called it ganz andere, (wholly other, something else), seemed to emerge
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spontaneously along with an instantaneous knowing-how-it-is-with-you-and-I-andall-of-us
that made even vicious killers appear sympathetic. Is this what the
Charismatic New Testament Book Churches mean by redemption through
forgiveness of others, requiring the genuine sincerity of this thought before
qualifying for Communion? Is this Christ’s undemanding gift of grace as in Romans
4: where Paul observed that all of us fall short of the full glory of God unless justified
freely by His grace. Was this the New Testament’s spiritual technological advance
from the Old Testament’s and Koran’s eye-for-an-eye? Did this chemically triggered
transcendent experience differ significantly from the supernatural transformation of
individuals by the Holy Spirit of Christian revivalist teachings? Martin Marty,
University of Chicago’s Professor of Modern Church History, dates the
institutionalization of this personal transformation in the United States to the post-
Civil War period. Did this mean that the mysteriously selfless love of Christian
agape and the altruism of E.O. Wilson’s sociobiology lay waiting in the brain and
could appear spontaneously, by grace, without lawful directive, repetitive recitation
or the discipline of catechism?
As one might have suspected, the urgency of my inner and outer search for a
new spiritual ecology of mind was driven by more personal needs. My spiritual
hunger was made acute a couple of years before our laboratory’s DMT discovery
when as a 30 year old Assistant Professor of Psychiatry and Neuroscience at UCLA
in West Los Angeles, I was living in a small, heavily mortgaged house in Brentwood
with my graduate student wife and two young sons. A testicular lump was an
accidental discovery made while showering. After surgical biopsy and radical lymph
node dissection, the professor of urology gave me a diagnosis of right testicular
choriocarcinoma. All by itself, my testicle had given birth to a mass containing all the
embryological tissues of a fetus, and had thrown in some maternal placental cells
as lagniappe. Unlike now, when the group of testicular neoplasms are treated
successfully with a high survival rate (think Lance Armstrong), at that time, follow up
research of this young man’s disease by the Army Medical Corps promised a fiveyear
survival rate of only 5% to 10%. The news filled me with fear and the ensuing
hopeless resignation detached me from life with a dread broken up only by
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episodes of rageful envy of everyone else in the world that had been spared. My
wife escaped into an alcoholic flirtation with her major professor; my sons grew
increasingly ensconced in the generous and kind neighborhood homes of their
playmates. I metered as many hours as possible in equity growing, long lonely days
in a small, dark, couch filled, university office, listening to Beverly Hills, Brentwood
and West Los Angles citizens as they psychoanalyzed their mysterious lack of
emotional fulfillment from materialistic fulfillment. Legend has it that Gautama’s
sudden insight about the universality of this sated, bored condition occurred in 528
B.C. after 49 days of sitting in the lotus position under the bodhi tree, now called
ficus religiosa. In contrast with Buddha’s illumination, my psychoanalytic traininginduced,
Freudian-Darwinian instinctual conflict, driven by fears of starvation and
castration, drew me tighter into the world of meaningless, coin flip probabilities.
Our house was a block away from a West Los Angeles synagogue and we
knew the Rabbi and his family well. Our sons played together frequently. The Rabbi
tried to bring comfort to me on my death watch, with hours of discussions about
trans-individual, ethnic belonging and a deeper foray into philosophical humanism.
Both felt completely irrelevant to my condition. As an intern tending to those dying at
night in Ochsner Foundation Hospital in New Orleans, it seemed to me that Jews
tended to die more noisily than Catholics. For my personal escape from low-lying
dread, I needed the metrically linear time of chronos to become the metric-free,
topological, continuous surface of the twisted circular ribbon of a Mobius loop, with
the view from each moment a kairos, a stretchable infinity of each moment’s internal
multiplicity of times.
The ruthlessly reasonable Hebraic historicity, configured by the tooth-for-atooth,
Mosaic and Roman talion law, the reciprocal, economic, exchange-calculating
brains of Barkow, Cosmide and Tooby’s The Adapted Mind (1992) and the terrifying
stories of the Five Books of Moses, made the hopelessness of this sinner’s plight
inevitable. It felt like my dichotomous choice of God-type was between One of
merciless fairness and the He and She of unconditionally forgiving generosity. The
mind set of logical problem solving applied to the question about which of these two
represented the true character of God lead to a momentarily distracting, metaphoric
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ecclesial exercise: what were the minimal number of four magical cards need we
turn over with preconditions or results on the upsides and downsides if what was
showing was: (1) Beatifically good; (2) Cursed with extraordinarily bad luck; (3) Not
dependent upon personal virtue; (4) Inordinately fortunate in all of life’s trials. The
pay-as-you-go God people would need to pick up (1) and find fortunate life and (2)
to find the fate of the non-believer to establish that God was coldheartedly true and
fair with the results of flipping (3) and (4) being none contributory. The grace-to-allsinners
God people need to turn over card (3) to find good life and (4) to find
sometime sinners nonetheless fortunate to confirm their belief in the unconditionally
of the loving generosity of God and making finding out about the underside of cards
(1) and (2) unnecessary. This liturgical discussion and gamble with God’s cards,
perhaps a caricature of the Talmudic, rational discussions with the rabbi, felt
irrelevant to my spiritual needs.
Missing was mysticism’s promise of the disappearance of I into a union with
the divine, the Heart Sutra’s eternal emptiness of form and the eternal form of
emptiness that gifts with spiritual perspective and not-necessarily-logical intuition
about unseen Absolute Reality. Forced either-or, binary, card-turning cognition in
the search for God’s logic is unrewarding. As the Dalai Lama, in his Heart of
Wisdom Teaching, says, “…all phenomena are emptiness, without defining
characteristics, they are not born, they do not cease…" In trying to penetrate the
mystery and promise of this emptiness, it was difficult to surrender my internal
parody of what sounded like that day’s Southern California New Age stuff about
global nonaggression, sexual politics, Beadles music, distressed jeans and pot. In
the synagogue of my neighborhood, experience with a deeply felt, never-you-mindabout-anything
God of detachment with love, was not on the menus of Friday night
or Saturday morning services. All I could feel was a faithless and nonnegotiable
fear.
In the work of many mysticism-positive scholars, a classic being Evelyn
Underhill’s Mysticism, 1961, it has been speculated that this ineffable state as a
union with a powerful unknown, transcending description in language, becomes
more socially prominent during times of cultural efflorescence. She pointed to the
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flowering of mysticism in epochs of the high cultural achievements at the close of
the Classical Period in the Third Century, the Medieval Period in the Fourteenth
Century, the Renaissance in the Seventeenth Century and, now, as we know, in the
Western World toward the end of the Twentieth Century. An increase in general
acceptance of talk, writing and practice focused on mystical experience is said by
many to accompany historical high points in intellectual, literary and political
achievement. One might include as a component of our growing cultural richness,
the new science about chemical dialogues with the brain. Although no central
nervous system agents were ever allowed in the ashrams of Baba Muktananda, it
was common during some evening sessions of questioning, called satsangs, for him
to acknowledge that one or a few experiences with entheogenic agents can open
many recalcitrant folks to the existence of the God within. This, in turn, led them to
the drug free spiritual exercises, sadhana, of love, self-truth, and spontaneity (each
according to their nature) as well as abstinent discipline, meditation, chanting and
yoga to maintain the knowledge. We might speak of participating in the creation and
maintenance of the spiritual ecology of ones inner and outer being. Underhill said
that the cultural richness of an efflorescent epoch is taken inward and accompanies
personal and societal mutations into states and institutions involving higher spiritual
consciousness.
In addition to an increase in the common outward manifestations of having
had a mystical experience, such as an increase in compassion, forgiveness and
more respectful and reverential attitudes toward the Earth and all its creatures
(currently taking the forms of deep ecology, ecofeminism, herbal medicine, organic
farming and the like), these times bring more public consideration of the nature of
reality itself, apart from its material manifestations. The theme of the life’s work of
the Dominican priest, Thomas Aquinas, made master of theology by papal
dispensation in 1259, involved the existential recognition of this dichotomy of
existence, esse, and essence, nature and grace, the material world and God.
William James wrote famously about mystical experience penetrating the thin veil
between these two worlds. Those with a mystical orientation attribute reality to inner
experience in relationship to a transcendental, supernatural world. Whereas
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everyday events are subject to perceptual ambiguity and its attendant variety of
interpretations, mystical union is claimed to bring the existence and meaning of
Absolute Reality into direct experience. This kind of knowing is more akin to the
Platonic view of mathematics, that theorems have been everlastingly existent, from
before our physical world, then it is to the here and now, physically based, finite
computations involving the experimental machines of physics.
The philosopher-mathematician father of phenomenology, Edmund Husserl,
criticized the physics-want-to-be orientation of the 1860 empirical, objective
measure psychologies of Fechner and Wundt. He understood the best of their
findings as simply correlations between subjective and observable events. Using
mathematical discoveries as examples, Husserl spent his life arguing for the
possibility of abstract truths relevant to mind being more reliable and valid if grasped
via direct experience. Knowing by what the popular mid-twentieth century writer of
science fiction, Robert Heinlein, called grocking it. This is antithetical to the attitudes
of today’s human cognitive and brain sciences which disallow such knowing as
deeply suspect unless accompanied by objectively definable observables such as
changes in electrical or imaging indices of brain activity in one neural region or
other. The modern psycholinguistics of brain mechanics can be called
neolocationism. Using modern technology to measure regional blood flow, energy
metabolism and/or electrovoltage or magnetic field activity, stories of function are
spun that closely resemble those imagined more than a century ago by the first
locationists, such as Ramon Cajal. These neuroanatomists spent thousands of
hours looking at cell clusters and their connections in stained slides of human brain
tissue using microscopes and imagined their singular and integrated function.
Today, Lewis Judd, long time chairperson of the Department of Psychiatry at
UCSD in La Jolla, carries a full sized, polymeric, three-dimensional model of the
human brain when teaching his students about human subjective experience and
interpersonal behavior. In his weekly grand rounds, he explains that day’s
psychiatric patient’s problems pointing here and there at regions in this plastic
surrogate for our electrical jellied brain. Few, if any, of the psychiatry students in his
class was inclined to ask the foundational question: how it is that a finger point and
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a name of a brain place can describe, much less explain in the language of physical
or physiological mechanism, a patient’s illogical thoughts, feelings of hopelessness,
irrational rage or prayerful gratitude. There remains a wide gap between ideas
about the mechanisms of human symbolic processing and those involving the
structures and functions of neuronal components and their connectivities in the
brain, particularly when perceived as regionally segmented meat. Yet this report of
Professor Judd’s finger-pointing plastic brain ritual should not elicit surprise since
iconic manipulation is certainly not new to the practices of priesthood.
In contrast with neuropsychiatry’s behavioral attributions to brain parts as an
explanatory pantheon of mysterious doers, absent of mechanical specifics, the
fields of physics turn to more abstract and general mathematical and statistical, socalled
phenomenological laws, such as those of thermodynamics and statistical
mechanics. The accounts of Feynman’s abstract and general thermodynamic
development of conservation of energy as well as equilibrium thermodynamics
discussed previously serve as relevant examples. These abstract models have
been found to capture the behavior common to diverse physical systems involving
(often still unknown) differing physical mechanisms. Consistency of description,
reliability, weighs in before predictive validity, which, with maturation of the research
area, gradually becomes detailed mechanistic understanding with the eventual goal
being derivation from the first principles of physics. The painful truth is that that in
spite of evocative claims made to the contrary in the 1990-2000 Decade of the
Brain, this level of understanding at the interface of neurobiological hardware and
software remains unbreached. Some recent attempts are interesting.
One of the current research themes about real single neurons in real brains
(in contrast with the silicon chip modules used in neural network computer
simulations), involve widely distributed neurons that discharge in temporal
synchrony. These phenomena have been described by Max Planck’s Wolf Singer,
Christoff Koch of California Institute of Technology and Florida Atlantic University’s
Steven Bressler and others with words such as synchronization, phase locking,
coherence and binding. Binding is an intuitively seductive word that premises that
two, even widely spatially separated, brain regions that manifest neuronal signals of
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activation locked together in time are assumed to be functionally integrated. Another
time-dependent neuronal characteristic of current interest involve neurons or
neuronal clusters that beat with almost strict periodicity, the oscillatory pacemakers.
For example, the program of research by Professor Al Selverson at University of
California at San Diego, among others, has elucidated the role of these rhythmic
pattern generators, both autonomous and those emerging from particular patterns
of network connections. A wide variety of functional links involving neuronal
pacemakers has been demonstrated. They range from the oscillatory transport of
calcium through membrane channels in neurons and heart muscle, smooth muscle
oscillations of the pylorus muscle of the stomach, the neuronal ganglion driven
chewing motions of the jaws of invertebrates and the retina-to-brain hypothalamic
cells gating human circadian rhythms coupling our body’s hormonal clocks to light
cycles.
Though regular rhythmicity in neuronal discharges is an intuitively attractive
idea and relatively easy to quantitate using simple sine wave trigonometric
transformations, in the real brain it is statistically rare. The commonest neuronal
discharge pattern observed is that of intermittent bursting, clusters of neuronal
discharges in time in which the inter-discharge intervals irregularly stretch and
contract like the bellow pleats of a syncopated accordion. Bursts of repeated firing
of some unpredictable length followed by silences of equally mysterious durations.
Their behavior can be represented as statistical measures using non-normal, long
tailed distributions and in-between entropies described previously. For a whole
human example, although the rhythm of manic depression is commonly thought to
involve periodic cycles, careful study using motility patterns of the timing through life
of these episodes of extreme mood states by Professor Allan Gottschalk at the
University of Pennsylvania and others have demonstrated an irregularly intermittent
bursting pattern in manic-depressive episodes, getting more frequent with age.
Neuronal inter-discharge intervals seldom demonstrate what is called a regression
to the mean like the normal distribution of heights, as one increases the number of
people measured, the tighter the distribution around the mean. Neurons, much like
our own irregular pattern of doing things (in spite of our plans), the statistical
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distributions of neuronal interspike intervals have increasingly long tails. Contrary to
the behavior of a normally distributed observable, the larger the series of neuronal
spike observed, the more likely that a longer interspike interval than had been seen
before will occur. Counter-intuitively, long intervals tend to be followed by more long
intervals as more shorts follow short intervals. Manic attacks cluster in time as does
a number of other brain and body diseases. Maybe it is intuitively obvious that bad
stuff tends to cause more bad stuff and good stuff is self-propagating. Having
suffered recently does not mean fate owes you one. The brain’s syncopated
segmentations of time can be translated into a creatively arrhythmic dance.
What makes neurologizing conversations like these about subtle human
experience possible are the human subjective scenarios we have agreed to short
hand with names of brain parts and neurochemicals. The how is where conceptual
connection is filled with post 19 th Century Spanish microscopic neuroanatomist,
Santiago Ramon y Cajal-like, intuitions about the functional role of brain structures:
we think motor automaticity and pacing when hearing the brain place names such
as caudate, putamen and cerebellum; we think limbic lobe when musing about
sexuality, rage and depression; we short hand left versus right hemispheric places
for verbal and sequential versus intuitive and geometric shape cognition; we point to
the frontal lobe for the future work of executive control, anticipation and paranoia;
the hypothalamus for primitively expressed appetites and to the brain stem for our
vital functions such as breathing and blood pressure. With respect to the brain
juices, we say dopamine for aggressive activity, norepinephrine for attention and
sensory discrimination and serotonin for hunger, mood and sexual inclination. No
matter how avant guarde our experimental techniques such as monitoring local
functional blood supply by fMRI, regional brain glucose utilization maps, timedependent
changes in skull surface voltage using a cap studded with
electroencephalographic, EEG, leads, monitoring these voltage field via their
transverse magnetic fields by the frozen helmets of magnetoencephalography,
MEG, we conclude our work by calling forth named but still enigmatic brain parts
and their juices as mysteriously powerful little men and women executing
remarkably complex and subtle tasks, sometimes even when called upon.
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Current neurochemical research using molecular biological tools such as
mice knockouts (the ablation of specific proteins though interference with their
nucleotide-mediated protein biosynthesis), for example, the production of animals
missing a subunit of their hippocampal glutamate receptors associated with the loss
of some memory functions, conclude the memorial mechanism to be a specific
cellular region, such as hippocampal CA3 cells. Technology advances but continues
to support a primitive philosophic animism of named brain parts which pop science
icons like the late Francis Crick called “The Amazing Hypothesis.” He and his fellow
brain philosophers implicate brain mechanisms such as the amygdaloidal nucleus
man who can emotionally color even affectually neutral information that is
transported through him. Imaging data showing amygdala man lighting up is used to
tell us that circulating sensory information through the differentially behaving
amygdaloid nucleus is used for fight or flight interpretive significance. Emotionally
expressive human faces light up inferior parietal cortex. The Iowa University
Professors, the husband and wife Damasios, have located even the criminal
psychopath man in specific locations in the brain. As we have argued, perhaps ad
nausem, using multimillion-dollar imaging and molecular biological technology and
no new thoughts that weren’t around during the era of the 19th Century’s
neuroanatomists, specific brain regions continue to gain implicative properties like
the task-specialized gods of the Roman and Greek pantheons. Crick implied that
God is a brain part.
At the same time, those of us that have been in the brain business for a
while, recall skyscraper window washers, standing steady, high up on rope lashed
planks, suffering from congenital absence of the cerebellum, the supposed sine qua
non brain part supporting motor coordination and balance in humans. More
generally, there is much evidence that if young enough and willing to work, many of
the functions of missing parts of the brain can be taken on remarkably well by other
brain parts thought not to be involved in these functions at all. In addition, since
evidence of neuronal responding to loud noise or bright light perturbation can be
found almost everywhere in the hyper-connected human brain, because anticipation
and brain time inversions make before and after indicate little about human
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neuropsychological causality, and inhibitory on or off and activating on or off are a
priori functionally equivalent with respect to the logic gates of information encoding,
transport or storage, the modern study of brain mechanisms in emotion, cognition
and behavior remains almost as mysterious as ever.
* * *
The only human mind-brain observations that are doubted consistently, and
treated as unpublishable by the editors of the journals of science, are those that
result from direct human experience using subjective reports from within. They are
called unscientific. Often ignored are logically consistent mathematical and
computational contexts, which, as abstract and general tools of thinking and
imagining, have the capacity to frame, rigorously define and describe thinking about
both the subjective and objective aspects of brain-generated phenomena. These
mathematically configured metaphors can lead to consistencies in description, this
is behaving like that, in what are called equivalence relations expressed both as
intuitive imagery; for a concrete example, a one holed bagel and one handled tea
cup are topologically equivalent because, sculpting in clay, they can be smoothly
transformed into each other. We have seen that invariant measures in computable
statistical flows can come out of a mess of data. Professor Paul Rapp of the
University of Pennsylvania has been able to mathematically encode the verbal
content of the patient’s free associations and the therapist’s responses, using tape
recordings of hours of psychoanalytical treatment. Examples of quantifiable qualities
found useful in this regard involve a variety of characteristic statistical patterns in
what are called entropies and information as well as various measures of what with
a wide range of definitions is called complexity. These quantifiable properties,
measures, can help in the struggle with the intrinsic tension of Absolute Reality
between the “eternal emptiness of form and the eternal form of emptiness.” We
resort to measures of entropy, information and complexity when confronted with our
ignorance, “emptiness,” great or little, with respect to either cause or result, about
what exactly is going on. Entropy in its forms relevant to information quantifies our
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ignorance, the emptiness and its mystery. Computations of the entropy of systems
in motion convert questions and answers concerning the detailed workings of the
leg’s neuromuscular machinery to global statistical descriptions of more abstract
thematic motifs, forms, expressed in the dance. Patterns of behavior of these
properties can suggest intuitive ideas and imagery about global mechanisms,
approach/avoid, smooth/discrete, wild/tame, as well as correlated and objective
physical observables.
To learn more about this abstract, topology tinged (none numeric) style of
model building, we can go to school on a long studied physical example. It connects
a simple and well understood real world observable with abstract statistical patterns
resulting from motions using the one-to-one correspondence (the equivalence
relation called isomorphism) between their entropies. As we have discussed, the
Stanford mathematician and Field’s Medal Winner, Donald Ornstein, proved that in
statistical studies of even point-to-point unpredictable, chaotic systems, entropy is
the only isomorphism. The hardware of this physical example is what the statistical
physicists call a dilute gas of some fixed number, n, of uniform hard spheres,
moving scatterers, that, absent of dissipative friction, wander continuously around,
changing their directions when bumping into each other. In a two dimensional
bounded arena of randomly rolling balls, this game has been called Sinai’s billiards.
It was named for previously mentioned Ya Sinai, an eminent Russian
mathematician He is now at Princeton and was previously a student of Andrei
Nikolaevic Kolmogorov, the Russian guru of many of the Twentieth Century’s worldclass
Russian mathematicians. Kolmogorov axiomatized the field of probability and,
more relevantly, initiated the theory of statistical descriptions, the ergodic theory, of
nonlinear dynamical systems. In the language of statistical physics, we will see that
the same system produced by high number of elements executing Newton’s
deterministic laws can be generated by a so-called random system such as that
resulting from flipping a suitably biased coin. Our example can also serve as a
metaphor, used extensively in the mathematical biology of the late Professor Art
Winfree, for the temporal features of life on a topological circle: the natural
irregularities of the recurrent beat of the heart, the in and out breathing of lungs, the
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up and down voltage of brain waves, the pendulum swings of our blood hormone
levels, the cyclic procession of our days, months and years and at large scale, our
body’s journey from dust to dust.
The angular deviation theta, θ� �from the initial reference direction of a single
moving sphere, gets rotated to a new angle theta, θ
→ θ
’ �by a collision with another
sphere. It has been shown that the new angle θ ’ is the previous angle, ��times twice
the average distance traveled between collisions called the mean free path, here
symbolized by delta, δ, divided by the diameter, D, of the sphere. Algebraically,
θ ’ �=�
2δ θ ��the new angle is equal to twice the mean free path divided by the diameter
D
of the spheres times the original directional angle of the sphere’s motion. �If we
symbolize the time between collisions with tau, τ, after an elapsed time of
experimental observation, t, we can say that the deviations from the initial direction
of the sphere changes like ( 2 δ � t/τ . The exponent, t/τ, represents the time of the
D
experimental observation divided by the average time between collisions of the
spheres, i.e. the time we’ve been watching, t, is expressed as units of inter-collision
interval, τ. Of course, the circular deviation in the angle from the initial direction
rotates repeatedly around a circle as the number of collisions increase. If a point on
a circle marks the angular change resulting from each collision and the system runs
long enough, it has been shown that the circle will eventually be completely covered
by points.
An estimate of the entropy, S, being generated by each sphere labeled with
some index i, Si, is positive because the recurrent motion is deviating continuously
from the initial direction. It can be computed for each sphere as the logarithm of the
intercollision time-averaged deviation from the initial direction, S i = 1 log( 2 δ
) and the
τ D
entropy of the whole n hard sphere system is the sum of the n entropies, which can
be expressed as n× S i . If we keep books by registering the points when each
sphere’s  ’ makes a stop on the top half of the sphere’s circle as 1 and the bottom
half as 0 (and we must arbitrarily decide between 0 and 1 if it falls exactly on the
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division between top and bottom and do so in a consistent way), then we can keep
score with a random looking binary series such as 11001001010…. that describes
the sequence of rotations. The advantage that accrues by doing so is that this coin
flip counting eliminates details in favor of a computable over all measure and
supports several forms of entropy calculations for its use in deciding if this system is
behaving like that system, an equivalence relation. One can imagine a series of coin
flips with 1 being heads and 0 being tails such that the statistics of a characteristic
series is determined by the fairness of the coin. As noted above, Donald Ornstein’s
famous theorem says that the entropy of these kinds of hardware and software
systems is the only general basis for finding correspondence between
characterizations of two such irregularly behaving systems. The important idea here
is that a series of 1’s and 0’s may not be identical but the two systems can be
isomorphically equivalent with respect to their entropy.
Notice again that the physical process of hard spheres bouncing off each
other on a flat surface has been captured by an abstract representation in binary
numbers that, like a series of coin flips, can be quantified as entropies (which would
be maximal for an ideal, fair coin). After describing the process of real number
representation by the binary code, we will show how entropies can be computed for
these binary series. We remind ourselves that we are struggling to obtain some kind
of knowing in a representative system manifesting the tension and mystery between
emptiness and form.
We can translate all finite real numbers into this language, making them
accessible to standard entropy computations. The following discussion of the
process of transforming numbers into binary series is in the spirit of the famous
number theory theorem that every natural number (the positive integers such as 1,
2, 3, 4…) can be expressed as the sum of at most four squared numbers. Encoding
any number by a series of 0’s or 1’s in what is called a binary transformation, begins
with its separation, called partition, into a sum of powers of 2, for example, 100 = 64
(2 6 ) + 32 (2 5 ) + 4 (2 2 ). A short hand description of this sum begins with a form
indicating the presence or absence of each successive power by a 1 or 0 coming
before the relevant power of two; i.e. 100 = 1 × 2 6 + 1 × 2 5 + 0 × 2 4 + 0 × 2 3 + 1 ×
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2 2 + 0 × 2 1 + 0 × 2
0 (in which the last term, arbitrarily, is 2 0 = 1, since anything to
the power 0 = 1). This can be written even more simply as a series of 0’s or 1’s,
their presence indicating whether the power represented by each place in the left to
right descending sequence of powers of two participates in the sum of the partition.
It is in this way that in binary numbers, 100 = 110010. As another example, if we
similarly partition the decimal number 729 = 512 (2 9 ) + 128 (2 7 ) + 64 (2 6 ) + 16 (2 4 ) +
8 (2 3 ) + 1(2 0 ), we find that its binary transformation results in 729 = 1011011001,
the 0’s representing the descending powers of two that are absent in the powers of
two partition. One can compute the binary representations of lower valued numbers
immediately; for example, 4 = 1 × 2 2 + 0 × 2 1 + 0 × 2 0 so that there is a 1 in the
multiply-the-power-of- two column and 0 the power 1 and power 0 columns so in
binary representation, 4 = 100. Similarly, 6 = 1 × 2 2 + 1 × 2 1 + 0 × 2 0 making the
binary transformation of 6 = 110.
It was the co-inventor (with Isaac Newton) of the calculus, Gottfried Wilhelm
Leibniz, in about 1665, who fully developed the binary representation of all decimal
numbers. In a state of wonderment about the simplicity, power and completeness of
this 1 and 0 encoding, he is said to have the beliefs that 0 symbolized the
emptiness of the universe’s beginnings, 1 represented the complete fullness of God
and that this transformation served as metaphoric evidence consistent with God’s
creation of the universe out of nothing.
The simplicity of binary expressions as in the dynamics of hard spheres or
rotations on the circle as well as the transformations such as 729 = 1011011001
make them propitious for exemplifying the methods for computing the entropies of
the growth rate of the possible, called the topological entropy, H T , and the probable,
the metric entropy, H M , which was introduced in a previous chapter called “Sensual
In-Between Entropies.” The following exemplify the computations of measures of
topological and metric entropies, H T and H M , another computable idea called
algorithmic complexity, AC and finally, the well known (to statisticians) standard run
score, src. Their descriptions have as their purpose a demonstration for the reader
that these apparently abstract, perhaps nebulous sounding, words can be
transformed into well-defined, concrete, quantitative and computable form of reality.
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If acceptance of this idea does not constitute a problem for the reader (and you do
not find it fun to follow along with a computer math program and/or a pencil), then
the following several paragraphs can be quickly scanned or skipped entirely.
The computations of H T and H M begins with keeping track of how many 0 →
1 and 1 → 0 transitions are found going from left to right in the binary series. For
example, in the binary expression of 729, 1011011001, one starts counting with a
1→ 0 transition followed by a 0 → 1 transition and then a 1 → 1 transition and so
on. A useful way to record the count is via entries into a 2 × 2 matrix for score
keeping in which the horizontal rows are labeled 0 on top and 1 below and the
vertical columns are labeled 0 on the left and 1 on the right. The number of each
kind of transitions (from the vertical label to the horizontal label) are counted and
summed in the appropriate box of the two box by two box matrix; for examples: for a
0 → 0 transition, a tally mark is entered in the upper left corner of the matrix; for a 0
→1 transition, a tally mark is entered in the upper right corner; a 1→ 0 tally goes in
the left lower corner and a 1→ 1 is tallied in the right lower corner. The resulting
transition incidence counting matrix, M t for the 729 binary transformation series
looks like M t = 1 3
indicating one 0 → 0, three 0 → 1, three 1 → 0, and two 1 → 1
3 2
transitions have been tallied. Although this series alone is too short for computing
reliable statistical measures, if we assume that the pattern of transitions observed in
this short series is stationary, that is its transition behavior will remain the same if
the binary series continued on to be infinite in length, the assumption being that the
dynamics of now will be the same as always, 729 will stay 729, then we can use two
forms of this transition matrix in the computation of the topological entropy reflecting
the growth rate of the possible, HT, and the metric entropy from the statistical
weights of allowed choices among them, the probable, H M .
To obtain the entropy representing the growth rate over time of the new
possibles, the computation of H T , the topological entropy, involves first transforming
M t into an transition incidence matrix, M t,i a 0 or 1 matrix indicating whether each
box has been entered at all (or not). Since in the binary representation of 729, all
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four boxes of M t are occupied, the M t,i =
1 1
1 1
indicates that all four kinds of
transitions are possible. Since we remain in the context of a 0,1, two state system,
the growth rate of the possible equals the logarithm, base two, of the sum of the
entries in the boxes of the left-top-row to right-bottom-row diagonal called the trace
and HT = log 2 (1 + 1) = log 2 (2) = 1. Consistent with intuition, since every transition is
possible, the topological entropy of M t as indicated in its M t,i is maximal (= 1).
Another expression equal to the sum of the trace (the sum of the upper left to lower
right diagonal) in a square matrix, is its leading eigenvalue, most often symbolized
with a lambda, λ 1 . The logarithm of the leading eigenvalue of the transition
incidence matrix is equal to its topological entropy. Symbolically, H T (M t,i ) = log 2 (λ 1 )
= log 2 (2 ) = 1. Standard elementary linear algebra texts describe how to compute
eigenvalues, these relations and related operations as well as their foundational
theorems.
Before computing the entropy of the distribution of probabilities among the
possibles as the metric entropy, H M , let us notice again that the occupancies in the
four entry boxes of the transition matrix M t are not uniform, M t =
1 3
3 2
. This leads
naturally to the intuition that for this series of binary transitions, HM, in contrast with
H T , will not be maximal, i.e. not equal to 1 and the nonuniformity of H T and H M is a
computational expression of what we mean by a state of in-between entropy. These
entropies are identical and their difference = 0 for transitions reflecting maximal
entropy, as might be realized in a very long series of fair coin flips in which the
entropies = 1. Entropy will be minimal when flipping a two headed coin, here the
entropies = 0. More compactly, the non-uniform probabilistic, metric entropy,
differing from the maximal topological entropy indicates that the system is in a
dynamical state of in-between entropy, written as H T - H M ≠ 0.
In the computation of the metric entropy, H M , the M t is transformed into a
transition probability matrix, M t,p , called a Markov matrix named for one of the two
great Russian mathematicians, both students of Pafnuti Lvovich Chebyshev, the
Markov brothers. The entries of each row in the M t are transformed into transition
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probabilities, so that the sum of the decimal fraction parts of all the boxes in each
horizontal row add up to 100%, or as a real number, 1.00. Recall that in the
example we’ve been using, the binary expansion of the natural number 729, the
1 3
transition incidence matrix is M t = and its Markov matrix is top row, 1/4, 3/4
3 2
and bottom row 3/5 , 2/5, i.e. M
t,p =
0.25 0.75
. Matrix multiplication of Mt,p by itself
0.60 0.40
repeatedly is equivalent to tracking the temporal evolution of the transition matrix’s
probabilities until the resulting matrices move toward, converge onto, a steady state;
each self matrix multiplication step represents what results from the passage of one
unit of time. The convergence to equilibrium values is continuous and gradual.
When the steady state is reached, both rows become identical. For this example,
M t,p × M t,p or M t,p 2 =
0.5125 0.4875
; M
0.3900 0.6100
t,p 4 =
0.4527 0.5472
; Mt,p 8 0.4445 0.5554
= ;
0.4377 0.5622 0.4443 0.5556
M
t,p 16 =
0.4444 0.5555
0.4444 0.5555
which for the first four decimal places remain the same for
additional times of self multiplication. Note the convergence of the top and bottom
rows to the same asymptotic values. Books discussing the multiplicative and other
behavior of these nonnegative matrices are numerous and frequently appear in
matrix algebra texts under the rubric of the Frobenius-Perron theorems.
Using the entropy formalism of Claude Shannon as developed previously, H M
is computed as the sum across either of the identical rows of each probability times
its logarithm, �ρ � �× log(ρ � �����ρ 2 × � �log(ρ 2 )) remembering from above that we are working in
base 2 logarithms and to change the minus sign (resulting from taking the
logarithms of decimal fractions) to plus: H M (M t,p ) = .4444 × log(.4444) + .5555 ×
log(.5555) = .9911 The nonuniformity of the box occupancy probabilities is reflected
in the difference between the topological (maximal estimate) and metric (minimal
estimate) entropies and is therefore quantifiable and computable: H T - H M ≠ 0 = 1.00
- 0.9911 = 0. 0089. If the maximal and minimal estimates of the entropy were equal
and all the probabilities boxes in each row asymptotically contained the same
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probabilities as in M t =
0.5 0.5
, it would retain these values across an infinite
0.5 0.5
number of self multiplications such that HM = .5 × log(.5) + .5 × log(.5) = 1 and H T -
H M = 1.00 – 1.00 = 0. 0.
Complexity is a more general and variously defined descriptive expression
than that of the topological and metric entropies and as such brings with it many
kinds of definitions and computational approaches. One choice that’s intuitively
appealing assumes that the relative complexity of an expression representing, say
an outcome of an observation or experiment, is reflected in the minimum length of
the most compressed program (algorithm) from which, given a suitable dictionary of
symbolic equivalencies, one can reconstitute the original expression. Increases in
what some have called algorithmic complexity, AC, are reflected in the growth of
this minimally descriptive symbol series length. Karen Selz’s approach to
compression and AC, similar to one proposed by Paul Rapp, involves the
identification and symbolic representation of repeated blocks of symbols called
words. For example, given an arbitrary, exemplifying binary series:
011011101010001010101001001010011, we first find the longest repeated word
[1010100] and represent it with the symbol, a, yielding a shortening in the original
series, 011011a010a1010011. The next longest repeated word is [011] is replaced
with b, yielding a further compression, bba010a1010b. The next remaining binary
word is of length equal to the previous one, [010], which, when replaced by c results
in the series bbaca1cb. This can be further compressed to the final representation
with four symbols and for the sequentially repeated b, one exponent of degree two,
b 2 aca1cb. From this representation and a dictionary of letter equivalent words, the
original binary expression can be recovered. For a quantitative index of the
algorithmic complexity, AC, of the compression, Selz computes the sum of the
number of distinct symbols plus the sum of the natural logarithms of the exponents:
4 + log (2) = 4.6931. The binary representation of 729, 1011011001, discussed
above, is compressed by making two [101]’s = a and two 0’s = b resulting in a 2 1b 2 1.
Having three distinct symbols, a,b, and 1, and two exponents of two, its algorithmic
complexity is equal to, AC = 3 + 2 × log(2) = 4.38.
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In addition to H T , H M and AC, if computable in a meaningful way, the
deviation of the binary series under study from the idealized random behavior of a
fair coin could serve as another index of complexity. Common descriptions of the
amount of randomness in a series are indices of run length If a run length is defined
by number of elements in a series of the same symbol before it stops, counting the
number of run boundaries by reading along the binary series and counting the
number of switches from 0 →1 or 1 → 0, then the binary expression of 729,
1011011001, has six runs. The great analytic probabilist, William Feller, among
many others, including the distinguished 18 th Century Swiss family of
mathematicians, the Bernoulli’s, proved that computing a standard run score, srs,
involves three terms, the theoretical expectation, E, of the number of runs, r, that is
E(r), the number of runs actually observed, Obs(r) and the variance of the
expectation of the number of runs, Var( E(r). If the srs is less than zero, then the
binary series is more random than that resulting from the flipping of a fair coin.
Interestingly, when a normal group of subjects are instructed to simulate what they
think of as a random coin flip determined series of 0’s and 1’s, their srs tends to be
lower than zero, over-estimating the degree of irregularity that randomness
represents. Long runs occur by chance far more often than intuition would dictate. If
srs is more than zero, than the binary, coin-flip series is more ordered than random.
If srs equal to zero, the binary series is not discriminable from fair coin flipping
randomness.
The expected number of runs, E(r), can be estimated by a fraction formed by
twice the product of the number of heads times tails divided by the sum of the
heads and tails to which is added one. That is, E(r) = 2 × 6 × 4 + 1 = 5.8. The average
6+
4
variation around this expectation called the variance, Var, of the expectation,
Var(E(r)), is estimated by a fraction formed by (take a breath) twice the product of
the number of heads times tails × twice the product of the number of heads times
tails minus the number of heads and minus the number of tails, all over the product
of the sum of the heads and tails squared, times the sum of the number of heads
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(2× 6× 4)(2× 6× 4 −6−4)
and tails minus one. That is, Var(E(r)) = = 2.03 . From these
2
(6 + 4) × (6 + 4 −1)
three terms, we compute srs =
Er () − Obsr () 5.8−
6,0
= =− 0.140 . We conclude that
Var( E( r) 2.03
the standard run score of the binary series is less than zero and therefore more
random than the expected random behavior of a fair coin.
Recall from the last chapter that Karen Selz, Martin Paulus and others have
shown that various personality types and psychiatric diagnoses are associated with
characteristic deviations of srs from zero. When the winners of the 2002 Annual
World Rock, Paper Scissors Championships held in Montreal Canada were
interviewed, they said that sensing their opponent’s characteristic style of deviations
from randomness in what we would call the continuum from maximal to minimal
entropy determined their successes. We characteristically use all of these measures
to estimate quantitate the deviation from randomness standard run score, srs,
algorithmic complexity, AC, as well as H T and H M ,, the topological and metric
entropies.
* * *
The encounter with mystical Absolute Reality, though sought by arduous
contemplative and other practice, emerges spontaneously, most often during times
of apparent mental emptiness, detachment, a state in which rationally instructive
thought and the choral background of brain voiced, emotion-ladened, commentary
have disappeared into the entropic soup of formless silence. It is this indescribable,
ineffable, stillness that we think serves as the psychophysiological anlage of
mystical experience. The mathematical systems yielding quantitative metaphors,
descriptive ideas about dynamical entropic statistical emptiness and form inspire the
use of mathematical structures in place of localized lumps in brain meat as
personalized icons of doing.
Our wedding of well-defined mathematical objects to metaphoric elements of
more general nonverbal intuition has a long tradition. Rene Thom’s 1990 book,
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Semiophysics, discusses mathematical mechanisms and their representations in
mind and the real world, analogizing mathematical objects and the intuitions they
generate to mechanical tools. Similar ideas are found among the four liberal arts of
the ancients: Number, Geometry, Music and Cosmology. The epistemologies of all
four require, then and now, the intuitive use of mathematical objects, conscious or
unconscious. Examples can be found in conceptual issues of Geometry and
Number with implications for relationships between man’s physical and
psychological worlds. One set of articulations were attributed to the shapes of
Platonic solids found among the Neolithic stone circles in Aberdeenshire, Scotland,
2000 years before Plato. Each symbolized particular physical and psychological
themes. All manifested equal edges and every face of each solid was the same
perfect polygon. The solid with four equilateral triangles manifesting four vertices
and faces, the tetrahedron, represented the physical element, Fire, and the
personal psychological climate of a choleric, fiery nature. A Platonic solid composed
of eight equilateral triangular faces, two tetrahedrons annealed, the octahedron,
signified Air in physical composition and optimistic hopefulness in psychological
disposition. Six square faces together making a cube, evoked the elemental
physical component, Earth, and its human expression as a phlegmatic, apathetic
personal style. Twenty faces, all equilateral triangles, constitute an icosahedron
indicating Water and a dominant feeling state of melancholic sadness. Like
onomatopoeic words and pictorial script, the three dimensional geometry of these
Platonic solids feel like what they came to symbolize.
The personality styles symbolized and evoked by the Platonic solids continue
to be used to this day. For example, they compose the basic elements of the
constitutional categories of remedy in homeopathic medicine as introduced over
200 years ago by Dr. Samuel Hahnemann in his classical Organon of the Medical
Art. The assignment of clinical remedy in homeopathic treatment combines
consideration of the presenting physical symptoms and signs, the what, with
intuitive discernment of the patient’s constitutional type, the who. To the
homeopathic physician, tetrahedral fire is suggested by the traits of personal
magnetism, courage and inspiration as well as egotism, strong desire and rage.
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Octahedral Air people intellectualize objectively in confident and insensitive
aloofness. Those symbolized by cubic Earth are realistic and practical, a what-yousee-is-what-there-is
belief along with rigid, materialistic ways. Icosahedral Water
types experience emotions strongly and are sensitive, intuitive, nurturing and can be
overly sensitive and dependent.
What intuitions and observations relevant to self, subjective and objective,
emanate from the stylistic properties of feelings as derived from a time series of
observations of their associated actions suggested by their statistical measures, H T ,
H M , AC and srs? The yield is rich and unexpected. We find an enjoining of values of
these measures, characteristic and invariant for each person, with the brain and
behavioral actions of entheogenic agents and Zen meditation in contrast with
worldlier focused attitude adjusting experiences and drugs. The range of their
potential values helps rationalize a person’s inclinations along the continuum of
attachment and detachment. This quantifiable dimension augers positively and
negatively with respect to the requirements for mystical experience as poetically
described by the ambivalent warrior prince, Ardjuna, in conversations with Lord
Krishna in the Bhagavad-Gita, the most famous and influential component of the
Mahabharata of Hindu scripture, A similar theme relevant to the occupancy of a
propitious range of values for the measures, H T , H M , AC and srs, is found in what is
often called the Second Nobel Truth as explained by the Buddha, Siddhartha
Gautama, in lectures recorded in a deer park near Benares. We begin with the
results of some drug experiments conducted by behavioral neurophysiologists and
end with suggestions about the intuitive relevance of the conceptual content of
these measures to the universals of mystical experience and perhaps to elements
of spiritual transformation.
As described previously, the brain and behavioral process of habituation is
characterized by a decrease in the strength of an observable response to the
repetition of an evocative stimulus. Imagine the decrease in our startle responding
when a once unexpected loud noise continues to occur. Sir Charles Sherrington,
the early Twentieth Century British pioneer in neurophysiology showed that animals
and humans gradually stopped the withdrawal of their limbs with stimulation of its
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skin when it was repeated several times. Columbia University’s Nobelist in the brain
sciences, Eric Kandel studied the neural mechanisms of habituation as a primitive,
accessible and fundamental example of learning, the association of a nonresponse
to a usually evocative stimulus, in Aplysia californica. The sea snails learned not to
respond to a local irritation with a gill-withdrawal response when exposed to it many
times. They learned to stop paying attention to the perturbation. The background
noise appears to disappear after a little time in the Mall. Though his exploration of
its synaptic mechanisms involved the neural circuit of the gill-withdrawal reflex in the
marine snail, its generality and human relevance is well established. Hundreds of
papers can be found reporting the results of studies of habituation in normal
humans under all kinds of circumstances as well as in psychopathological
conditions. That it samples something both fundamental and persistent is suggested
by studies in children by one of Kandel’s students, Michael Lewis. He found that the
rate of habituation of a startle response to a bright light in one-year-old human
infants predicted success in many kinds of learning and other cognitive functions
when the children were tested again at the age of four. Pavlov’s experiments
studied habituation of the classically conditioned salivary response to meat powdercoupled
bell sounds in dogs in which the bell was followed by nothing, not only led
to inhibition of the salivary response with unreinforced trial repetition but
generalization of the inhibitory state such that dogs were observed to freeze in
motionless catatonic states for hours. In the language of our statistical measures,
the fixation of the dog’s behavior would manifest minimal entropy in the form of H T =
H M = 0 and the lowest complexity values for AC and srs. Entheogenic agents like
LSD or mescaline inhibit the process of habituation and fixation, maximizing the
entropy of behavioral measures, H T , H M → 1 and high complexity values for AC and
srs.
Mark Geyer and David Braff, Professors at the University of California in La
Jolla and Michael Davis, a Professor at Yale’s School of Medicine, found that
entheogenic agents, such as mescaline and LSD, as well as naturally occurring
indoleamines, such as DMT, which occurs naturally in human brain, prevented
habituation of startle responding in mammals. Each sound repetition was treated as
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though it were new. The baby is Buddha is an Eastern philosophical aphorism that
captures the fresh spiritual state of each moment’s openness and readiness, the inbetween
entropies for new information surprise. Geyer and Martin Paulus found that
entheogenic agents such as Ecstasy also increased the complexity of the patterns
of spontaneous motor movement made by rats exploring a bounded space. Recall
that they partitioned the floor to document the exploratory motion in the context of a
sequence of location transitions, readying the data for the computation of some of
the measures previously described. Following the administration of entheogenic
agents, the partitioning of the space that the animals were exploring, into a lattice of
discrete boxes and the encoding of each square with a symbol, the computable
entropic and complexity measures such as H T , H M , AC and srs were increased. In
contrast, the administration of amphetamine-like stimulants led to a different kind of
behavioral activation than that induced by entheogenic agents. The measures of H T ,
H M , AC and srs reflected decreases in entropy and complexity. As University of
California’s David Segal and others documented in the 1960’s, high doses of
amphetamine led to animals into in a minimal entropic state, they were frozen in
stereotyped rocking, nodding and circling motions. High dose amphetamine-treated
humans develop rigid fixation of ideas, low H T , H M , AC and srs, in man this is seen
as inescapable obsession and paranoid delusion. There is considerable medical
evidence that Hitler took large doses of amphetamine (Benzedrine) daily for the last
20 years of his life.
The entheogenic drug-induced phenomena of naïve openness and absence
of fixation, states of high entropy and complexity, behavior generating higher than
control measures tending toward maximal values of H T , H M , AC and srs , are
subjectively reflected in the results of personal experiments of University of
Chicago’s Heinrich Kluver as described in his Mescal and Mechanisms of
Hallucinations (1966). Observing himself after the self administration of a crude
preparation of peyote cactus, he said that it led to glad feelings of unfamiliarity and
a marked reduction in his tendency for boredom (habituation), a detachment from
old ways of thinking and a new openness to a rush of seen again for the first time
experiences. Everything in his personal world, no matter how mundane, became a
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source of new interest and fascination. New thoughts replaced old ideas in a
continuing process of new formulation. All of these things feel like they emerge
spontaneously, making ideas about being born again and personal renewal
concrete. We remember that Timothy Leary and his wife in their privately circulated
pamphlet, Neurologic, described their entheogenic drug-induced escape from the
habitual order as supported by the learned and established “…mental-manipulative
and socio-sexual brain circuits…,” an escape to a fresh new planet of possibilities.
Louis Lewin, the early Twentieth Century German pioneering ethnopharmacologist
described his subjective responses to peyote as a flood of lively, numerous, random
fantastic creations of perception and thought, all demanding his fresh attention.
To complement these subjective reports, experimental tasks involving
habituation, such as the disappearance of a brain wave sign of arousal to sound or
light stimulation, called alpha blocking, the eyes-closed resting pattern of 8-14
cycles per second, hz, waves perturbed into the arousal pattern of >20 hz, did not
habituate when the subjects were pretreated with entheogenic drugs. This finding
was also true for the results of years of meditative practice. In his 1974
Psychophysiology of Zen, Hirai reported that Soto Zen monks, after many years of
practice in mindful, one pointed, be here now meditation, unlike normal controls,
continued to show alpha blocking surprise, brain wave arousal patterns, throughout
the course of repeated stimulation with auditory clicks.
James Austin in his monumental book, Zen and the Brain (2000) summarizes
other studies of habituation in TM practitioners and other mediators in which eyes
open versus eyes closed, the set and setting and variations in other experimental
variables blurred these results to some degree. He develops the case that years of
meditation-induced brain states of emptiness, we would say of maximal entropy and
minimal form, set the stage for the ecstatically insightful flood accompanying the
sudden insight into a Zen koan’s solution or the transcendent startle induced by a
roshi’s shout. A meditative struggle concerns how one can think about not thinking.
That is, thinking of nothing. This is generally thought to be the most important part
of Zen meditation, called zazen. Achieving high values for brain and behavioral H T ,
H M , AC and srs supply the formless infrastructure for ecstatic transformation.
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In healthy people, an awareness of self is not lost during this time of invasion
by and fusion with what feels like an independent agency. At full force, the mystical
experience is transfixing, tending to paralyze movement and speech, and at the
same time bringing with it the capacity for clear sensory and sensory-integrative
lucidity. This new seeing brings previously unnoticed things to attention and makes
old things new. Perhaps most striking is the passive (unsought) experience of the
unification of erstwhile disparate, apparently unrelated thoughts and feelings. The
yield can be the sudden emergence of deep relationships between apparently very
different constructs, beliefs and formalisms leading to unanticipated and unsought
integrative connections. In mathematics, this experience can lead to entirely new
kinds of theorems and proofs; in the physical and biological sciences, a previously
unseen organization of the data generating new global relationships and potential
scientific laws. In our spiritual life, the ineffable richness of the direct experience of
God.
Mysticism-negative interpretations of these experiences have always been
attendant. To the extent that the mystic’s inward turn is seen as a detachment and
implicit derogation of the external, consensually real world, it is often seen as
alienating from established institutions of religion and government. Psychoanalytic
practitioners may label it a regression to primary narcissism. Most churches tend to
discourage its practice as counter to the dominant social hierarchy and its
governance. Governments pass laws against its practice and manifestations, a
current example being modern Chinese governmental reactions to the Tibetan
Buddhism of the Dalai Lama and the yogic practices of the Falon Gong. Agencies of
established society such as the institutions of licensed medical practice make the
dominance of the inner world of mysticism subject to diagnoses ranging from the
narcissistic character disorders to interpretations of the reported extraordinary
experiences as manifestations of schizophrenia, manic-depressive disorder or
temporal lobe epilepsy. Rejection and fear of the transcendent states lead to
uninformed and politicized anti-narcotic laws, grouping heroine and cocaine with the
entheogenic (recall: engendering connection with the sacred within) agents such as
the Huichol Indian’s peyote and the Amazonian Indian’s yage, obstruct and socially
118
taint the personal use of plants and practices that facilitate access to the mystic
way. Rational, socially responsible and otherwise kind and tolerant Presbyterians,
Unitarians and Reformed Jews can be suspicious and rejecting of what appears to
them as the politically tinged mass hysteria of praying in tongues and other rituals of
Charismatic Christian rebirth and renewal or the ecstatic states of Orthodox Jewish
chant-dancing.
Modern brain and behavioral scientists, remaining under the philosophical
spell of logical positivism and its requirement for operational definitions and
(external) experimental disconfirmability, operate from the position of strong doubt
when mystical experience is addressed. What is striking and strange about how
science plays the game of mysticism research is exemplified by the publishable
increment in credibility concerning a meditation-induced change in state of
consciousness when Boston University’s William Benson reported the
accompanying relaxation response, a sudden decrease in heart rate---much like the
dive reflex of a seal or what the heart rate does when you duck your head suddenly
forward into a sink full of water. Decades are spent getting professorial tenure for
research yielding things we have already experienced and know directly and for
ourselves. Recall that the existence of visual imagery in the human, doubted by an
experimental psychology of the time in which William James self-exploratory
observations were viewed as revolutionary, was made more credible by evidence
for the existence of a subjective spatial metric: verbally reporting subjects, when
timed, took longer in their minds to go from one room to another one that was down
the hall then going to the room that was immediately next door.
We use brain chemical, pharmacological, neurophysiological and
neuroanatomical localization and computation of characteristic statistical patterns in
time dependent brain and behavioral observations to the same end.
Further Readings for SOME ENTHEOGENIC ENTROPIES
119
Phantastica: A Classic Survey on the Use and Abuse of Mind-Altering Plants. Louis
Lewin, Park Street Press, Rochester, Vermont, 1998 (First published in 1924)
Indole(ethyl)amine N-methyltransferase in the human brain. M. Morgan (Poth) and
A. J. Mandell, Science 165:492-493, 1969
Enzymatic formation of tetrahydro-beta-barboline from tryptamine and 5-
methltetrahydrofolic acid in rat brain fractions. L.L Hus and A.J. Mandell, J.
Neurochemistry 24:631-636
The Sacred and Profane, The Nature of Relgion. Mircea Eliade, Harvest Books,
Harcourt, San Diego, 1957
Hashish and Mental Illness. J. J. Moreau, Raven Press, N.Y. 1973 (First published
in 1848)
The Neurochemistry of Religious Insight and Ecstacy, A.J. Mandell in Art of the
Huichol Indians, Fine Arts Museum of San Francisco, Abrams, N.Y. 1978
Altered States of Consciousness: A Book of Readings. Charles T. Tart, John Wiley,
N.Y. 1969
Soul; God, Self and the New Cosmology. A. Tilby, Doubleday, N.Y. 1992
Pihkal: A Chemical Love Story. Alexander Shulgin and Ann Shulgin, Transform
Press, Berkeley, CA 1991
Psychochemial Research Strategies in Man, A. J. Mandell and M.P. Mandell,
Academic Press, N.Y. 1969
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The Biology of Transcendence, J. C. Pierce, Park Street Press, Rochester,
Vermont, 2002
Psychiatry and Mysticism, S.R. Dean, Nelson-Hall, Chicago, 1975
Zen and the Brain, James H. Austin, MIT Press, Boston, 2000
Perspectives in Biological Dynamics and Theoretical Medicine. Eds. S.H. Koslow,
A.J. Mandell and M.F. Shlesinger, Ann. N. Y. Acad of Sci. Volume 504, 1987
Consciousness and the binding problem, W. Singer, Ann. N.Y. Acad. Sci. 929:123-
146.
Mixing properties in Human Behavioral Style, Karen A. Selz, U.M.I., Ann Arbor, MI.
1992
Dynamical Systems and Ergodic Theory, M. Pollicott and M. Yuri, London
Mathematical Society, 1998.
Introduction to the Modern Theory of Dynamical Systems, A. Katok and B.
Hasselblatt, Cambridge University Press, Cambridge, 1995
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CHAPTER 6:
PENTECOSTAL PHASE TRANSITIONS
By their late teens, my two offspring, sons of an Alcohol Anonymous, born
again, originally Christian Science mother and a spiritually struggling and mostly
secular Jewish psychiatrist father, had been unfulfilled in their hungry search for the
experience of a personally meaningful God. After years of perhaps too academic
conversations with their parents, visits to a variety of houses of worship, talks with
University of California religion professors and evenings with a Ph.D. psychologistrabbi
and friends at the neighborhood synagogue, they turned somewhere else.
Some of their high school friends who were Evangelical Christians took them to
their Assembly of God, Pentecostal and other Christian, direct experience of God,
churches. They came to love what they sometimes called their Wednesday night
and Sunday morning “rock and roll,” services.
Struggling with the post-Vietnam cynical mistrust of authority and the
marijuana apathetic nihilism of the 60’s and 70’s, and clearly not enticed by what
they regarded as their father’s vacuous mélange of New Age Eastern Religions and
secular brain science, they spoke about their sudden and life-changing experiences.
They studied, memorized and quoted the Scriptures as part of their commitment to
their word churches. As erstwhile cynical teenagers, now positive and brimming with
faith, I secretly called it denial, they described what was happening to them as New
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Birth. They told me that, paraphrasing Paul in Romans, they had been saved and
were living New Life, not earned by good works as in Hebraic Law, but by faith
through God’s Grace. Jesus had “paid their bills” through His sacrifice at
Gethsemane. They both tried to explain inexplicable feelings of new energy, the
unseen hand of spiritual guidance and peace. One told me that the wind of the Holy
Ghost had taken him to the front of the pulpit, tearfully, thankfully, on his knees, to
accept Jesus as his personal Savior. They described how they had opened their
lives to the spiritual strength of living in Jesus.
Many things about them changed: their tastes in food, from hamburgers to
vegetables and fruit; from the jazz of John Coltrane and McCoy Tyner and the
cynicism of Frank Zappa’s “…only fourteen and knows how to nasty…,” to playing
strum guitar and singing the hymns of Wednesday night healing services; from t-
shirts hanging out of raggedy, Southern California, boutique store purchased,
stressed jeans, to polished dark shoes, starched white shirts and gray or tan khaki
slacks, sometimes with ties. They became cool, respectful, rational and more
distant with me. They repeated often the scriptural story about young Jesus,
accidentally separated from his parents on a visit to Jerusalem. When by standers
asked Him about where His parents were, He answered, “I have no mother and
father.” They told me that they, like God’s son Jesus, were filled to completeness
with the Father and the Holy Ghost.
On one hand, their experiences sounded like those of the activated mind
state of Abraham Abulafia, a suddenly emergent Nevesh and my father’s
metaphysical talks about personal transformation. My personal secularcomputational
brain God spoke to me of the mechanisms of sudden personality
change, a phase transition in complex systems, in the context of the nonlinear
dynamics of brain and behavior. On the other hand, their global changes in mind felt
both alien and threatening. When I came to learn their churches’ full list of
expectations, rules, requirements and sociopolitical policies, I found that I could not
identify with this system of spiritual knowing at all. It felt rigid, righteous, unforgiving,
even angry, and it frightened me. I never anticipated that my culturally enriched,
intellectually sophisticated sons would be quoting Pat Robertson and Jerry Falwell.
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The Freudian psychoanalyst of my younger days tried to write off these (to me)
cataclysmic changes as manifestations of male sons’ unconscious oedipal strivings
to father kill and thus become. After some mulling, my theory did not wash.
They spent time accompanying themselves on guitars, singing hymns and
shouted Corinthian Paulisms to small curious crowds gathered in beach parking
lots, city parks and inner city street corners of Southern California. They passed out
pamphlets containing New Testament tracts and formulaic aphorisms promising the
post-repentance blessings of Jesus. The eldest, articulate, bright and prematurely
worldly, had been an ardent memorizer and appreciator of Shakespeare, especially
the mystical Tempest, the music of Aaron Copeland and Igor Stravinsky, the
improvisations of Charlie Parker and Cannon Ball Adderley and the provocative
literature of the time including Jack Kerouc’s On the Road and Hunter Thompson’s
Fear and Loathing in Las Vegas. They loved riffing with the Voltairean pungency of
Frank Zappa’s lyrics. Now, nihilistic humor had become an anathema.
Several weeks after my eldest son’s transformation, I found him in the
garage using a hammer and an empty barrel for disposal as he destroyed his
modern jazz and early rock record collection. He ridded himself of all of his fiction
and most of the nonfiction books in his young but relatively large personal library.
His new energy and high purpose emerged as a clearly defined set of rules of
behavior, a strong stand against abortion, frequent talk about the need to escape
from the contaminating influence of MTV culture, as well as our years of talk about
the biological and physical sciences. Both boys were particularly critical of my
Darwinian flavored attempts at scientific explanation of man’s inner life using the
selective and adaptive neurobiology of brain mechanisms and behavior. They spent
increasing amounts of time with Church friends, seldom seeing their old ones. The
eldest’s college goals turned from plans for a U.C. Berkeley equipped career in
literature and creative writing to a none spiritually challenging, objective and
practical, Christian free market finance and accounting degree from U.C.’s Business
School.
Gone were shared magical hours of intellectually stimulating, humorous,
even scholarly discussions. In place of evidential talk in areas of philosophy,
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literature and science, their opinions and claims derived exclusively from biblical
quotation. Their particularly favorites were Paul’s letters and some of the later
prophets, particularly Jesus-auguring Isaiah. “In the beginning was the word…”
became the real reality. The meaning of life was Scripture as explicated by their
book church pastors. They scribbled notes in the margins of their Bible pages
during sermons They were displeased when I interpreted the wild imagery and 666
symbolism of Revelations from the point of view of the historicity of encoded political
messages, meanings hidden for the safety of the early Jews in their world of Greco-
Roman governance. Twenty-five years, before the glut of books by Tim LaHaye, my
well-educated sons claimed that Revelations was literal and foretold the coming
tribulation that augured the end of the world and ascension to heaven of the
believers. My youngest, since childhood a well-read history buff, now viewed New
Testament scripture as sui generisly, divinely and literally true. They said the
conduct of their lives their meaning had been clarified by the biblical truths revealed
to them by The Book. What I did not say was that much of the talk seemed to me to
be an intellectually and spiritually impoverished miasma of cant and righteousness.
At the same time, their remarkable transformation appeared to be the expression of
a powerful and mystical force, the scientific understanding of which has been the
ostensible focus my life’s work. Why did their alterations appear so alien, strange
and forbidding?
Born to a home of psychoanalytically and scientifically oriented political
liberals, these precociously bright and worldly sophisticated young men were
suddenly transformed into, unrecognizable to me, radical Christian
Fundamentalists. They are now in their late thirties and remain just as ardent,
Christian patriotic, Right Wing voters to this day. The eldest is now an executive in
Morris Cerullo’s San Diego based, worldwide missionary movement, raising money
for revival and media ministries. He travels to and is involved with hundreds of
Fundamentalist Christian churches in countries ranging from Argentina and Africa to
the Middle East and Russia. He hasn’t allow me to contact his children, my
grandson and granddaughter, because, in vague talk and mostly silent implication, I
and people like me are seen as sources of potentially satanic, worldly
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contamination. He feels wronged by the way I am. He once chided me about what
he saw as my futile spiritual search in what he called the “health food” Eastern and
brain religions. My youngest, only a little less ardent and critical, visits occasionally,
and, hands in the air and speaking in tongues, prays to the Lord for my salvation.
Of course, this sudden and long lasting personal transformation in the
direction of Fundamentalism is well known and almost commonplace in modern
American and European Jewish, Christian and Moslem college educated middle
class families. The Saudi Arabian World Trade Center bombers were, mostly, well
supported children of the educated middle class We recall the famously tragic
American radical Moslem, Richard Reid, the would be airplane shoe bomber. My
stomach clenched as I heard Richard’s sophisticated and obviously caring father
share his confusion and struggle to rationalize what had happened to his son. The
commonality of this kind of spiritual and life transformations in the educated young
makes each event no less painful. On the other hand, we know that healing
transformations in the name and spirit of the Christian God can lead to quite positive
realities. They are effective in even quasi-secular disguise as in Alcoholics and
Narcotics Anonymous, Synanon and in the rehabilitation of the Charismatic
Christian, ex-alcoholic, Southern Methodist politician, George W. Bush.
Paul Holmer, Professor of Theology at Yale Divinity School gives thanks to
the evangelicals who “…keep alive the radical breach that the gospel is from the
nous of this world…they (Fundamentalists, Evangelicals) look marginal if you are
churchy…intolerant if you are ecumenical…anti-intellectual if you are trying to
systematize… in their roughness and …abrasiveness.” I bring personal and painful
witness to these claims. To get to the personal meaning and mechanisms of these
transformations, I had to start from somewhere. I am wedded to the belief of the
Jewish ecstatic, Abraham Abulafia, and not those of Moses Maimonides, that the
human mind in an altered state of activated intellect, man’s Nevesh, can understand
such mystical happenings. I would continue to work at it.
One of the early personal church experiences with my sons’ religious path
came after accepting an invitation to go with them to a Sunday service at their
current charismatic church. By then, the eldest was married with children, the
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youngest, unmarried, was teaching bilingual mathematics in high school. I had
waited several years for this occasion.. The meeting took place in a large, gray,
unmarked warehouse building that was crowded in back with high stacks of storage
cartons. The large, cement floored, open space in front of the storage boxes was
occupied by rows of metal folding chairs. They faced an unadorned, elevated
wooden platform upon which was a lectern and microphone. Behind the lectern
stood a casual array of a dozen or so young people, singing hymns and playing a
variety of instruments. These included piano, two or three guitars and upright bass,
tenor saxophone, trombone, trumpet, mouth organ and two snare drums. Sounding
a bit like a Salivation Army Band, they played and sang, “They cast their nets in
Galilee just off the hills of brown; such happy simple fisher folk, before the Lord
came down…the peace of God, it is no peace, but strife closed in the sod. Yet let us
pray for but one thing, the marvelous peace of God.”
The building, used for commercial storage, packaging and mass mailings
during the week and a Charismatic Christian word church on Sunday, was located
at the rear of an unfinished strip mall. A new and well-polished yellow Cadillac
Deville was the only vehicle parked in the no parking zone immediately in front of
the entrance to the warehouse. My youngest explained that the car belonged to Carl
Austin, the self-discovered and declared pastor, who spontaneously rose up to lead
without academic religious training or a conventional ordination. The bright yellow
car was explained as evidence of the power of God. Paraphrasing Mark, my son
told me “…he who does not doubt in his heart and believes that those things he
says will come to pass, he will have whatever he says…whatever things you ask for
when you pray, believe that you receive them, and you will have them.” The car
served as a glorious instantiation of the church’s major promise of the rewards of
faith.
Pastor Carl Austin, a tall, blonde, portly man in his early thirties with a
resonant tenor voice, was the youngest of several children of a poor Midwest farm
family. He had been a state college drop out and without a career or a job. His
sermons contained stories about how he had caught spiritual fire at a revival
meeting conducted by Kenneth Hagin of Kenneth Hagin Ministries, aka Rhema
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Bible Church, Tulsa, Oklahoma. The pastor’s witness of the Holy Ghost acting
through his life was his personal cure, by transformative Grace, of a triad of selfdestructively
sinful addictions: alcohol, gambling and promiscuity. Self-chosen and
self-declared, he now served this two and a half year old growing congregation of
over 200, mostly young, working families. The young men in attendance at the
warehouse church were in shirts and ties, very unlike the more casual garments of
even dressy occasions in Southern California at that time. Women were dressed
simply and modestly. Most of the children were in Sunday school in a small
neighboring store in the strip mall during the adult service. The few that
accompanied their parents were remarkably well behaved I was told that most
families tithed 10% of their income. They quoted Hebrews, “…king of the
righteous…to whom also Abraham gave a tenth part of all….” They believed that
their tithe would be returned manifold and the yellow Cadillac Deville served as
Pastor Carl Austin’s personal evidence. From these funds, the congregation
supported the pastor, his car, the rental expenses of the Sunday warehouse church
and an orphanage in a small Mexican border town. Some of these children, several
neurologically disabled, were bussed to the Sunday service for healing. They sat
together in a section in the front of the congregation and were the beneficiaries of
the second Sunday collection plate, passed around after the first one that was
designated for the church and its pastor.
The first Sunday sermon I heard in the warehouse followed several awkward
minutes of Pastor-directed warm up hugs of neighboring strangers while the choir
sang hymns. The songs were accompanied by instruments playing the melody in
unison sans harmony, and accented by the beats of two loud drums. As the volume
and pace of singing increased, I saw several episodes of ecstatic looks and fainting,
dying in the Lord and shouts of praise with upraised hands. The intermittent
elevation of the hands during prayer and song appeared to be spontaneous. I was
told that the arms were up as antennae, feeling the energy of Lord all around us.
The pastor’s topic was forgiveness. From Ephesians, “…let all bitterness, wrath,
anger, clamor, and evil speaking be put away from you, along with all malice… be
kind to one another, tender hearted, forgiving one another, just as God in Christ
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also forgave you.” In the middle of his sermon, which built slowly in tension and
volume, the pastor introduced a forty-ish, sparkly eyed, somewhat overweight, dark
haired, slightly made up woman who the Pastor said was a witness for the ultimate
in Christian forgiveness. She was someone from whom all of us could learn. She
was the mother of the 7-year-old boy that he, the Pastor, had, four years before,
accidentally killed during a drunken driving episode in his “other life.” That was the
one he was living before he was saved. I was told that he presented her in a service
at least once a year. The woman said that her successful struggle for forgiveness
led to her being saved. She quoted Ephesians, ”And you who were dead in
trespasses and sins hath he quickened.” She looked radiant and hugged the pastor.
When my sons introduced me to him as we filed out at the end of the service, the
pastor told me that my visit was important to the congregation. He told me that Jews
were special in Charismatic Christianity since we would play an important role in the
return. He said he hoped he would see more of me. My boys seemed pleased to
have invited me.
I accompanied them to their church most Sundays, and often for what they
called the “rock and role healing services” on Wednesday night, for over two years.
Within three or four months I found myself, the first time while awakening out of a
deep sleep, mumbling sounds that I was told sounded like some unknown
language, I was praying in tongues. At some services it happened spontaneously
accompanied by an almost ecstatic feeling accompanying the surrender of willful
control. This was usually accompanied by the release of new energy. I recall
thinking that the spontaneous, nonsensical linguistics shorted out my verbal and
obsessionally logical left brain allowing the unbridled expression of my hysterical
right brain. Sometimes in agreement with an insight offered in a sermon or when
particularly moved by a hymn, I found my hands lifting skyward, right hand and arm
higher than left, with a high feeling of trust and delicious surrender of conscious
cognitive control.
Reading the New Testament’s Acts, I learned that we were re-enacting the
scene of the Apostles in the upper room. Those gathered there were the ones
chosen by the risen Jesus to be able to see Him, the list including Peter, James,
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John, Andrew, Philip, Thomas, Bartholomew, Matthew, James, Simon and Judas.
“…they were all filled with the Holy Spirit and began to speak with other tongues, as
the Spirit gave them utterance…” The secular psychoanalyst in me tried to make an
analogy with the joyful jazz lyrics of Ella Fitzgerald’s scat singing, I’d done a little of
that during my small jazz group pianistics as an a adolescent. I thought about how
verbally paralyzed stutterers could be articulate when singing what they mean when
they could not talk it. I wondered about the relevance of the spontaneous poetry of
slams and Hip Hop rapping. We attended what my sons called charismatic black
Baptist churches in South Los Angeles and Long Beach. These often four hour
services usually featured two wonderfully harmonic echoing choirs with organ and
drum punctuation of the speech-singing, sermonizing Reverend. Large and
beautifully dressed black women sang operatically and danced gracefully down the
aisles. I joined my sons in this joyful noise for these long services and, exhausted, I
was forced to go home for a Sunday afternoon nap.
In spite of what could be regarded as validating experiences with the real life
Holy Spirit, I continued to be generally confused and even more deeply estranged.
An inner voice kept recalling my spiritual failure as a parent and being traitorous to
my Jewish ethnic identity by Christian church attendance. I tried to understand how
my sons had traveled from where I thought we were living together to this entirely
new world. How did it happen? Could the path going there and back be
meaningfully reconstructed and then reversed? This idea is consistent with the
medical dictum that knowing the cause, the treatment logical follows. My education
had shown me such assumptions of reversibility need not be true.
Contrary to the beliefs of early physical mechanics, medical psychiatric
history takers and psychoanalysts reconstructing childhood events, the modern
physics and mathematics of complex systems says phase transitions in complex
systems are probably not reversible, at least not simply so. One of the features of
global changes in complex systems, often called bifurcations or phase transitions
(think heated water going suddenly to a boil), is their dramatic discontinuities in
behavior. Knowing only the initial and end state, phase transitions in complex
systems do not allow for point-to-point backtracking or specific linear-causal
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understanding. These discontinuous and global transformations are the stuff of
miracles, especially for physicists. Even with respect to initial and end-states, rather
than using straight forward phenomenological observation, the mathematical and
physical theories of phase transitions are usually dependent on not necessarily
intuitive, derivative physical quantities. Their verbal representations are often not
concrete but metaphoric. This retreat to derived and abstract, far from the primary
data computables, may be more evidence of man’s many insufficiencies in
understanding of the mysteries that are often placed in the spiritual realm.
* * *
Driven by an effect that contributes to cause, like the faith-driven
abandonment to God that generates more faith, a drop of water hanging from a
faucet is pulled down by its own gravitational field as the thinning neck of the drop
facilitates its own further thinning. A gobbet connected by a thick neck to the main
drop begins to separate. The neck between them thins and breaks, and one
becomes suddenly and irreversibly two. A continuous structure has suddenly
become discontinuous in finite time at what is called a singularity. Since the single
measurable feature that dominates the water’s behavior around this singularity is
the diameter of the thinning neck, a derivative physical, one-dimensional
observable, neither the details about where it all began (called the initial conditions)
nor the path it followed to get to the moment of fracture, are predictively relevant
with respect to the sudden transition. Considering this kind of phenomenon going on
in our brains, choosing between theories of behavior that involve changes in brain
cell groups and/or brain chemicals versus those that involve behavioral quantities,
may be neither possible nor necessary. The challenge is to place the problems of
cataclysmic change in brain and behavior in sufficiently abstract and universal terms
that can be represented in some low dimensional, computationally accessible space
of variables.
The simplification and stereotypy of behavior around singularities reduce the
number of features that are required to discuss the dynamics of change in what
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would otherwise be a complicated beyond reach situation. One of the properties
found around singularities, is the loss of absoluteness in contextual characteristics
such as the scale of the observation. We no longer can say that what we are
studying happens in inches or miles, in seconds or days, now or in the past. In the
place of a single unit of relevant measurement, we have a distribution of spatial and
temporal feature sizes that stretch toward both the infinitely small and the infinitely
large.
We can illustrate a dynamical transition involving the passage of the system
through a singularity by using the metaphor of another kind of water experiment. If
we pour a small amount of water through a filter full of coffee grounds, or watch our
coffee maker do it, the first spurt of water makes an incomplete path of wet grounds
in the bed of dry ones. The next bit of water soaks this path more thoroughly and
may form additional and multiple, new and branching, incompletely penetrating
paths. Eventually, on just one more of these pourings, a connection in the paths
occur, such that the water snakes all the way through the coffee grounds and the
first brown drop of coffee falls into the pot. At this flow singularity and opposite to
the dynamic of a faucet water drop, a discontinuous system of pathways becomes
continuous in finite time in a process called percolation,
Trying to set up a predictive model, we can count the number of water
deliveries that occur before the first drop finds its way through. Repeating the
experiment many times yields a span of the number of pours required to reach the
singular point of percolation. If we do the experiment enough times, the distribution
of the number of pours required to reach percolation will range from one toward
infinite. In the neighborhood of the transition, time as recorded as the number of
small pouring events may stretch.
In aa comparable system, as elegantly described by Detrich Stauffer in his
Springer-Verlag book on percolation, multiple hot spots in the woods can suddenly
fuse into a forest fire. Isaiah said, “…glorify the Lord in the growing fires of dawn…”
Faith fires spreading through a faithless dense forest, its hot irregular front damped
by the disbelief of water-filled leaves, or disillusionment gaps of already burned out
trees, can, under the right motivating conditions of dryness, wind velocity, tree
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density, kindling temperature and desperation-induced willing of faith, sweep
through the entire woods in a sudden blaze. This is the spirit of percolation.
Computer simulations of percolating blazes generate a multiplicity of life times of
forest fires near the singularity that represents the transition to a global
conflagration.
Mentioned previously is Rudolf Otto’s 1917 book about the characteristics of
religious experience, Das Heilige, The Sacred, which described phases in the
discontinuous transition from everyday life to the wholly other (ganz andere) reality
of the world of the sacred. They include intense, numinous experiences of fearsome
ambiguity, dawning awareness of awesome mystery, revelation and appreciation of
the majestic power and finally, entrance into a reality of an entirely other place and
time than the natural and secular which Mircea Eliade called profane. In his 1958
book, Patterns in Comparative Religions, this well-known historian of religion called
the revelatory occurrence of sacred reality an hierophany. Eliade’s classic work,
The Sacred and the Profane, contrasts the homogenous, spiritually formless and
relative world of the profane with the results of passage through spatial and
temporal singularities to a place and time that are not of this world.
Poincaré said that the brain did not know of absolute space, but rather
established a model of it through internal reconstructions of sequential sensory
experiences that accompanied our exploratory movements. Activity generates the
internalized, partial differential, equations (describing changes in the observable
with motions in space) required for representing the dynamical cartography of the
world. It was Poincaré’s habit to topologize the dynamics of motion in mathematical
problems that lacked analytic solutions. In this way, simple algebraic operations
replace some of the insoluble problems of the calculus. Eliade’s sacred space
defining singularity in the plane that breaks profane homogeneousness, a center
point that is no longer a circle, can be viewed also as Poincaré’s topological center.
His topological brain theory found expression in the formal representation of internal
space as the invariant product of an organism’s displacement groups of imagined or
real physical movements around such singular fixed points. The operational object
called groups defines this kind of algebraic, mathematical structure and motion.
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associated with the loss of habitual temporal-spatial contextual moorings. A mind at
time one and the same mind at time two are unconnected. They are wholly other.
In much the same sense, for Eliade, sacred time, like space, is neither
homogenous nor linearly continuous. Sacred time is circular, recoverable and
reversible. Past, primordial, mythical time can exist in the present. Religious
festivals are recurrently ontological, allowing the recovery of the sacred time such
that their past and present expressions are the same. Rebirth is new birth. In the
language of the North American Indian Tribe, the Yokuts, the term for world
(cosmos) and year are the same. A year and the world has gone by, only to start
again. The Dakota Tribe says that the Year goes around the World. As Elaide has
said, “…at each New Year…the world (is) recreated and to do this is also to create
time…the sick man becomes well because he begins life again with its sum of the
energy intact.” Healing by becoming another or renewed self may become a frontier
science in the yet unexplored field of phase transition medicine.
The quality of separateness, discontinuity in states, as occurs in the samedifferent
inside world, is much like that found in the stages of anesthesia. Each
stage of anesthesia is ganz andere from the others. In Stage I anesthesia, fast
frequency, low voltage brain waves are observed and accompanied by a two
Martini-like, mildly activated, sedated but exhilarated high. Stage II, the next deeper
stage of anesthesia, is marked by the sudden emergence of intermittent bursts of
high amplitude brain waves, and animals and man demonstrate bizarre postures,
hallucinatory phenomena, fixed staring, and sometimes movements that look like
acting out some symbolic drama. This stage marks the beginnings of the loss of
responsiveness to painful stimuli. In the sudden drop into Stage III, a low voltage
mix of mostly slow and some fast brain waves can be seen associated with
depressed consciousness, complete insensitivity to pain, slow regular respiration
and an unexcitable cardiovascular system. Stage IV is the deepest stage of
anesthesia. This state is characterized by very low voltage, almost flat brain waves,
a loss of spontaneous breathing, the collapse of blood pressure and, finally, cardiac
irregularities and death in cardiac arrest. These are both discontinuous and global
brain state phase transitions.
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primary process by Freud and his followers. This forgotten language of the
unconscious, an archaic needs and fear-driven tongue lurking beneath our
supposedly objective discourse, comes to dominate themes of communication in
the middle of these unfinished spiritual transitions. The Rorschach Test of master
meditaters and LSD users overflow with conflictual primary process images, as
does the talk of patients on the verge of schizophrenic decompensation. The
primitive symbolism of primary process provides the major current in the overwritten
prose of the hyper-religious temporal lobe limbic epileptics described previously and
called the Geschwind Syndrome and in the regressed and iconic transference
concerns of patients with tendencies for global and sudden phase transitions,
prostitute to saint, righteous obsessional to conscienceless psychopath, called
borderline personality disorder.
Primary process represents a dynamical brain state, one unburdened by
linearly predictive connections with reality. It is a state without even a transient
single defining physical time or other fixed measure of order. It is without the causal
logic or knowledge of an outside reality that a brain implies in supposing to know. Its
primitively instinctual style and goals contrast with more physically time-locked,
reality oriented thinking which Freud called secondary process and Penn-Lewis
referred to as ordinary and religiously lawful “reasoning faculties.”
An absence of absolute time and space scales with which the executive ego
orders internal and external time and events, and therefore their relations, results in
primary process thinking characterized by condensations of several, often
incompatible, representations into one. Dueling, conflictual and simultaneous
feelings and thoughts float from their relevant objects to others. In the transitional
transcendent state, there may be confusion of self with others, of objects with their
labels, of parts with the whole and of symbols with the things that they symbolize.
This facilitates living in the spirits of the Father, the Son and the Holy Ghost at the
same time. Mixed inextricably with saintly awareness and charisma, there are
signatures of instinctually driven and configured primary process. Freud’s classical
work on slips of the tongue concerned the intrusion of these instinctual thought
stream condensations from the world of the ganz andere and displacements into
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everyday life. In this intense and quasi-fluid state, saintly priests slip seamlessly into
sexual predation; an ecstatic Jewish Orthodox fundamentalist shoots 29 praying
Moslems in a cave near Abraham’s burial plot for Sarah in Hebron; what were
lovingly mystical, Jelaluddin Rumi’s Afghanistan (Balkh) descendents become
people bashing and women stoning morality police; committed and mesmerizing
Christian televangelists attend peep shows and seek child pornography; devoted
Islamists crash airplanes into tall New York buildings.
In the physics of condensed matter, two common forms of multi-molecular or
polyatomic cooperative arrangements are the crystalline condition and in some
ways its opposite, the amorphous glassy state that results from rapid cooling