Copyright 1975, European Journal of Parapsychology. Reproduced with permission.


D.J. Bierman and J.M. Houtkooper

University of Amsterdam

(Originally published in European Journal of Parapsychology, Vol.1 No.1, 1975)

ABSTRACT: An experiment has been done on PK with an electronic random number generator coupled to a minicomputer. The task of the subject was to influence the RNG and to raise the frequency of the target alternative. Feedback was visible. Fourteen unselected subjects participated in the experiment.

The overall result is significant, having a one sided probability P=.026 when using the trial as a unit and P = .0013 when using only the sign of the deviation per run-pair. The variable conditions in the experiment are: RNG frequency (about 100 and 1000 Hz), runlength (3 to 12 seconds) and display characteristics. Short runs give considerable contributions to the overall effect, while long runs (9 and 12 seconds) contribute only slightly. This is consistent with pilot studies. Results are discussed in the light of a new theoretical approach, which amounts to an extension of quantum mechanics.


The obvious lack of reproducible experiments is in our opinion one of the main reasons for the slow progress in parapsychology. One can maintain certainly that during some experiments with talented subjects results have been obtained which proof beyond any reasonable doubt the existence of psi. However, experiments in which the influence of different variables are studied, are not expected to yield consistent results. Indeed it is not unusual that upon replication some of the effects observed in the first experiment are found to be reversed in the replication experiment.

A method to get reproducible results may be found in large scale experiments, i.e. many subjects and/or many trials. Recent experiments of Levy et. al. (1973) and Schmidt (1973) are examples of this "large scale" direction. It is remarkable that in both kinds of experiment the interaction is studied between a living entity and a machine. It may be that such a system is most promising for getting reproducible results, as one half of the agent-percipient pair is a machine, which behaviour is known to a larger extent than that of a human being or an animal. If we discuss the reproducibility of experiments we mean that a given experiment should be repeatable in any laboratory, without the need for the same subjects.

The proposal for a theory of psi-phenomena by Walker (1972) is our reason for the invisible versus visible trials in the present experiment, in connection with retro-PK. The theory, which is an extension of quantum mechanics, is in our opinion still incomplete, as it does not give a compelling argument for the proposed association of "hidden variables" connected to different quantum mechanical processes. In the case of PK, these processes are proposed to take place in the brain of the subject and in the random number generator. However, many aspects of this theory are attractive. Concerning the present work it can be shown that for the relatively simple situation of a PK experiment, trials are expected to be influenced as they are observed, by either subject or checker/experimenter (Feather & Brier, 1968). We will refer to this conjecture as the "observational hypothesis on parapsychological phenomena" (OHPP). We do not go into details here, for the fact of using'visible and invisible trials in our experiment can also be interpreted in a more classical way as a search for a differential effect on feedback conditions.


Our apparatus (see figure 1) consists of a random number generator (RNG) which is coupled to a clock pulse generator (CPG), which governs the rate at which the binary random numbers are generated. The random numbers are fed into a minicomputer in the form of pulses on two channels, corresponding with the two alternatives possible. Other peripheral apparatus of the computer are: a magnetic tape drive, a display terminal with a storage CRT and a paper tape reader. The magnetic tape is used to store the frequencies of both alternatives in chosen time intervals. We use the display terminal to give commands to the computer and to display the excentricity of the events for each visible time interval.

This is done in the following way: For each time interval a point is displayed on the screen with the horizontal coordinate dependent on the frequencies of both alternatives. If one alternative occurs more than the other, the point lies in the left half of the screen and viceversa in the right half of,the screen. The distance from the vertical middle line indicates the magnitude of the scoring. Subsequent points lie a fixed distance below each other. Immediately after the time interval is finished the point is projected, together with a line segment connecting it to the previous point. Thus the subject sees a broken line, showing the result of each time interval as it develops during a run. The target alternative is indicated by an arrow, displayed in the corresponding half of the screen before the run is started.

The paper tape reader is used to feed the parameters of a series of runs into the computer. Finally, there is a connection between the computer and the CPG by which the computer can switch the frequency of the CPG between two values (in this experiment about 100 and 1000 Hz.

It has to be mentioned that it is difficult to obtain a RNG which shows no deviations from ideal behaviour, that is, P = .5 , and no dependency between subsequent trials.

Figure 1 belongs here.


The variables applied in this experiment are, apart from target direction:
1. Frequency or rate of the RNG
2. Length of the time intervals
3. Number of time intervals per run
4. Display memory decay time
5. Visible versus invisible trials
Ad 2 and 3: By combining the length of the time intervals and the number of them, we obtain a single variable called runlength.
Ad 4: The display memory decay time governs the.way in which the subject gets the feedback. The two extreme conditions are a) At any moment the momentaneous performance is displayed, and b) that at any moment the total performance from the start of the run up to the actual moment is displayed (a cumulative way of displaying).

In this experiment some intermediate cases of display memory decay time are chosen. These are determined by the constant A, which we call the display memory parameter. The horizontal deflection on the display screen (X), after M intervals, is proportional to the exponentially decaying critical ratio:

X_M= Sum(I=1...M) {EXP(-A(M-I))(N_1I - N_2I)} / (Sum{EXP(-A(M-I))(N_1I + N_2I)})^(1/2)

where N_1I, N_2I are the number of pulses on channel 1,2 during the Ith visible interval.
It can be seen that the value of A governs the decay time of the CR.
Ad 5: The invisible and visible trials are obtained by programming alternating invisible and visible intervals. Of both, the results are registered on magnetic tape, but the results of the invisible intervals are not added to the display memory and hence are not shown on the visual display.

Thus far the "real time" experiment has been described, that is, the type of experiment in which the subject is trying to influence events that are being produced by the RNG at the same time. To implement the idea of retro-PK, another program has been written to display the invisible trials registered during a previous series. For the subject this situation could not be discriminated from the real time experiment. The important difference was the direction of the target arrow, which is opposite to the direction in the real time experiment. This is done to be able to distinguish the influence of direct PK in the real time experiment, which should give a positive deviation, from the influence of retro-PK in the play-back experiment, giving a deviation with the negative sign. It has to be mentioned that interpretations that include psi-missing complicate the picture.

The target side of a run is displayed beforehand by an arrow in the target direction, together with five vertical lines indicating the CR = -4, -2, 0, +2, +4 boundaries. A control run is indicated by the absence of an arrow.

Each run is started by the subject by pressing a key on the keyboard of the display terminal.

The number of runs and the values of the above-mentioned parameters are fed on paper tape into the computer before each series. In this way various experiments can be done with our setup.


The experiment consists of two parts, which we call part A and part B. In part A, invisible trials are just registered and later on analysed, while in part B the invisible trials are displayed later on as just the third part of the experiment (see above).

Part A consists of 18 runs and part B consists of 12 runs. For the values of the parameters of the runs see table 1.


Values of parameters in the experiment

Part APart B
RunTargetRunlength (S)Frequency (Hz) Display memoryRunlength (S)Frequency (Hz) Display memory
2left31000long4100 short
3right31000short4100 long
4control3100long41000 short
5right3100long41000 short
6left3100short41000 long
7control121000short9100 short
8left121000long9100 short
9right121000short9100 short
10control12100long91000 long
11right12100long91000 short
12left12100short91000 long
Note: The actual frequencies in this experiment are 956 Hz and 93 Hz. The number of intervals per run is in part A: 60, of which 30 visible and in part B: 20, of which 10 intervals are visible. The values of the display memory parameter A are: Display memory long (more cumulative display) Part A: 0.1336; Part B: 0.2878. Display memory short (more momentaneous display) Part A: 0.2878; Part B: 0.6931.

Fourteen subjects, members of the study centre for experimental parapsychology, volunteered in this experiment. Subjects 1 to 8 were tested in the morning session, subjects 9 to 14 in the evening. During the evening session no slow RNG frequency was used due to a disconnection of the cable between the computer and the clock pulse generator.


Only the runs with a target direction will be analysed. The control runs can be incorporated as a separate target condition in an analysis of variance, which will be called for in further experimentation, but in the present exploratory phase a simple straightforward analysis will suffice. The overall result per subject, split for visibility, is given in table 2. In the tables, one sided probabilities are given. Of the 56 independent deviations in his table, 38 are in the target direction. The results are also scored in another way. The runs no. 2 and 3, 5 and 6, etc. are considered as units. A unit is a hit if over both runs together there are more trials in the target direction than in the nontarget direction. We give the result of scoring per run-pair in table 3. In both table 2 and 3 the visible trials score higher than the invisible trials, but the difference is not significant.

Finally we give the results split for RNG-frequency, runlength, visibility and display memory parameter in table 4.


Results per subject split for visibility and total results

Part APart B
SubjectTotal no. of trialsDeviation (Vis.) Deviation(Invis.)Total no. of trialsDeviation (Vis.)Deviation(Invis.)
143958+148-827225 +71+178
243995+226+8927245 +134+141
344021+22-30127270 -19+123
444067+70-12527281 -49+38
544097+30+11727274 +40-66
644083+236-24327290 +97-91
744105-69+1227290 +164-190
844091+6+13327304 -112+30
980236+122-6449669 +79+166
1080267-91+3249661 +23-176
1180285-276+43749688 +44+86
1280294+132+10649679 -157-22
1380302+50-22449725 +69+62
1480342+293+6149739 +252+429
Total834143+899+22516340 +636+708
No. of trialsDeviationCRP
Note: We give deviations in tables 2 and 4 as the number of trials in the target direction (hits) minus the number of trials in the non-target direction (misses). The number thus obtained, is exactly twice the usual deviation, the number of hits minus the chance expectation of the number of hits.


Runpair scoring

FeedbackNo. of runpairsHitsMissesRateCRP


Scoring for different conditions

Variable: ValueTotal no. of trialsDeviation (Vis.)Deviation (Invis.)Deviation (Total)
Frequency: low50672+174-18+156
Frequency: high1299811+1361+748+2109'
Runlength: 3 sec.119160-245+4051+160
Runlength: 4 sec.158880+532'+274+806'
Runlength: 6 sec.238320+1065'-127+938'
Runlength: 9 sec.357482+104+434+538
Runlength: 12 sec.476641+79-256-177
Display memory: long675241+849-108+741
Display memory: short675242+686+838+1524'
Note: ' indicates P less .05


Efficiency (1000xCR^2/duration) in experiments with visual feedback

Present study3004.29


Before and after the morning and evening sessions long runs without a subject were checked on randomness of the RNG. We tested our RNG for zeroth, first and second order effect, that is, bias, alternating and "one skipping alternating". The results of these checks were consistent with a previous series of tests in which we found on a total of 101211635 trials that there are slight deviations from ideal behaviour in our RNG: P = .50037 (bias is .074 percent) and excess alternating over persisting is .153 percent. One skipping alternating shows no detectable deviation from chance. The first effect is compensated for by balancing the number of trials for each target side. The second effect gives rise to a slightly smaller variance of the results, so that the critical ratios will be slightly conservative when applying the standard tests .


The first result to be discussed is the overall result. In table 2 and 3 we find one-sided probabilities of .026 and .0013 so that e can reject the null hypothesis. Remarkable is the (nonsignificant) enhancement of the significance when we use only the sign of the deviation in the target-direction per run-pair. alogous effects have been observed in a number of other experiments (Brier & Tyminski, 1970; Houtkooper, 1967).

The difference between the visible and the invisible trials is important for the experimental verification of the OHPP. However, we consider the present experiment rather as an exploratory investigation than as a crucial test, for the resultant direction of the "will" of the subject (psi-hitting or psi-missing) cannot yet be predicted with any reliability.

The results of the invisible trials of part A were only observed by the two experimenters. Their "will" was probably directed towards enhancement of the deviations in the target-direction. According to the OHPP, the effect in the invisible trials of part A is caused by the experimenters, however the effect is negligible (see table 2). On the other hand the invisible trials of part B were observed later by the subjects themselves, but their "will" was directed opposite to the direction during production of the same run. So the question can be put: "What influence on the invisible trials is greater, the (labeled) positive influence during the production of the run or the negative influence during the play-back?". We infer that the positive influence is predicted by the straightforward classical explanation (as we call it) while the negative influence is predicted straightforwardly by the OHPP.

As the outcome of the invisible trials of part B is slightly positive (CR = 1.39), the classical explanation is very slightly favored over the OHPP. Of course, explanations considering OHPP with psi-missing can be put forward, but this stretches the imagination. On the other hand, when considering a classical explanation, one has to take into account that the subjects were not aware of the invisible trials at the time of the experiment.

The data in table 4 give no significant effect of RNG-frequency, runlength, visibility or display memory parameter. We notice that visible trials are on itself significant (P = .032), while invisible are not (P = .19). As for runlength we observe that the visible trials at a runlength of 6 seconds are significant (CR = 3.09; P .001). The nonsignificant scoring on the long runlengths of 9 and 12 seconds is consistent with the results found in our pilot studies. In these, we found that of runlengths of 3, 4.5, 13.5 and 42 seconds, only those of 4.5 seconds showed a significant deviation (P = .01).

We have calculated the efficiency of this experiment (see table 5). If we compare it to the efficiency figures obtained in Schmidt's experiment (1973) our efficiency seems rather low. In the first place Schmidt uses selected subjects in his experiment, about which he does not indicate the criteria on which selection takes place. That causes that his experiment cannot be exactly replicated at another place in the world. For this reason we did no selection on our subjects.

Schmidt does not take into account the time invested in the selection of his subjects. Furthermore his setup was such that experimenter and apparatus should be available any time the subjects considered themselves capable of producing good runs. In our setup the whole experiment took 7 hours including introduction of the subjects to the experiment. As we took for .each subject just half an hour, introduction and atmosphere were rather unpersonal and hurried. It is our feeling that a further study with subjects 2,3 and 14 may enhance the efficiency to a level comparable to that found by Schmidt. However, if this selection remains necessary the duration term in a honest efficiency calculation should take into account this fact, so that other laboratories that plan to replicate indeed get a good impression in how much time they can expect to obtain a significant result. Maybe it is sensible to avoid attaching too much meaning to efficiency in one sense or another before it has been shown to be a reliable measure. Meanwhile it is juggling with the few parameters available like trial rate, duration and obtained CR, while wishing to increase the last.


Levy, W.J. and Davis, W.J., Introduction of an activity-wheel testing cage into rodent precognition work. J.Parapsychology, 37, 1973, p.253

Schmidt, H., PK tests with a high speed random number generator.J. Parapsychology, 37, 1973, p.105

Walker, E.H., Foundations of paraphysical and parapsychological phenomena. 15th Annual Convention of the Parapsychological Association, Ediburgh 1972.

Feather, S.R. and Brier, R.M., The possible effect of the checker in precognition tests, J. Parapsychology,32, 1968, p.167

Brier, R.M. and Tyminski, W.V., Psi application: Part 2. The majority vote technique - analyses and observations. J. Parapsychology, 34, 1970, p.26

Houtkooper, J.M., Eerste uitkomsten van een onderzoek aan het psychokinetisch plaatsings effekt. (First results of an investigation on the psychokinetic placement effect). Tijdschrift voor parapsychologie, 35, 1967.

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