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the shifted distribution behaves as a function of the sequence length,
[n]
, and knowing that
[z]
is distributed normally, the evaluation of Equation
(4) reduces to the evaluation of the
expectation of ln(zf(Aps) +
zs).
Or,
In [z f(AP s ) + zJ
(5 )
Let us now consider a general class of binary RNG models where the mean
of a binomial distribution
is shifted by an amount:
pa
=
0.5
(1 + a)
.
and
AP S
p
- 0.5
=
0.5
a
,
a
where
[a]
is an RA strength parameter.
That
is to say, the properties of the RNG device are
modified by RA such that the mean probability of producing a hit has been shifted from 0.5
to pa.
There are many other models that we might consider, but this particular one has been
proposed by the PEAR group.
They report that
if n = 200,
[a]
is approximately 0.001. 10
. 11
In other words,
this model implies that individuals cause the mean probability
of producing a hit to be constant, regardless of the sequence length.
(The logarithm term in
Equation 4 does retain an n-dependency through the z s term even though Apa does not.)
RA
perturbs the device on a bit-by-bit basis that
is independent of the number of bits in the
sequence.
Figure 4 shows the result of evaluating Equation
(4)
for various values of
[a]
compared to the MCE line.
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c.
Theoretical Considerations for the IDS Model
Equation
(2) represents the MCE condition in which no psychoenergetic
interaction
is present.
Because one premise of the IDS model
is that no causal interactions
occur, there
is only one term in Equation
(2) that can possibly account for a non-causal, but
psychoenergetic effect,
The 0.5 ln(p0q0 ) and the -0.5 ln(n) terms are consequences of the
standard deviation for the unperturbed distribution of Ap; therefore, the only remaining term,
the expected value for ln|z|, must contain the IDS considerations.
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In general terms, the expected value for ln|z|
is given by
In
| z
|
(6)
The function g(z,n)
is the distribution that reflects a subject’s ability to select subsequences,
leading to z-scores.
For example,
if a subject were always able to select subsequences
(regardless of sequence length) leading to
z = 2.15, then g(z,n) contains no n-dependence
and
is a Dirac delta function at z = 2.15.
If g(z,n)
is simply a Gaussian with a mean of zero
and a standard deviation of one, then Equation
(6) reduces back to the null hypothesis.
To
determine predictions under the IDS model, Equation
(6) must be evaluated for different
assumptions for the function g(z,n).
Consider the case in which g(z,n)
is not a function of the sequence length.
Then, g(z,n) = y(z).
Equation
(6) becomes a sequence length independent constant, which
can only affect the intercept of a straight line, regardless of any details of y/(z).
Figure
shows the RA hypothesis from Figure 4 and an example of the IDS case described above.
Suppose, however,
g(z,n) does contain some n-dependencies.
Even under
the IDS hypothesis, we might expect this to be the case.
Recalling that IDS
is a
psychoenergetic decision algorithm, we can imagine that better “decisions”
result when a
lot of
“information”
is available, or the reverse: “decisions”
are inaccurate
if there
is not enough
“information.”
It
is possible that inaccurate “decisions”
are made in the presence of too
much “information”
as well.
Elementary information theory tells us that the amount of information in a
sequence of length
[n]
is proportional to
[n]
if the bits in the sequence are independent.
Therefore, we can equate “information”
in the above paragraph with the sequence length.
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We now examine the case in which g(z,n)
retains a sequence length
dependency.
To define g(z,n), we transform the coordinates similar to what was done in the
RA derivation.
Let
Az
=
z
- z 0
Az s
=
Z a -
Z 0
Az a
=
Z
- z a
= Az - Az s
,
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where
za is the mean of a “shifted” Gaussian z-score distribution having a standard deviation
of o.
Z0
is the mean of the “unshifted” z-score distribution
(i.e.,
zo = 0.0).
Using this
transformation, g(z,n) becomes
g(z.n)
-0.5
e
/ Az a (n) \
V
cr(n)
/
Let zeta be given by
Then Equation
(6) becomes
In
| z
|
where
Azs
o-o
(o-o =
1)
,
(7 )
We notice that Equation
(7)
is of the same form as Equation
(5)—including
their relative n-dependencies.
Thus, depending upon the parameters involved in both
equations, we would be generally unable to differentiate between RA and n-dependent IDS.
d.
IDS vs. RA
in Perspective
The IDS model appears to have the sensitivity to differentiate between some
causal processes and some informational ones.
In particular, the most obvious causal model
(i.e., the “interaction”
is, on the average, the same for each bit in the sequence) contains
vastly different predictions than the most obvious IDS model
(i.e., sequence length
independent of the z-scores).
There
is another class of RA models that have attracted attention:
pa
=
°- 5 (
1 +
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This particular form of
[p»] leads directly to an n-independent zs -
a.
F(Aps)
in Equation
(5) becomes
r
a 2
1 1/2
f(Ap
s )
=
[l - -g-
J
~
•
This function
is approximately equal to one for most actual cases
(i.e., a = 0.1, n > 200).
We note here, that
it may be possible to separate even this RA model from IDS
at small
sequence lengths.
Thus, Equation
(5) reduces to a sequence length independent constant and
is equivalent to the IDS case of g(z,n) = y(z) in Equation
(6).
Therefore, RA
(of this form)
and IDS are indistinguishable.
All other forms of n-dependent RA contain a strong
n-dependence in the
zs term.
To separate RA from IDS in this case, requires a different approach
altogether.
Suppose that RNG experiments continue to produce significant results that appear
to be independent of
all known physical parameters
(e.g., source type— (3 decay, noise,
distance, shielding,
etc.).
Further, suppose that PRNG experiments continue to produce
significant results.
We would then argue that IDS
is the preferred choice for a mechanism
because:
•
Precognition can be shown to be true by separate and fundamentally
different experiments.
•
IDS can be shown to be possible (PRNG results).
•
Results of one of our RNG experiments 1 suggest that human-mediated
RA must be able to switch on and off within
1 ms.
•
There
is no known force in nature that can interact equally with the
weak nuclear and electromagnetic forces.
To us,
it would seem more parsimonious to assume that humans are more able to anticipate
the unperturbed natural fluctuations of an RNG, rather than generate
forces
that must
conform to such a set of attributes.
3.
Analysis and Hypothesis Testing
The
first step,
after data reduction,
is to determine
if we are justified in continuing
with a linear analysis.
To accomplish this, we calculate the linear correlation coefficient for
all data points
[ln(n), ln|Ap|], and determine
if there
is a significant correlation
(i.e.,
[r]
significantly different than 0.0) and,
as a side interest, determine
if the correlation
is
significantly different than expected
[i.e., Equation
(3)].
If the correlation
is significantly different than 0.0, we
fit the data with a straight
line, where the intercept
is determined at the average value of ln(n)
for the data
set.
By
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transforming the data about the average value of ln(n) slope and intercept hypotheses testing
may be done separately.
To determine
if the observed line
is significantly different from the
MCE line, we use an ANOVA technique. 12
The F-ratios (from the ANOVA)
for the two
tests are given below.
Let
n k = ln(s k
), where
sk
is the sequence length for the kth data point.
Let n be the average
value for the nk
over [m]
data points,
or
k=l
The F-ratios are given by
F (slope)
m
(b
b’)
2 x
A
dfl =
1; df2 = (m - 2)
,
and
F (intercept)
dfl =
1; df2 =
(n - 2)
where
[a] and
[b]
are the intercept and slope for [m]
data points,
(ln(n),
ln| Ap|).
[a’] and
[b
]
are the intercept
(at nk = n) and slope
for the MCE line.
A
is given by
A
m
m
mm
^M k + ma 2 + b
2 2 n k
+
2 a b 2n k -
2 a ]^M k
k=l
k=l
k=l
k=l
m
2 b 2n kM k
k=l
m - 2
M k
is the observed value of ln|Ap|
for the kth data point.
If the F-ratio for the slope
is not significant, then we can conclude that the
z-scores do not have a sequence length dependency.
Furthermore,
if the F-ratio for the
intercept
is significant, then there
is evidence in support of the IDS model.
Deviations from
this scenario
will be discussed below.
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B.
The SRI Pseudorandom Data
In 1985, Radin and May described a protocol that could be used as the pseudorandom
portion of a comprehensive test of the IDS model, and presented pilot data that appeared to
support the IDS model. 13 We have modified and extended that original proposal to form the
basis of our pseudorandom investigation.
1.
Justification for a Pseudorandom Number Generator Experiment
We have proposed an elaborate model (IDS) that predicts significantly different
results from those expected from an RA interaction.
As part of a systematic investigation of
the validity of the model, we must determine
if an IDS “interaction” can be demonstrated,
in
principle, under conditions that preclude RA.
Because there has been no evidence to date to support the idea that computer
hardware
is susceptible to a putative RA interaction, we assume that a purely pseudorandom
number generator (PRNG), which
is seeded by a computer clock, constitutes an environment
that precludes RA.
2.
PRNG Experiment Description
The primary concept for this experiment
is to study |Ap|
as a function of sequence
length.
To accomplish this, we design a PRNG experiment in which a single
trial contains the
following steps:
•
Select a sequence length,
[n], from a limited menu of lengths.
•
Collect
[n]
bits from a PRNG that has been seeded from a
computer system clock at the moment when the participant presses
a button.
•
Calculate |Ap| and a z-score, and display the z-score to the
participant.
•
Store raw data for later analysis.
Since the data
will be analyzed in logarithmic form, we chose the following 10
sequence lengths because they are relatively evenly spaced when they are expressed as
logarithms, and they did not allow Ap = 0.0
(i.e., the ln|Ap|
will remain finite):
101, 201,
501,
1001, 3501, 7001, 10001, 35001, 70001, and 100001.
While we may have wanted to
explore larger sequence lengths than 100001, we were limited by the speed of the Sun
Microsystems Model 3/160-C computer, and by human factor considerations.
The delay
between a button press and the display of the result was approximately
1.5 seconds.
This
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delay was constant in spite of the actual sequence length chosen,
in order for a given trial to
maintain a double blind condition with respect to sequence length.
At the
first trial of a series, the above sequences were placed in a random order
and stored as part of a data
file.
The sequence length,
for a given
trial, was taken in order
from this randomized
list.
Thus, the sequence length ordering was repeated every 10
trials.
The PRNG that was used
(a Kendel
shift register feedback algorithm) has been
studied extensively theoretically by Lewis 14 and experimentally by May.
This algorithm meets
the accepted tests for “randomness” 15 and was checked further in this particular experiment
using control trials.
The low order 15
bits from the system clock were used as seeds for the
PRNG.
For each
trial, the seed, sequence length, number of ones in the sequence,
z—score, time
(to the nearest second), and date of the trial were stored as part of a data
file
for later analysis.
C.
The Princeton Engineering Anomalies Research Data*
In order not to “pre-select” data to support (or not)
a given hypothesis, we obtained all
of the data to date (September 1986) from one of PEAR’s best RNG participants. A subset
of these data has been reported previously, but we have a complete set as of this writing. 10
A single trial was defined as a continuous collection of binary bits from a “true” RNG
(i.e., the sequence was derived from the noise associated with a back-biased PN junction).
For the data under study there were two trial lengths, 200 bits and 2000 bits.
To avoid
problems of a possible single dimensional “bias”
in the hardware, a target bit was toggled at a
rate such that each new bit from the generator was compared to the one’s
(Is) complement
of the previous target bit.
Data were collected in two fundamental modes, manual and
automatic.
In the manual mode,
a single button press resulted in a single
trial.
During the
automatic mode, a single button press resulted in 50 consecutive
trials.
In the IDS formalism,
is the total number of bits (sequence length)
resulting in a single button press
is the
independent variable.
Thus, there are only 4 allowed values for this independent variable:
200, 2000,,
10000, and 100000.
*We wish to express our appreciation to R. Jahn, R. Nelson and B. Dunne for providing
access to their data and for their assistance in transferring
it to our computer system.
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For
all sequence lengths, data were collected as a function of “aim”
•
pk+ — The participant attempts to force matches between the target bit
and “response”
bit from the generator.
•
pk
The participant attempts to force mismatches between target bit
and “response”
bit from the generator.
•
BL — The participant makes no attempt to modify the bits from the
generator.
These data are referred to by PEAR as the baseline data.
The order of “aim” was determined in two modes: the volitional modes,
in which the
participant chooses the order of the triad, and the random mode,
in which an RNG
determines the order of the triad.
Table 2 shows the data
files that were used for the IDS
analysis. A few of the button presses produced results in which the number of matches
between target and response bits was exactly equal to one-half of the sequence length.
Those
special cases are ignored in our analysis to avoid computing logarithms of zero.
The analysis
will focus upon the specific aim regardless of volitional/random control of the aim.
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Table 2
RAW DATA FOR OPERATOR 10—PRINCETON UNIVERSITY DATA
Sequence
Button
Number
Data Set
Length
Presses
z=0
200
5918
332
All PK +
2000
15014
286
(A PK)
10000
2065
1000000
597
200
3088 mm
All PK +
2000
7219
iSSHI
(PK+)
10000
1028 mi
1000000
299
l
200
2830
170
All PK -
2000
7795
155
(PK-)
10000
1037
1000000
298
200
1471
Volitional PK +
2000
4913
(V_PK+)
10000
330
1000000
105
'
200
985
Volitional PK -
2000
5203
(V_PK-)
10000
328
1000000
100
200
1617
Random PK+
2000
2306
(R_PK+)
10000
698
1000000
194
200
1845
105
Random PK-
2000
2592
(R_PK-)
10000
709
1000000
198
200
0 IHEH
All Baseline
2000 Hal
(BL)
10000
1000000 HSIIHuH
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IV
RESULTS AND DISCUSSION
The results of the SRI pseudorandom number generator experiment and the PEAR
experiment will be discussed separately here and then compared in Chapter V, Conclusions
and Recommendations.
A.
The PRNG Experiment Results
In 1985, Radin and May reported pilot results for two participants
(I.D.
105 and I.D.
531) who were selected on the basis of past successful performances in similar tasks. 1
For
example, Participant 531 was the most significant contributor in our 1979 RNG experiment.
In the 1985 pilot experiment, Participants 531 and 105 contributed 500 and 298
trials,
respectively.
The analysis showed that neither of the participants produced sequence length
dependencies different from MCE
(i.e.,
a slope of -0.5).
However, the analysis revealed that
both individuals showed independently significant evidence for IDS
(i.e., the intercepts were
significantly above MCE at the p < 0,005 level for each participant).
Thus, our tentative
conclusion from these data
is that IDS appears possible,
at least with these two participants.
During the FY 1986 program, we conducted the experiment in two phases:
a screening
and an experiment phase.
For the pilot phases, we asked 20 individuals to contribute 100
trials each under the protocol described above.
All but 4 of them completed this task.
For
availability reasons, the 4 participants contributed varying numbers of trials
(less than 100).
We had decided to select 7 individuals from within the pilot group to participate in a formal
PRNG IDS experiment.
The criterion for being included in the formal group was that the
participant had to produce a significant increase above MCE of the variance of the z-score
distribution over 100
trials
(the MCE variance =
1.0).
Of the
16 participants who finished the 100
trial series, only one, 531, met the above
requirement (variance =
1.37, p < 0.008).
The second best performer, however, produced a
variance =
1.21
(p < 0.07).
Judging from the 1984 study, we would not expect to see a
significant intercept with only 100
trials, and none were observed.
While
it
is particularly interesting that Participant 531 maintains his/her consistent
performance, we
felt that we should continue the pilot screening until we are able to select 7
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significant participants.
Thus,
at this point, we do not have any results to report for the
formal experiment.
B.
The PEAR Results
1.
Data Reduction and Analysis
Using the exact binomial procedure described in Chapter
III, we have computed
the MCE lines for the various data sets
(see Table
3).
These MCE lines were used as the
basis for the IDS analysis that follows.
Table
MCE FOR EACH DATA SET
Variable
Data Set
A_PK
PK+
PK-
BL
V_PK+
V_PK-
R_PK-
Intercept (X=0)
-0.9514
-0.9502
-0.9525
-1.0923
-0.9379
-0.9498
-0.9575
-0.9545
Intercept (X-bar)
-4.8845
-4.8688
-4.8999
-5.4789
-4.8738
-4.9533
-4.8616
-4.8331
Slope
-0.5380
-0.5381
-0.5378
-0.5208
-0.5402
-0.5387
-0.5365
-0.5370
X-bar
7.263
7.233
7.293
8.420
7.242
7.397
7.219
7.164
We have analyzed the PEAR data from a “top down” perspective
(i.e., beginning
with the most combined data and ending with the most condition specific data).
The
first
requirement from Chapter
III
is that we must determine
if a linear analysis
is appropriate for
these data.
For
all data
sets, the linear coefficient was strongly significant
(i.e.,
r ^ -0.6
for
all data
sets) when compared to
r =
0.
Therefore, we are justified in continuing with the IDS
analysis.
Table 4 shows the results of this analysis
(the data set abbreviations are taken from
Table
2).
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Table 4
RESULTS OF THE ANALYSIS OF THE PEAR RNG DATA
Variable
Data Set
A_PK
PK+
PK-
BL
V_PK+
V_PK-
R_PK+
R_PK-
Trials
23594
11634
11960
3971
6819
6616
4815
5344
Mean-Z
Z-Variance
p-of-Variance
-0.0067
1.018
0.024
0.0180
1.016
0.110
-0.0308
1.019
0.070
-0.0097
1.035
0.062
0.0185
1.002
0.454
-0.010
1.025
0.083
0.018
1.036
0.038
-0.056
1.012
0.274
Stouffer’s Z
p-of-Z
-1.031
0.849
1.946
0.026
-3.367
3. 80(-4)
-0.613
0.730
1.516
0.065
-0.821
0.794
1.219
0.038
-4.124
1.86(-5)
MCE
X-bar
Intercept
Slope
7.263
-4.8606
-0.5380
7.233
-4.8420
-0.5381
7.293
-4.8754
-0.5379
8.420
-5.4778
-0.5208
7.242
-4.8502
-0.5402
7.397
-4.9349
-0.5387
7.219
-4.8305
-0.5365
7.164
-4.8017
-0.5370
DATA
Intercept
Slope
-4.8606
-0.5317
-4.8469
-0.5471
-4.8737
-0.5157
-5.4580
-0.5276
-4.8574
-0.5449
-4.9338
-0.5167
-4.8319
-0.5486
-4.7989
-0.5144
F-Intercept
p-value
0.06
0.784
0.32
0.570
0.03
0.859
0.21
0.649
0.42
0.626
0.01
0.920
0.01
0.913
0.024
0.878
F-Slope
p-value
2.01
0.155
2.09
0.148
12.20
4.79(-4)
0.26
0.609
0.24
0.626
4.16
0.041
2.20
0.137
8.34
0.004
df-2
23592
11632
11958
3969
6817
6614
4813
5342
The meaning of MCE and data variables and their associated F-ratios have been discussed in
Chapter
III.
The z-score variables are included here in order to make comparisons with the
results published previously for part of these data. 10
The mean z-score
is the average value of
the z-scores for
all the
trials shown in each column; the MCE
is zero.
The variance for the
z-score
is calculated for the same data; the MCE
is one.
Note that both of these quantities
were not calculated as absolute values.
The Stouffer’s z-score
is the proper way of combining
all the z-scores to test against the MCE hypothesis: no psychoenergetic functioning.
The
Stouffer’s z-score
is given by16
z s
where
[n]
is the number of trials.
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2,
Discussion of the PEAR Results
We note that our analysis
is consistent with PEAR’s in that the difference between
the PK+ data
(the participant was tasked to force more matches than MCE regardless of the
origin of the “aim” request—volitional or random) and PK- data as measured by the
Stouffer’s z-score
(zdiff = 3.75, p < 8.6 x 10-5
)
is highly significant.
While the magnitude of
the effect
is small,
it
is, nonetheless, persistent and
statistically robust.
We are able to discuss the IDS analysis for
all of the PEAR data by examining the
most deviant (from MCE)
data
set.
Figure
6 shows the best
fit line
for the PK- data
compared to
its MCE.
We plot this particular data set because
it produced the most
significant deviation
(p < 4,79 x 10-4
) from the MCE slope.
While the slope of the data
line
is significantly more positive than the MCE slope,
the intercept
is not significantly different.
In effect, the data line has rotated about
its
intercept point
(i.e., sequence length = 1470).
Yet, the Stouffer’s z-score indicates strong
evidence
for some form of psychoenergetic functioning
(p < 3.8 x 10-4
)
for this data
set.
The resolution of this apparent inconsistency involves understanding a fundamental, and
unfortunate, problem with these PEAR data in general.
Their data were not collected to provide a specific test of our IDS model.
Thus,
the sequence lengths that were chosen and, more importantly, the number of trials collected
at each sequence length, were not optimized for our test.
In the extreme,
if
all the data were
collected at a single sequence length, our IDS analysis
is completely inappropriate
(i.e., the
IDS formalism requires testing as a function of sequence length),
To
first order, these PEAR
data suffer from the same problem,
Sixty-five percent of the total data shown in Figure 6
were collected at a single sequence length
(i.e,, 2000).
When we examine these data
at each
sequence length, we find that the Stouffer’s z-scores are -2.98, -0.80, -2.87, and -2.69
for
sequence lengths of 200, 2000,
10000, and 100000,
respectively.
Thus, most of the data for
this set are not significant, even though when they are combined across sequence lengths, they
are highly significant.
The situation described above
is similar for
all data
sets; none of the data
sets
produced significant intercepts,
Because the data were not collected uniformly as a function
of sequence length,
it
is
difficult to interpret the results of analysis. We
feel that
it
is
premature to speculate upon forms of either RA or IDS models that can
fit these data.
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|AP|
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V CONCLUSIONS AND RECOMMENDATIONS
In this report, we have developed a detailed model (IDS)
for psychoenergetic
functioning.
In particular, we have provided a mathematical formalism by which random
number generator experiments may be used to test the concept.
Preliminary results using pseudorandom number generators (PRNG)
, indicate that an IDS
ability appears possible.
Many more data are required using PRNGs to confirm these
preliminary results.
It
is anticipated that by 3rd quarter, FY 1987, we
will be able to
complete the PRNG experiment.
The PEAR data represent the largest amount of RNG data currently available.
The
PEAR group have reported strong statistical evidence of psychoenergetic functioning within this
massive data base
(i.e.,
1.12 x 108 binary bits).
It
is unfortunate that the data were collected
in such a way that an IDS analysis
is inconclusive.
We strongly recommend that RNG data be collected with an equal number of trials as a
function of sequence length.
The protocol should be similar to the one in use in our PRNG
experiment,
in which a double-blind condition
is maintained with respect to sequence length.
We conclude with some speculation.
Suppose,
after many experiments of different
varieties, we could demonstrate that the philosophical concepts behind IDS were true. We
would call into question any experimental results from any discipline that claim
cause-and-effect relations based upon statistical inference.
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