Extended Analysis: September 11 2001 in Context

The main formal prediction for this event is essentially the same as that made for the terrorist bombing in Africa in August 1998. That specified a period beginning a few minutes before the bombing, and including an aftermath of "a few hours." The actual time was from 10 minutes before the bombing to three hours after. We use in this case 10 minutes before the first crash to four hours after, which makes the aftermath period roughly the same following the last of the major cataclysmic events. The measure we use is the Chi-square representing the magnitude of the departure of the eggs' data from theoretical expectation, which is accumulated over the time defined for the analysis.

The resulting graph of data from the formal prediction shows a fluctuating deviation during the moments of the five major events, as ever-increasing numbers of people around the world are watching and hearing the news in stunned disbelief. Times of the major events are marked by boxes on the line of zero deviation. The uncertain fluctuation of the EGG data continues for almost half an hour after the fall of the second WTC tower. Then, at about 11:00, the cumulative deviation takes on a powerful trend that continues through the aftermath period and ultimately exceeds the significance criterion, with a final probability of 0.035 (Chi-square is 15314 on 15000 degrees of freedom. The number of eggs at the time of this analysis was 36.) As we will see, this significant departure from expectation continues over many more hours.

It is instructive to compare the graph of the same data, but plotted as the simple cumulative Z-score, which represents the sign of the deviations and not only their magnitude. In principle, this display could be completely different in its general appearance compared with that of the formal measure, which shows the accumulating absolute deviation. As we see in the following figure, there is considerable similarity. Again early in the period of disbelief and shock there is no strong trend, but at about the time of the collapse of the first tower, a powerful trend indicating high correlation among the eggs begins, and persists for two hours. For that period of time the slope of the line is extraordinary. If it were not selected by inspection, but had been an a priori prediction, its associated chance probability would be 0.000075; odds of less than 1 in 10000.

By the end of the day (midnight, GMT) 35 eggs had reported data, and the following figure looks at the full day in New York, beginning at midnight, Eastern daylight time, which corresponds to 04:00 GMT. The scale of hours in this graph indicates the time in New York, and the major events are marked on the zero line of expectation. The figure displays the cumulative deviation of the squared Z-scores (the cumulative deviation of Chisquare). It shows a continuous positive trend which culminates in a probablity of 0.024 for the 20 hour period. Corresponding pseudo-data computed for this day are included in the figure for comparison. The trend of the EGG dat begins well before the first attack, as early as 5 or 6 in the morning. It is noteworthy that the variance analysis, below, also shows a striking inflection a few hours before the attack.

Over the next days, we looked at longer periods of data to see the magnitude of the response of the EGG network to this tragic, horrifying event. These figures do not correspond to formal predictions, but are extensions of the formal method of analysis to look at the context and achieve a more general understanding. The next graph shows three days surrounding the attack. Statistically, this cumulative departure from random behavior is associated with a probability of 0.005 (261060 on 259200 df).

Next, a longer period of time surrounding September 11, with the attack marked and a small probability envelope for comparison to see the sharpness of the increase in non-random deviation. The slope of the graph beginning just before the attack to the end of the 13th is extreme. An estimate for the probability can be made, and lies between 0.003 and 0.0003.

The strong slope has a clear trend, and begins with a distinct inflection at a point well before the attacks began. If we extrapolate the slope itself, it passes through the inflection at about 04:00 on the 11th, suggesting that the terrorist attacks might have already begun to register on the EGG network some four or five hours before the first World Trade Center tower was hit.

A valuable tool for explorations is smoothing, where a average is calculated within a window that is moved across the data sequence. This is typically used to see whether there may be a concentration similar values, or clusters of extremes. In the September 11 data there is some concentration of strong deviations around the major events, with a peak at 10:13 EDT. This first figure shows the raw odds against chance for the squared Stouffer Z-scores for each second of the day. The maximum Z-score is 4.81 and a Z this large would appear by chance one time in about two weeks of seconds.

For a broader perspective, the next set of analyses used a different measure. Instead of looking at the shift of the mean values of the REG devices, we ask whether the variability among the eggs changes. Is there an increase or decrease in the range of scores that may be correlated with the event of the attack? The procedure used for visualization is the same as before, but we plot the accumulated deviation of the variance across the 35 or 36 eggs from its expected value.

I have been continuing to analyze data from the Global Consciousness Project to confirm and then extend what Roger Nelson and I have found, associated with the events of 9-11.

For the technically inclined, the steps in creating the basic z-score plot were as follows:

0) download raw data from the GCP site (http://teilhard.global-mind.org)

1) calculate an empirical mean and sd for each GCP egg (i.e., RNG), over each day

2) calculate one z-score per egg, based on above mean and sd, per second, using daily empirical mean & sd

3) calculate sum of z-squares for all eggs in non-overlapping 5-minute periods, per day

4) keep track of number of degrees of freedom (same as # eggs reporting), for step 3

5) calculate chi-square for sum of z-squares for 6 hour sliding window, with right edge of sliding window at "present time"

6) calculate z-score equivalent for step 5

7) draw the plot

This graph shows results for a 6-hour sliding window, in terms of z scores, from Sept 6 - 13. In this graph, positive z's mean the RNGs became "more ordered" than expected by chance. Negative z's mean the RNGs became "more random" than expected by chance. The peak value in this graph is 9:10 AM, Sept 11. Between the beginning of the tragedy and 7 hours later this data shows a drop of 6.5 sigma (odds against chance of 29 billion to 1). Such large changes will eventually occur by chance, of course, but this particular change happened during an unprecedented event, suggesting that this "spike" and "rebound" were not coincidental.

This shows the one-tailed odds against chance associated with the above z-score plot, in log space. The peak is at 9:10 AM. The "0" in the x-axis shows the start of each day.

This shows the two-tailed odds against chance associated with the above z-score plot, in log space. The first peak is at 9:10 AM, the second is at 4:20 PM. I show this to emphasize that unexpected negentropic and entropic changes both appeared during the crisis.

This shows the result for the z-score plot above when pseudorandom data are substitued for the real data.

This shows the one-tailed odds ratio plot when pseudorandom data are substitued for the real data.

This shows the two-tailed odds ratio plot when pseudorandom data are substitued for the real data.

There were four planes taken by the terrorists. Only three made it to their destructive destinations. The fourth was apparently brought down to crash in western Pennsylvania by passengers who attacked and overcame the terrorists, in a deliberate sacrifice of their own lives. We did not make a formal prediction about this event, but it certainly deserves analysis from the point of view of the EGG network. We do not have precise timing information, so the times selected for analysis here are speculative and selected with emphasis on the dramatic trends.

The first of the two following figures shows the data during what was likely the buildup and the struggle. The spike at the end is driven by a one-second trial during which the eggs were so highly correlated as to produce a Z-score of 4.8, which has odds of less than 1 in a million. Such an extreme score might happen by chance once in 15 days; the odds of ocurring during the 1.5 hour span of the terror attacks is about 1 in 200.. The second figure shows 15 minutes immediately preceding the crash. We will never know whether this picture reflects anything of what was happening in reality, but I like to imagine it represents an acceptance of the sacrifice.

What is the difference in the Chisquare and Variance graphs. How does one change the "deviation" calculation to arrive at "variance"?

The Chisquare figures show the cumulative deviation of the second-by-second Z-scores (squared), compounded across the N eggs (N=36 to 38 at this time). That is, for each second, the Z's for all the N eggs are added and normalized by sqrt(N), then the resulting Z is squared to yield a Chisquare with 1 df, and finally the Chisquares-1 (Chisq=1 is the expectation) are cumulatively summed, to represent the departure from expectation.

The Variance figures show something similar, but instead of the compounded Z across eggs, the variance (squared standard deviation) is computed across the N eggs for each second. The sequence of Variance-50 (Var=50 is the expectation) is then cumulatively summed as before.

The Chisquare figure displays extreme departures, in either direction, of the trial scores of the egg from what is expected by chance. The Variance figure displays the degree of variability among the trial scores for the eggs. Chisquare addresses movement of the central value of the distribution, Variance represents changes in the range or width of the distribution.

What is the difference in the the analyses by Roger Nelson and Dean Radin?

The most important difference is in the treatment of the data at the finest scale. Neither way is superior, but there is a difference in what is expected or hypothesized about the behavior of the eggs in the presence of a possible influence. The two perspectives are complementary, and though they are not fully independent, using both contributes to our confidence that the apparent effects are not accidents or mistakes.

For each second, Roger calculates what is called a Stouffer Z across the eggs as described above. This means that in order to produce a large deviation, the eggs have to have a positive correlation ­ to be doing the same thing. This composite Z is squared, so it does not matter whether the average value is shifted to the high or low direction, but there must be some excess deviation and there must be a tendency toward inter-egg consistency in the direction of deviation. The result is a single squared Z-score, which is Chi-square distributed, for each second.

Dean calculates a Z-score for each egg separately, and squares these individual Z-scores. He then sums the squared Z's across the eggs, producing a a single Chi-square for each second. In this case, the eggs are not expected to show a positive correlation, and a high score requires only that there is a tendency for excess deviation in either direction; no inter-egg consistency in the direction of deviation is predicted. Again, the result is a single squared Z-score, which is Chi-square distributed, for each second.