RReductions eductions of informational entropy in continuous data froma networked of synchronized, true random sequences generators in in correspondencecorrelation with major world news events

R. D. Nelson,**, D. I. Radin,? R. Shoup,? P. Bancel§?

**?Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey  , 08544, USA

?Institute of Noetic Sciences, Petaluma, California, 94952, USA

??Boundary Institute, San JoseLos Altos, California,, ?????, 94024CA, USA

§???????Paris, France


At some 40 sites around the world, data are recorded from a network of true random number generators attached to time-synchronized computers connected through the Internet.  These generators produceing continuous, independent sequences of random numbers that are collected into an archival database.[1]  We examine this archive to determine the nature and frequency of statistical aberrations in long-term, consistently generated sequences.  Samples taken during calibrations or resampled[2] at arbitrary timesthat meet robust criteria for randomness in samples taken during calibrations or resampled at arbitrary times.[3]  Duringrandomness, but during certain pre-specified time intervals  predicted predictively identified periods there are, on average, significant departures from randomnessof distribution parameters from random expectation indicating structure in the data matrix.  These aberrations are correlated with major events in the world and with a quantitative index of daily news intensity, but not with electromagnetic field fluctuations.  This non-random behavior of true random sources remains unexplained, and we suggest that other technical and natural sources should be subjected to similar analysis.  Here we describe focused analyses of the data corresponding concentrating to on the disasters of September 11, 2001, ; the results indicate that reveal substantial deviations from chance expectation in statistical parameters and informational entropy, and further analyses show that these are not attributable to identifiable physical interactions.

            Research grade, hardware-based trulyQuantum indeterminate, electronic random number generators (RNG) with are designed with protectionshielding from environmental influences such as electromagnetic fields or fluctuations in temperature are designed to produce cryptographically secure random sequences with near-maximal entropy.2, [4]  Yet, under certain circumstances, such devices have shown surprising departures from theoretical expectations.  It is generally assumed that no shielding is required against intense variations in the perceptual or cognitive environment, in spite ofThere is controversial but substantial evidence that distortions of statistical distribution parameters may be correlated for unknown reasons with psychological statesconditions of importance to humans.[5], [6]  To address this this putative physical-psychological interaction in a rigorous wayamong other issues, a long-term, international collaboration was instituted in 1998 to develop a network to continuously collect standardized RNG data continuously continuously over a period of years.  The design required spatially distributed, independent sources, employing secure data-collection and networking software and high-quality RNG devices designed for serial computer interfacing.2, [7]  The resulting matrix of random numbers can be correlated with longitudinal data from many disciplines: cosmology, earth sciences, meteorology, economics, even with and other metrics of human activity.  We find no overall relationship with physical timeseries, but there is evidence that alterations in the statistics of random data may be correlated with operationally defined measures of human attention to major world events. 

On events. 

On Sept. 11, 2001, our this world-spanning network of RNGs displayed striking nonrandom structure in several statistics.  Though it is the most extreme human event case in the three-year database, the apparent "imposed" effect on the informational structure is not unique to this day, but is found also in correspondence with other major world events.  The correlations are cleardemonstrable , but it is not obvious clear yet how they arise, or whether there is some directan instrumental link with the world events or the intensely focused world attention.  At this point we feel it is appropriate to present an empirical description of methods and results, to invite comment and independent analysis.  The project is fully described on a dedicated Web site that presents results for a number of other examples of apparent structure where theoretically there should be none under the null hypothesis, accumulated over a period of three years.1  The Web site provides access to the original data for researchers who wish to confirm our analyses or examine the data from other perspectives.


Three types of electronic RNG devices are employed in the networkused.  All use a quantum indeterminate level process as the primary source of random events: thermal Johnson noise in resistors, or quantum tunneling in solid state junctions.  They are designed for professional research and pass an extensive array of standard tests for randomness, based on calibration samples of a million 200-bit trials.2  The devices are shielded from biasing influences across most of the electromagnetic spectrum, and utilize stable components and sophisticated circuit designs to protect against environmental influences and component interaction or aging.  In addition, the raw bit sequence is subjected to a logical XOR against a known pattern of an equal number of 0 and 1 bits to guarantee an unbiased mean output.  Custom software collects data at a rate of one 200-bit trial per second into time-stamped files on the local disk, with computer clocks synchronized to standard Internet timeservers.  Secure data packets are assembled and transmitted over the Internet to a server in Princeton, NJ, for archiving in daily files containing the data for each node for each second, registered in coordinated universal time coordinates (UTC).

            Standardized analysis protocols used to examine the RNG outputs may be are used to examine the random data during periods corresponding to major news events such as the disaster on Sept. 11.[8], [9]  For example, in one analysis the deviations of the 200-bit sums, or trial means, for each of the individual nodes, can be are normalized as

Zi = (mi-μ?)/σ?m, and these Z-scores are combined as Zs =Σ? Zi/N, where N is the number of nodes.  Given these algebraic composite Zs representing each second, a meaningful summary statistic for the period of interest is the sum of the squared Zs, which is a χ?2-distributed statistic quantity with degrees of freedom equal to the number of seconds.  This measure is responsive reflects to an excess of correlated deviation among the nodes, and will tend to  to be large if the independent RNG devices are subjected to a common influence that changes their output distributions in a parallel fashion.

            On Sept. 11, with 37 RNGs reporting, a trend to larger deviations began at about 04:00 EDT early in the morning and continued for more than 50 hours50 hours, until roughly noon on Sept. 13.  A "cumulative deviation" (cumdev) plot, such as is used in process control engineering to identify changes in monitored parameters, shows a striking departure from expectation of the χ?2 measure (Figure 1).  The trace displays an unexceptional random walk for several days preceding September 11 but then changes dramatically.  The aberrant trend beginning just before the World Trade Center (WTC) attack is unique in in the three-year database.:  a A trend with this slope continuing for so long would happen by chance only once in about 2300 days.  , and we find no other period of similar deviation in the actual data.  A corresponding analysis using of a “clone” database with pseudo-randomlyalgorithmically generated clonereplicareplacement cell entries[10] corresponding toof the Sept. 11 dataset shows no unusual trend, which rulesruling out analytical artifacts., and there is no other period of similar deviation in the three-year database. 

Figure 1:  Cumulative deviation of χ?2 based on the composite meanshift across RNG devices for each second, Sept. 7 through 1315, 2001. Day boundaries are in UTC and t The terrorist attacks are is marked with a boxrectangle on the line of zero deviation.  A parabolic curve beginning at the time of the attacks provides a 5% probability comparison.s  A segment of the parabolic envelope of 95% confidence with origin at 08:45 EDT (12:45 UTC), provides scale for the persistent trend of the random walk. 

            Low pass filtering with windows of 10 to 60 minutes shows substantial, persistent increases in this measure in extended bursts from approximately 04:00 to 05:00, 08:30 to 12:00, and 12:45 to 14:30 EDTD. 

T.  Spikes in the unfiltered, one-second composite deviations indicate an excess of inter-node correlations.  To test more generally for intercorrelations of the independent nodes, all possible correlations among the RNGs were calculated for each day's data over a period of a year, and each correlation then was transformed to a Fisher Z-score. The day with the largest value on this mean intercorrelation measure is Sept. 11, and it differs significantly from the mean of the distribution for all days from Dec. 1, 2000 to Dec. 31, 2001, t = 3.67 (p = 0.00012).

            The aberrant behavior of the data array on Sept. 11 is more sharply The defined in the variance (σ2) across the independent RNG devices. also exhibits  unusual structure, as shown in Figure 2.  There shows is a notable structure, with change a major departure from random fluctuation beginning about four hours before the first attack.  At that time, the variance increases over expectation by a striking amount, and it continues to exhibit excess until about 11:00 EDT, shortly after the fall of the second WTC tower.  Then the variance then undergoes a precipitous decrease that persists for several hours until about 18:00 EDT.  Over the course of approximately seven hours from 06:30 to 13:3011:00 to 18:00, the change from maximum to minimum maximum to minimum cumulative deviation is equivalent to 6.8.5  standard errors (σm)sigma.  Monte Carlo analysis determines that such an extreme monotonic trend in less than 8 hours would occur with a chance probability of approximately less than 0.002.  Similarly, aA bootstrap permutation analysis, reordering the actual data, yields an similar estimate of p = 0.0048 0009 for the peak excursion, based on 10,000 iterations.  For the Sept. 11 clone data the corresponding estimate is p = 0.756.  Figure 2 also shows the pseudo-random clone data in a visual comparison.  There are no similar, long-lasting trends in these "control" data.. 


Figure 2:  Cumulative deviation of variance (σ2variance ) across RNG devices, relative to the empirical mean value, across RNG devices for each second, on Sept. 11, 2001.  The truly random data from the network are contrasted with a pseudo-random “clone” dataset computed for the same array of data elements processed with the same algorithms.  TAxis labeling is in EDT; times of the terrorist attacks are indicated with rectangles boxes on the zero line.

            Figure 2 also shows the pseudo-random cloned data for Sept. 11 for comparison; there are no similar, long-lasting trends in these "control" data. To assess the generality of the variance effects in the actual data, we S separateding the RNGs into subsets on the basis of their location, as well as by random assignment.  The results indicated that  shows that similar aberrant trends are exhibited generally across the independent devices.  Computation of a complexity measure used to reduce dimensionality in neurophysiological data shows that a parameter closely related to variance is by far the largest contributor in a standard three-parameter representation.[11]  To aid in visualizing the variance excursions over long-extended periods, low-pass filtering with smoothing windows of one to six hours were applied to data from July through October 2001, and a six-hour window was applied to all days for a year.  The results clearly show that Sept. 11 is unique: no aberration of comparable magnitude occurred on any other day from Dec. 2000 to Nov. 2001.

            The next question is whether there is are any temporal correlations in the datacross-temporal linkage.  The sequential autocorrelation function is generally used as a check for independence of successive events.  In the Sept. 11 data we discoverThere are no short lag time anomalies in the autocorrelation function of the composite meanshift or variance on Sept. 11 for short lag times; the data appear to be independent on a time scale of seconds.  The aAutocorrelation function is, of course, also sensitive to extended excursions, and to cyclic or sustained fluctuations.  Figure 3 shows the autocorrelation function of the composite variance during the 24-hour UTC window for Sept 11, using 5-second blocks. The function was computed via Fourier transform for as a function of lag,lags from 1 second up to fourthree hours.  , during It shows a strong departure from expectation, witha 14-hour window from 04:00 to 18:00.  This period was selected to include the clusters of aberrant data that appear to drive the deviations of distribution parameters.  The autocorrelation that is consistently positive and highly significant for lags up to about one hour, thenslightly less  it drops slightly over the second hour, after which it drops to the expectation level.  The deviation is so persistent hat the trace penetrates a 10-6 probability threshold, implying a probability less than 0.001.  The return to zero correlation fFor lag times greater than two hours it drops to the expectation level of zero, implying implies that the deviant periods driving theis sequential a autocorrelation temporal linkage were on the order of one to two hours longin length..  The overall probability of such a large accumulation of excess autocorrelations in this 14-hour window is on the order of 1 part in 109. [measured how?]  Windowing the full 24-hour day yields a probability of 10-5.   For comparison, the figure includes traces showing the same computations for ten other days from September 5 to 15, all of which fall within a 95% confidence envelope.  These results imply a reduction of informational entropy in the nominally random data during and around the time of the Sept. 11 disaster.



Figure 3:  Autocorrelation of GCP scores for Sept. 11, 2001, contrasted with the same calculation for 10 surrounding days.  The variance of the trial scores across RNGs was converted to an approximate Z-score in 5for each -second blocks for the 24-hour UTC day.  The autocorrelation function for this time series was computed over lags of 5 sec to 3up to four hours.  Deviations from theoretical expectation for this normalized function are plotted here as a cumulative trace, summing the squared, normalized correlation coefficient, less its expectation..  Excess correlation is evident for lags up to 2 hours, and the maximum cumulative deviation has a chance probability of 10-5.  At lags longer than 2 hours, the autocorrelation reverts to normal.

This overview of the evidence for structure in a large array of nominally random data collected on Sept. 11, 2001 should be placed in the context of the long-term research project, but space does not permit a detailed presentation of the full corpus.  In brief, Tthere have been over 95 formal analyses of data associated with world news events such as the African embassy bombings in 1998, four New Year transitions, several natural disasters including earthquakes and floods, Internet-promoted large-scale meditation eventspeace meditations, and political events with international impact.  The results show the statistical variations expected of low signal- to- noise measures, but about two-thirds of the cases have a positive outcome relative with respect to the null hypothesis, and 21% are independently significant at or beyond the 5% level.  The composite probability that chance fluctuation can account for the total deviation from expectation across these focused analyses 95 replications of this experiment is less than one part in a 107.  Based on the intercorrelation measure described earlier, these major news events tend to occur on days with significantly higher intercorrelation among the RNGs.  To assess this relationship more generally, an objective metric was constructed based on an independent survey of news events.[12]  The count of characters in the summaries of news items was taken to represent the news intensity.  Over the one-year period from Dec. 2000 through Nov. 2001, this measure, though diffuse, is correlated with daily mean intercorrelations of the RNG data at r = 0.15, t (362 df) = 2.94, p = 0.002.[13]


Figure 4:  Correlation between daily news metric and daily RNG intercorrelation values.  Sept. 11, 2001 is associated with a news metric value of 398 in this graph.

            Alternative explanations for these departures of nominally random data from their expected values must be addressed before we seriously consider the anomalies to reflect human reactions to events such as the Sept. 11 disaster.  The electromagnetic spectrum is an obvious candidate.  Could mMajor changes in the electrical supply grid that were caused by the destruction, or and there was an enormous surges in cell-phone activity, or and an unusualan coherence increase in radio and television broadcasting coherence somehow have affected the RNG network?.  Because the devices are distributed around the world, their average distanceseparation from the physical disruption was on the order ovaries greatly (fmean distance, 6400 Km), but the effects is described above are broadly distributed across the network.  The appearance of strong deviations well prior to the attacks presents yet another conundrum, but it is inconsistent with EM field explanations.  More definitive is the instrument design, which includes physical shielding from EM interference down to about 1 Hz, and in addition, includes a logic stage that literally eliminates first-order biasing from electromagnetic, environmental, or other physical causes.  These indications are confirmed by analytical results.  Empirical computations based on RNG outputs according to local time the timeseries of daily intercorrelations show that there is no correspondence with expected diurnal variations in the power grid and no diurnal or other known cyclic patterning.10  12  We can find no evidence that physical influences arising from the extreme conditions of Sept. 11 were responsible for the structure found in these RNG data. 

            ODefinitive answers to the questions posed by these findings will not be easy to find because our analyses point to anomalous departures from expectation in nominally random data that are related, de facto, to global events of great importance to human beings.  The LocatingTo identify the source of the deviations we must account for excess inter-node correlations, persistent changes in composite variance, and long-term autocorrelations, all indicating significant alteration in the informational entropy of the data array.    The aberrations in the RNG data are correlated with objective measures of news intensity, but not with any likely physical variables.  Although the observations reported here are apparently quite unconventional, the evidence is strong sufficiently compelling enough to justify deeper investigation, and we invite other researchers to examine the data in a broad-based search for better understanding.  We would be grateful for access to other continuously recorded, nominally random data sequences that can be examined for aberrations similar to those reported here. 



This work was supported in part by the Institute of Noetic Sciences, with financial contributions from numerous individuals.  Computing and technical support were provided by the Princeton Engineering Anomalies Research program, Princeton University.


Correspondence and requests for materials should be addressed to R.N. (email: rdnelson@princeton.edu.)

[1]Nelson, R. D. (1998). The Global Consciousness Project, http://noosphere.princeton.edu

[2] Princeton Engineering Anomalies Research. (1998). Construction and Use of Random Event Generators in Human/Machine Anomalies Experiments.  PEAR Technical Report 98002, Princeton University.

[3] Princeton Engineering Anomalies Research. (1998). Construction and Use of Random Event Generators in Human/Machine Anomalies Experiments.  PEAR Technical Report 98002, Princeton University.

[4] Schmidt, H. (1970). Quantum-mechanical random-number generator. Journal J.of Applied Physics, 41, 462-468.

[5] Radin, D. I. & Nelson, R. D. (1989). Evidence for consciousness-related anomalies in random physical systems.  Foundations of Physics, 19, 1414-1499.

[6] Jahn, R. G., Dunne, B. J., Nelson, R. D., Dobyns, Y. H., and Bradish, G. J. (1997). Correlations of random binary sequences with pre-stated operator intentions:A review of a 12-year program. Journal ofJ. Scientific Exploration, 11, pp. 345-367

[7] Vincent, C. (1970). The generation of truly random binary numbers.  Journal ofJ. Physics E, 3, 594-598.

[8] Nelson, R. D. (2001). Correlation of global events with REG data: An Internet-based, nonlocal anomalies experiment. J. Parapsychology, 65, 247-271.

[9]Nelson, R. D. (2002). Coherent Consciousness and Reduced Randomness:  Correlations on September 11, 2001. Journal of Scientific J. Scientific Exploration, in press.

[10] Walker, J. (2000). An automatically generated pseudo-random clone of the GCP database.  Retrieved Dec. 21, 2001, from the Internet: http://noosphere.princeton.edu/pseudoeggs.html.

[11]Wackermann, J. (1999).  Towards a quantitative characterization of functional states of the brain: From the non-linear methodology to the global linear description.  International Journal of Int. J. Psychophysiology, 34, 65-80.

[12]InfoPlease "Year in Review", Dec. 2000 through Nov. 2001. Retrieved January 15, 2002 from the World Wide Web: http://www.infoplease.com.

[13]Radin, D. I. (2002). Evidence for relationships between random physical events and world news events. Journal ofJ.  Scientific Exploration, in press.



This work was supported in part by the Institute of Noetic Sciences, Petaluma, CA, USA, with financial contributions from numerous individuals and the Lifebridge Foundation.  Computing and technical support have been provided by the Princeton Engineering Anomalies Research program, Princeton University, Princeton University, Princeton, NJ, USA.  We thank our colleagues, Greg Nelson, Princeton Gamma Tech, Princeton, NJ, USA;, John Walker, Fourmilab, Neuchâtel, Switzerland,; and Paul Bethke, Oconomowoc, WI, USA, for the implementing the secure processing architecture and software, and our 65 other colleagues worldwide who host the distributed network.


Correspondence and requests for materials should be addressed to R.N. (email: rdnelson@princeton.edu.)