SHANNON ENTROPY AS AN INTRINSIC TARGET PROPERTY: TOWARD A REDUCTIONIST MODEL OF ANOMALOYS COGNITION

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• Publication Date: April 22, 1994
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Shannon Entropy as an intrinsic Target Property V2.22 April 1994
Shannon Entropy as an. Intrinsic Target Property:
Toward a Reductionist Model
of
Anomalous Cognition
by
Edwin C. May, Ph.D.
S. James P. Spottiswoode (Consultant)
and
Christine L. James
Science Applications International Corporation
Cognitive Sciences Laboratory
Menlo Park, CA
Abstract
We propose that the average total change of Shannon's entropy is a candidate for an intrinsic target
property. We analyze the results of two lengthy experiments that were conducted from 1992 through
1993 and find a significant correlation (Spearman's e = 0.337, df = 31, t = 1.99, p < 0.028) with an
absolute measure of the quality of the anomalous cognition. The 1993 result replicated the similar find-
ing from the 1992 study. We describe the methodology, the calculations, and correlations in detail and
provide guidelines for those who may wish to conduct similar studies. In addition, we provide circum-
stantial evidence which leads us toward a reductionist view of anomalous cognition.
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Shannon Entropy as an Intrinsic Target Property V2. 22 April 1994
Introduction
The psychophysical properties of the five known senses are well known (Reichert, 1992). At the "front
end," they share similar properties. For example, each system possesses receptor cells that convert
some form of energy (e.g., photons for the visual system, sound waves for the audio system) into electro-
chemical signals. The transfer functions are sigmoid; that is, there is a threshold for physical excitation,
a linear region, and a saturation level above which more input produces that same output. How these
psychophysical reactions translate to sensational experience is not well understood, but all the systems
do possess an awareness threshold similar to the subliminal threshold for the visual system.
Since all the known senses appear to share these common properties, it is reasonable to expect that if
anomalous cognition (AC)' is mediated through some additional "sensory" system, then it, too, should
share similar properties. For example, a putative AC sensory system should possess receptor cells that
have a sigmoidal transfer function and exhibit threshold and saturation phenomena. As far as we know,
there are no candidate neurons in the peripheral systems whose functions are currently not understood.
So, if receptor cells exist, it is likely that they will be found in the central nervous system. Since 1989, our
laboratory has been conducting a search for such receptor sites (May, Luke, Trask, and Frivold, 1990);
that activity continues.
There is a second way in which receptor-like behavior might be seen in lieu of a neurophysiology study.
If either an energy carrier for AC or something that correlated with it were known, then it might be
possible to infer sigmoidal functioning at the behavioral level as opposed to the cellular level. Suppose
we could identify an intrinsic target property that correlated with AC behavior. Then, by manipulating
this variable, we might expect to see a threshold at low magnitudes and saturation at high magnitudes.
To construct such an experiment, it is mandatory that we eliminate, as much as possible, all extraneous
sources of variance and adopt an absolute measure for theAC behavior (Lantz, Luke, and May, 1994).
We can reduce one source of variance by considering what constitutes a good target in an AC experi-
ment. Delainoy (1988) reported on a survey of the literature for successful AC experiments and catego-
rized the target material according to perceptual, psychological and physical characteristics. Except for
trends related to dynamic, multi-sensory targets, she was unable to observe systematic correlations of
AC quality with her target categories.
Watt (1988) examined the target question from a theoretical perspective. She concluded that the "best"
AC targets are those that are meaningful, have emotional impact, and contain human interest. Those
targets that have physical features that stand out from their backgrounds or contain movement, novelty,
and incongruity are also good targets.
In trying to understand these findings and develop a methodology for target selection for process-ori-
ented research, we have constructed a metaphor. Figure 1 shows three conceptual domains that con-
tribute to the variability in AC experiments. The engineering metaphor of source, transmission, and
detector allows us to assign known contributors to the variance of specific domains. Without controlling
The Cognitive Sciences Laboratory has adopted the term anomalous mentalphenomena instead of the more widely knownpsi.
Likewise, we use the terms anomalous cognition and anomalous perturbation for ESP and PK, respectively. We have done so
because we believe that these terms are more naturally descriptive of the observables and are neutral in that they do not imply
mechanisms. These new terms will be used throughout this paper.
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V2.22 April 1994
or understanding these sources, interpreting the results from process-oriented research is problemati-
cal, if not impossible.
Figure 1. Information-transfer Metaphor
For example, suppose that the quality of an AC response actually depended upon the physical size of a
target, and that affectivity was also a contributing factor. That is, a large target that was emotionally
appealing was reported more often more correctly. Obviously, both factors are important in optimizing
the outcome; however, suppose we were studying the effect of target size alone. Then an "attractive"
small target might register as well as a less attractive large target and the size dependency would be con-
founded in unknown ways.
Our metaphor allows us to assign variables, such as these, to specific elements. Clearly, an individual's
psychological response to a target is not an intrinsic property of a target; rather, it is a property of the
receiver. Likewise, size is a physical property of the target and is unrelated to the receiver. Generally,
this metaphor allows us to lump together the psychology, personality, and physiology of the receiver and
consider these important factors as contributors to a detector "efficiency." If it is true that an emotion-
ally appealing target is easier to sense by some individuals, we can think of them as more efficient at
those tasks. In the same way, all physical properties of a target are intrinsic to the target and do not
depend on the detector efficiency. Perhaps, temporal and spatial distance between target and receiver
are intrinsic to neither the target nor the receiver, but rather to the transmission mechanism, whatever
that may be.
More than just nomenclature, our metaphor can guide us in designing experiments to decrease certain
variabilities in order to conduct meaningful process-oriented research. Some of the methodological
improvements seem obvious. If the research objective is to understand the properties ofAC rather than
understanding how an AC ability may be distributed in the population, then combining results across
receivers should be done with great caution. To understand how to increase high jumping ability, for
example, it makes no sense to use a random sample from the general population as high jumpers; rather,
find a good high jumper and conduct vertical studies (no pun intended). So, too, is it true in the study of
AC. We can easily reduce the variance by asking given receivers to participate in a large number of trials
and not combining their results.
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May, Spottiswoode, and James (1994) suggest that by limiting the number of cognitively differentiable
elements within a target, the variance can also be decreased. A further reduction of potential variance
can be realized if the target pool is such that a receiver's emotional/psychological response is likely to be
more uniform across targets (i.e., reducing the detector variance as shown in Figure 1).
Having selected experienced receivers and attended to these methodological considerations, we could
then focus our attention on examining intrinsic target properties. If we are successful at identifying one
such property, then all process-orientedAC research would be significantly improved because we would
be able to control a source of variance that is target specific. The remainder of the paper describes two
lengthy studies that provide the experimental evidence to suggest that the average of the total change of
Shannon's entropy is one such intrinsic target property.
Approach
The AC methodological details for the two experiments can be found in Lantz, Luke, and May (1994).
In this section we focus on the target calculations and the analysis techniques.
Target Calculations
Because of the analogy with other sensorial systems, we expected that the change of entropy would be
more sensitive than would be the entropy alone. The target variable that we considered, therefore, was
the average total change of entropy. In the case of image data, the entropy is defined as:
Nk pp ((,,,,
Sk = - ZP.k1092(P.k), (1)
m-0
wherepmk is the probability of finding image intensity m of color k. In a standard, digitized, true color
image, each pixel (i.e., picture element) contains eight binary bits of red, green, and blue intensity, re-
spectively. That is, Nk is 255 (i.e., 28-1) for each k, k = r, g, b. For color, k, the total change of the
entropy in differential form is given by:
dS, = IVSk I ? dr + ltdt. (2)
We must specify the spatial and temporal resolution before we can compute the total change of entropy
for a real image. Henceforth, we drop the color index, k, and assume that all quantities are computed
for each color and then summed.
Tb compute the entropy from Equation 1, we must specify empirically the intensity probabilities,p,,,. In
Lantz, Luke, and May's 1993 experiment, the targets were all video clips that met the following criteria:
? 'Ibpic homogeneity. The photographs contained outdoor scenes of settlements (e.g., villages, towns,
cities, etc.), water (e.g., coasts, rivers and streams, waterfalls, etc.), and topography (e.g., mountains,
hills, desserts, etc.).
? Size homogeneity. Target elements are all roughly the same size. That is, there are no size surprises
such as an ant in one photograph and the moon in another.
? Affectivity homogeneity. As much as possible, the targets included materials which invoke neutral
affectivity.
For static targets, a single characteristic frame from a video segment was digitized (i.e., 640 x 480 pixels)
for eight bits of information of red, green, and blue intensity. The video image conformed to the NTSC
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Shannon Entropy as an Intrinsic Target Property V2. 22 April 1994
standard aspect ratio of 4 x 3, so we arbitrarily assumed an area (i.e., macro-pixel) of 16 x 12 = 192 pix-
els from which we calculated the p,,,. Since during the feedback phase of a trial the images were dis-
played on a Sun Microsystems standard 19-inch color monitor, and since they occupied an area approxi-
mately 20 x 15 cm square, the physical size of the macro-pixels was approximately 0.5 cm square. Since
major cognitive elements were usually not smaller than this, this choice was reasonable-192 pixels
were sufficient to provide a smooth estimate of they,,,.
For this macro-pixel size, the target frame was divided into a 40 x40 array. The entropy for the (ij)'th
macro-pixel was computed as:
N-1
S;, Z P. log2(PM ),
M-0
wherepm is computed empirically only from the pixels in the (i, j) macro-pixel and m is the pixel intensi-
ty. For example, consider the white square in the upper left portion of the target photograph shown in
Figure 2.
Figure 2. City with a Mosque
The green probability distribution for this macro-pixel (3,3) is shown in Figure 3. The probability densi-
ty and the photograph itself indicate that most of the intensity in this macro-pixel is near zero (i.e., no
intensity of green in this case). Ina similar fashion, the Sj are calculated for the entire scene. Since i and
j range from zero to 40, each frame contains a total of 1,600 macro-pixels.
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Shannon Entropy as an intrinsic Target Property
20 40 60 80 100
Intensity (m)
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Figure 3. Green Intensity Distribution for the City Target (Macro-pixel 3,3).
We used a standard image processing algorithm to compute the 2-dimensional spatial gradient for each
of the 1,600 macro-pixels. The first term in Equation 2 was approximated by its average value over the
image.
The total change of entropy for the dynamic targets was calculated in much the same way. The video
segment was digitized at one frame per second. The spatial term of Equation 2 was computed exactly as
it was for the static frames. The second term, however, was computed from differences between adja-
cent, 1-second frames for each macro-pixel. Or,
aS;1 AS;1(t) - S;1(t + At) - S;;(t) (3)
at At At I I
where At is one over the digitizing frame rate. We can see immediately that the dynamic targets will
have a larger AS than do the static ones because Equation 3 is identically zero for all static targets.
In Lantz, Luke, and May's 1992 experiment, the static targets were digitized from scanned
photographs. This difference and its consequence will be discussed below.
AC-Data Analysis
Rank-order analysis in Lantz, Luke, and May's (1994) experiment demonstrated significant evidence
forAC; however, this procedure does not usually indicate the absolute quality of theAC. For example, a
response that is a near-perfect description of the target receives a rank of one. But a response which is
barely matchable to the target may also receive a rank of one. Table 1 shows the rating scale that we used
to assess the quality of theAC responses, regardless of their rank.
To apply this subjective scale to an AC trial, an analyst begins with a score of seven and determines if the
description for that score is correct. If not, then the analyst tries a score of six and so on. In this way the
scale is traversed from seven to zero until the score-description seems reasonable for the trial.
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Shannon Entropy as an Intrinsic Target Property
Thble 1.
0-7 Point Assessment Scale
V2.22 April 1994
Score
Description
7
Excellent correspondence, including good analytical detail, with essentially no
incorrect information
Good correspondence with good analytical information and relatively little
6
incorrect information.
Good correspondence with unambiguous unique matchable elements, but
5
some incorrect information.
Good correspondence with several matchable elements intermixed with
4
incorrect information.
Mixture of correct and incorrect elements, but enough of the former to indicate
3
receiver has made contact with the site.
Some correct elements, but not sufficient to suggest results beyond chance
2
expectation.
1
Little correspondence.
0
No correspondence.
Anomalous Cognition Experiment - 1992
In Lantz, Luke and May's 1992 experiment there were no significant interactions between target condi-
tion (i.e., static vs dynamic) and sender condition (i.e., sender vs no sender); therefore, they combined
the data for static targets regardless of the sender condition (i.e., 100 trials). The sum-of-ranks was 265
(i.e., exact sum-of-rank probability of p < 0.007, effect size = 0.248). The total sum-of-ranks for the
dynamic targets was 300 (i.e., p < 0.50, effect size = 0.000).
Entropy Analysis
Tb examine the relationship of entropy to AC, two analysts independently rated all 100 trials (i.e., 20
each from five receivers) from the, static-target sessions using the post hoc rating scale shown in Table 1.
All differences of assignments were verbally resolved, thus the resulting scores represented a reason-
able estimate of the visual quality of the AC for each trial.
We had specified, in advance, for the correlation with the change of target entropy, we would only use
the section of the post hoc rating scale that represented definitive, albeit subjective,AC contact with the
target (i.e., scores four through seven). Figure 4 shows a scatter diagram for the post hoc rating and the
associated AS for the 28 trials with static targets that met this requirement. Shown also is a linear least-
squares fit to the data and a Spearman rank-order correlation coefficient (,o = 0.452, df = 26, t =2.58,
p