Copyright 1981, Journal of Parapsychology. Reproduced with permission. You may download and print one copy for personal use only. For additional copies or subscription information, write or Journal of Parapsychology, 402 N. Buchanan Blvd., Durham, NC 27701, USA.



(Originally published in Journal of Parapsychology, Vol. 45 No. 2, June 1981)

ABSTRACT: Previous experiments in PK with prerecorded targets emphasize an apparent noncausal mature of PK. Theoretical models suggest that noncausality may be the very essence of psi and that the effects, unplausible as they appear, may well fit into one logically consistent picture. Nevertheless, we have so far very little theoretical and experimental experience in dealing with noncausal systems. A further study of the more exotic matures of PK may help us further. Two questions are studied in this context:

l. If the target events in a PK test are not individually generated but are derived by a causal algorithm from one randomly determined seed number, can there still be a PK effect? Can PK focus seemingly backward in time on the moment when the one random seed number is generated, as theoretical models suggest?

2. Does it make a difference whether or not the seed number is looked at by some human observer, before the subject makes his PK attempt? This is part of the general question whether a preinspection of the data in PK experiments with prerecorded targets can affect the outcome.

These questions are also of immediate practical interest for the computer-oriented PK researcher. If one can use a seed-number algorithm for the target sequence and if even a preinspection of the seed numbers does not matter, then one can design particularly simple and controllable PK experiments.


Psychokinesis has been observed in the laboratory as a mental influence upon truly random processes occurring during dice falls or in electronic random generators based on radioactive decay or electronic noise.

Many natural random processes can be adequately simulated with the help of computer-generated quasi-random numbers: A sequence of such numbers r_1, r_2, r_3, . . . starts from a "seed number" r_0 and calculates the successive r_n's by some algorithm, r_n+1 = F(r_n) where F(x) is a suitable algebraic expression.

The first question to be studied in the following is whether PK effects can be observed with quasi-random numbers as targets when only the seed number is produced by a truly random process. Intuitively one might doubt this possibility because the PK effort made during a test run would seem to have to be focused backward in time onto the random generation of the one seed number. On the other hand, a mathematical psi model described earlier (Schmidt, 1978) supports such a focusing concept. This model takes the feature of noncausality as the very basis of psi phenomena and derives from this a number of intuitively implausible but nevertheless logically consistent implications. In particular the model predicts PK to operate in this experiment as efficiently as in the conventional case where each target event is momentarily generated by a separate truly random process.

The second question to be investigated is whether an inspection of the seed numbers by the experimenter, previous to the test sessions, might have a bearing on the test scores. The general question whether such an inspection of the prerecorded PK targets might inhibit the success of the subject's later PK effort had been raised previously (Schmidt, 1976) but not yet studied experimentally- and the mentioned mathematical model leaves the question unanswered as well.

The experiment to be described used about 512 PK target numbers for each test run. These numbers were derived from one seed number which was generated by a truly random process. The seed numbers for all runs in the main experiment were obtained in advance, and then one-half of the seed numbers were inspected by the experimenter. This inspection did not give any clues to tbe outcome of the test runs; but, theoretically, the experimenter would have been able to calculate from the seed number the PK target sequence and the final run score.


The experiment uses random numbers modulo 16, as they would result from the throwing of an unbiased "16-sided die." In a test run a sequence of such random numbers is generated at a typical rate of 8 per second. The basic feedback display is provided by a circle of 16 lamps wherein only one lamp is lit at any given time. With each generated random number the light moves by one step in a clockwise or counterclockwise direction in the following manner: The light, beginning at the top of the display, jumps continually clockwise for each generated random number (RN) until after a RN = 3 has been obtained. Then the light begins moving counterclockwise until after a RN = 12 has appeared. This process continues until a total of 16 clockwise-counterclockwise pairs of light motion have been completed. In the basic test arrangement the subject tries to make the light move more clockwise than counterclockwise, i.e., to extend the time periods of clockwise motion and to shorten the periods of counterclockwise light movement. At the end of a run, display counters give the numbers H and M of light jumps in the desired clockwise and opposite direction, respectively.

Note that the test situation (including the psychological conditions and the mathematical evaluation) are quite different from earlier experiments (Schmidt, 1971) in which a light performed a random walk around a lamp circle so that each individual jump was independent of the previous jump being given by a binary decision. In the present set-up the light moves for an average of 16 steps in the same direction before inverting its motion. Thus the random generator produces essentially a sequence of 32 random time intervals, and the subject's task is to lengthen the odd-numbered intervals and to shorten the even-numbered ones.

The equipment permits some additional forms of feedback. By the flip of a switch, the counterclockwise light motion becomes inhibited, and the subject sees periods of clockwise motion alternating with periods during which the light is at rest. The goal in this case is to keep the light moving most of the time.

An auditory feedback is provided by a gong tone which sounds at the beginning of each period of clockwise light motion and persists until the light reverts (or stops). Thus the subject's goal is to sustain each gong tone as long as possible and to shorten the quiet intermissions between gong tones. (The gong tone has an exponentially decaying component, which provides the pleasant gong-character and a constant component which insures the persistence of the tone until the clockwise light motion ends.)

An inverter switch is provided for subjects who want to aim in the opposite direction, i.e., to make the light move more counterclockwise in the original arrangement. The switch simply interchanges clockwise and counterclockwise motion in the display so that the light starts moving counterclockwise, and the subject succeeds by having more counterclockwise than clockwise motion.

The other display forms are similarly inverted so that in the stop/go mode the subject has to keep the light still rather than moving. Similarly, with the gong display, the goal would be to keep the gong quiet most of the time.

Thus the random number sequence used in a test run appears as a sequence of 16 strings of hits alternating with 16 strings of misses. The sequence starts with a hit string, and a hit or miss string continues until after it has encountered a "3" or "12," respectively.

The subject's goal is always the same-to make the total lengths of the hit strings greater than the length of the miss strings.


The test machine contains in a memory chip (INTEL 2716) a large supply (up to 1,000) of binary 16-digit numbers which have been generated by a truly random process (using radioactive decays as the source of randomness).

A microprocessor (INTEL 8035) in the test machine executes the algorithm for deriving quasi-random numbers r_1, r_2,... from a seed number r_0. The particular algorithm chosen can be written as

r_n+1 = B*r_n (mod p)
with p = 2^19 - 1 = 524,287
B = 242,293.

Remember that for two integers A,B the equation A = B (mod P) means that (A - B) is divisible by p. Thus r_n+1 is obtained from B*p as the remainder left at division by p. In a BASIC program the relationship would read

r_n+1 = B * r_n - p * INT(B*r_n/p).

In binary notation the prime number p appears as a sequence of 19 1's, and all r_n's can be written as binary 19-digit numbers.

The number B is chosen as a primitive root of the equation x^p-1 = 1 (mod p). (For further clarification see Hardy & Wright, 1945, or some other text on elementary number theory.) The smallest primitive root is x = 3, but B = 3^(5^6) (mod p) is more suitable because it lies farther inside the available number range (1,...,2^19-2). Then for any seed number r_0, different from 0 and p, the quasi-random number sequence has maximal cycle length, i.e., th numbers r_1, r_2,...,r_p-1 are all different and r_p = r_1.

For a test run a 16-bit binary number is taken from the store of prerecorded binary numbers. The 16 bits serve as the most significant bits for the 19-bit seed number, and the three least significant bits are always taken as 1, 0, 1. This guarantees that the seed number different from 0 and p. From the seed number a sequence of approximately 512 numbers r_1, r_2, r_3,... is derived, and from each of these 19-bit numbers only the four least significant bits are selected to determine one random number RN in the range (0,...,15). These numbers represent the mentioned decisions of a "16-sided electronic die."

Note that the algorithm executed by the microprocessor provides a cyclical quasi-random sequence of 2^19 - 2 binary 19-bit numbers and that this sequence contains every possible 19-bit number, with the exception of 0 and p, exactly once. Thus by choosing a seed number (different from 0 and p) we specify an entry point into this cyclical sequence, and the approximately 512 numbers following the seed number determine the outcome of the test run.

Thus, by choosing a favorable seed number we can pick out a section of the number chain which is favorable for success in the experiment. And since each section used in a test run comprises only about 1/1024 of the total chain length there is sufficient opportunity for such favorable sections to occur.


Exploratory work for the described experiment was started at the beginning of 1980. During 1979 the present experimenter had pursued several different pilot studies, none of which seemed promising. Thus the experimenter spent much of his time in building equipment for other experimenters and in preparing the new set-up to be used for the present tests.

Initial results with the new equipment were promising. Therefore, the whole test series could be undertaken in a general spirit of optimism. Whereas the main part of the experiment was exclusively aimed at establishing the existence of PK with prerecorded seed numbers, both with and without previous inspection, the initial tests were concerned with determining psychologically favorable test conditions. The subjects were encouraged to use a wide variety of approaches in order to avoid monotony. A session typically comprised about 8 to 10 test runs wherein each test run lasted either about 40 or 80 seconds, depending on the speed setting for "fast" (about 12 steps per sec.) or "slow" (about 6 steps per sec.).

Various psychological settings were explored, including the following:

1. Subject looks at the light display in the stop/go mode and tries to keep the light moving most of the time.
a. Subject visualizes a lively mountain stream or some other continual, easy-going motion. Subject feels that the light wants to move like the stream, without stopping.
b. Subject listens to lively music, standing up and feeling his body swing and move with the beat. The subject sees the light as part of the general movement but tries not to become anxious when the light stops temporarily.
c. Subject is asked to remember a situation wherein he was highly successful and experienced the exuberant feeling of winning (for example, in a sports competition). Subject tries vividly to associate this feeling with the task of keeping the light moving.
d. Subject relaxes while the light is moving but makes a tense, muscular effort to get the light moving again whenever it stops. This approach was aimed particularly at practitioners of martial arts.

2. In all the previous settings the gong tone feedback might be used in conjunction with the light display. But the tone display seems to be most appropriate for mentally relaxed or meditative approaches. Three typical approaches tried are as follows:
a. The subject listens to the tone, trying to "hang on" to the tone as long as possible. During the (unwanted) intermissions the subject patiently concentrates on imagining how the next gong will sound.
b. The subject meditates for a short period before each test run begins. Then the subject "meditates" on the tone, trying to experience each tone to its fullest.
c. The subject aims for the opposite goal-to keep the quiet periods long and the tones short. The mental picture involves the quiet periods going deeper and deeper into a quiescent mental state from which the subject is aroused periodically by the gong tones. Subjects may be instructed to slump down physically in the quiet periods and to straighten up with each renewal of the gong sound.

At the preliminary stage, apart from many less supervised and documented test runs, one formal test series of prespecified length was done. This series utilized the present experimenter as subject and differed from the main experiment insofar as none of the prerecorded seed numbers was inspected before the test session. Ten sessions of five runs each were held on different days. In five sessions a meditative, relaxed approach was used., In the other five sessions the approach was forceful and dynamic, frequently accompanied by lively music. These two types of sessions were alternated. A total of H' = 13,577 hit events and M' = 12,263 miss events were obtained. The difference, (H - M) = 1,314, corresponds to a CR = 2.12, significant at the .02 level. The values obtained for H' - M' under the relaxed and forceful conditions were similar (733 and 581, respectively).


For this experiment it was decided to perform a total of 100 test runs with predominantly unselected volunteers, and to complete another 50 test runs with a few particularly promising, selected subjects. It was decided to evaluate these two groups separately. Therefore, prior to the test sessions, two blocks of 100 and 50 random numbers (blocks U and S respectively) were generated using radioactive decay as the basic source of randomness. These blocks of numbers were recorded in different sections of a memory chip (INTEL 2716). Each binary 16-digit random number was to determine the seed number for one test run with the selected (S) or unselected (U) group of subjects.

A computer printed the generated seed numbers in a format of eight 6-digit seed numbers per line as shown in Table A in Appendix B. In order to distinguish between preinspected and uninspected seed numbers a templet was attached to the TELETYPE printer so that only the (odd-numbered) seed numbers in columns l, 3, 5 and 7 were visible. The experimenter read these numbers aloud and then closed his eyes, ripped off the printout, and inserted it into an opaque envelope for storage.

A selector switch on the test machine allowed experimentation under three conditions labeled P (play), S (selected subjects), and U (unselected subjects). In the play mode (P) the seed number for the test run was obtained by activating a true random number generator in the machine; whereas, in the Settings S and U the seed number was taken from the corresponding memory block. The seed numbers in the memory were accessed in the sequence in which they were recorded, and each number was automatically checked off so that it could not be used twice.

Most sessions were begun with a number of play runs to acquaint the subject with the different psychological approaches and forms of feedback. These play runs were not systematically recorded.

After the play runs a flexible number (average: eight) of test runs were done with seed numbers from block S (for the most promising subjects) and from block U for the others. The decision when to terminate a session was made rather subjectively, depending on the scores and the subject's and experimenter's mood and confidence. In a few cases where the subject appeared uncomfortable and prone to psi-missing under all conditions, the session was terminated after the play runs. A total of 11 subjects contributed to the U group. Subjects could participate in more than one session. Four subjects were selected for the S group. Three of these were known to the experimenter from previous work. The fourth was a newcomer who impressed the experimenter with his confidence and his proficiency in martial arts. He was the only one in this group to obtain a negative score.

Table 1 gives the results. It shows that the total score of the S group is significant with CR = 3.42 at the .0005 p level and that the half of the runs for which the seed numbers were preinspected is still significant with CR = 2.68 at the .005 p level. For the group U of unselected subjects the scores are lower: The total significance for the U group is CR = 2.19 at the .05 p level, and the contribution of the runs with preinspected seed numbers provides a CR = 1.45. Further information on the statistical evaluations and machine randomness tests can be found in Appendix A. A printout of all 150 seed numbers is provided in Appendix B as basis for any further analysis of the data one might wish to perform.

Table 1
Section P: Pilot study
Section U: Tests with predominantly unselected subjects
Section S: Tests with highly selected subjects.
H' and M' tally the total lengths of the hit and miss strings respectively. for each section. The CR values are calculated from equation (A6) in Appendix A.



The experiment obtained significant PK effects in a situation where the complete history of a test run was determined by a prerecorded seed number. The possibility of PK in this setting is in agreement with abstract theoretical psi models. The PK mechanism in this case might be tentatively interpreted in the sense that the subject's PK effort made during the test session was focused backward in time towards the moment when the random selection of the seed number occurred. But such intuitive interpretations have to be handled with caution.

Perhaps the most interesting question to be studied in this experiment was whether PK effects could still be found in cases where the seed number was inspected by a human observer before the subject made his PK effort.

This question is related to an argument that one might perhaps interpret PK effects on prerecorded targets still within a causally operating world if one is willing to abandon the concept of an absolute physical reality, independent of the human observer. Based on some still controversial interpretations of quantum theory one argues that perhaps there is no absolute physical reality; i.e., that things become physically real only when there is a human observer to take notice. Then in a PK experiment with prerecorded targets the decision for a "head" or a "tail" would not be made when the targets are generated and the results are recorded. Nature would be rather in a macroscopically ambiguous state until the later time when the subject, while receiving feedback for his PK effort, would notice the "head" or "tail." Then the PK effect would not have to reach into the past because the decisions were made "really" during the PK test session. If the consciousness of the human observer would play such a vital role in determining what is physically real, then an inspection of the prerecorded targets, or the seed numbers in our case, should make nature's decision final and absolutely real at this stage. And then the subject's later PK effort would find the decisions already made such that no cauSal PK mechanism could succeed in obtaining high scores. The experimental results, the appearance of a PK effect even with the preinspected seed numbers, refutes this chain of arguments, but the results are still consistent with the mentioned abstract mathematical psi models.

The use of randomly selected seed numbers from which a long sequence of targets is derived by algebraic processes has a practical advantage for experimenters working with minicomputers. Since only one random seed number is required for a whole test run, this seed number can be determined by the random times at which a few computer keys are pressed at the start, but no more sophisticated truly random generator is required.

SCHMIDT, H. Can an effect precede its cause? A model of a noncausal world. Foundation of Physics, 1978, 8, 463-480.
SCHMIDT, H. Mental influence on random events. New Scientist and Science Journal, 1971, 50, 757-758.
SCHMIDT, H. PK effects with pre-recorded targets. Journal of the American Society for Psychical Research, 1976, vol 70, 267-291.
HARDY, G. H., & WRIGHT, E. M. An introduction to the theory of numbers. Oxford: Clarendon Press, 1945.

(RPKP note: Appendices A and B will be included in due course)

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