equation explains the
mismatches between labels and biological outcomes in blind “public demonstrations” of Benveniste’s experiments;
the apparent “jumps” of “biological activity” from sample to sample are easily described. Indeed, the probability for
the label AC to be associated with “↑” decreases from 100% to 50% and the probability for the label IN to be
associated with “↑” increases from 0% to 50%. It is as if the “biological activity” randomly moved from some
samples with the “active” label to samples with the “inactive” label.
In summary, all characteristics of Benveniste’s experiments are described in this modeling: “success” of
experiments with internal supervisor such as Bob and “failure” with external supervisors such as Eve.
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We have seen that:
1)( ProbBsuccess
for experiments supervised by Bob
 
E)( Prob)( Prob)( Prob ACINsuccess
for experiments supervised by Eve.
We can easily calculate that the difference between these two probabilities of “success” is equal to:
)( Prob)( Prob2( Prob)( Prob )
EB ACINsuccesssuccess
We can do the same calculations with Prob (failure). Similarly, we have seen that:
0)( ProbBfailure
for blind experiments supervised by Bob
)( Prob)( Prob2)( ProbEACINfailure
for experiments supervised by Eve.
The difference between these two probabilities of “failure” is equal to:
)( Prob)( Prob2( Prob)( Prob )
EB ACINfailurefailure
Therefore, ProbB (success) and ProbB (failure) for experiments with Bob can be written as follows:
)( Prob)( Prob2)( Prob)( Prob EB ACINsuccesssuccess
)( Prob)( Prob2)( Prob)( Prob EB ACINfailurefailure
The term 2 × Prob (IN) × Prob (AC) is equivalent to an “interferenceterm. The logical structure of the modeling of
Benveniste’s experiments is thus reminiscent of the results that are obtained with Young’s two-slit experiment (or
with an interferometer of Mach-Zehnder). In Young’s two-slit experiment, according to non-detection vs. detection
of the path of the photon trajectory (slit A or slit B), interferences are observed on the screen or not, respectively. In
the modeling of Benveniste’s experiments, the role of the slits A and B is played by the labels IN and AC. In a
previous article, this analogy with the self-interference of a single photon has been depicted in detail [26].
In Young’s two-slit experiment, the indistinguishability of the paths of the photon through slit A or slit B is
responsible for the interference patterns (constructive interferences are comparable to “success” and destructive
interferences to “failure). In the present modeling, we observe the following probability transition (Figure 4):
2/1)| ( Prob1)| ( Prob successINsuccessIN
2/1)| C( Prob0)| ( Prob successAsuccessAC
The “paths” IN and AC are distinguishable in the initial position; indeed, if “success” is observed, then the
probability of “path” IN is equal to one and the probability of “path” AC is equal to zero. In contrast, in a stable
position, the “paths” become indistinguishable with probability equal to 1/2 for each label.
It is interesting to note that we find here the notion of probability amplitude. Indeed, in quantum logic, the
probability of an event is obtained by squaring its probability amplitude. As described in Figure 5, in experiments
supervised by Bob (which give the same results as open-label experiments), the probability of “success” is obtained
by making the sum of the probability amplitudes of the two paths that lead to success and then by squaring it. For
blind experiments supervised by Eve, the probability of success is obtained by squaring the probability amplitude of
each path that leads to “success” and then by making the sum of the probabilities of the two paths.
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Figure 5. Classical or quantum-like probability of “success”. The probabilities of “success” are different according
to quantum-like or classic probability. Indeed, quantum-like probability is calculated as the square of the sum of the
probability amplitudes of the different possible “paths”. Classical probabilities are calculated as the sum of the
squares of the probability amplitudes of the “paths”.
The achievement of a stable position as depicted in Figure 4 supposes first that the perceptions of the observers are
independent and second that there is no physical “barriers” in the macroscopic world that would block the transition
of the probability of success from 1/2 to 1. For this purpose, we have to examine the two key macroscopic systems
in the modeling, namely the experimental system and the experimenters/observers. Finally, we have to wonder
whether they have something special for observing these phenomena. In other words, is any experimental system
always appropriate? Are some experimenters more “gifted” than others? As a first step, we examine more deeply the
origin and consequences of independent perceptions.
10.1. Independence of perceptions
A key condition of the modeling is the independence of perceptions of the different observers. The independence of
two events, E1 and E1, is written as:
)(E Prob)(E Prob)E(E Prob 2121
As a consequence, the independence of the two events is only partial if:
d)(E Prob)(E Prob)E(E Prob 2121
(with 0 < d < 1)
If, as in Figure 3, the probability to observe the event “success” is the same for the two observers; the joint
probability is Prob (success) = p2 + d. The probabilities of the other experimental situations can be easily calculated.
For example, the situation (not allowed in the macroscopic “reality”) where one observer perceives “success” and
the other one perceives “failure” is p (p2 + d) = p × (1 – p) d = pqd (Figure 6). Equations (8) and (9) for the
probability of “success” can be modified:
)(Prob 11
psuccess nnnn
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Beauvais The Lessons from Benveniste’s Experiments
   
dεqδqεpδpnnnnnnnn 2Δ 1111
Figure 6. General case for joint probability of “success” of two observers according to the degree of independence
of perception of “success” of each observer. Parameter d varies from 0 to pq according to the more or less
independence of perception of “success”. When d = 0, perceptions are independent and quantum-like probabilities
arise. When d = pq, the probability of perception of “success” is equal to p as in classical probability.
When the value of d gradually changes from d = pq = 1/4 to d = 0, one progressively moves from classical to
quantum-like probability and Prob(success) increases from 1/2 to 1 (Table 3). Parameter d varies according to the
distinguishability of the “paths” IN and AC (as in Young’s two-slit experiment). In Figure 4, d = pq in the initial
state (paths are distinguishable) and d = 0 in the stable state (paths are indistinguishable). With the values of data
from Benveniste’s experiments reported in Table 1, we can calculate that d = 0.07.
Table 4. From classical to quantum-like probability by varying the value of d = pq.
Value of d*
Prob (success)
Stable position #1
Stable position #2
Classical vs. quantum-like probability
Pure classical
Pure quantum-like
In Benveniste’s experiments, d = 0.07 for a stable position ~0.92 according to the results of Table 1.
* See Figure 6.
There is also an important consequence of the coexistence of (1) independence of perceptions and (2) intersubjective
agreement. If the perceptions of the two observers are independent, but are nevertheless correlated after
measurement, this means that the perceptions do not pre-exist, but are created by measurement (i.e. interaction with
the macroscopic environment). This is one of the most counterintuitive features of quantum logic: a measurement of
a quantum (-like) system both creates and records a property of the system.
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Beauvais The Lessons from Benveniste’s Experiments
In the stable position, the “paths” IN and AC are undistinguishable; in quantum logic, these two states are said
superposed and quantum (-like) interferences are observed. Talking about what observers really perceive has no
sense; the only reality is the macroscopic world, that is, after asking observers what they perceive. In other words,
we cannot compare perceptions that remain definitely out of reach, but we can compare answers that belong to the
macroscopic “reality”; we can thus construct and share a common modeling of the world exte rnal to our senses and
10.2. Are some experimental systems more frequently associated with an experimenter effect?
We have seen that the experimental systems used by Benveniste’s team were asymmetrical (the “resting state” of the
system was associated with the “inactive” label). Moreover, the “signal” (i.e. the state of the system associated with
the “active” label) was present in the experimental background noise.
Laws of physics must be respected during the transition of probability of “success” from 1/2 to 1. When calculating
Prob (success) as depicted in Figure 4, we supposed that elementary random fluctuations were possible and
accumulated up to a threshold sufficient for the transition. In some devices, the probability fluctuations of outcomes
are allowed, but only around a fixed value or up to a maximal value. For the establishment of a relationship as
described in the modeling, it must be possible to go freely from an initial point (such as “↓”) to a final point (such as
“↑”) after a series of random fluctuations. A pollen grain which is only submitted to Brownian motion on the surface
water is a good picture of such a system. The fact that Benveniste’s experiments were performed in the context of a
laboratory of biology was perhaps not fortuitous. Indeed, biological systems exhibit many degrees of freedom and
consequently, they frequently exhibit a large “flexibility”.
10.3. Are some experimenters more exposed to an experimenter effect?
The observation of high “success” rates requires maintaining a stable position (Figure 4). A stable position is the
consequence of a question which permanently underlies the experimental process, specifically: “Is Prob (↑ AC) >
(↑ IN)?” Moreover, we have seen above that a stable position is characterized by the indistinguishability of the two
“paths” IN and AC. How these requirements could be translated in terms of mental cognitive processes?
If labels (IN and AC) and biological outcomes (↓ and ↑) are separately perceived by the experimenter, in the absence
of any definition of “success”, classical probability applies as described in Figure 7A. In contrast, if the
experimental situation is perceived in an integrated manner (i.e. as a relationship between labels and biological
outcomes), the logical structure of the results is comparable with Young’s two-slit experiment as described in Figure
7B. In this case, “success” is perceived as a new “object” which is not the simple addition of the separate
perceptions of labels and biological outcomes. This situation is also reminiscent of the Necker cube which does not
appear as a simple collection of lines on a 2D surface, but is immediately perceived as a 3D cube by a human
observer (Figure 8).
Some experimenters are probably more “talented” than others for performing such a task, namely maintaining
expectation/perception of a shape rather than its separate elements. Training is certainly also important in order to
structure mental processes for this purpose. Thus, experimenters working with Benveniste were dedicated to a
biological system and they have repeated the same experiments day after day for years. Implicit learning – a well-
known unconscious process during learning tasks could also play an important role. Note that only one “gifted”
experimenter is sufficient in the modeling; the joint probability with another observer (not particularly “gifted”) will
nevertheless achieve a stable position since independence of perceptions of the different observers and
intersubjective agreement are still present.
The implementation of the experiments on the “memory of water” by teams which were poorly trained, more or less
motivated, more or less concentrated and whose daily work was not dedicated to this theme of research could be one
of the reasons of the failure of the diffusion of Benveniste’s experiments. In contrast, the circumstances were quite
different in Benveniste’s laboratory. Indeed, the stakes were important, the experimenters were highly trained and
committed in these manipulations and the “survival” of the group depended on “successful” experiments. Such
situations could be favorable to the development of mental states necessary for maintaining stable position.
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Beauvais The Lessons from Benveniste’s Experiments
Figure 7. “Success” as a new “object”. If labels (IN and AC) and biological outcomes (↓ and ) are separately
perceived (i.e. are not connected by any definition of “success”), classical probability applies (A). In contrast, if the
experimental situation is perceived in an integrated manner, then the perception of the experimental situation is
reminiscent of the logic of Youngs two-slit experiment (B). In this latter case, “success” is perceived as a new
“object” which is not the simple addition of the separate perceptions of labels and biological outcomes.
Figure 8. Analogy with Necker cube [27]. A human observer immediately perceives the lines on the left as a cube
(with two possible positions in space as shown on the right). The perception of a 3D cube needs an observer who is
committed in the interpretation of the left figure. Thus, the perception of the 3D figure can be considered as a first-
person perspective whereas the description of the 2D lines is a third-person perspective. In this last case, a detached
observer (i.e. uninvolved in the perception/interpretation process) describes another observer who stares a paper
sheet where lines have been printed [28].
The present modeling benefited from readings of articles on quantum cognition [29-34], quantum Bayesianism
(QBism) [35, 36], relational interpretation of quantum physics [37, 38], convivial solipsism [39] and hidden-
measurements interpretation of quantum physics [40] (these references are not exhaustive). The modeling of
Benveniste’s experiments based on an involvement of the observers has two purposes. The first one is an attempt to
close the controversy by suggesting that the disputed Benveniste’s experiments could have been a misinterpreted
epiphenomenon of a more general phenomenon. The experimenters were thought to be impartial observers of the
world but, according to this interpretation, they were themselves an essential part of the experimental process that
they studied. In other words, they described what they constructed and they constructed what they described.
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Beauvais The Lessons from Benveniste’s Experiments
Therefore, this reappraisal of Benveniste’s experiments suggests that these results deserved attention even though
the hypothesis of “memory of water” was not supported. The second purpose is to propose to extend this modeling
to situations that potentially could involve unnoticed experimenter effect. Indeed, the modeling based on the
involvement of the observers in experimental outcomes could give a theoretical framework for some improbable,
unexplained or poorly reproducible results. More fundamentally, it could also enlighten the relationship between
mental states and macroscopic states.
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Full-text available
When human polymorphonuclear basophils, a type of white blood cell with antibodies of the immunoglobulin E (IgE) type on its surface, are exposed to anti-IgE antibodies, they release histamine from their intracellular granules and change their staining properties. The latter can be demonstrated at dilutions of anti-IgE that range from 1 x 10(2) to 1 x 10(120); over that range, there are successive peaks of degranulation from 40 to 60% of the basophils, despite the calculated absence of any anti-IgE molecules at the highest dilutions. Since dilutions need to be accompanied by vigorous shaking for the effects to be observed, transmission of the biological information could be related to the molecular organization of water.
Previous studies suggest that the biological activity of agonists can be transferred to water by electromagnetic means [1-7]. Since July 1995, in keeping with these results, we have digitized, recorded, and 'replayed' to water the activity of acetylcholine (ACh) or water (W) as control. ACh and W were recorded (16 bits, 22 KHz), for 1-5 sec, via an especially designed transducer, on the hard disk of a computer equipped with a Sound Blaster 16 card. Files were digitally amplified and the signal of digitally recorded ACh or W was replayed for 15 min, via the transducer, to 15 ml, W-containing plastic tubes. W thus exposed (dACh, dW) was then perfused to isolated guinea-pig hearts. In 13 open experiments, coronary flow variations were (%, mean + SEM, nb of samples): W+dW(not stat. diff.), 3.3 + 0.2, 20; dACh, 16.2 + 1.0, 33, p = 4.1 e- 10 vs W+dW; ACh (0.1 M), 23.4 + 2.8, 12, p = 5 e-3 vs dACh. In 25 blind experiments: W-fdW, 3.6 + 0-3, 61; dACh, 20.4 + 1.3, 58, p = 1 e-16 vs W+dW; ACh (0.1 M), 28.1 + 2-3, 24, p = 3 e-3 vs dACh. Atropine inhibited the effects of both ACh and dACh. Moreover, we have recently transferred specific digital signals via telephone lines. These results indicate that the molecular signal is composed of waveforms in the 0-22 Khz range. They open the way to purely digital procedures for the analysis, modification and transmission of molecular activity.
Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.