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CORRELATIONS OF CONTINUOUS RANDOM DATA

WITH MAJOR WORLD EVENTS

R. D. Nelson,aD. I. Radin,bR. Shoup,cP. A. Banceld

aDepartment of Mechanical and Aerospace Engineering

Princeton University

Princeton, New Jersey, 08544, USA,

E-mail: rdnelson@princeton.edu

bInstitute of Noetic Sciences, Petaluma, California, 94952

cBoundary Institute, Los Altos, California, 94024

d108, rue St Maur, Paris, France F-75011

Received 18 July 2002; revised 4 October 2002

The interaction of consciousness and physical systems is most often

discussed in theoretical terms, usually with reference to the epistemo-

logical and ontological challenges of quantum theory. Less well known

is a growing literature reporting experiments that examine the mind-

matter relationship empirically. Here we describe data from a global

network of physical random number generators that shows unexpected

structure apparently associated with major world events. Arbitrary

samples from the continuous, four-year data archive meet rigorous cri-

teria for randomness, but pre-speciﬁed samples corresponding to events

of broad regional or global importance show signiﬁcant departures of

distribution parameters from expectation. These deviations also cor-

relate with a quantitative index of daily news intensity. Focused anal-

yses of data recorded on September 11, 2001, show departures from

random expectation in several statistics. Contextual analyses indicate

that these cannot be attributed to identiﬁable physical interactions and

may be attributable to some unidentiﬁed interaction associated with

human consciousness.

Key words: physical random systems, correlations in random data,

quantum randomness, consciousness, global events, statistical anoma-

lies,

1

Fig. 1. Locations of host sites for the RNG nodes. Distribution is op-

portunistic because the network depends on voluntary collaboration.

1. INTRODUCTION

Quantum indeterminate electronic random number generators (RNG)

are designed to produce random sequences with near maximal entropy

[1, 2]. Yet under certain circumstances such devices have shown sur-

prising departures from theoretical expectations. There are contro-

versial but substantial claims that measurable deviations of statistical

distribution parameters may be correlated, for unknown reasons, with

conditions of importance to humans [3, 4]. To address this putative

correlation in a rigorous way, a long-term, international collaboration

was instituted to collect standardized data continuously from a glob-

ally distributed array of RNGs [5]. First deployed in August 1998, the

network uses independent physical random sources designed for serial

computer interfacing [6] and employs secure data-collection and net-

working software. Data from the remote devices are collected through

the Internet and stored in an archival database. The geographic loca-

tions of the 50 host sites comprising the network as of late 2002 are

shown in Fig. 1. The data archive, continuously updated, is freely ac-

cessible through the Internet and can be investigated for correlations

with data from many disciplines: earth sciences, meteorology, astron-

omy, economics, and other metrics of natural or human activity.

In addition to making the database available to the scientiﬁc

community, the collaboration maintains ongoing experiments to test

the conjecture that deviations in the random data may correlate in

some way with human activity. The primary experiment measures

deviations in the variance of the network output during brief, pre-

designated examination periods corresponding to collective human

events of major importance. After nearly four years of operation, we

2

ﬁnd that, whereas the data overall meet standard criteria for random-

ness and device stability [6], the data corresponding to the speciﬁed

periods tend to exhibit anomalous deviations from expectation. As of

June 2002, the statistical signiﬁcance of the cumulative experiment,

comprising over 100 replications of a protocol testing the conjectural

hypothesis, attains a level of ﬁve standard deviations. This apparent

correlation of the output of true random sources with a socially deﬁned

variable remains unexplained. However, in view of the increasing sig-

niﬁcance of this cumulative statistic, we feel it is appropriate at this

point to present a description of methods and results and to invite

comment and independent analysis. In this report we summarize the

overall results and provide a detailed assessment of the data recorded

on September 11, 2001, which constitute a particularly well-deﬁned

case study. The results show that substantial deviations from chance

expectation in several statistical parameters are present in the archive

for this day.

2. METHOD

The RNG devices employed in the network rely on quantum level pro-

cesses as the source of random events. All but two of the units are

based on quantum tunneling in solid-state junctions. Those not based

on tunneling use classical Johnson noise in resistors. The devices are

designed for professional research and pass an extensive array of stan-

dard tests for randomness, based on calibration samples of a million

200-bit trials. They are well shielded from electromagnetic (EM) ﬁelds,

and all 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

exclusive-or (XOR) against a pattern of an equal number of 0 and 1

bits to guarantee an unbiased mean output. Data bits are collected by

custom software on the local host into 200-bit trial sums at the rate

of one trial per second. The trial sums theoretically distribute as a

binomial (200, 1/2) distribution (mean = 100, variance = 50). The

software records the trial sums into time-stamped ﬁles on the local disk,

with computer clocks at most nodes synchronized to standard Internet

timeservers. Data packets with identiﬁcation and timing information

and a checksum are assembled and transmitted over the Internet to

a server in Princeton, NJ, for archiving in daily ﬁles that contain the

data for each node for each second, registered in coordinated universal

time (UTC).

A standardized analysis protocol is used to examine the random

data during periods corresponding to global events such as the disas-

ter on September 11, 2001 [7, 8]. Fully speciﬁed examination periods

are entered into a prediction registry, accessible through the Internet

3

[9]. These periods comprise collectively about 1% of the full database.

Roughly two-thirds of the registry entries pertain to scheduled events

and are registered before the event occurs; all are entered before the

archive is examined. Our analyses employ standard techniques of clas-

sical statistics, which can be found in introductory statistics texts [10].

The analysis proceeds by converting the raw RNG trial sums to a stan-

dard normal deviate, or z-score, as z= (trialsum −100)/√50. The

unit of the z-score is the standard deviation of the normal distribution,

σ= 1. A composite network Z-score representing the signed depar-

ture of the composite mean of all nodes for each second is computed

as Z=Pz/√N, where Nis the number of devices reporting for each

second. From this, a network variance cumulative is computed as the

sum of (Z2−1). Similarly, a device variance cumulative is computed

as the sum of (z2−1) over all devices per second. Note that these

quantities are deﬁned with respect to the theoretical trial sum variance

of 50. Substituting an empirical trial sum variance yields essentially

identical results.

The standard protocol is to compare the variance of the network

output, Z2, with its theoretical expectation for the designated periods.

Large excursions of this measure reﬂect an excess of correlated devi-

ation among the nodes if, for example, the independent RNG devices

are subjected to a common inﬂuence that changes their output dis-

tributions. This analysis tests for accumulating positive excess of the

network variance, and 93% of the entries in the prediction registry are

of this sort. A smaller number of formal examinations address the de-

vice variance, which has become a more useful statistic as the number

of online devices in the network has grown. It shows changes in the

absolute magnitude of the deviations of individual devices from expec-

tation. The Z2measure and the device variance calculation are both

additive chi-squared statistics [10], which permits the aggregation of

results from all the individual cases into a single composite statistic.

3. RESULTS

3.1. Composite Distribution

The aggregated outcome of the formal analyses for 109 registry entries

as of June 2002 yields a statistic with a probability value on the order

of 10−7, and a corresponding equivalent z-score of ﬁve normal devia-

tions (5 σ). Importantly, this aggregate result is not due to outliers

or a few extraordinary replications, as is demonstrated by translating

the individual experimental results to their equivalent z-scores. The

z-scores for the 109 experiments distribute smoothly, and are well ap-

proximated by a Gaussian ﬁt (mean = 0.53±0.1, standard deviation =

1.10). Truncating the distribution by successively removing the highest

4

and lowest scores yields mean values within one standard error of the

full distribution value. The smoothness of the distribution implies that

the aggregate result is due to a small but consistent accumulation of

statistical weight under application of the experimental protocol.

While the continuing experiment will allow further testing of the

experimental hypothesis, the distributed character of the current result

suggests ad hoc approaches to examining the database. In particular, if

the conjectural hypothesis is valid, independent designations of global

events other than the experimental prediction registry should also show

correlations with the database. A preliminary analysis of this type is

presented below. A further implication of a distributed eﬀect is that

data segments immediately neighboring the registered examination pe-

riods may be expected to show statistical deviations. A full analysis is

beyond the scope of this paper. However, as a concrete example of this

approach, we present several post hoc analyses of the data for Septem-

ber 11, 2001, which stands out as one of the most important entries in

the registry in terms of global impact socially and psychologically. Our

strategy is to compare the data surrounding registered examination pe-

riods against appropriate control samples from the full database. Note

that, while we provide probability estimates for the analyses as a guide

to the reader, these do not imply explicit hypothesis tests.

3.2. Network Variance

On September 11 the global network of 37 online RNGs displayed

strong deviations in several statistics. The registered prediction for

this event designated an examination period from 08:35 to 12:45 (EDT

local time). The network variance cumulative for this period attains

a modest p-value of 0.028 (equivalent z-score of 1.9 standard devia-

tions). However, a trend exhibiting substantial excess in the network

variance measure began early in the morning and continued for more

than two days, until roughly noon on September 13. A cumulative de-

viation (cumdev) plot, such as is used in process control engineering to

identify changes in monitored parameters, shows a notable departure

from the expectation for this statistic, which is a horizontal random

walk (Fig. 2). The trend beginning at the time of the World Trade

Center attack and maximizing 51 hours later is statistically unlikely,

as shown by iterative resampling analysis. Deviations with this slope

and duration occur with probability 0.012 in random resampling from

the 11 days of data shown in Fig. 2. This analysis underestimates the

strength of the deviation, however, because of the substantial average

bias of this 11-day segment. Relative to theoretical expectation, the

corresponding estimate is p= 0.002. Resampling from a ﬁducial 400-

day segment of the database from December 1 2000 to January 4 2002,

during which the number of online devices is comparable to that on

September 11, yields an estimate of p= 0.003. Applied to a control

database with algorithmically generated pseudo-random data [11], the

5

5 6 7 8 9 10 11 12 13 14 15

September Days (EDT)

-500 0 1000 2000

Cumdev (Z^2-1)

Attacks

Network variance

0.05

Fig. 2. Cumulative deviation of network variance for each second,

September 5 through 15, 2001. Day boundaries are in Eastern Day-

light Time (EDT). The terrorist attacks are marked with a pair of

vertical dotted lines at 08:45 and 10:30 on September 11. A segment

of a parabolic envelope of 5% probability with its origin at the level

of the random walk at 08:45 (horizontal dotted line) provides scale for

the persistent trend.

cumulative Z2analysis shows no unusual trend, ruling out possible

artifacts in the analysis procedure itself. This extended positive excur-

sion of the September 11 network variance suggests that the database

may indeed contain correlations lying outside the explicitly speciﬁed

examination periods.

3.3. Inter-Note Correlation

To test more comprehensively for correlated deviations among the in-

dependent nodes in the network, we have examined the average daily

node-to-node correlations within the 400-day database. The correla-

tions were calculated for data sequences with a similar time scale to

that of the experimental examination periods, typically several hours

in length. The squared z-score sequences for each device were low-pass

ﬁltered and all possible (Pearson) correlations among RNG pairs were

calculated for each day’s data (00:00 to 24:00, EDT) in the ﬁducial

database. Each pair correlation was transformed to a Fisher Z-score

[10] and a mean daily value for the correlations was calculated. These

values give a measure of the average strength of correlations between

node pairs, on the time-scale of the smoothing window, on any given

6

day in the 400-day period. The result shows that the daily mean for

September 11 deviates markedly from the mean of the distribution for

all days (t-score = 3.81, p= 0.00009, ﬁlter window = 2 hours) and that

this positive correlation is the largest occurring in the dataset. The re-

sult is robust against changes in the size of the ﬁlter window over a

range of one to eight hours. It is appropriate to correct the proba-

bility value for the freedom allowed in choosing the starting point of

the consecutive 24-hour data periods. With all possible starting peri-

ods considered, the Bonferroni-corrected [10] p-value is approximately

0.00024, corresponding to an equivalent z-score of 3.5.

3.4. Device Variance

The exceptional nature of the September 11 data is more sharply de-

ﬁned in the variance across the independent RNG devices. Figure 3

is a cumdev plot of the device variance relative to its empirical mean,

showing a broad peak centered on the time of the September 11 events.

Beginning at about 05:00 EDT the second-by-second variance increases

sharply and the cumulative deviation continues to rise until about

11:00, when the variance shifts to values below expectation in a trend

that persists until about 18:00. A bootstrap permutation analysis, re-

ordering the actual data, yields an estimate of p= 0.0009 (z-score =

3.1σ) for the peak absolute excursion, based on 10,000 iterations. A cal-

culation relative to theoretical expectation for this excursion occurring

in a 24-hour period gives a similar value of p= 0.0007. In contrast, for

the September 11 pseudo-random control data [11] the corresponding

estimate is p= 0.756, reﬂecting chance behavior (the small negative

peak visible near the time of the attacks is well within the range of

expected ﬂuctuations).

A daily measure of variance excursions, closely related to the

measure shown in Fig. 3, shows that September 11, 2001 has the great-

est deviation from expectation of any day in the database from August

1998 to June 2002. For this measure we apply a 6-hour low-pass ﬁlter

to the raw variance to capture the eﬀect of the long monotonic trends

seen in the cumulative deviation ﬁgure. The result on September 11,

2001 shows a change of 6.5 σover a period of about 7 hours. The same

procedure applied uniformly to the full database shows that September

11, 2001 is unique among the 1336 days of collected data (p= 0.0007,

or 3.18 σ).

3.5. Autocorrelation

We can assess the unusual behavior of the variance from another per-

spective by calculating its autocorrelation, which is sensitive to the

details of the trends over time that deﬁne the shape of the curve. The

autocorrelation function for the September 11 data shows a substantial

response driven by extended monotonic excursions in the raw device

7

0 2 4 6 8 10 12 14 16 18 20 22 24

Time (EDT)

-2000 0 2000 4000 6000

Cumdev (Var-Mean(Var))

Device variance

Pseudo control

Attacks

Fig. 3. Cumulative deviation of device variance across RNG nodes, rel-

ative to the empirical mean value, for each second on September 11,

2001. The truly random data from the RNG array are contrasted with

a pseudo-random control dataset computed for the same array of data

elements processed with the same algorithms. Axis labeling is in EDT.

Times of the terrorist attacks are indicated with boxes on the zero line.

variance. As shown in Fig. 4, the autocorrelation cumdev displays a

rapid increase up to a lag time of about one hour, with a more modest

rising slope continuing for up to two hours of lag. Inspection of the

previous plot (Fig. 3) conﬁrms that the strong, persisting deviations in

the data occur on a timescale of one to two hours. An indication of the

likelihood of several such excursions occurring on one day, as happened

on September 11, is given by the magnitude of the cumulative devia-

tion of the autocorrelation: the trace in Fig. 4 repeatedly penetrates a

0.0005 probability threshold. For comparison, the ﬁgure includes traces

showing the same computations for 60 surrounding days, nearly all of

which remain within a 5% probability envelope. Computations for the

ﬁducial 400 days, considering all possible starting points for the con-

secutive 24-hour blocks over which the autocorrelation is calculated,

show no other days with trends outside a 1% envelope. Applying a

Bonferroni correction for the selection of starting points, a p-value of

0.001 (3.1 σ) can be assigned to the autocorrelation on September 11.

3.6. News Correlation

We observe by inspection that world events noted in the prediction

registry tend to occur on days with signiﬁcantly higher average pair

correlations among the RNGs. To assess this relationship quantita-

8

0 1 2 3 4

Hours of Lag (1-sec increments)

-20 0 20 40 60

Cumdev (Autocorr)

0.05

Sept 11 data 0.0005

Other days

Fig. 4. Cumulative deviation of autocorrelation of the device variance.

The cumulative sum is shown as a function of lag time for September

11, 2001, contrasted with the same calculation for 60 surrounding days.

The autocorrelations were calculated for 24 hour EDT days over lags

of up to four hours.

tively, an objective metric was constructed based on an independent

daily assessment of newsworthy events by a professional news service

not associated with this project [12]. The count of letters used in the

daily summaries of news items was taken to represent the news “inten-

sity”. Over the one-year period from Dec. 2000 through Nov. 2001,

this measure, though diﬀuse, is correlated with daily mean pair cor-

relations of the RNG data at r= 0.15, t(362df)=2.94, p= 0.002,

z-score = 2.9 [13]. We note that this statistic is independent of the

selection of events in the prediction registry, but fully consistent with

the results for the pre-speciﬁed analyses since it correlates a measure

of the importance of world events with deviations in the database.

3.7. Source Distribution

To characterize the source distribution of the deviations, we examined

data from individual RNGs, as well as subsets of RNGs designated by

location or by random assignment. The departures from expectation

are distributed generally across the independent devices and there are

no signiﬁcant outliers that dominate the statistics. A complexity mea-

sure used to reduce dimensionality in multi-channel neurophysiological

data [14] was computed with the RNG devices treated as channels.

This measure shows that a parameter closely related to variance at

9

the device level is by far the largest contributor in a standard three-

parameter representation. In the time domain, our analyses of the

400-day database indicate that, in contrast to the result for longer lag

times, the data exhibit no signiﬁcant autocorrelations on a time scale

of seconds for either the network or device variances, or for individual

RNGs. This indicates that the observed anomalies are not driven by

short time characteristics of the RNG electronics.

4. DISCUSSION

In summary, we ﬁnd evidence for a small, but replicable eﬀect on data

from a global network of random generators that is correlated with

designated periods of intense collective human activity or engagement,

but not with any physical sources of inﬂuence. The 109 experimental

replications as of June 2002 distribute normally, but have a shifted

mean z-score of 0.53, representing a ﬁve σdeparture from expectation.

We attribute this result to a real correlation that should be detectable

in future replications as well as in analyses using correlates independent

from the project prediction registry.

The random generator network has been conceived to produce

stable output under a variety of conditions and it is unlikely that en-

vironmental factors could cause the correlations we observe. Conven-

tional mechanisms might be sought in environmental factors such as

interactions due to major changes in the electrical supply grid, surges

in mobile phone and telecommunications activity, or unusual coher-

ence in radio and television broadcasting, all of which may accompany

periods of intense regional or global attention. However, the instru-

ment design includes physical shielding of the RNG devices from EM

interference, and at all nodes the data pass through a logic stage that

eliminates ﬁrst-order biasing from electromagnetic, environmental, or

other physical causes. The devices are distributed around the world,

so their separation from sites of physical disturbance varies greatly

(for example, the mean distance of the RNGs from New York is 6400

Km), yet the eﬀects described here are broadly distributed across the

network. These logical and empirical indications are conﬁrmed by ana-

lytical results. Time series analysis based on 365 days of RNG outputs

registered at local time shows that there is no correspondence with

expected diurnal variations in the power grid or other known cyclic

patterning (p= 0.30) [13].

Barring demonstration of a conventional interaction that can af-

fect the random generators on a global scale, we are obliged to confront

the possibility that the measured correlations may be directly associ-

ated with some aspect of consciousness attendant to global events. In

particular, this evidence, if conﬁrmed, would support the idea that

some processes in nature that have been assumed to be fundamentally

random are in fact somewhat mutable. If the present understanding of

10

quantum randomness is called into question, there are profound the-

oretical and practical implications [15, 16, 17]. However, there needs

to be signiﬁcant replication and extension of our results before these

novel theoretical positions can be seriously considered. Although some

progress can be made to elucidate the form that an explanatory theory

might take [18, 19], it clearly must be guided by further experimenta-

tion and deeper examination of the data in hand.

The post hoc analyses presented here indicate possible exten-

sions of this research. For example, the September 11 results imply

that there is a correlation between the intensity or impact of an event

and the strength of deviations present in the data. The September

11 event is arguably the most extreme in the database in terms of its

social, psychological, emotional, and global impact. As the analysis

has shown, it also exhibits the largest and most consistent deviations

in the database on the statistical measures we have investigated. It

will be important to develop strategies to test this conjecture over the

full set of replications and in newly acquired data. The September 11

analysis also suggests that the eﬀect detected in the formal replications

is distributed over the database and is not isolated to the prediction

periods. The statistical signiﬁcance of these excursions is limited to

roughly three normal deviations. Thus, as isolated, post hoc analy-

ses, none of these individually would be suﬃcient to conclude a causal

or other direct link between the September 11 events and the mea-

sured deviations. In light of the formal result, however, these analyses

do suggest that independent metrics spanning the database and con-

sistent with the experimental hypothesis may reveal other correlations

with our statistical measures. This suggestion is supported by the news

index analysis in which deviations in the RNG data correlate with an

objective measure of news intensity. It is likely that more sophisticated

metrics with optimized statistical power could provide independent ver-

iﬁcation of the results generated by the ongoing experiment as well as

the capability to probe secondary correlates in the data.

Our ﬁndings are summarized in Table I, which includes an in-

dication of their likelihood in the context of the comparison standards

used. To identify the source of the deviations we must account for

excess inter-node correlations, persistent changes in composite vari-

ance, and long-term autocorrelations, all indicating signiﬁcant alter-

ation in the informational entropy of the data array. Although the

aggregate result attains a level of ﬁve normal deviations, signiﬁcant by

any standard, extensive further replication is needed before proposals of

a causal or otherwise direct link between human consciousness and the

output of the network generators can be convincingly advanced. We

present this work as an invitation to other researchers to examine the

data in a broad-based search for better understanding. The observa-

tions reported here are unexplained and may seem to defy conventional

modeling, but the evidence is suﬃciently compelling to justify further

investigation. More detailed analyses of the accumulating database

11

are proceeding. We would be grateful for access to other continuously

recorded, nominally random data sequences that can be examined for

correlations similar to those reported here.

Table I. Summary of statistical measures

Measure Probability Comparison standard

Network variance, 9/11 0.003 Resampling: 400 days

Device variance peak, 9/11 0.0009 Permutation: control p= 0.756

Autocorrelation, 9/11 0.001 400 control days: p > 0.01

Inter-node correlation, 9/11 0.0002 Student t: 400 days

News intensity correlation 0.002 Student t: 365 days

Diurnal variation 0.30 Time series: 365 days

Composite Chi-square 2.7×10−7109 Replications to June 2002

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