Signal processing analysis of forcedchoice ESP data:
evidence for psi as a wave of correlation.




Abstract:  Signal processing methodology was applied to forcedchoice ESP data. This methodology, which has been used successfully in a variety of other scientific disciplines, appears to have yielded information about psi not available by classical methods. In the ESP experiments reported here, a form of cross correlation of guesses with targets revealed the presence of periodic maxima. Upon computing the number of matches between guesses and targets at all possible displacements, we found that most of the matches were in clusters that recurred regularly and periodically throughout the whole range of displacements. Fourier analyses of the cross correlations were performed to quantify the harmonic patterns. The power maxima were then compared to Monte Carlo simulations of the experiments. In the linear and circular correlation analyses of grouped data from selected subjects, the mean power was statistically significant (p [less than] .002 and p [less than] .001, respectively). We termed the observation of a significant harmonic pattern in the correlation of targets and guesses a "correlation wave." Also, two post hoc analyses of grouped data from unselected subjects revealed that only subjects with visual (rather than verbal) cognitive styles guessing highimagery targets had significant or nearsignificant correlation waves (p [less than] .037 and p [less than] .063). Therefore, within the context of these experiments, guesses and targets were related in a meaningful way by wave functions, possibly suggesting the operation of a natural, lawful process. Psi has repeatedly been found to be unconstrained in ordinary ways by space, time, and causality. These properties of psi suggest that psi should appear as a pattern throughout the entire range of data rather than be locally confined to one or a few places in the data, as it is usually described. Our results suggest that psi may be an oscillatory correlational field, dependent upon or interacting with mental factors and target characteristics and capable of organizing information or even macroscopic objects in contextually meaningful ways. 


Subject: 
Signal processing
(Usage) Extrasensory perception (Research) Statistical hypothesis testing (Usage) Correlation (Statistics) (Usage) Parapsychology (Research) 
Authors: 
Don, Norman S. McDonough, Bruce E. Warren, Charles A. 
Pub Date:  12/01/1995 
Publication:  Name: The Journal of Parapsychology Publisher: Parapsychology Press Audience: Academic Format: Magazine/Journal Subject: Psychology and mental health Copyright: COPYRIGHT 1995 Parapsychology Press ISSN: 00223387 
Issue:  Date: Dec, 1995 Source Volume: v59 Source Issue: n4 
Accession Number:  18445602 
Full Text: 
INTRODUCTION This study began with the serendipitous discovery of apparently nonrandom patterns in displaced ESP data gathered during a longdistance test of clairvoyance with Olof Jonsson, a selected subject who has a long history of participation in ESP tests (Don, McDonough, & Warren, 1992). The subject attempted to guess the order of five symbols (star, wave, cross, square, and circle), each repeated five times, in a computerrandomized, 25card Zener deck located approximately 1500 miles away. For purposes unrelated to the signal processing methodology used here, we examined ESP displacements of 24 to +24 lags from the intended target. Displacements occur when a subject in an ESP experiment identifies stimulus material other than the intended, or focal, target. For example, in a forcedchoice, cardguessing task, guesses that significantly often match the symbol on the card immediately following the target card would be referred to as exhibiting a forward displacement (+1 lag). Similarly, guesses matching the symbol on the card immediately preceding the target cards would be referred to as backwardly displaced (1 lag). Such displacement effects have a long history in parapsychology, dating at least to the middle of the last century (Alvarado, 1989), although rarely have displacements of greater than 2 lags from the target card been studied. Nonetheless, this study is not the first to examine an extended range of displacements. For example, Russell (1943) and Tart (1978) also did so, but they did not use the methods of signal analysis, as we did. Therefore, they did not address the possible presence of periodicities or wave effects. Our study is also not the first to report periodic psi effects. Investigators from the Netherlands have reported cyclical effects in psychokinesis data (Jacobs, Michels, Millar, & MillarDe Bruyne, 1988; Michels, 1987); however, these studies dealt with the time course of focal effects and not with cyclical effects as a function of lag, as we did. Carington (1935) published a report involving displacement analysis that presaged the methodology in our study (see footnote 9). His study came to our attention only after the present study was completed. A pattern of alternating bands or clusters of matches and mismatches extended throughout the matrix and seemed to parallel the main diagonal (the focal hit line). The clusters seemed to fall into a pattern suggestive of a wave or ripple effect like that seen in water. The effect was present throughout the entire structure of the data, which differentiates this from the ordinary displacement effects near designated targets that have been studied extensively in parapsychology. This finding was unanticipated. Since visual inspection suggested that there was a nonrandom, periodic structure to the data, we applied the standard methods of signal analysis to determine the character of the patterns. We used signalanalytic methods to examine the entire range of data instead of just counting symbol matches at one or a few places in the data, which would be a local analysis. By this means, we were able to analyze mathematically the apparent periodic data structure. Signal processing procedures have also been employed fruitfully outside of engineering in disciplines as far flung as paleontology (Cutler, 1995), astrophysics (Arp, Keys, & Rudnicki, 1993), and MRI image analysis (Bretthorst, 1990), yielding information not available by standard methods. The signalanalytic methods, described in "Methods and Results: Experiment 1," revealed the existence of a wave with statistically significant power when compared to a Monte Carlo simulation of Zener card guessing with 25card decks. We termed this the "correlation wave." Our efforts to validate the existence of the ESP correlation wave and understand its characteristics and determinants are reported herein. METHODS AND RESULTS: EXPERIMENT 1 Experiment 1: LongDistance Guessing of Zener Cards A doubleblind test of clairvoyance was conducted long distance by telephone with the first selected subject, who was about 1500 miles from our lab during all phases of the experiment, which lasted only onehalf hour. One newly purchased deck of Zener cards, never seen by the subject, was shuffled seven times. Each card was placed in a separate opaque envelope with an inner opaque liner, and a unique number (125) was written on each envelope. This procedure was carried out by an associate of the laboratory while she was alone in her office. The 25 Zener cards, each in its own numbered envelope, comprised the target set. This same target preparation procedure was followed in Experiments 24. The first author, Experimenter 1, then telephoned the subject, who by prearrangement had agreed to be available at that time. After he answered, the call was put on hold, and Experimenter 1 then ran a computer program that generated a list of pseudorandom numbers (125). The laboratory associate who had placed the cards in envelopes was given this list; she ordered the envelopes accordingly and returned them to Experimenter 1. Experimenter 1 then reconnected the call to the subject, a tape recorder was turned on, and the subject proceeded to guess the targets in order from the beginning of the series; Experimenter 1 wrote down his guesses. This process took about four minutes. The call was then terminated, and Experimenter 1 checked the list of guesses he had written down against those on the tape recording. Experimenter I then opened the envelopes and listed the actual order of the targets. The target list was made with the subject's guesses obscured, and it was double checked. No feedback to the subject was provided during the experiment; he was informed only of his focal score several weeks later. The original purpose of Experiment 1 was to study focal scoring (8 focal hits out of 25 trials, p [less than] .109, onetailed exact binomial) and displacement effects within [+ or ]2 lags of the focal target. Note that in closeddeck data, the binomial yields a reasonable approximation of the appropriate p value. In addition, we explored post hoc all possible lags of the displacement data from 24 to +24. Figure 1 shows a correspondence between the subject's guesses (along the ordinate) and target symbols (along the abscissa). Matches are displayed as diamonds, and mismatches by no entry (blanks). Since for each guess on the ordinate there are five possible target symbols on the abscissa, there are five diamonds in each row of the matrix, and a total of 625 cells in the correspondence matrix. Instead of the more or less random distribution of diamonds and blanks beyond the focal region that might be expected by chance variation, it was observed that they tended to fall into alternating bands centered about the main diagonal of the matrix. To analyze the data for the possible presence of a periodic pattern, a form of cross correlation(1) was computed. (We also refer to these as linear correlations.) Starting in the lower right corner of the matrix (the precognitive half) and proceeding to the upper left corner (the retrocognitive half), an alternating pattern of high and low hit densities was revealed. That is, for each of the 49 possible lags (24 to 1; 0; +1 to +24), the number of hits (matches) divided by the number of possible hits (which range from 25 for the focal to I for lags [+ or ]24) was computed, yielding the hit densities. For example, in Figure 1 the 1 lags lie along the line parallel to and immediately to the left of the 45degree diagonal (9 hits out of a possible 24; hit density was 9/24 = 0.375). By using hit densities, we reduced the twodimensional problem of pattern recognition in Figure 1 to one dimension. Next we examined the periodicity in the cross correlations by computing the power spectral density (PSD) of the hit densities with a Fast Fourier Transform (FFT) on the hit densities. In this way we quantified the harmonic patterns (waves) apparent to the eye in Figure 1 (Bracewell, 1986; Brigham, 1974; Gottman, 1981; Oppenheim & Schafer, 1989). The decimationintime FFT algorithm is described in Oppenheim and Schafer (1989, pp. 587598). The PSD is computed from the squares of the magnitudes of the spectral lines in the first half of the FFT divided by n squared. The PSD reveals how much power is present in the data at each of the possible frequencies. In the more common situation in which the data are in the time domain, the frequency range is determined partly by the rate at which the data are sampled, whereas the frequency resolution is determined by the time interval over which each data sample is collected. The signal analytic methods used to process the hit densities are illustrated in Figure 2. In Figure 2a, the (raw) hit densities, as computed from the correspondence matrix, are plotted. What would normally be considered the DC offset was removed by subtracting the mean hit density from the hit densities observed at each of the 49 lags, as seen in Figure 2b. A Hanning window(2) was applied in Figure 2c, which has the effect of tapering the ends of the signal. Because the FFT algorithm used in our PSD calculation required an integral power of 2 points, the 15 remaining data slots were filled ("padded") with zeros, consistent with standard practice (Bracewell, 1986). In Figure 2d, the effect of filling (padding) the ends of the signal with zeros is illustrated. Then 64point PSDs were computed, as seen in Figure 2e. Waves are commonly represented in terms of changes over time, but they can also be represented in terms of patterns in space or other variables. Because the trials were not precisely timelocked and no time information was recorded, the Figure 1 correspondence matrix includes no temporal information (except for the incidental increase in time from trial 1 to trial 25). The data are not temporal but are a function of trialtotrial separations. Therefore, the waves here are a function of lag number and may be said to exist in lag space. Because the data exist in a spatial(3) rather than temporal domain, instead of power by frequency variables, the power spectrum is a function of the number of cycles at each lag (the wave number, k). The inverse is the number of lags per cycle (LPC), which is the wave length ([Lambda]). There were three salient peaks in the PSD with periods of 2.78 LPC, 10.67 LPC, and 12.80 LPC [ILLUSTRATION FOR FIGURE 2E OMITTED]. The positive phase and the negative phase of each wave, corresponding to matches and mismatches, are most easily viewed for the 10.67 and 12.80 LPC waves. The power for all other lines in the spectrum was at least a factor of 2 less. In Figure 1, although the 10.67 cycle of lags was the most easily discerned visually, it had the second highest power, the maximum power being at 2.78 LPC. To assess its statistical significance, the maximum power spectral component of the PSD was compared to a 1000value Monte Carlo simulation. The actual experimental guess sequence was duplicated 1000 times (with the digits 15 substituting for Zener symbols) and paired with 1000 simulated, closeddeck target sequences generated by a random process.(4) Cross correlations and hit densities were computed, then 1000 PSDs (one for each simulated experiment) were calculated, and the maximum power value from each PSD was taken,(5) regardless of which spectral line yielded the greatest power. The simulated data had a mean of 0.000695 relative units and a standard deviation of 0.000309. The 1000 power maxima were then rank ordered from largest to smallest value. The probability of observing simply by chance a power maximum as large as or larger than the experimental maximum is given by the proportion of simulated maxima that exceed the experimental observation in value. The power maximum in Experiment 1 (0.001309 relative units), observed at 2.78 LPC, was exceeded by only 47 of the 1000 simulated maxima, corresponding to a probability ([p.sub.max]) of [less than] .048.(6) (See Table 1.) The existence of the significant [p.sub.max] was termed a correlation wave. The 95% confidence interval for the proportion of simulated power maxima greater than the experimental observation ranged from .034 to .060. (The 95% confidence interval of the true proportion (p) was estimated by the formula [Mathematical Expression Omitted] where [Mathematical Expression Omitted] = proportion of samples greater than the observation, [Mathematical Expression Omitted], and n = the number of samples in the Monte Carlo calculation.) To summarize, hit densities  which were cross correlations (computed in this case by counting symbol matches) scaled by the number of possible matches at each lag or displacement  were Fourieranalyzed to determine whether there were periodicities with statistically significant power. The maximum power spectral line, observed at 2.78 LPC, was compared to simulated data and was found to rank between 47th and 48th out of 1000 simulated power values. On the basis of Experiment 1, we hypothesized that in the spectral analysis of the cross correlation of guesses and targets of forcedchoice data of the Zener type, the maximum power spectral line is significantly greater than that produced by random fluctuations. That is, the entire range of guesses and targets is related by a wave function. This hypothesis was tested in Experiments 25 by comparing the mean of the powerspectral maxima of these four experiments to a Monte Carlo simulation of means as described below. Also reported are [p.sub.max] values and 95% confidence intervals for individual experiments. Because three of the four data sets used to test the hypothesis were gathered under conditions different from those in Experiment 1, each will be described briefly. [TABULAR DATA FOR TABLE 1 OMITTED] METHODS AND RESULTS: FOUR CONFIRMATORY EXPERIMENTS Experiment 2: Replication of LongDistance Guessing of Zener Cards An exact replication of Experiment 1 with the same subject was conducted one month later. There were 7 focal hits out of a possible 25 (p [less than] .220, onetailed exact binomial). A new Monte Carlo simulation was generated, as above, by pairing 1000 repetitions of the Experiment 2 guess sequence with 1000 newly generated closeddeck target sequences. Compared to this 1000point distribution of power maxima, the maximumpower spectral component observed in Experiment 2 was 4.26 LPC (0.001608 relative units), [p.sub.max] [less than] .009. The 95% confidence interval ranged from .003 to .014. Experiment 3: First Card Matching Experiment Experimenter I attempted to replicate partially the above two experiments with several modifications, using himself as the subject. When the target preparer returned the stack of randomized targets to Experimenter 1, each target in its own opaque envelope, instead of guessing each of the 25 targets in downthrough fashion, Experimenter 1 shuffled a second deck of Zener cards seven times with the intent of matching the order of those in the envelopes. This was done because in the past Experimenter 1 achieved better success in psi tasks presumably involving more unconscious processes, such as bulk matching, in contrast to individual target guessing. After the seventh shuffle, Experimenter 1 wrote down the order of symbols in the shuffled deck. Then he opened the envelopes and wrote down the order of the enclosed cards, with the first list obscured. Both lists were double checked by Experimenter 1. There were 7 focal hits (p [less than] .220, onetailed exact binomial). PSDs were computed, and the statistical significance of the maximum power line was assessed as above, except that the 1000value simulated distribution repeatedly paired the shuffled sequence found from card shuffling in Experiment 3 with 1000 newly generated random target sequences (power = 0.000765 relative units, [p.sub.max] [less than] .447). The 95% confidence interval ranged from .415 to .477. Post hoc inspection of the hit density data revealed a band of aboveaverage scores (lags 0 through 4) bracketed by bands of belowaverage scores, similar to Experiment 1, suggesting that the wave effect, if it existed, damped out beyond the focal cycle. Experiment 4: Second Card Matching Experiment For the purpose of replication, Experimenter 1 repeated Experiment 3 nine days later, again with himself as the subject and using the same protocol. There were 9 focal hits out of a possible 25 (p [less than] .047). The PSD yielded one power peak at the 8.00 LPC (power = 0.001265 relative units, [p.sub.max] [less than] .046, as compared to a 1000point simulation using Experiment 4 guesses). The 95% confidence interval ranged from .032 to .058. Experiment 5: PearcePratt Data Hubert Pearce was a highscoring subject tested in the laboratories of J. B. Rhine in the 1930s (Rhine & Pratt, 1954). One sample run of 25 guesses drawn randomly from the PearcePratt distance series was examined.(7) This analysis was carried out to determine whether the wave was the result of an experimenter effect, because Experimenter 1 had been involved in Experiments 14. There were 10 focal hits out of a possible 25 (p [less than] .017, onetailed exact binomial). There was one salient spectral line at 9.14 LPC (power = 0.001591 relative units, [p.sub.max] [less than] .011, calculated as above). The 95% confidence interval ranged from .004 to .016. The hit density data, plotted in Figure 3a, was smoothed with a threepoint moving average [ILLUSTRATION FOR FIGURE 3B OMITTED], which clearly revealed the periodicity. In Figure 3c, the PSD of the hit density data prior to smoothing yielded a wave length of 9.14 lags, which matched the periodicity apparent to the eye in Figure 3b. STATISTICAL SIGNIFICANCE OF THE FOUR CONFIRMATORY EXPERIMENTS Analysis of Mean Maximum Spectral Power for Grouped Data From the four 1000value Monte Carlo simulations used in the evaluation of Experiments 25, random samples of size four were drawn (one power maximum from each experiment), and their means were computed. (Note that it was the power maxima, not the cross correlations, that were averaged.) One thousand such means were then rank ordered. The mean of this distribution was 0.000711 relative units. The mean power maximum for Experiments 2, 3, 4, and 5, was 0.001307 relative units and was exceeded by only one of the simulated means (p [less than] .002). The 95% confidence interval ranged from .000 to .003. Therefore, the correlation wave hypothesis derived from Experiment 1 was now replicated and confirmed in new data. OTHER ANALYSES Tests on Other Salient PSD Peaks Observed in Experiment 1 The above analyses focused on the power maxima observed in the PSDs of experimental data. However, PSDs may sometimes have more than one salient peak (for example, as seen in Figure 2e showing the PSD of the Experiment 1 data set). Indeed, as mentioned earlier, it was not the power maximum observed at 2.78 LPC that first caught our attention, but rather it was another PSD component with a longer wavelength, but slightly less power, which we first noticed in the correspondence matrix. It can be seen in Figure 2e that this other component is actually comprised of two adjacent peaks at 10.67 and 12.80 LPC. Smoothing the Experiment 1 hit densities by taking a fourpoint moving average, as demonstrated in Figure 4, enhances the visibility of the slower components observed at 10.67/12.80 LPC. The statistical significance of the power in the secondary PSD peak (p [less than] .014), observed at 10.67 LPC (0.001245 relative units), was assessed post hoc by comparing it to a Monte Carlo distribution of 1000 simulated power values, each calculated exactly as described above except that the simulated values in the distribution corresponded to the second highest spectral lines instead of the power maxima, as was done previously. This Monte Carlo distribution had a mean of 0.000546 relative units and a standard deviation of 0.000233. It was not necessary to compare the tertiary spectral line, observed at 12.80 LPC (0.001231 relative units), to an analogous Monte Carlo simulation (made up of thirdhighest power values); it is certain that it too would be significant because its power exceeded all but 14 values in the distribution used to test the secondary line. Therefore we may conservatively estimate its significance at p [less than] .015. Tests to Determine Whether the Wave Effects were Localized With one complete cycle in the hit densities, such as a focal hit band and an adjacent miss band, the PSD yields a complete spectrum. To test whether the results of the linear correlation analyses were due only to such localized effects near the focal band, Experiment 1 hit densities from lags 1 through +7 (which by visual inspection appeared to be one cycle) were replaced by the mean value for all 49 hit densities (0.19506). The PSD yielded the same three peaks in the spectrum found for the whole data set, but with reduced power. Furthermore, the data were also divided into three sets: the one just cited and two other sets, on either side, one all negatively and the other all positively lagged. PSDs revealed that for all three sets of data, the same peaks occurred with power levels of the same order of magnitude. It therefore appeared that the wave effect was not localized just at the focal region of the data set in Experiment 1. Also, the maximum power levels in Experiments 2, 4, and 5 were of the same order of magnitude as in Experiment 1. Inspection of their respective hit density data revealed alternating runs of above and belowchance hits scores, similar to Experiment 1, suggesting that the wave effect was also not focally localized in these data sets. On the other hand, inspection of the hit densities for Experiment 3, which had a nonsignificant correlation wave, suggests the presence of only one cycle localized near the focal. A complete analysis of the effect of localized and nonlocalized waves on correlation wave power awaits future research; however, results of the circular correlation analyses, described below, also suggest that the correlation waves that we observed were not dependent upon localized effects. Autocorrelations on the Experimental Target Strings An autocorrelation was performed on the target sequence used in Experiment 1 to determine whether significant periodicities existed in the target sequence itself. Hit densities computed on the resulting signal were then processed as before; that is, the data mean was subtracted, a Hanning window was applied, the ends of the signal were padded with zeros, and a 64point PSD was computed. The maximum spectral component was observed at 2.78 LPC, the same as the power maximum observed for the whole Experiment 1 data set. The power maximum (0.00231231 relative units) was nonsignificant when compared to a Monte Carlo simulation of power maxima computed on autocorrelated, random target sequences (p [less than] .731). This Monte Carlo distribution had a mean of 0.003100 and a standard deviation of 0.001166. Analogous autocorrelations on the target strings used in Experiments 2, 3, 4, and 5 yielded power maxima of 0.002796 (p [less than] .497), 0.002480 (p [less than] .659), 0.002551 (p [less than] .628), and 0.003212 (p [less than] .361) relative units, respectively. Circular Correlation Analysis The data sets were limited to 25 guesses and targets, and so the hit densities computed on these data were affected by the diminishing populations at highorder lags. Because the population diminishes from 25 at the focal to 1 at lags [+ or ]24, the standard error accordingly grows large. However, the use of the Hanning window, which weights the highestorder lags with a function that diminishes to zero, reduced the contribution of data from lags with n less than 10 to nearly zero. If larger data sets had been available, then only subsets of data with robust ns at each lag, surrounding the focal, would have been analyzed. One solution to this problem was the use of circular correlation (cf. circular convolution,(8) Oppenheim & Schafer, 1989), which preserved an n of 25 for each lag. Guesses were arranged uniformly on a circle, and targets were arranged on a concentric circle. Starting with guess 1 adjacent to target 1, the number of matches of symbols at all 25 adjacent positions across the two circles were counted. Next, the circles were displaced 1 lag, so that guess 1 was adjacent to target 2, and the symbol matches at all 25 positions were counted. The matches at progressive lags were computed for all possible 25 lags (024). The existence of significant circular correlation in our data would mean that the same periodic signals or patterns were found throughout the entire data ranges in both guess and target data sets. Because both ends of the data were joined, the maximum power spectral component of the wave would also be continuous across the data boundaries. Displacement analysis treats the data with a linear model that preserves the forward (+ displacements) and backward ( displacements) directionality of causality. In a circular analysis, the contribution to the measured effects is derived from a circular process, and so there is no directionality to causality. For example, correlating the guess data set, g(i), with the target data set, t(j), when the latter is rotated one lag produces the following set of comparisons: g(1)t(2), g(2)t(3), . . ., g(25)t(1).(9) We undertook this confirmatory analysis to avoid the diminishing population problem in the tails of our data, but not knowing whether there was circular continuity in the data. There was no reason to expect such effects in our data, even though the linear hit density analysis for grouped data was significant, and we had shown that the periodicity was spread somewhat beyond the focal band. Therefore, circular correlation analysis was undertaken on all five data sets to determine whether the group mean PSDs calculated from the circular correlations were significant compared to a Monte Carlo calculation. For each of the five data sets, the circular correlation and the PSD were computed. Twentyfive point Discrete Fourier Transforms (DFTs) were used (Oppenheim & Schafer, 1989, p. 532). In contrast to the frequency analysis of the linear correlations, padding with zeros was not necessary because the DFT does not require that the number of data points be integral powers of 2, as did the FFTs used in the linear analyses. Neither was a Hanning window applied to the data, because there was an adequate sample size (n = 25) at all lags, and the other effects of windowing were of no relevance to us. As with the linear correlations, the DC component was excluded from further computations. The mean of the maximumpower spectral lines from the five data sets was compared to another 1000value Monte Carlo simulation. Each value in this Monte Carlo distribution was a mean of five randomly drawn power maxima, one from each of the simulated experiments. The circular correlation analyses were performed on the same simulated experiments that were used in the linear correlation analysis, described above. The mean maximumpower spectral value for the five experimental data sets was 5.1076 relative units,(10) and the mean of the simulation was 2.4224 (p [less than] .001). It was not possible to calculate the 95% confidence interval because the mean maximum value exceeded all of the simulated maxima in this distribution. Experiment 6: Unselected Subjects Additional forcedchoice data, originally collected by the late James Crandall (1987), were analyzed for the presence of a correlation wave. In that study, the subjects were 52 undergraduate psychology students; lists of low and highimagery words served as psi targets. Also, subjects were classified as having either a visual or verbal cognitive style on the basis of scores on Paivio's (1971) Individual Differences Questionnaire. These analyses, which used circular convolution, have been published elsewhere (Don, McDonough, & Warren, 1994). The results, reprinted in Table 2, indicate the possible presence of a correlation wave in two of the eight subgroups of subjects. The mean maximum spectral power was significant for the 14 subjects classified as visualizers scoring above mean chance expectation (MCE) on focal targets when guessing highimagery targets (p [less than] .037), and it was marginally significant for the 12 visualizers scoring below MCE on focal targets when guessing highimagery targets (p [less than] .063). Mean maximum spectral power was nonsignificant for subjects classified as verbalizers, regardless of focal scores, and for all subjects when guessing lowimagery targets. As in the previous analyses, statistical significance was determined by comparing each experimental observation (group mean) to a 1000value Monte Carlo simulation comprised of the means of 1000 randomly selected groups, each with group size equal to that of the experimental group in question.(11) [TABULAR DATA FOR TABLE 2 OMITTED] DISCUSSION It has long been held that psi is not bounded by the ordinary constraints of space, time, and causality. The results of this study are in accord with that belief: Under certain conditions, psi appears to be spread throughout all the data and not localized merely at one place, for example, to focal targets. Further, psi appears as a wave in the correlation between guesses and targets, that is, a "correlation wave." We may think of each guess as distributing the five symbols that match it and the 20 that do not in such a way that the preceding and succeeding guesses become coordinated into a regular, periodic pattern of matches and mismatches that runs throughout the whole data set. The patterns created in this way by the correlations are twodimensional [ILLUSTRATION FOR FIGURE 1 OMITTED] such that each experiment is a unity created out of all the guesses and all the targets taken as a whole. Even though subjects may pause, ponder, hesitate, or waver while guessing each trial, psi seems to transcend this apparent level of action by merging all elements of a defined experiment into a closed unity. In our data, these elements included the behavior of the subjects and the physical arrangement of decks of cards or lists of words. Perhaps the most striking, as well as the strongest of all our results, was from the circular correlation analysis. This analysis implies that the correlation waves were continuous across the data boundaries  the wave form at one end of a data set matched up with the wave form at the other end. This finding seems to suggest that psi acts to complete experiments, in the present case by adjusting the distribution of symbols to achieve the wave continuity. Because the symbols were printed on fullsized playing cards, their apparent arrangement by psi is provocative. We may think of the wave continuity across the data boundaries as further evidence for the unifying function of psi, in this instance by seamlessly transcending the data boundaries. These findings were determined using the methods of signal analysis rather than the conventional measure of psi, which involves counting matches between guesses and targets at one or only a few of the lags. Signal processing procedures have also been employed fruitfully in fields as varied as electrical engineering, paleontology, astrophysics, and MRI image analysis, there too yielding information not available by classical methods. In paleontology, a signal processing approach has yielded precise temporal information from the fossil record which had been smeared by the mixing of sediments (Cutler, 1995). In astrophysics, another signal processing method was used to analyze data exhibiting unexpected periodicities in the red shift (Arp, Keys, & Rudnicki, 1993). Another example is its use on data from magnetic resonance imagers (MRIs) to detect frequencies and for image processing (Bretthorst, 1990). Is the correlation wave merely a measurement artifact? For example, were significant periodicities in the cross correlation of guesses with targets merely an artifact of strong autocorrelations in either the guess or the target sequences alone? The experimental guess sequences can be assumed to be nonrandom (Burdick & Broughton, 1987) and thus might have artifactually produced correlation waves of greater power than those produced by truly random data. However, if this were so, then correlation waves of comparable power would also have been present in the simulated (Monte Carlo) distributions, since the actual guess sequences were used there too, and the experimental data would not have stood out as significantly different. Nor were periodicities in the experimental target sequences a likely explanation of the observed results. Tests on the autocorrelations of the experimental target sequences indicated that, although periodicities were indeed present, these did not have significantly greater power than those from the autocorrelation of random target strings. Also, it is worth reemphasizing that the simulated data were processed in exactly the same way as the experimental data. Thus, any artifactual periodicities introduced by the methods of analysis cannot be responsible for the observed differences between experimental and simulated data sets. Similarly, design features, such as the use of five symbols and 25 trials per experiment, were common to both experimental and simulated data sets and hence could not have been responsible for the observed effects. Corollary to this, Experiment 3, which did not have statistically significant spectral power, was analyzed exactly the same way as the other experiments with selected subjects, all of which were significant. Another question involves aliasing artifacts, which introduce spurious low frequency periodicities into time domain data when sampled too slowly. As we have shown in the Methods and Results section, our data were in the spatial domain, not the time domain, and were not sampled. If real then, the correlation wave would appear to be a phenomenon different from psi displacement as it is conventionally interpreted. Following confirmation of the existence of an overall significant correlation wave, followup tests showed that the wave effect observed in Experiment 1, and then in Experiments 2, 4, and 5, was present throughout the entire structure of the data. This finding differentiates the wave effect from displacement effects near designated targets, which have often been studied in parapsychology. Nor can we easily modify the ordinary concept of displacement to account for the present data, for example, by considering the correlation wave to be simply the waxing and waning of a very broad displacement effect extending over the entire range of targets. Although the results of the linear analyses (using hit densities) might be accommodated in this way, the observation of significant wave effects in the circular analyses is less amenable to a displacement interpretation because the circular method scrambles together lags of different length. The results of the circular correlation analyses suggest instead that the correlation wave somehow transcends the data boundaries, so that the wave form at one end of the data matches up with the other end. This would be evidence for a new form of nonlocality for psi. Traditionally, displacement effects have been viewed as the flawed focusing of psi on targets adjacent to the intended target (Crandall & Hite, 1983). They are seen as discrete expressions of psi on a subset of targets. On the other hand, the correlation wave appears to be a more global expression of psi, relating all guesses to all targets. Alternatively then, displacement as it is traditionally measured may occur when a correlation wave is phase shifted with respect to the focal target. This is a testable hypothesis. In some data sets, such as Experiment 1, multiple salient spectral peaks were observed. Post hoc analyses on the secondary and tertiary spectral components observed in Experiment 1 indicated that the peaks were, if anything, even more outstanding relative to simulated data than was the power maximum. In other data sets, such as Experiment 5, there was only one salient spectral line. Also, as seen in Table 1, the wavelength at which the power maxima was observed varied widely among the experiments. It is not altogether clear at this early stage of investigation why some data sets have only one salient peak whereas others have more than one, or why the salient peaks appear at one rather than another wavelength. Further study is required to understand these differences and under what conditions they occur. Experiments 1, 2, and 5 dealt with subjects' guesses and the order of symbols in their respective decks of cards, and so in those cases the harmonic relationship may be interpreted as a psi information effect. However, Experiments 3 and 4 each involved two physical decks (a "guess" deck as well as a target deck), and statistically significant harmonic power was found in Experiment 4. That is, the physical arrangement of the cards in the two decks was in harmonic relationship, a finding that may be interpreted as a largescale psychokinetic effect. These results suggest that psi may propagate as a wave of correlation both in clairvoyance and in psychokinesis. We have demonstrated with three selected subjects and five data sets that there is strong statistical evidence for the existence of correlation waves. However, the small sample size raises the issue of generalization: How widespread is the phenomenon? Attempting to address this issue, we examined data from 52 unselected subjects in Experiment 6, finding significant correlation waves for a group of psi hitters (on focal targets) and nearsignificant correlation waves for a group of psi missers. Thus, even unselected subjects who are not high scorers may show evidence of correlation waves in their data. However, we note also that nonsignificant correlation waves were present for six other groups of unselected subjects. Because these analyses were post hoc and were not corrected for multiple numbers of statistical tests, these results must be considered only tentative. Nonetheless, the results of this experiment offer some support for the generalizability of the correlation wave hypothesis to unselected subjects, at least for a subset of those subjects. Moreover, the results of the analyses on the data of unselected subjects were consistent with those of the selected subjects in two potentially important ways. First, among unselected subjects, only those with a visual (as opposed to verbal) cognitive style had a significant correlation wave effect. Furthermore, although they were not tested on the Paivio Individual Differences Questionnaire to determine whether their cognitive styles were verbal or visual, two out of three of our selected subjects (contributing four out of five of the data sets) also claimed to use visualization techniques when performing forcedchoice psi tasks. Second, the results indicated the presence of a correlation wave for unselected subjects only when highimagery (i.e., easily visualizable) targets were used; and of course the Zener symbols used in the testing of our selected subjects were also highly visualizable. These results suggest that the use of visualization, and visualizable targets, may be necessary for the correlation wave phenomenon to occur. Clearly, this latter finding requires replication. Another possibility is that the correlation wave of subjects with a primarily verbal cognitive style is more focused or particulate than with visualizers, where it is more diffuse and holistic, perhaps reflecting the differences between left and right hemisphere brain function. Therefore, do verbalizers have wavelets, more localized than the waves of visualizers? This possibility is highly speculative at this point, and the definitive answer to this question must await future research; however, such a wavelet was found about the focal in Experiment 3. We encourage other investigators to look for correlation waves in ESP data. Data of the Zener card type are not difficult to collect, even with strict controls for possible sensory leakage. The experiments may be performed using cards, word lists, or modifications of computerized systems like the ESPerciser (Psychophysical Research Laboratories, 1985). Signal processing methods require specialized training, but there are many qualified persons, especially in certain fields of engineering, who could be tapped for collaboration. However, the results of Experiment 6 suggest that the subjects' cognitive styles must be assessed and that robust effects may be found only with strong visualizers and highimagery targets, whether the focal score is above or below MCE. Even so, a subject who is classified as having a visual cognitive style may not always invoke visualization and therefore may not produce correlation waves in every data set. This situation occurred in Experiments 3 and 4; in the first instance the same selected subject did not use a visualization strategy, and in the second he did. One way of dealing with this manipulation of mental state would be to monitor the EEG over visual areas to determine brain function during experiments. Experimental data could then be classified as associated (or not) with visualization. Additionally, exploratory EEG studies should be undertaken to determine whether there is physiological evidence for the presence of meditative or altered mental states associated with correlation waves. Another important question to be addressed is whether psi always propagates as a correlation wave, even though its wavelike character may go unnoticed in standard experiments. Or is there a parallel here to the dual nature of light  that is, under some conditions is it a wave, and under others is it not? We also touched earlier on the possibility that localized wavelets may occur under certain conditions, particularly for verbalizers, who presumably engage the two cerebral hemispheres differently than visualizers do. The question of differential hemispheric function is also addressable by EEG studies. The analysis of wavelets could be part of such a study. Finally, other questions to be investigated include: (1) whether phaseshifting of the correlation wave accounts for psi missing and the psimissing displacement effect (PMDE), and (2) whether high (or low) hit scores at any displacement involve entrainment among adjacent displacements (i.e., a significant reduction [or increase] of hit scores or spectral power in the PSD at adjacent displacements), which is another characteristic of certain wave processes. In summary, we report evidence of significant periodicities in the correlation of guesses with targets in forcedchoice ESP data, an effect we termed the "correlation wave." We have made efforts to rule out the possibility that the correlation wave is artifactual, but clearly further studies will be required to confirm this. If real, our results have profound implications for understanding psi. They suggest that psi is an oscillatory, correlational field, at least under certain mental conditions, detectable with multiple, identical, and visualizable targets. Within the context of an experiment, the correlational field meaningfully associates information and even macroscopic objects into a unity. These are harmonic associations, suggestive of a natural, lawful, organizing process. 1 Cross correlations are usually computed as the summed, lagged multiplications of two numeric sequences (Bracewell, 1986; Oppenheim & Schafer, 1989). Since our data were symbolic rather than numeric, symbols were represented as fivedimensional unit vectors (e.g., star = (1,0,0,0,0); cross = (0,1,0,0,0); and so forth. The summed, lagged dot products were computed, yielding integer results in the range of 025. For each lag, these were divided by the maximum possible number of matches at that lag, yielding a hit density between 0 and 1. 2 Because the data sample is finite rather than infinite, by weighting the data at both ends of the sample by a function that gradually approaches 0, artifactual ripples in the FFT, and therefore in the PSD, are reduced. In addition, because the higher order displacements account for small percentages of the possible observations, weighting these with the Harming window (Oppenheim & Schafer, 1989) reduces their influence in the data set. For our data, the data values from lags 15 (n = 10) through 24 (n= 1) and 15 through 24 became almost zero. 3 The change of a variable with time, measured from a fixed position, is the ordinary timedomain description of the variable, that is, in terms of frequency and period. The spatial domain description occurs at a fixed time when a wave is described in terms of space variables, that is, the rate of change of phase with distance (wave number) and wave length. 4 Each of the 1000 simulated target sequences was generated as follows: A hardware RNG, developed at the Foundation for Fundamental Research on Man and Matter (FREMM) employing two independent noise diodes, was attached to the serial port of a 486 computer and was sampled approximately every 3 ms. The bit level output of the RNG was compared (using "exclusive or" logic) to a similar pseudorandom number generated algorithmically (see below) in order to mitigate the effects of a potential malfunction of the hardware RNG (although none were known to exist). The result (a new integer from 0 to 255) was scaled to yield a digit between 1 and 5, inclusive. Because we were simulating closeddeck targets, sequences of 25 simulated targets were restricted to five occurrences each of the digits 1 through 5 (substituting for the five Zener symbols). After the fifth occurrence of any digit, subsequent occurrences were discarded, and the process was repeated until an acceptable digit was generated. The pseudorandom numbers were generated using the RAND function of Microsoft C/C++, version 7.0, seeded once at the beginning of each run with the C/C++ TIME function, which gives the number of seconds elapsed since midnight (00:00:00), December 31, 1899. A new set of 1000 random target sequences was generated in the same way for each of the analyses of Experiments 25 and for the autocorrelation calculation. 5 Each of the PSDs yielded 32 spectral lines (i.e., numerical power values). The first line (the DC offset) and the second line (64 LPC) were not physically relevant to the analysis of possible cyclic patterns among the 49 lags or displacements. Therefore they were excluded from further analysis. 6 The [p.sub.max] was calculated as (less than) the number of simulated maxima that exceeded the experimental maximum plus one, divided by the number of samples in the Monte Carlo distribution. Thus, [p.sub.max] for Experiment 1 was calculated as less than (47+ 1)/1000, or .048. 7 This sample run was run #1 from the archival raw data recorded September 21, 1933, located in the Parapsychology Collection, Container 541, Manuscript Department, Perkins Library, Duke University, Durham, NC. 8 Circular convolution is an analogue of circular correlation in which the order of one of the signals is first reversed before counting matches. 9 Only after our study was completed did we learn that in 1935 Whately Carington used a form of circular analysis in part of a study of precognitive guessing (Carington, 1935). Describing the analysis he performed on runs of hits, he stated: "I have allowed myself the slight latitude of treating each [data] sheet as a 'ring'  that is to say, of pretending that the first guess follows on the last . . . . This avoids trouble with end effects" (pp. 9596). Carington found, as did we, that hits tend to cluster among the displacements or lags. He analyzed only runs among focal scores and lags 1 and 2 because of the daunting amount of calculations required by hand. However, his desire to persist seems clear: "If my strength were as the strength of ten and I could command a fortyeight hour working day, I would pursue the point a few stages further" (p. 98). He commented prophetically  if not precognitively  that "refinements of this kind will have to wait until we have a machine which will score guesses and throws (or other events) mechanically." He further stated that "the provision of such a machine . . . appears to me to be almost indispensable for the proper prosecution of this class of work and of paragnostic studies generally" (p. 98). 10 The PSD algorithm used in all calculations up to this point differs from the DFT calculation employed here. Because of this and other factors affecting the scale of the results of PSD and DFT calculations, the latter values are several orders of magnitude larger than the former. 11 The experimental data of the unselected subjects were compared to simulated target sequences generated by a PSILAB II RNG (Psychophysical Research Laboratories, 1985) instead of the FREMM RNG used in the above analyses. Also, the PSILAB II RNG output was not combined with pseudorandom numbers as in the above analyses. However, extensive testing of the output of the PSILAB II RNG indicated no significant deviations from randomness, either in tests of frequency or serial dependency, of the output stream. 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