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Exploring Relationships Between
Random Physical Events and Mass Human Attention:
Asking for Whom the Bell Tolls
DEAN RADIN
Institute of Noetic Sciences,
101 San Antonio Road, Petaluma, CA 94952,
DeanRadin@Noetic.org
Abstract—Exploratory study of the outputs of continuously operating truly
random number generators (RNG) located around the world indicated that the
largest daily change in variance in the year 2001 occurred on an unprecedented
day in United States history, September 11, 2001. Calculation of correlations
between all possible pairs of RNG outputs on a per-day basis showed that the
largest daily average correlation also took place on September 11. Comparison
of daily RNG correlations for 250 days that made headline news in 2001
according to a commercial news service vs. similar measures for 115 non-
eventful days showed a larger average RNG correlation on days with major
news events (p 50.011). More generally, the correlation between an objective
metric of daily news vs. the daily average RNG correlation was significantly
positive (p 50.001). Potential environmental artifacts were examined and
found to be implausible explanations for these results. One interpretation of
these findings is that mind-matter interaction effects previously observed only
in focused laboratory studies may be detectable outside the laboratory,
potentially at a global scale.
Keywords: randomness—attention—mind
Introduction
As I grew up I became increasingly interested in philosophy, of which [my family]
profoundly disapproved. Every time the subject came up they repeated with unfailing
regularity, ‘‘What is mind? No matter. What is matter? Never mind.’’ After some fifty or
sixty repetitions, this remark ceased to amuse me.
—Bertrand Russell
Generations of philosophers have vigorously debated the questions that taunted
Bertrand Russell, so far without much resolution. In an experimental approach to
this question, investigators have examined the outputs of electronic noise-based,
truly random number generators (RNG) before, during and after highly focused
or coherent group events. The group events studied included intense
psychotherapy sessions, captivating theater presentations, religious rituals,
popular sports competitions, like World Cup Soccer, and high-interest television
broadcasts like the Academy Awards (Bierman, 1996; Blasband, 2000; Nelson,
1995, 1997; Nelson et al, 1996, 1998a, 1998b; Radin, 1997; Radin et al, 1996;
Journal of Scientific Exploration, Vol. 16, No. 4, pp. 533–547, 2002 0892-3310/02
533
Rowe, 1998; Schwartz et al, 1997). Results of these studies suggest in general
that mind and matter are entangled in some fundamental way, and in particular
that focused mental attention in groups is associated with negentropic
fluctuations in streams of truly random data.
Unlike laboratory investigations of mind-matter interactions involving RNGs,
where typically one individual is asked to mentally intend the output of an RNG
to deviate from chance, the present experiments study groups of coherent minds
that are paying attention to external events and explore whether these moments
are associated with analogous states of coherence in matter. RNGs are used as
the ‘‘matter’’ in these experiments because methods for detecting statistical order
in sequences of random events are well established, techniques for generating
and recording truly random bits are well understood, and several hundred
independently replicated, previously reported laboratory studies provide support
for the hypothesis that under certain conditions, mental intention and random
events can become significantly correlated (Radin & Nelson, 1989, in press).
In 1998, Roger Nelson initiated the Internet-based Global Consciousness
Project (GCP) to significantly expand this line of research by providing
numerous parallel, continuous streams of truly random bits from well-calibrated,
noise-based RNGs located around the world (Nelson, 2001). In these studies,
mass mental coherence is inferred to take place as a result of major news events
which attract widespread attention, and it is around these times that negentropic
changes are predicted to occur in the RNGs. This hypothesis has been formally
tested in the GCP data by examining whether the cumulative deviation in
variance across the random bit streams shifts from chance expectation, usually
by examining RNG data from just before an event of widespread interest to a few
hours afterward. As of May 2002, some 104 such events had been formally
tested, with overall significant results (p ,3310
27
)
1
. With growing support
for the GCP mind-matter interaction hypothesis, I was motivated to examine the
data over longer time periods than had been previously studied, with special
interest in exploring how RNG outputs behaved on days with major news events
as compared to relatively uneventful days.
Devices and Data
A more detailed account of the hardware and software that comprises the GCP
network can be found in Nelson (2001, 2002). The following brief description
will suffice for the present analyses. The GCP RNGs are not software-generated
pseudorandom numbers, but hardware circuits that rely on inherent electronic
noise as a source of randomness. Of the three different types of RNGs employed
in the GCP network, one uses noise in resistors and the other two use quantum
tunneling in solid-state junctions. The RNGs are designed for professional
applications requiring highly reliable generation of truly random bits, and
each has passed standard tests for randomness (e.g., Marsaglia’s DIEHARD test,
no date) as well as calibration tests consisting of one million 200-bit trials.
534 D. Radin
All of the RNGs are solid-state circuits housed in electromagnetically shielded
boxes, and the noise-based random bit sequences are compared to an equal
number of 0 and 1 bits with a logical exclusive or (XOR) to ensure that the mean
output is unbiased regardless of environmental conditions, component interac-
tion, or aging.
Each RNG is attached to a personal computer which collects random bits into
one ‘‘trial’’ per second, where each trial is the sum of 200 random bits. These
trials theoretically follow a binomial distribution with mean 5100 and variance
550. Each computer records its trials into time-stamped files, and all computer
clocks are synchronized to standard Internet time servers. Packets of data with
RNG site identification, per-second timing information, and a checksum to
ensure data accuracy are assembled and transmitted over the Internet to a central
server in Princeton, New Jersey, USA, for archiving.
The GCP network of RNGs started with a few RNGs in 1998, and it has
slowly increased in size over time as individuals are found who are willing to
host an RNG on their personal computer. As of May 2002, the network consisted
of approximately 50 RNGs located throughout North America, Europe, South
America, Asia, Africa, and Australia. The number of RNGs reporting daily
fluctuates by one or two occasionally, when the computers hosting the RNG are
taken offline or used for other tasks.
Analyses
Never send to know for whom the bell tolls; it tolls for thee.
—John Donne
The analyses presented here were exploratory, and as such, the results will be
useful primarily in developing future hypotheses. A non-mathematical way of
thinking about these analyses is as follows: Imagine that each RNG is
continually generating numbers that, when collected into a histogram, form
a bell-shaped curve.
2
We are interested in how the shape of this bell curve
changes over time, and especially in how external events might be associated
with those changes. We are, in effect, studying relationships between the
‘‘ringing’’ of the bell during the course of human events. To borrow John
Donne’s poetic phrase, we are asking for whom the bell tolls.
There are four simple ways that a bell curve can deviate from a theoretically
perfect bell shape. The curve can be (1) shifted to the left, (2) shifted to the right,
(3) squashed flat (i.e., the top of the bell pushed down), or (4) squashed thin (the
sides of the bell pushed toward the center). The first two possibilities are not
suitable for our purpose because we have no a priori way of predicting which
direction the curve might shift (or in our metaphor, which direction the bell
might swing). So our analyses focus on the second two methods.
In the analyses described below, the ‘‘variance’’ method is concerned with
how a bell-shaped curve formed by data from all of the RNGs fluctuates from
Exploring Relationships 535
one day to the next. The ‘‘intercorrelation’’ method is concerned with the
similarity in shapes among many bell-shaped curves, one curve for each RNG,
and how those similarities fluctuate from day to day.
Variance Analysis
This analysis explored changes in variance among all reporting RNGs for
each day in the year 2001. The procedure was as follows:
1) Download the daily raw data files for each day in 2001 from the GCP Web
site (http://noosphere.princeton.edu/data/extract.html as of May 21, 2002).
The data files are in the form of a matrix, where the columns identify the
RNGs and the rows list the per-second trial outputs.
2) Calculate the daily trial mean and standard deviation for each RNG
running each day. Exclude individual RNG trial values <50 or >150,
whole RNGs with daily empirical trial means .103 or ,97, or whole
RNGs with daily trial standard deviations .6or,8. Extreme individual
trials and deviant daily means and standard deviations were excluded from
further analysis to ensure that the data were being collected from properly
functioning RNGs. This is necessary because the RNGs are physical
devices connected to PCs and the Internet, and as such they are not
expected to perform perfectly all the time. Still, the GCP network has
proven to be remarkably reliable. In more than three years of continuously
collected data, over 99.5% of the database falls within expected thresholds
for truly random data. The few exceptions include RNGs with overly
restricted variance (typically due to RNG circuits that failed) or an
occasional impossibly high or low individual trial value (typically due to
a malfunctioning PC serial port).
3) Use the daily trial mean and standard deviation for each RNG to calculate
a Student t-score with 199 degrees of freedom (199 df) per RNG, per
second, where t5(x2
xx)/s,xis a per-second trial value from RNG
number r,
xx is the daily trial mean for RNG r, and sis the daily trial
standard deviation for RNG r. In practice these tscores are almost
identical to standard normal deviates, z5(x2100)/
ffiffiffiffiffi
50
p, where 100 is
the theoretically expected mean and s5
ffiffiffiffiffiffiffiffiffi
Npq
p5
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
200 3:53:5
p5
ffiffiffiffiffi
50
p, the theoretically expected standard deviation.
4) Because t(199 df) ’z, calculate one t
2
value per RNG per second. These
t
2
values are effectively chi-square distributed.
5) Sum the t
2
values from Step 4 across all reporting RNGs per second,
keeping track of the number of t
2
values that are summed. Call this
summed value T, and the number of summed t
2
values N; thus Tis chi-
square distributed with Ndf.
6) Sum 300 contiguous Tvalues from Step 5 to form a single value that
consolidates 5 minutes of the per-second data; call this value T
5
. Do the
same for the Nvalues; call this N
5
. Repeat this procedure to create a total
536 D. Radin
of 288 non-overlapping T
5
and N
5
values per day. This step is performed
to compress what is otherwise a very large daily data set (e.g., for 36
reporting RNGs, there are 86,400 seconds per day 336 RNGs 5
3,110,400 per second trials reported, vs. 288 5-minute periods per day 3
36 RNGs 510,368 data elements per day). T
5
is chi-square distributed
with N
5
df.
7) Sum 72 contiguous T
5
values from Step 6; do the same for the N
5
values.
Call these summed values W
T1
and W
N1
. Then shift right by 1, create
another sum of 72 T
5
values, call these W
T2
and W
N2
, and so on. This
procedure creates a sliding window (the equivalent of 6 hours of real-
time), where the W
T
values are chi-square distributed with W
N
df. A total
of 288 272 5216 sliding windows are created to cover each day’s data.
8) Calculate a zscore (standard normal deviate) for each sliding window in
Step 7 as z5
ffiffiffiffiffiffiffiffiffi
2WT
p2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2WN1
p(Guilford & Fruchter, 1973, p. 517),
where W
T
is the chi-square value and W
N
is the degrees of freedom.
Variance Results
To demonstrate that over long periods of time the composite RNG variance is
well-behaved, Figure 1 shows the distribution of zscores for each 5-minute
segment (i.e., the T
5
and N
5
values formed in Step 6 above) for all GCP random
data generated between January 1, 2001, and November 30, 2001. We expect to
see a normal, bell-shaped curve with mean approximately 0 and standard
deviation approximately 1, and this is what we observe.
To examine slower fluctuations in the time-varying RNG output variance, and
to consolidate the data into time lengths more appropriate to the way in which
humans tend to respond to important news events (i.e., in terms of hours rather
Fig. 1. Distribution of zscores associated with 5-minute summaries across all RNGs from January
1, 2001, through November 30, 2001.
Exploring Relationships 537
than minutes), the data are smoothed with a 6-hour sliding window, as described
in Step 8 above. Figure 2 illustrates the effects of this smoothing for data
collected between June 16, 2001, and September 20, 2001. This curve may be
thought of as (roughly) a visualization of the ‘‘ringing’’ of our bell.
The ordinate in Figure 2 is in terms of zscores. Values between z522
and 12 are basically noise, but values outside this range are statistically
interesting. In particular, in Figure 2 notice that something unusual happened
one day in September. On that day the curve deviated beyond z,23 and
z.13. Figure 3 shows this anomaly in more detail. It happens that this curve
peaks more than an hour before a jet hit World Trade Tower 1 in New York City
at 8:46 AM EDT, September 11, 2001, and the curve drops to its lowest point
around 2:30 PM, roughly 8 hours later.
3
A 6.5 (or greater) drop in zscores within
an 8-hour period, as observed on September 11, is unique throughout the year
2001. In metaphorical terms, our bell rang more loudly on this day than any
other day in 2001.
Intercorrelation Analysis
The GCP network of RNGs is analogous to a set of buoys that we scatter
across an ocean to detect a tsunami, a colossal singular wave. To continue our
bell motif, let’s say we attach a little bell to each bouy, and we use a radio to
send the sound of each bell to a central monitoring location.
Because buoys are tossed about by local currents and winds, if we listen to
their collective sounds, most of the time we will hear nothing but random
tinklings. However, on rare occasions the bouys will sing out as one great chord.
Fig. 2. zScores associated with 6-hour sliding windows, as described in Steps 7 and 8 above, for
RNG data collected between June 16, 2001 (noted as ‘‘616’’ on the x-axis) and September
20, 2001. This 3-month time-span was used to place the September 11 results into context.
538 D. Radin
During such times we have an anomalously positive correlation among all the
bouys, and we have good reason to believe that a tsunami has occurred.
In a similar fashion, I examined all correlations among all possible pairs
of GCP RNGs to see how they behaved on a daily basis over the year 2001,
from January 1, 2001, through December 31, 2001. My expectation was that
September 11, 2001, might be the GCP equivalent of a tsunami given the
unprecedented degree of world-wide attention precipitated by the events of
that day.
Procedure
1. For each RNG, determine z-scores as z5(x2100)/
ffiffiffiffiffi
50
pfor each trial,
where xis the per-second RNG trial data. The very small percentage of
cases in the GCP database with known RNG data problems were, of
course, excluded from this step.
2. Create a z-squared value per RNG per second.
3. For each RNG, sum 300 contiguous z-squares to create a single, 5-minute
consolidation of the per-second trial, and repeat this for all 288 non-
overlapping 5-minute periods per day. As in the initial variance analysis,
call this sum of z-squares T
5
and the associated degrees of freedom N
5
.
Note that this step differs from the initial variance analysis because these
288 T
5
and N
5
values are created for each RNG separately.
4. Smooth these 5-minute segments, per RNG, using the equivalent of a
6-hour sliding window.
5. Calculate a Pearson product moment correlation rbetween all possible
pairs of smoothed curves, among all RNGs, per day; e.g., among 36 RNGs
there are 630 possible pairs.
6. Normalize each resulting rfrom Step 5 using a Fisher ztransform, then
Fig. 3. Smoothed z-scores across 36 RNGs running from 8:00 PM September 10, 2001, to 8:00 PM
September 11, 2001. No other day in the year 2001 showed as large a drop in zscores as
observed on this day. The x-axis is in hours, Eastern Daylight Time.
Exploring Relationships 539
determine the daily mean and standard deviation of these transformed
rvalues.
7. Use a Student t-test to compare each day’s daily mean normalized
ragainst the null hypothesis of r
0
50.
Intercorrelation Results
Figure 4 shows the daily mean Fisher zscores (i.e., daily intercorrelation
values) for each day between December 1, 2000, and December 31, 2001. Figure
5 shows the odds against chance associated with t-tests of the daily values. The
peak daily value occurred on September 11, 2001. This suggests that our ‘‘bell’’
rang loudest on this day because of the collective simultaneous bell tones issuing
from all of our RNGs around the world.
One question that may arise when examining these results is whether the large
intercorrelation value observed on September 11 may have been due to unusual
environmental artifacts, such as increased cell-phone usage, which affected
some RNGs. If this were the case, then we might expect to see a few very high
intercorrelations on that day for RNGs located in say, North American cities, but
most of the other intercorrelations, say for RNGs located in the South Pacific,
Australia or Asia, would be near chance. If this were the case, then we could
predict that the standard deviation of the RNG intercorrelation values on
September 11 would be inflated. However, Figure 6 shows that this stand-
ard deviation was unremarkable as compared to all other days; thus, from
this perspective there is no compelling reason to believe that the large
Fig. 4. Daily average RNG intercorrelations. The peak value is September 11, 2001.
540 D. Radin
intercorrelation observed on September 11 was due to localized environmental
artifacts.
This finding is supported by Figure 7, which shows the histogram of all RNG
intercorrelations on all days (the bell-shaped curve centered around 0) as
compared to the histogram of intercorrelations observed on September 11, 2001
(the jagged line). The environmental artifact hypothesis predicts that the
distribution of intercorrelations for September 11 would be skewed by a few
large high correlations among some neighboring RNGs. Instead, the histogram
shows what appears to be a normal distribution that is shifted to the right. A
t-test of the mean difference between these two distributions results in t53.714,
p50.0001 (one-tailed). This implies that all of the RNGs were ‘‘ringing’’ in
unison a bit more than usual, rather than just a few RNGs ringing in
exceptionally close synchrony.
One might argue that these results depend on a fortuitous selection of a 6-hour
smoothing window (Step 4 in the analytical procedure). To address this
possibility, I varied the window smoothing length from 5 minutes to 12 hours,
then determined t-scores of the difference between the Fisher zintercorrelation
means for September 11 vs. the grand mean for all other days. Figure 8 shows
the results. The value z53.7, associated with the difference between the two
distributions shown in Figure 7, appears on this graph at the window size of 6
hours. The analysis indicates that the optimal window length is actually about 8
hours rather than the 6 hours I employed, but more importantly it shows that all
window lengths greater than 10 minutes resulted in significant differences. This
suggests that the significant intercorrelation observed on September 11, 2001,
was not due to a fortuitous selection of window length.
Fig. 5. One-tailed odds against chance for values observed in Figure 4.
Exploring Relationships 541
News Analysis Method
Given the interesting exploratory results associated with September 11, 2001,
the next question I addressed was whether the GCP hypothesis would generalize
to less dramatic days. To investigate this question, I examined how the RNGs
behaved on 25 single-day events listed in the GCP event registry (multi-day
events were excluded from this analysis), from December 1, 2000, through
December 31, 2001. The GCP hypothesis predicts that the average daily
intercorrelations for these days, as compared to all other days, would be
significantly larger. A t-test supported the prediction, p 50.016 (one-tail),
and this difference remained significant after excluding September 11, 2001
(p 50.024).
While this result points in the right direction, many of the events entered into
the GCP registry were there because someone guessed that a given event might
be associated with a change in randomness in the RNGs. While such guesses
were valid because they were made in advance of examining the GCP data, one
could argue that this opportunistic method of registering events overlooked
many other events that also attracted mass attention, and more importantly it
provokes the criticism that the method of selecting newsworthy events was too
subjective.
Thus, to form an objective measure of ‘‘newsworthy events,’’ I took all news
events listed in the ‘‘Year in Review’’ month-by-month feature on the InfoPlease
Web site, www.infoplease.com, for the one year period from January 1, 2001,
through December 31, 2001. This Web site lists headline news in five
categories: world news, US national news, and a combined business, science and
society category. InfoPlease is affiliated with ESPN, Time, and the Reuters news
Fig. 6. Standard deviations for daily average Fisher zintercorrelations.
542 D. Radin
service; thus, the information on the site is assumed to be reasonably accurate.
Of greater importance, the news items were selected by the InfoPlease editors
completely independently of the GCP. This Web site was selected over other
potential online news sources, such as CNN, because it provides a comprehen-
sive day-by-day list of news events, whereas most other sites list important news
stories, such as ‘‘the economy,’’ without providing day-to-day historical details.
For the 1-year test period, a total of 394 news events were listed; these took
place on 250 days. The GCP hypothesis predicts that these 250 days would have
a larger mean intercorrelation value than the remaining 115 non-newsworthy
days. A t-test confirmed the prediction, p 50.011, one-tailed.
A still more generalized way of examining the GCP hypothesis is to see
whether the ‘‘amount’’ of daily news would be positively correlated with the
daily RNG intercorrelation means. To test this idea, I observed that in the
InfoPlease list of events, the minimum number of news events occurring on
a single day was 0, and the maximum was 5. Each of those events was
accompanied by a text description; the number of characters in those
descriptions summed over all events per day ranged from 72 to 1,193. I used
these text counts as indicators of the amount of news per day in the sense that
many news events on the same day would lead to larger values. I also explored
using the number of events per day as a simpler news metric (the correlation
between the total number of characters per day and the total number of events
per day was r50.90, so I used the text count value as the primary metric
because it provided a more continuous variable to work with).
News Analysis Result
Figure 9 shows the correlation between the daily news metric and the daily
mean intercorrelations. The correlation is small, but as predicted it was
Fig. 7. Histogram for all Fisher zintercorrelations from December 2000 through December 2001
(the smooth, bell-shaped curve), and the intercorrelations observed on September 11, 2001.
Exploring Relationships 543
significantly positive: r50.16, t(363 df) 53.08, p 50.001, one-tailed. If
September 11 is removed from consideration: r50.15, t(362 df) 52.88, p 5
0.002, one-tailed. And if all of the non-news days are removed (these are seen in
Figure 9 as a column of points at 0 on the x-axis), the correlation remains
significant: r50.11, t(248 df) 51.76, p 50.040, one-tailed. A Kendall tau
nonparametric correlation between the number of listed news events per day vs.
the daily RNG intercorrelation value was also significant: r50.062, n 5365,
p50.037, one-tailed.
Discussion
As mentioned above, one mundane explanation for the present results is that
world events that captured mass human attention were associated with unusual
surges of electrical power and use of telecommunications equipment, and this in
turn might have created unusual environmental conditions that influenced the
RNGs. While environmentally-induced artifacts are conceivable, there are four
main arguments against this explanation: (1) in the case of September 11, the
cross-RNG variance peaked over an hour before the terrorist events began to
unfold, (2) the RNG intercorrelations reflected common changes among RNGs
located around the world, (3) the RNGs are powered by voltage-regulated
computer power supplies, and many PCs are further isolated from line power
through surge suppressors and battery-powered, uninterruptible power supplies,
and (4) the RNGs are designed to exclude first-order biases (i.e., drifts of the
mean) through the use of XOR logic.
Fig. 8. Effect of window size length on differences between the distribution of all daily
intercorrelation values vs. the distribution for September 11, in terms of a one-tailed
z-score.
544 D. Radin
These items argue against an artifactual explanation, but we can indirectly test
the effects of electromagnetic interference on the RNGs by examining their
outputs according to local clock time. That is, if the electromagnetic
environment influenced the RNG circuits, then we would expect to see
differences in RNG behavior between night and day. During the day, human use
of electronic devices peaks, as does wide-spectrum electromagnetic noise,
electric field strength, non-ionizing radiation, etc. During the night, all of these
effects decline.
Figure 10 shows the z-score equivalent for variance across all RNGs,
consolidated in 0.1-hour bins according to the local time of each RNG, over the
entire month of September 2001. This graph summarizes 89.6 million 200-bit
samples from all RNGs reporting in September 2001, for a total of 17.9 billion
random bits. This provides enormous statistical power to identify diurnal
influences, but no day-night differences or trends are observed: between 8:00 PM
and 8:00 AM (night) and 8:00 AM and 8:00 PM (day), z(difference) 50.53, p 5
0.30, one-tailed. This provides no support for an electromagnetic artifact hypo-
thesis.
Besides possible environmental artifacts and a global mind-matter interaction
effect, what else might account for the observed results? One possibility is that
these results might be due to chance. Another is that the results are due to
a fortuitous choice of analysis methods. Follow-up tests with new data will help
evaluate the viability of these possibilities.
Conclusion
Throughout history, philosophers have debated the perplexing, dualistic
nature of subjective versus objective. In the 20th century, quantum theorists
Fig. 9. Correlation between daily news metric and daily RNG intercorrelation values, p 50.001,
one-tailed. September 11, 2001, is associated with a news metric value of 398 in this graph.
Exploring Relationships 545
found themselves forced to seriously reconsider classical assumptions about
observer vs. observed, and about mind vs. matter (Jahn, 1981; Jahn & Dunne,
1987; Stapp, 1999; Wilber, 1984). In the latter half of the 20th century,
investigators developed increasingly rigorous methods for explicitly testing
postulated mind-matter interactions (Radin & Nelson, 1989, in press). And as
the 21st century begins, it appears that a cautious answer to the question used to
taunt Bertrand Russell may be, ‘‘Yes, mind does matter.’’ As for the observations
discussed in this paper, whether they turn out to be a fluke due to the uncertainties
of exploratory data analysis or something more interesting will be resolved by
formalizing these analyses and testing them in future GCP data.
In sum, these analyses explored a new twist on the enduring riddle, ‘‘For
whom does the bell toll?’’ The answer according to this analysis resonates with
John Donne’s words in the 16th century: ‘‘No man is an island. The bell tolls for
thee.’’
Notes
1
See the Web site http://noosphere.princeton.edu and Nelson (2001) for further
details.
2
More precisely, a normal distribution that approximates the underlying
binomial distribution.
3
There is no easy answer for why the peak in this curve occurred before the
terrorist attacks; the observable fact is that it did.
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