Robert G. Jahn et al- Count Population Profiles in Engineering Anomalies Experiments

8/3/2019 Robert G. Jahn et al- Count Population Profiles in Engineering Anomalies Experiments

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Journal o f Scienti f ic Explorat ion . Vol. 5, No. 2, pp. 205-232, 1991 0892-3310/91 $3.00+.00Pergamon Press plc. Printed in the USA. 1991 Society for Scientific Exploration

Count Population Profiles in EngineeringAnomalies ExperimentsROBERT G. JAHN, YORK H . DOBYNS, and B R E N D A J. DUNNE

Prin ce to n En gin eer in g A n o m a l i e s Research , Pr ince ton UniversityAbstractFour technically and conceptually distinct experiments a ran -dom binary generator driven by a microelectronic noise diode; a determin-istic pseudorandom generator; a large-scale random m echan ical cascade;and a digitized rem ote perception protocoldisplay strikingly similar pat-terns of count deviations from their corresponding chance distributions.Specifically, each conforms to a statistical linear regression of the formd n / n = d(x - ), where dn/n is the deviation from chance expectation ofthe population frequency of the score value x divided by its chance fre-quency, is the mean of the chance distribution, and 8 is the slope of theregression line, constant for a given data subset, but parametrically depen-dent on the experimental device, the particular operator or data concatena-tion, and the prevailing secondary conditions. In each case, the result istantamount to a simple marginal transposition of the appropriate chanceGaussian distribution to a new mean value ' = + Ne , where N is thesample size, or equivalently to a change in the elemental probability of thebasic binary process to p' = p + e, where p is the chance value and e = d/4.Proposition of a comm on psychophysical mechanism by which the con-sciousness of the operator may achieve these elemental probability shifts isthwarted by the complexity and disparity of the several technical and logicaltasks that would be involved. More parsimonious, albeit more radical, ex-plication may be posed via a holistic information-theoretic approach,wherein the consciousnessadds some increment of information, in the tech-nical sense, into the particular experimental system, which then deploys itin the most efficient fashion to achieve the experimental goal, i.e., the voli-tion-correlated mean shift T he relationship of this technical inform ationtransfer to the subjective teleological processes of the consciousness remainsto be understood.

IntroductionOver the past twelve years, the Princeton Engineering Anomalies Research(PEAR) program has accumulated very large data bases on a number ofhuman/machine experiments, including a variety of microelectronic ran-domand pseudorandom binary generators, a macroscopic random mechan-ical cascade, and an assortment of analogue experiments using optical, me-chanical, and fluid dynamical devices. For the most part, attention has beenfocused on anomalous shifts of the mean values of the statistical outputdistributions of these machines, compared to their calibration behavior and/

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206 R. G . Jahn, Y . H . Dobyns, and B . J. D unneor theoretical expectations, in correlation with prerecorded intentions oftheir human operators. Full descriptions of the specific equipment utilized,its qualification and calibration, the experimental protocols, safeguardsagainst spurious artifacts, data collection and processing techniques, the de-tailed results, and their interpretation are available in many references(Jahn, Dunne, & Nelson, 1987; Dunne, Nelson, & Jahn, 1988; Jahn &Dunne, 1987; Nelson, Dunne, & Jahn, 1984, 1988a). In briefest summary,the following hierarchy of effects has been established:

1. Systematic anomalous deviations of the output distribution means ofsuch devices can be replicably achieved by a large number of common hu-man operators.2. T he scale of the anomalous effects are invariably quite sm all tanta-m ount to a few bits per thousand displacement from chance expectation inthe binary machinesbut over large data bases can compound to highlysignificant statistical deviations.3. The primary correlate of these deviations is the pre-stated intention ofthe operator. Randomly interspersed accumulations of data taken underthree states of intentionto get higher values; to get lower values; to main-tain the chance valueshow clear and systematic separations from one an-other and from the chance expectation.4. The form and scale of these "tripolar"separationsare identifiably oper-ator-specific. Some operators achieve in both high and low intentions; somein just one; some in neither; some regularly obtain shifts inverse to theirintentions;some even produceanomalousdataunder the null intention.B utthese results are sufficiently characteristic of the individuals that they mayreasonably be termed operator "signatures."5. T he dependence of the results on the particular machines employed isless clear. Some operators seem to transfer their signatures across two ormore devices, others show substantial differences from one device to an-other, but in most cases the scales of achievement are preserved.6. Sensitivity of the effects to a variety of secondary technical parameters,such as length or pace of the experiment, form of feedback, whether theoperator chooses the direction of effort or is instructed by a random selector,etc., is also found to be quite operator-specific. Some operators' perfor-mances are profoundly affected by such options; others seem oblivious tothem.7. Twooperators attempting to influence the machine in a cooperativefashion do not simply compound their signatures; rather, their joint resultstend to be distinctively characteristic of the particular pair.8. These effects can be obtained by operators widely displaced from themachinesup to distances of several thousand miles. In a nu m ber of cases,the characteristics of a given operator's "remote" data closely concur withhis "proximate" data.9. In some cases, remote effects can alsobe obtainedwhen the operator's


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Count population profiles 207effort is substantially displaced in time from the actual operation of themachine.10. Although little systematic correlation with psychological or physiologi-cal indicators has been attempted in this laboratory, there appears to be littledependence of individual operator achievement on personality, style, orstrategy. A ll of the over 100 operators so far employed in these studies havebeen anonymous and uncompensated, and none has claimed extraordinaryabilities before or after the experiments. W hen their individual effect sizes arearrayed in ascending order, the distribution covers a continuous range onlyslightly displaced from chance (Dunne, Nelson, Dobyns, & Jahn, 1988).

Although most of the data treatment and interpretation of these experi-ments has heretofore concentrated on the anomalous deviations of the out-put means, some incidental attention has also been paid to the behavior ofhigher moments of the experimental distributionsvariance, skew, kurto-sis,goodness-of-fit, and other more elaborate statistical criteria in the hopeof illuminating some aspectsof the physical, psychological, and epistemologi-cal mechanisms of these phenomena. T he ultimate assessment of this type,however, must entail systematic examination of the complete distributionprofiles, at whatever incremental scale the particular experimental readoutpermits. For our ensemble of random event generators, for example, basedas they are on binary combinatorials, the most natural incremental units aresimply the integer count reports that distribute about the sample mean, e.g.,for 200-sample binaries, the populationsof counts... 98,99,100,101,102...,etc. From such detailed distributions one may then determine whetherthe shift of the mean is driven by an excess or deficiency of nearby counts,counts in the tails, counts near the standard deviation, or by some regularlydistributed pattern of differences or by a totally random array. O ne m ay alsoinquire whether individual operators invoke identifiably different count pat-terns for their achievements,and how replicably so, thereby supplementingtheir cumulative deviation mean signatures in characterizing their individ-ual effects.U nfortunately, given the highly stochastic nature of the process, themarginal scale of the anomalous effects, and the number of parameters thatcan influence operator performance, monumental amounts of data must beaccumulated before any credible systematic trends in the individual countpopulations can be identified, and it is only relatively recently that our totaldata base has reached adequate dimensions to support such an effort T odate, the microelectronic random event generator (R EG ) ensemble of ex-periments has compounded to some six million trials, encompassing 108operators, three machines, and three major protocol variations. From thisreservoir, a number of sufficiently large and self-consistent data subsets m aynow be extracted, including some individual sets for a few of our moreprolific operators, that can reasonably be submitted to this count distribu-tion analysis.


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20 8 R. G. Jahn, Y. H. Dobyns, and B. J. DunneCount Population Profiles in REG Experiments

T he theoretically expected count distribution for any random binary gen-erator trial follows from the B ernoulli binomial combinatorial

where n(x) is the frequency of count x, N is the number of binary samplesper trial, and p is the elemental binary probability of each sample. For all ofthe experiments described here, N = 200, and all machines are designed toprovide p = 0.5. T he corresponding binomial distribution is very well ap-proximated by the Gaussian function(2)

with mean = N p = 100 and standard deviation s = [Np(1 - p ) ] = 7.0707. . . .Al l calibration data conform appropriately to these theoreti-cal expectations, within an empirical uncertainty on p of 5 X 10 -5 (Nelson,Bradish, & Dobyns, 1989).For virtually all composite or individual operator data subsets for whichstatistically significant anomalous deviations of the mean are found, thecorresponding count distributions appear, well within the inherent experi-mental noise, to retain essentially Gaussian profiles, albeit centered about adisplaced mean ' = 100 + dp, where d is characteristic of the particularsubset, the intended direction of effort, and an assortment of prevailing sec-ondary parameters. The essential question we wish to examine here iswhether the detailed forms of these translated distributions can provide anyinsight into the basic nature of the anomalous phenomenon.Given the tiny scale of d, it is best to deal in terms of the d i f f e r e n t i a lcount frequencies between the displaced distributions n'(x) achieved by theoperators, and the chance distribution, n(x) i .e., dn(x) = n'(x) n(x) .Figure 1 shows sets of such d n ( x ) profiles for an overall R EG data base ofsome 3.8 million trials performed by 92 operators over a period of elevenyears under the tripolar intentions of high, low, and null, compared to anappropriate set of calibration data.In thiscase, the null intentionand calibra-tion deviations are found to conform very well to statistical chance expecta-tion, as evidenced by the essentially randomalternation of positive and nega-tive values, and by the small number that exceed the two-tailed .05 confi-dence envelopes sketched on the graphs. T he high and low intention data, incontrast, show clear distributions of imbalance consonant with the totalmean shifts for these subsets. From these displays it is evident that the m eanshifts are being broadly supported by a preponderance of the individualcount deviations, rather than by more localized excesses or deficiencies inthe tails or elsewhere.

(1 )


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Count population profiles 209

Fig. 1a. Count frequency deviations. A ll diode REG: high, low.

Figure 2 shows the patterns of count frequency deviations for a singleoperator's contribution to this same data set Although these distributionsare considerably noisier because of the smaller data base size, similar firstconclusionsmay be drawn.From a full array of such graphs for all individualoperator contributionsto thisand all otherR EG data subsets, it m ay be quitegenerally concluded that significant anomalous displacements of the meanare almost invariably broadly distributed across the corresponding countdistributions, rather than appearing as more localized departures fromchance expectations.Temptations to search for yet more subtle features in these differentialcount patterns are largely deterred by the inherent statistical noise whicheven for these very large data sets tends to obscure any secondary regulari-


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210 R. G. Jahn, Y. H. Dobyns, and B. J. Dunne

Fig. 1b. Count frequency deviations. A ll diode R EG: baseline, calibration.

ties. It is possible, however, to take another analytical step that may help toilluminate the basic nature of the process underlying these anomalies.Namely, if the count data are re-plotted as proportional deviations, i.e., asthe differences between the operator-generated distributions and the chancedistribution, normalized by the latter, ( d n / n values in x,) a particularlysimple functional relationship tends to emerge in most cases. The data ofFigure 1 are regraphed in this form in Figure 3. (Countsbelow 85 and above115 have now been excluded because their populations are too small toprovide stable estimates.)D espite their large stochastic swings, each of thesepatterns can be statistically well fit by a linear regression of the form(3)


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Fig. 2. Count frequency deviations. D iode R EG: Operator 010.i.e., by a straight line through the mean count,with characteristic slope 5. (Inthese and subsequent figures, Z1 is the z-score denoting the significance ofthe linear term in the regression; Z2 denotes the improvement that would bemade by retaining a quadratic term. Other details of the regression calcula-tion are presented in the Appendix.) A s shown in Figure 4, this form alsoobtains at the level of the individual operator data of Figure 2, and has beenconfirmed over many other composite and individual data sets not shownhere. In virtually all cases, the linear fit is statistically sufficient; the qua-dratic, cubic, and higher terms are usually not needed.This striking result is most parsimoniously consistentwith the hypothesisthat the displaced distribution is still Gaussian, but with its elemental binaryprobability,p = 0.5, somehow altered to a newvalue,p' = 0.5 + e,where thesize of e is characteristic of the subsetor individualoperator.This can be seen


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212 R . G . Jahn, Y . H . Dobyns, and B . J. Dunne

Fig. 3a. Proportional frequency deviations. A ll diode REG: high, low.

most directly by partial differentiation of the G aussian function with respectto the mean value, , holdingx constant as parameter:

Inserting

and

(4)

(5)(6)


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Fig. 3b. Proportional frequency deviations. A ll diode REG: baseline, calibration.

yields(7)

In other words, a single incrementaldistortion of the elemental binary proba-bility, commensurate with the overall mean shift of the Gaussian, manifestsas the observed linear displacements of dn/n.This does not, of course, imply that each count deviation contributesequally to the overall shift of the distribution mean. For this assessment onerequires the first moment of the deviations about the m ean, which we mightterm the leverage distribution, L(x) = dn(x- ). Empirically, thisdistribu-


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214 R . G . Jahn, Y . H . Dobyns, and B . J. Dunne

Fg4. Proportional frequency deviations. DiodeR EG: O perator 010.

tion is found to reach a maximum at a count somewhat outsideof the firststandard deviation. A theoretical leverage distribution can be computedfrom the linear fit of Eq . (7) and the Gaussiann(x) approximation (2).(8)

where C subsumes both the constant coefficients and the bias parameter, e.For our values of n and a , thisfunction has maxima at (x ) = \2s, i.e.,atthe counts 110 and 90, consistent with the experimental distributionssketched in Figures 5 and 6 for the overall diode data base and the singleoperator, respectively.It is temptingto leap from the generic result of relations (3) and (7) tospeculate on possible modes of interaction of the consciousness of the hu-man operatorwith the R EG noise source, whereby the elemental probability


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Fig. 5. Count leverage on mean shift. A ll diode REG: high, low.

of the microelectronic processes occurring therein might be altered by theindicated amounts. It should first be noted, however, that considerable elec-tronic processing is applied to the output of the primary noisediodeprior tothe bit-counting stage, including the imposition of an alternating templatethat compares the raw randombit stringwith a regularly alternatingcriterion(+, -, +, , + , ) and countsthe coincidences of sign. It is these coincidentcount distributions that constitute the experimental data and are used asfeedback for the operators. While this strategy has the powerful technicaladvantage of eliminating any possible influence of remanent D C bias thatmight escape the extensivevoltage regulation failsafe system, it considerablycomplicates and delimits the modalities by which the operators' influencemay be imposed. In particular, introduction of a simple systematicbias inthe raw noise pattern or the primary bit string will not avail. Rather, the


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216 R . G. Jahn, Y. H. Dobyns, and B. J. Dunne

Fig. 6. Count leverage on mean shift. Diode REG, Operator 010.

effect must be exercised much further along in the preparation of the outputcount sequence.This complexity of interaction is underscored by similar treatment of re-sults from "pseudorandom" versions of the R EG experiments. Early in theR EG program, in an effort to assess the sensitivity of the observed effects tothe specific nature of the noise source, a number of other microelectronicsources were developed, among them a hard-wired array of shift registersthat produces a deterministic string of pseudorandom digits (Jahn, Dunne,& Nelson, 1987; Nelson,Dunne, & J ahn, 1984).Thiscontinuously runningstring, which repeats itself every thirty hours, can replace the diode randomsource in the composite REG circuit box by a flip of an external switch,leaving all other functions of the experiment, includingits feedback and dataprocessing, identical. O verall results using this pseudorandom version, in


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Count population profiles 217terms of intention-correlated, operator-specific shifts of the mean, are essen-tially the same as with the electronic diode noise sources.Since the only evident mode of operator influence on the output distribu-tions of such a deterministic device is via the points of incursion into the bitstring, examination of the count population patterns should be particularlyinteresting. Figure 7 shows dn/n for the entire pseudorandom data base ofsome 700,000 trials. (No individual operator has yet generated sufficientdata on thisdevice to support this analytical treatment.) Note once again thelinear fits of magnitude consistent with the overall mean shifts. Clearly, if weare to retain the image of an induced bias in the underlying elemental proba-bility, its mode of attainment must be extremely subtle. This point will befurther illustrated in the context of the more substantially different experi-ments discussed in the next section.

Fig. 7. Proportional frequency deviations. A ll pseudo-REG.


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218 R . G. Jahn, Y . H . D obyns, and B . J. D unneBin Populations in a Random Mechanical Cascade Experiment

R EG experiments like those described above have served as the bench-mark studies of the PEAR program since its inception. From these haveradiated a number of ancillary experiments designed to explore systemati-cally the dependence of the anomalous phenomena on various technical,aesthetic, and procedural parameters, such as the scale of the machine, itsphysical domain, the character of its feedback, the quality of its randomicity,etc. Of these, the most extensively developed and deployed counterpart tothe microelectronic R EGs has been a room-size "Random Mechanical Cas-cade" (RMC)apparatus, shown in Figure 8a, wherein 9000 polystyrenespheres are allowed to trickle downward through an array of 330 nylon pegsto distribute themselves am ong 19 collecting bins lined across the bottom ofthe device. Photodetectors track the entrance of each ball into each bin andappropriatecomputational programs recordanddisplay on line thegrowingbin populations, followed by the terminal distribution properties.

Fig. 8a. Random Mechanical Cascade Apparatus.


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Count population profiles 219T he detailed mechanics of the ball trajectories through the peg maze aremuch too complex to permit calculation of a theoretical bin populationdistribution, but when properly aligned, the machine yields calibration dis-

tributions sufficiently close to Gaussian to allow analysis by conventionalparametric statistics (Figure 8b). Even so, various environmental vagaries,most notably hydroscopic changes in ball and peg resilience and long termball and peg wear, preclude comparison of active experimental distributionswith any fixed reference. Rather, data are invariably taken and processed ona tripolar differential basis wherein operator efforts to shift the distributionto the right or to the left, or to take an undisturbed null, are compared locallywith one another.Further details on the design, operation, andcalibration of this machine,and full presentations of the large bodies of operator-specific and compositedata, are available in the references (Nelson, Dunne, & Jahn , 1988a). Mostbriefly, anomalous effects quite comparable in scale and character to thoseobtained on the R EG devices are found in these R MC experiments. In fact,the entire hierarchical list of salient effects sketched in the Introductionwould apply equally well to this macroscopic mechanical faculty. O f primaryinterest here, however, are the interior details of the terminal output dis-tributions.By its design and by its inherent statistical leverage, the R MC is even betterdisposed than the REGs to display of incremental count distributions,namely via the individual bin populations themselves. Indeed, although theabsolute number of experimental runs of this machine are substantiallysmaller than for the REGs, there are fewer bins than R EG counts, and thebin population data are actually somewhat less stochastic and easier to pro-cess. Figures 9 and 10, for example, show the mean differences in bin popula-

Fig. 8b. R MC baseline mean bin totals on theoretical Gaussian.


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220 R . G . Jahn, Y . H . Dobyns, and B . J . Dunne

Fig. 9. Mean bin population differences. A ll RMC.tions for right versus left efforts for the entire R MC data base presented inDunne, Nelson, and Jahn (1988) and Nelson, Dunne, and Jahn (1988a),and for the same individual operator, respectively. Note once again that alarge number of the bins contribute substantially to the overall mean shift,rather than leaving the burden to any particular few.A s before, it is instructive to display these population decrements in dn/nform, where the reference n here is the average of the right and left effortpopulations for the corresponding bins. T he results, like those shown in

Fig. 10. Mean bin population differences. RMC, Operator 010.


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Fig. 11. Mean proportional bin population differences. A ll RMC.

Figures 11 and 12 and for many other subsets not shown, again lend them-selves to a simple linear regression of the form(9)

where B is the bin number from extreme left to extreme right (10 is thecenter bin) and 5 is the slope of the fit. (The significant quadratic correction,

Fig. 12. Mean proportional bin population differences. RMC, Operator 010.


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222 R.G . J ahn , Y . H . Dobyns, and B . J. DunneZ2 = -2.214, in Figure 11, is attributable to the spurious effect of the R MCsidewalk, which tend to distort the end bin populations somewhat. If thecalculations are repeated with bins number 1 and 19 excluded, Z2 drops to-0.754; if 2 and 18 are also excluded, Z2 becomes 0.132. In both cases thevalue of Z1 and d remain nearly the same.)T he conformance of a large body of data on this macroscopical mechani-cal R MC device to the same form of linear d n / n relationship found for themicroelectronic and pseudo REG results must have important implicationsfor comprehension of the generic anomaly at work in these vastly disparatesystems. In the previous section we commented on the technicalcomplexityof the task facing the operator in attempting to impose his characteristicincrement, e, on the basic binary probability, p, to achieve the observedoutpu t results in the microelectronic and pseudorandom R EGs. To this wenow must add the yet more imposing complexity of the R MC system, wheretheelemental probabilityis deeplyburied in ahostof technical features, suchas the ball inlet conditions, the configuration and resilience of the scatteringpegs, and the high unpredictability of the ball/ball collisions that supple-ment the ball/peg interactions. Indeed, although we have on occasion madesome attempts to interpret the observed bin population distributions of thismachine in terms of a"quasi-binary" combinatorial, it is quite clear that thebasic scattering events span wide ranges of elemental probability, and com-pound in a highly hierarchical and non-linear fashion, so that the resem-blance of the output distributions to the Gaussian must be far more fortui-tous than fundam ental. In this light, the similarity of the observed bin popu-lation deviation patterns to those of the REGs becomes even moreremarkable than simply the scale and genre differences of these classes ofmachine would suggest In fact, it makesany common mechanistic interpre-tation so implausible as to require a more paradigmatic resolution.

Application toRemote Perception DataT he ubiquitous appearance of the count population patternsuncovered inthe various human/machine experiments outlined above and the implica-tions thereof for the basic mechanisms involved can be projected even fur-ther by one final example drawn from a substantially different sector of ourresearch program. For over twelve years, this laboratory has also carriedforth a coordinated experimental and theoretical component concernedwith the acquisition, evaluation, and interpretation of data in a variety of

protocols subsumed under the nomen of "Precognitive Remote Perception"(PRP)the acquisition of information about physical target scenes, remotein both space and time, by common human percipients, using other thannormal sensory processes. T he primary focus of this effort has been thedevelopment of analytical judging techniques to quantify the anomalous


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Countpopulationprofiles 223information contained in the several hundred formal target perceptions ac-quired in these experiments.These analytical strategies, fully described in asequence of publications (Jahn, D unne, & Jahn, 1980; Dunne, Jahn, &Nelson, 1983; Jahn et al., 1982; D unne, D obyns, & Intner, 1989), ultimatelyyield distributions of perception scores that can be compared with empiricalchance distributions for the same scoring methods. Such pairs of score distri-butions are found to correspond closely enough to Gaussian forms to allowparametric statistical evaluation of the mean shifts and higher moments,much like that applied to the R EG and R MC data. D espite the much smallersize of the PR P data base, the statistical significance of the mean shifts of thescore distributions are considerably greater than for the human/machineexperiments, w ith probabilities against chance ranging from 10 -6 to 10-12,depending on the particular data subset and scoring method.If the PRP experimental and chance score distributions are binned intodiscrete increments, they m ay be subjected to the same dn and d n / n analy-ses used for the R EG and R MC data. Figures 13 and 14 show the results ofsuch treatment of 277 formal PR P trials, ab initio encoded, employing aglobal target pool and both instructed and volitional protocols (Dunne,Dobyns, & Intner, 1989). T he similarities of form to the human/machinedata are unmistakable; the interpretation, however, is even more obscure.A ll of the PR P scoring methods are based on an array of thirty binarydescriptors ranging from very factual to very impressionistic details, such aswhether the scene is outdoors, whether it is noisy, whether people are pres-ent, etc., that are answered by the percipients after dictating their free re-sponse narratives. Each of these descriptors has a particular frequency ofoccurrence across the target pool of all scenes in a given data set. T he percip-

Fig. 13. PR P score frequency differences. A ll ab initio data.


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224 R . G . Jahn, Y . H . D obyns, and B . J. D unne

Fig. 14. PR P proportional score frequency differences. A ll ab initio data.

ient's responseto each descriptor iscompared to theproper statement for thegiven target, and that result is weighted in terms of the descriptor frequency.Thus, the linear d n / n pattern of Figure 14 is equivalent to a uniform slightimprovement in the statistical likelihood of the percipients' proper identifi-cation of the target descriptors, beyond their normal chance occurrenceacross the utilized target pool.Mechanistically, this seems far removed fromthe alterationofbitprobabilities in an REG, or from thesystematicmarginalmigration of balls in an RMC, yet the dn/n pattern similarities among themare unmistakable.

The tantalizingly similar simple patterns of the count deviations in thesefour disparate experiments, tantamount in each case to marginal transposi-tion of the chance Gaussian distributions consistent with incrementalchanges in their elemental binary probabilities, begs for some correspond-ingly simple common hypothesis for the attainment of these several empiri-cal anomalies. Yet, the individual complexity and collective differences inthe interior technical processes involved quickly render any such hypotheti-cal mechanisms extremely convolutedat best, suggesting thatamore genericand holisticapproach, even ifmore radical in its paradigmaticimplications,may ultimately be more productive. W ith no pretense of empirical verifica-tion or theoretical uniqueness, the remaining paragraphs o f f e r one such possi-ble representation.


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Count population profiles 225In a strictly technical sense, the only difference between the chance expec-tations of the various experimental outputs and their demonstrated anoma-lous results is a matter of information. In each case, the anticipated random

array of output digits, bin populations, or target descriptor scores has beenslightly ordered, thereby decreasing its overall entropy, and raisingits overallinformation content. Sincethe only empirically demonstrated primarycorre-late of this achievement is the pre-stated intention of the human operator, itis reasonable to assume that the source of this information increment is theconsciousness of that operator. Whether the process is regarded as a directtransfer of information from the operator's consciousness to the machine's"consciousness," or as an internal rearrangement of the total informationcontent of the bonded operator/machine systemalthough a philosophi-cally intriguing distinction in its own right is not of primary relevancehere.R ather, the essential feature is that the particular output pattern now findsitself obliged to assimilate this increment of information.In simplistic terms, the pattern has tw o options: it may retain a G aussiandistribution, displaced by the requisite amount to accommodate the fullinformation increment solely within its mean shift; or, it may distributesome or all of the information into an internal rearrangement of the countdistribution, e.g.,by changing its variance, developing a skew or kurtosis, orforming a more pathological pattern. In opting for the former reaction, asour empirical results indicate, the added information is utilized in the mostefficient fashion to fulfill the stated teleological task of the operator, in thiscase to shift the mean score, squandering noneof it in unproductive internaldistortions of the distribution. This option, which seems to be commonlyelected in all of the various experiments described, thus takes the form of a"minimum information" principle, with the consciousness of the operatorsomehow specifying the nature of the experimental goal, and the outputpattern deploying the minimum information necessary toachieve itA critical test of this hypothesis would be for the operators to address tasksother than shifts of the mean in otherwise similar experimental protocols,e.g., to attem pt to change the distribution variance, to develop asymmetries,or to overpopulate particular counts, to see whether the systems respond insimilarly efficient modes to f u l f i l l these volitions. U nfortunately, given thehuge data bases that would be needed to substantiate such statistical pat-terns, we are a long way from being able to validate the model in this moregeneral form. T he only relevant evidence in hand is from two operatorswho,in relatively smalldata sets, succeeded in significantly altering R EG distribu-tion variances, without substantially affecting the mean or other moments,and from a third who achieved similar effects on the RMC. O ne other opera-tor has had minor success in over-populating particular preselected R MCbins. Many more data of this sort are clearly required.A ny information transfer model for the observed phenomena inevitablyentails, energy transfer considerations as well, on purely physical grounds. O f


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226 R. G . Jahn, Y . H . Dobyns, and B . J. Dunnethe three recognized currencies of the physical w orldsubstantial matter(mass), energy, and informationthe relationship between the first two hasbeen unequivocally established via Einstein'smonumental equation and hasdominated much of twentieth century physical science. T he relationshipbetween energy and information has been less incisively formulated and lessextensively exploited, although models and empirical examples exist inmany physical sectors, notably the Second Law of Thermodynamics; thequantum mechanical exchange energy of covalent m olecular bonds; variouselectromagnetic resonance and coherence situations such as lasers andmasers; and,of course, fundamental information theory la Shannon and itsmany derivatives. T he classical separation of these three physical currenciesover most of scientific history is attributable to the huge size of the transmu-tation coefficients that relate mass to energy, and energy to information,respectively.In our experimental situation, the inversion of a small fraction of theinformation bits from their chance configurations or, equivalently, the shiftin the apparent elemental probabilities, alsohas energetic as well as informa-tive implications, although the former are of miniscule scale,again given themagnitude of the transmutation coefficient Nonetheless, what is of over-arching interest here is the possibility that the consciousnessof the operator,using that capacity for which it is most extraordinarily equippedthe pro-cessing of informationhas in these interactions entered proactively intothe affairs of the physical world, rearranging not only a portion of its infor-mation array, but thereby accessing its energy, and thence, by inference, itsvery substance. Extrapolating to more general implications, this modelwould thus suggest that the third side of the mass-energy-information trian-gle of physical currencies can provide a natural entry for hum an conscious-ness to participate in the construction of tangible reality, if we can but com-prehend the dynamics of transfer of the subjective information of the mindto the technical information of the cosmos.

ReferencesD unne, B . J., Dobyns, Y. H., & Intner, S. M. (1989). Precognitive Remote Perception III:Complete Binary Data Base with Analytical Refinements (Technical Note PEAR 89002).Princeton Engineering Anomalies Research, Princeton U niversity, School of Engineering/Applied Science.D unne, B . J., Jahn, R . G., & Nelson, R . D . (1983). Precognitive R emote Perception (TechnicalNote PEAR 83003). Princeton Engineering A nomalies Research, Princeton U niversity,School of E ngineering/A pplied Science.Dunne, B. J., Nelson, R. D., & Jahn, R. G. (1988).Operator-related anomalies in a random

mechanical cascade. Journal of Scient i f ic Expl ora t ion , 2. 155-179.D unne, B. J., Nelson, R. D ., Dobyns, Y . H ., & Jahn, R. G . (1988). Individual O perator Contri-butions in Large Data Base Anomalies Experiments(Technical Note PEAR 88002).Prince-ton Engineering Anomalies Research, Princeton U niversity, School of Engineering/A ppliedScience.


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Count population profiles 227Jahn, R. G., & Dunne, B . J. (1987). Margins o f reality. San Diego, New York, London: Har-court Brace Jovanovich.Jahn, R. G., Dunne, B. J., & Jahn, E. G. (1980). Analytical judging procedure for remoteperception experiments. J o u rn a l o f Parapsychology, 44 , 207-231.Jahn, R. G ., Dunne, B . J., & Nelson, R . D . (1987). Engineering anomalies research. Journal ofScienti f ic Exploration, 7,21-50.Jahn, R . G., Dunne, B . J., Nelson, R. D ., Jahn, E. G., Curtis, T . A ., & Cook, I. A. (1982).Analytical Judging Procedure for R emote Perception Experiments II: T ernary Coding andGeneralized D escriptors. (Technical Note PEAR 82002).Princeton Engineering A nomaliesResearch, Princeton U niversity, School of Engineering/Applied Science.Nelson, R . D., Bradish, G. J., & Dobyns. Y . H . (1989). Random Event Generator Qualifica-tion, Calibration and Analysis (Technical Note PEAR 89001). Princeton EngineeringAnomalies Research, Princeton U niversity, School of Eng ineering/A pplied Science.Nelson, R . D ., Dunne, B . J., & Jahn, R. G. (1984). An R EG Experiment with Large Data BaseCapability III:Operator Related Anomalies (Technical Note PEAR 84003).PrincetonEngi-neering A nomalies Research, Princeton U niversity, School of Engineering/ Applied Science.Nelson, R . D ., Dunne, B . J., & Jahn, R. G . (1988a). Operator Related A nomalies in a RandomMechanical Cascade Experiment (Technical Note PEAR 88001), and (1988b). O peratorRelated A nomalies in a Mechanical Cascade Experiment, Supplement: Individual O peratorSeries and Concatenations(Technical Note PEAR 8800 IS). Princeton Engineering Anoma-lies Research, Princeton U niversity, School of Eng ineering/A pplied Science.

AppendixError-Weighted Linear Regression

A ll of the data consist of many observations of a dependent variable yi,each associated with an independent variable value xi and involving a mea-surement uncertainty si. A linear model assumes that the data are of theform(D

where ei is an error term with mean zero. In an unweighted regression it isusually assumed that the error terms are all drawn from a common distribu-tion,whereas for the weighted regression employed here the ei are presumedto have variance s2i. It is further assumed that the various ei are independentT he goal of a regression analysis is to construct sample estimates bo of B 0 and

A least-squares approach that minimizes the total, normalized squarederror,

seems a natural choice in that it gives the error term a x2 functional formwhen the ei are normal, and includes the unweighted regression form as a

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228 R . G. Jahn, Y . H. Dobyns, and B . J. D unnespecial case. This total error may be minimized by finding zeroes of itspartial derivatives,

O n simplification, Eqs. (3) become a set of linear equations in two un-knowns,

which may readily be solved for b0 and b1 , yielding

Note that both b0 and b1 are l inear combinations of the y i , so that

where

and

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(3)

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(5)

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Count population profiles 229These k coefficients have the addition properties: S k0i = 1, S koixi = 0,S k1 i = 0, and S k1ixi = 1 , from which it follows that the expectation valuesof b0,b1are indeed the model parametersB0, B1 :

where the last equality follows from the addition properties of k0i and thefact that E [ e i ] = 0 for all i, by definition. A parallel derivation w ith the k1 ishows that E[b1] = B 1.In order to establish confidence intervals for the model parameters, it isalso necessary to know theirvariances.U sing s

2 [ x ] to denote the variance ofa formula x, w e note from the rules for variances of linear combinations thatBut, by the assumptions of the model,s2[yi]= s2[ei]=s2i.Therefore s 2 [ b 0 ]= S (k0isi)2 and,by a similar derivation, s2[b1] = S (k1isi)2. This allowsconfidence intervalson b0 and b1 to be established.In addition to inferences regarding the individual parameters, it is alsooften desirable to form joint inferences about the regression line that resultsfrom combining them. T he hyperbolic confidence band that results fromsuch calculations is an envelope about the regression line such that, with thestated likelihood, the actual model line Y = B0 + B 1x lies entirely within theenvelope. Establishing the confidence band requires calculation of the modelprediction variance s2[ Y] where Y = b 0 + b1x is the predicted value of theregression line at a given point x. The may becomputed as

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where the intermediate expansion is needed because, while the variancesof bo and b1 are known, they are not independent Given a formulafor s2[Y]. the locations^ of the confidence band limits are Y ^2F [ l - a; 2, n - 2]


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230 R. G. Jahn, Y. H. Dobyns, and B. J. Dunnesome non-random component of the data unaccounted for. T he simplestway to test this is by examination of the residuals after the regression lineprediction is subtracted from the data. A rescaling of the x axis values to x2,x3 or any other suspected contributing term can then be performed, and theresulting data fitted with a new regression line to be examined for significantslope.Theabsence of such a slope doesnot totallyguarantee that the contrib-uting term is not present, but only that the dataare insufficient to resolve it ifit is.

Regression Line and Mean ShiftA s demonstrated in the body of the text, if the theoretical frequency for thezth count value is denoted by ni; the empirical frequency is n 'i; the deviationof the ith count from the theoretical mean is xi; and the elementary successprobability is 0.5 + d then

(12)is the expected proportional shift in the population of the ith count value.T wo other quantities that are useful for this discussion are Pi, the actualpopulation of the ith count in a given dataset, and ti, the theoretical popula-tion expected in a dataset of N trials. Note that P, = An,-, f, = Nn f, and 2 t f= 2 P,:- N all hold as identities from their respective definitions. Alterna-tively 2 P, = # may be regarded as the definition of N.T o consider this in the context of the regression analysis above, we mayidentify y, = (P t t f)/;,- with the proportional shift in population for eachcount value. W e then note that under the null hypothesis P, is random withexpectation /, and standard deviation V//. Since a, are the standard devia-tions of y t for the regression analysis,


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Count population profiles 23 1ered to form one trial; therefore the number of binaries inquestionis 2/t. Theprobability of a hit in one binary is m/2n, where m is the empirical trialmean, so that

Combining (14) and (15), we obtain $ = (1/2/*) "2 n / X j - y , , which may beused in the right hand side of (12) to compute the predicted proportionalshift y, for each count value:

Now let us consider the linear regression fit that is computed for x, , y, , andf f f as defined above. First, since the bin probabilities are symmetric about thetheoretical mean, and x, is by definition the deviation from that mean,2 X f / f f j = 2 xtti = 0. This simplifies the formulas (5) for the regressioncoefficients to

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Noting that 2 P,- = 2 /,- = Wand P f = y^ + r/ are both required, weconcludethat 2 tg y,, = 0; this is in essence a constraint equation on y t that follows fromthe fact that the /, are normalized to the actual population. Applying thisrelation in (17) we see that b0 now vanishes identically. T he formula for b:may be simplified by noting that 2 tgxj is N times the trial variance. Sincethe number of binaries per trial is2u, from the binomial formula the trialstandard deviation is ^2ftpq = V/i/2 for p = q = 0.5. Therefore the trialvariance isjust ft/2 and 6, = 2 r, ^y,/^/*/^) = (2/n) 2 ,oc, J,. The regres-sion line prediction for the /th bin is thus Y f = (2//t)(2 n^y^x^ which isidentical to Eq. 16. In other words, the regression line and the mean-shiftprediction line are identical, unless the set of counts is incomplete, so thatcount-conservation conditions such as 2 P f = 2 *, are not perfectly obeyed.This latter situation actually arises in many cases, including those covered bythis paper, whenever extreme count values, i.e.,those in the tails of thedistributions, are insufficiently populated to allow stable estimates, and mustbe excluded.

One can also show that theregression line preserves the mean shift, or, toparaphrase, that a hypothetical data set,whose count population all fallexactly on the regression line obtained from an actual data set, has exactlythe same mean shift as that data set.From (14) the mean shift produced bythe actual data is dM = 2 n, x,yt. The various symmetries andconservation

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232 R. G. Jahn, Y. H. Dobyns, and B. J. Dunneconditions coerce the regression parameters to b0 = 0, bi = (2 ra,-x, > , )_ /(2 /xf ) . The predicted Y values for the regression line are then Yt= x,-(2 n j - X j - y ^ / C Z ,*;). B ut formula (14) for the mean shift applies to anyset of y i, so the mean shift for the hypothetical set Y i, can be calculated:

ReferenceNeter, J., and Wasserman, W . (1974). Applied l inear s ta t is t ical models. Homewood, Illinois:R ichard D . Irwin Inc.

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Robert G. Jahn et al- Count Population Profiles in Engineering Anomalies Experiments

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