organizations, Gurumayi took over the guru lineage of Siddha Yoga. Her lively
brother’s worldly preoccupations with jazz drumming and confessions of promiscuity
led to his giving up of the orange robe of the denunciate, sanyasi, for the blue robe
of worldliness, exchanging one kind of energy for another.
Brad Gooch who visited Gurumayi’s Ashram in Ganeshpuri, India, wrote in
his recent book, Godtalk, that she looks like a “synthesis of Indira Gandhi and
Bianca Jagger.” In what reads like a Hunter Thompson episode in an unwritten book
called Fear and Loathing Along the Guru Trail, Godtalk’s explication of Siddha Yoga
was dominated by yellow journalistic rumors such as the one about Baba’s use of a
gynecologist’s table with stirrups for non-ejaculatory Tantric practice with some
female followers. This unconfirmed claim remains, as Gooch says, in the realm of
“…he said, she said.” Gooch’s exploration almost ignores the deeper meanings of
Kashmir Shavism, Buddhism and Kundalini Yoga that compose the philosophical
foundations of Siddha Yoga. The importance of knowing, loving and becoming one
with the God within trivializes all but ungenerous or hurtful interpersonal behavior.
Even the tougher version of the Ten Commandments in Leviticus 19 would not
necessarily disagree.
When a Los Angeles Times reporter tried to chide Baba about being driven
about in his “worldly” Mercedes sedan, he explained that a very wealthy Indian
merchant had given it to him and “…I have to put my behind somewhere.” Similarly,
why would Gooch’s account of Baba’s Tantric practice, even if true, ruin the imago
of him in my mind unless I had already surrendered to the pantheon of good and
evil absolutes of Judeo-Christian taboo? My knowledge of these non-materialistic
meanings of apparent materialism began with one of the favorite finds of Baba’s
youthful days of guru hunting: Zipruanna, who, wearing only a loincloth spent all
day, every day, on a stool in the middle of a garbage dump. Remarkable changes
occurred in people who spent time there in his presence. Baba said the identity of
guru was established by the results experienced by those that spent time in his
presence. It could not be defined by the physical features or ritual conduct of the
48
interaction. People become spiritually energized and change in Zipruanna’s smelly,
garbage-filled presence. I keep a picture of him on my desk.
Gooch, in his implicitly and superficially righteous preoccupation with what he
considered disenfranchising human vulnerability, recalls how the medieval church
used the difficult to impossible vow of chastity for political control of their priesthood.
He seemed to have missed Baba’s lessons about the remarkably simple sounding
practices for mobilizing the energy of the God-receptive state. Once in this new
state, the rest of the metaphysical work almost takes care of itself. I, like many
others, adopted Baba’s mantra, Om Namah Shivaya, “I worship the God within me
(and you)” that he was given by his guru. The inner chant of this mantra brings me
to an internal quiet in which things become clearer. Meditation, chanting and service
to the guru was motivated by his promise that my egoistic concerns ranging from
the number of publications on my curriculum vitae, to the size and adroitness of my
penis, would disappear autonomously in the Baba state of bliss. This sounds very
much like the role of the transition to an “active intellect.” in Abraham Abulafia’s 13 th
Century Commentary on the Secrets. Arduous study of the spiritually dense writings
of Sri Aurobindo during the days with Professor Spiegelberg at Stanford gave me a
peak into the simple but difficult to execute idea of “simply” becoming the
transcendently comprehending state of existence-consciousness-bliss.
Whereas Baba would occasionally lapse into terse Sanskrit verse and its
multiplicity of potential meanings, Gurumayi keeps things simple. Sitting silently and
immobile at satsang for hours, she radiates transformational energy, shakti, that
makes ruminations about human affairs seem unimportant. The work is about
getting the self concerned head noise of ones preoccupations sufficiently out of the
way to allow the discovery of the God who has been waiting patiently within. A
fellow ashramite gave me a photograph of my first audience with Gurymayi. It
showed me on my knees in front of her. She appears to be dismissing me with a
baleful, almost disdainful look as my introducer, gesturing broadly, was, unasked,
reciting a list of my professional bona fides. The picture caught her waving me off
with a long, peacock-feathered stick. Obviously unimpressed, she is sending me
back to my all night, every night, tent cleaning labors at the Ashram. Rich Indian
49
businessmen, whose large donations were a major source of support of the
Ashrams, faired little better. They seldom received a personal audience or favorable
seating at Darshan, the evening public time of question and answers with the guru.
In contrast with the relatively easy public availability, mischievous play, provocative
humor and worldly sophistication of Baba, the ambience of Gurumayi is more
private, simple, serious and subtle. It is as powerful, but in another way.
In response to Gurumayi’s ascension to Siddha Yoga’s singular guru, I
imagined hearing Baba saying that God energy was at least androgynous, if the
dimension of sexual identity was relevant at all. Baba taught that divine energy, by
necessity, is expressed through a wide variety of particular personalities and
cultures and should not be confused with the details of its manifestations. This
included the sexual identity of the chosen Vehicle. Guramayi’s central theme, as I
understand it, concerns the simple, quiet and pervasive powers of love and faith.
Some say Baba took the path, marga, of selfless action, karma-marga, whereas
Gurumayi took the bhakti-marga, the road of loving devotion and faith. The third
marga is jnana-marga, my inclination, is the road of intellectual study and
knowledge. Aldous Huxley related the choice among these three categories of yoga
practice, to the physical and personality types of William Sheldon’s 1954 Atlas of
Man. Karma yoga corresponded to the mesomorphic body type and the assertive
boldness, high energy, and interpersonal callousness of the somatotonic
personality. Bhakti Yoga was the characteristic choice of endomorphic body types
with the viscerotonic personality traits of sociability, good will, tolerance and love.
Huxley associated Jnana Yoga with ectomorphic body type and the cerebrotonic
characteristic of shyness, sensitivity and intellectuality.
My summers with Baba at his temporary Ashram in Venice, California and
the permanent American Ashram in South Fallsburg, New York, were spent in daily,
very early morning, chanting of the gurugita after most of the night spent taking
down, cleaning and putting up large tarpaulin meeting tents. I was assigned this
simple, arduously manual, all night work after being interviewed and found out to be
a professor and chairperson of a medical school department. Baba instructed his
assignment committee that many if not all professorial egos would benefit from what
50
Andrew Carnegie famously called the dignity of real work. Spicy one dish vegetarian
meals, twice a day meditation and brief stolen naps consumed the rest of the day. I
found myself meditating for longer and longer times, chasing the promised Blue
Pearl that Baba said appeared behind the eyes near the supreme meditative end
point.
Beside care with the titration of meditation-induced interpersonal
disconnection, detachment with love is the desired end point of most Hindu and
Buddhist meditative practice, another set of “side effects” of the energy arising early
in the course of too much meditation is called kriyas, spontaneous episodes of
involuntary behaviors and postures of the body such as unprovoked chanting and
writhing and stereotyped hand positions called mudras. Baba told us one of his
kriyas took the form of spontaneous erections that occurred during his first
experiences with deep meditative states. I recall a woman physician and fellow
ashramite in Los Angeles telling me that her panties often got so soaked during
meditation that she worried about being stuck to her cushion. Beyond these initial
somatic overflows of Divine Energy, shakti, emerges a vision of the Blue Pearl,
bindu, Baba’s “gift from the Goddess Kundalini.” As he entered this stage, he said
that his mind filled with “joyous contentment.” Jewish mysticism of the 1300’s
acknowledged the neighborhood relations of Eros and the Sacred.
More formal and scientific uses of the word, energy, like all objects of thought
embeddable in a mathematical context, are abstract and relational. In his book,
Mathematics-The Music of Reason, Jean Dieudonne′ treats mathematical objects
as objects of thought. Dieudonne′’s book documents the 19 th Century transition
from concrete, visualizable, classical mathematics to abstract, nonvisualizable
relational ideas. This conceptual transition to abstract, relational thought objects that
are no longer representable by pictures or accessible to our senses of mathematics
and physics is yet to reach the concrete DNA-causal religionists of modern
molecular biology. In 20 th Century mathematics, Dieudonne′ observes that “…the
primary role in theory is played by the relations between mathematical objects
concerned rather than the nature of the objects themselves…these relations are
often the same for objects which appear to be very different and therefore they must
51
be expressed in ways which do not take these appearances into account…and can
be specialized at will…” DNA sequences are, as MIT molecular biologist, Eric
Lander observed, nothing more than an elementary “…list of parts…” In fact, since
about 1% of the nucleotides are relevant to functional genes, one might say that the
important members of this list of parts are distributed very thinly among many more
apparently unimportant ones. The next frontier will certainly involve an
understanding of the dynamics of the interactions among elemental parts and in
more abstract laws about molecular biological relations; a focus on the dynamics,
not the structural parts, that regulate and control their expression.
* * *
I made a pilgrimage to spend eighteen months within Rene’ Thom’s
penumbra, living among mathematicians in his “ashram” in Bures sur Y’vette,
France. Thom was one of the founders of the Institute des Hautes D’Etudes, IHES,
Institute for Advanced Scientific Studies, created to stanch the flow of high-level
scientific talent away from France after the Second World War. It is in Bures sur
Y’vette, deep in a green forested valley, 50 or so miles South of Paris, in a building
packed with small, thin walled, big windows-on-the-woods offices. Each office
contained a single hard chair, an old office desk, two walls of blackboards and a box
of white only chalk. The use of colored chalk was felt to be without mathematical
rigor because its use substitutes colors as dimensional descriptors for more
demanding abstract and formal representations. Color was cheating. Meditation in
this ashram was practiced by staring, pacing, scribbling, and humming, mumbling,
belching and farting through the Institute’s thin office walls. The building, though
almost completely occupied, was otherwise silent. The Institute was populated by
such world-class mathematicians and theoretical physicists that once inside that
building, I felt so intimidated that I almost never spoke above a whisper. Listening to
excellent William Thurston’s casual use of a tiled bathroom floor to motivate a
unique partition of a topological space, I was attacked by the awe of an early
morning visit to an almost empty Notre Dame Cathedral in Paris or standing in front
of Michelangelo’s radiant marble statue of Mary and Jesus the Infant in the Vatican.
52
Though the environment was one of tranquil academic scholarship, I lived charged
with anticipated performance anxiety about the seminars on the brain as a
dynamical system I was scheduled to present to these (I feared) ready-to-bedisdainful,
prize-winning, pure mathematicians and theoretical physicists.
My dorm-style sleeping room at IHES was, in winter, painfully cold and
drafty; the narrow iron bed’s thin mattress contained lumps of persistently disturbing
dreams, the small scratched table for work shim-irreparably wobbled. A faded
poster of Van Gogh’s garden was tacked crookedly on the door facing the toilet in
the dank, dimly lit small bathroom. A dwelling for distracted young mathematicians.
A retired but still famous Parisian chef cooked many course, elegant meals every
afternoon. The food was accompanied by so many liters of unlabeled red wine and
peer pressure to be French and socially drink it that it became a choice between
dulled, blunted,. sleepy post-prandial afternoons or living on bread, many cheeses,
apples and Perrier water, alone in my room. I chose the latter.
Thom’s gifts to us theoretically oriented non-mathematicians were
diagrammatic, easy-to-visualize pictures that allow the intuitive capture of counterintuitive
discontinuities in functions. How we might imagine that a smooth and
continuous change in a cause of something can lead to a big, discontinuous change
in the results. His system of topological (shape not size) diagrams was useful when
considering up to four causal variables and one to two dependent variables that
described how things behaved.
For an important real life example, in modern clinical pharmacology, the
smooth dose-response curve consistent with the physician’s intuition that if a little
drug didn’t work, a little more may do so, should become an up and down search for
the dose-region for the desired effect which may involve a lower amount than a
previously ineffective drug dose. The therapeutic effect may occur in the middle of a
narrow dose range with too much or no effect occurring out of this span. In many
physical systems, sudden and global transitions in state, from incoherent light rays
to coherent lasing and from laminar flow of fluids to turbulence, emerge
unexpectedly when causal parameter are moved into what some call the critical
region of the values of control parameters. Outside this region, cause and result
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were behaving linearly and smoothly whereas within this region we observe global
and dramatic changes via a forced discontinuity in what Thom called a catastrophe
and others use related words such as bifurcation or phase transition. The transitions
from painful fatigue to running rage and then to ecstatic transcendence feels like the
gifts from two kinds of Gods, the first, bearing the righteous lawfulness of the Old
Testament, the second bringing the empathic forgiveness of the New Testament
Jesus. Catastrophe and bifurcation theories predict and keep track of these
transitions using mathematically describable changes in global characteristics of the
“motion” using technical descriptors such as eigenvalues, germs and jets.
Thom taught me my first catastrophe, called the cusp, in words during our
late afternoon walks along a shadowed green wooded path on the grounds of the
Institute des Hautes Etudes, outside of Paris. My homework consisted of trying to
visualize his verbal descriptions. It was not until weeks later that he drew the
geometric object being discussed on the blackboard. With eyes twinkling and in his
provocatively playful style, he said,
“Imagine an empty rectangular box with the front edge of its roof buckled
into an `S’ and the back edge, an unfolded, left-to-right gradually rising simple
smooth curve. If one moves the causal force from low to high, from left to right along
the back of the box, the changing effect (represented by height) would be smooth;
moving from left to right in the front encounters a sudden drop off at the S shaped
buckling, a discontinuity in roof height indicating a discontinuity in effect. The energy
equivalent height of the roof graphically indicates the amount of result. The roof is
the manifold upon which the result of causal change is portrayed. The two
dimensional floor of the box represents a graph of the two causal parameters, the
increasing amount of normal factor going left to right along the `x’ dimension, the
increasing amount of splitting factor (taking one from the back to the front to the
region of the buckling) going back to front along the `y’ dimension.”
He gave me some examples of systems that showed cataclysmic changes in
effect from smooth changes of normal and splitting factors. About the onset of a
war: “At the back of the top surface of the box, the manifold, the normal factor
increasing from left to right is the amount of the perceived threat. The splitting factor
54
decreasing from front to back is the cost (and ability to pay) for war. Without the
financial capacity to make war, threat goes from left to right smoothly at the back of
the box as tension gradually increases without the onset of armed conflict. When
effective fighting capacity is cheap and/or already well funded, the country well
armed, the increases in threat go from left to right at the front edge of the box and
encounter the cliff of catastrophe and war is declared. Cost of, or ability to wage war
varies from the front to back, and serves as the splitting factor. Considering prison
riots, social tension is the normal factor and alienation (degree of identification with
prison authority) is the splitting factor.” Using factial expressions of dogs sketched
by the Konrad Lorenz, Christopher Zeeman then of Warwick Mathematics Institute
in England, considered countenances reflecting increasing rage as the normal
factor, the amount of fear was the splitting factor. Increasing rage at high fear
increased smoothly at the back of the box; at low fear, increasing rage falls off the
cliff to an animal attack at the front of the box.” He paced as he talked, occasionally
looking up to see if I was following him. He continued,
“A light above the box casts a shadow from the roof to the floor, outlining the
gradually widening fold created by the transition from the smoothly rising back of the
roof to its `S-shaped’ front. This triangle on the x-y causal floor is the region in which
the discontinuity in the result surface roof results and is called the bifurcation set. An
increasing amount of the causal `normal factor’ is represented from left to right
along the `x’ dimension, the results of which change smoothly at the back of the roof
but encounter a discontinuous jump up or fall down crossing the inaccessible
crevice in the `S’ fold at the front of the roof. Again, the triangular shadow on the
floor made by the fold indicates the parameter region in which discontinuous
changes in the result surface occur. The reason the parameter that determines the
front to back location of the left to right movement of the `normal factor’ is called the
`splitting factor’ becomes obvious. Its value determines whether the results induced
by increasing amounts of `normal factor’ will be smoothly changing or generate a
discontinuous jump. The entire visualizable object is called a cusp catastrophe and
it along with higher dimensional parameter region-inspired shapes such as the
55
swallowtail and butterfly buy back the smooth DE deterministic intuition lost with
discontinuous changes in results.”
He grinned mischievously as he asked, “Can you see it?”
Thom’s catastrophes serve as accessible and powerful theoretical settings
for the use of energy as a generalizable, one dimensional, dependent, resulting
effect, influenced by one or several, sometimes conflicting, independent, causal,
variables. For more examples: the weight of a ship (smaller to greater, left to right,
along the x, normal dimension) and the position of center of gravity (smaller to
greater, front to back, along the y splitting dimension) are causal with a jump in roofheight
energy from stability to capsizing, a discontinuity emerging from initially
smooth changes in stability. As above, gradually increasing tension (the left to right
normal factor) and alienation (the back to front (splitting factor) in inmates generate
a sudden increment in energy, from subtlety increasing tension in relative quiet to
the sudden outbreak in a riot in the prison population. Embryological notochord
somitogenesis, (that which become the vertebrate of the spinal column) has a
smooth (left to right) causal influence that Chris Zeeman named a normal factor. It
is the smooth growth of the material wave of mesodermal (to become muscle,
connective tissue and bone) tissue. Zeeman called the front to back dimensional
gradient of influence, the secondary wave of adhesiveness, the splitting factor. The
value of this secondary wave co-determined a critical-valued interaction between
these causal parameters leading to a discontinuous change in the “energy”
equivalent continuity of developmental growth and vertebral column segmentation.
A little more technically: Thom’s basic mathematical contributions were in
differential topology and analysis with particular emphasis on what is called
structural stability of surfaces representing and supporting actions called manifolds.
For example, in a graph of a function, say F(x), such that a change in cause x
determines what happens to the result y= F(x), the stability question involves what
happens when one perturbs F(x) with a littleδ, i.e. δ + F(x). Do the topological
properties of the surface representing the potential range of actions of the system
(such as nearness of an originally close point set, continuity and connectedness of
the surface, its dimensionality, its compactness as a generalization of finiteness)
56
remain the same after perturbation? Note that the inter-data point metric distances
are not considered. If they do, the two dynamical objects being compared are
topologically equivalent. The test of this equivalence requires the mapping one set
onto the other with, at most, smooth distortions of either or both surfaces.
In the context of catastrophe-related bifurcation theory, if a δ converts a
steady valued fixed point to an oscillating cycle on a manifold of potential actions,
also called a state space, then the fixed point system was not structurally stable. In
phase space, this is seen as a change-in-causal-parameter induced transformation
of a dot to a circle. If the one frequency circle is perturbed to a manifold of the
system’s actions consisting of two independent frequencies, the circle takes the
topological form of the crust of a doughnut, one frequency graphed spiral winding
around the doughnut, the other winding along the doughnut around its orifice, the
circle is not structurally stable. If δ distorts the frequency-amplitude relations on a
surface such that the manifold of possible actions is distorted from a doughnut to a
tea cup, both topological manifolds being one holed surfaces and therefore
topologically equivalent, the system is structurally stable. Perturbed systems that
maintain the sequence of points in time in sequential order (though the distances
between the points may be different), are generally structurally stable.
The seductive possibility, one which Thom realized so successfully, was
that in the language of distance-independent differential topological forms, there
would exist a small, finite set of shapes categorically describing the causes and
result parameter spaces from which, even without specific quantities, universal
qualitative (including discontinuous) behavior could be described and sometimes
predicted. A formal yet general categorical system within which a small set of
universal discontinuous changes in global qualities could be rationalized seemed
seductively applicable to the enlightenment transitions, spiritual transformations,
appearing suddenly after months and years of disciplined spiritual practice. The
Platonic view is that the universal forms of discontinuous change existed before
they could be about anything specific, before the universe was born.
In this era of nonlinear dynamics and dynamical system, common dynamical
scenarios give accounts of smooth changes in causes leading to discontinuous
57
changes in results. The Nobel Prize winning solid-state physicist, Phillip Anderson,
in a short but memorable piece in Science in the 1970’s said it tersely, “More is
different.” This general, qualitative mathematical theory of discontinuous change
models nicely the sudden delivery of the first and second second winds from
gradually and continuously increasing running distances as well as the abrupt
transmission of the guru’s “energy”, shaktipat, from smoothly increasing amounts of
chanting, meditation, guru service and Baba love. Gradually changing forces
leading to sudden changes in an energy-equivalent result are found in most
rigorous form in Rene′ Thom’s singularity-bifurcation-catastrophe theory applied to
rational mechanics and geometric optics. Here the existence of already solvable
computational formalisms makes this more qualitative approach superfluous. On the
other hand, the power of this both basic and applied mathematical orientation and
method lies in its approach to the qualitative understanding of variously induced
global and sudden changes in an energy-equivalent observable in biological,
psychological, spiritual and social systems, fields of study in which little abstract and
formal lawfulness presently exists. Oxford’s Chris Zeeman’s more accessible
applications of Thom’s deeper, more generally ramifying, almost mystical (due to
their apparent wide generality) results, include approaches to real world problems
such those above as well as the sudden change in excitable membrane potential
accompanying the generation of the heart beat and neuronal discharge;
mechanisms of opinion change, stock market crashes and, as noted above, the
social science of riots. Whereas Thom’s On Structural Stability and Morphogenesis
can be said to be scriptural, Zeeman’s Selected Papers, 1972-1977 constitute the
Book of Common Prayer of this church.
To review and place catastrophe and bifurcation theories in the context of the
differential equations of mathematical physics and biology, causal determinism
implied by differential equations conventionally requires continuity and smoothness
in behavior to be credible. Our intuitions as well as the formal conditions for the
generic differential equations of mathematics and physics imply that smoothly
increasing amounts of cause lead to smoothly increasing results and yield at least
local predictability: a little more leads to a little more, a little less leads to a little less.
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This smoothness-dependent intuition of determinism breaks down in nonlinear
equations as well as in a wide variety of the machines of experimental physics, from
the sudden coherent lasing of previously incoherent light to the vortices and
turbulence in suitably bounded rotating or flowing fluid. It took me a while for these
topological still shots and movies of the head to become real. Nevertheless, the
enrichment of intuition was well worth it. Of course one could smoothly increase the
normal factor weight of a ship until it gradually sank, but if one moved the center of
gravity splitting factor to an eccentric position in the ship in the parameter region of
the bifurcation set, a sudden global capsize before weight-induced gradual sinking
made sense. I could see it. Indeed, increasing normal factor tension in a prison
population that was identified, not alienated, from the officials and mores of the
penal institution, would increase social symptomotology gradually. However,
increasing the splitting factor of social and institutional alienation results in the
cataclysmic change of a riot with increasing tension. I could see it.
Do we need to know the causal equations to anticipate instability and
discontinuity in our lives? Zeeman making Thom’s thoughts accessible to us plain
mortals said no. He suggested that we could use several diagnostic
phenomenological signs to make a good guess about whether we are near or within
the bifurcation set. Depending upon the route that the causal variables take through
the shadow of the bifurcation set, we may see very large fluctuations in our
observable. The Dow or S&P stock indices in the neighborhood of a sudden large
change is often presaged, sometimes for weeks, by a marked increase in volatility,
fluctuations between extreme values. Theorists call the statistical properties of a
time series of values behaving this way anomalous variance. For several months, I
did psychotherapy with a genuinely spiritual Catholic priest who only some Sundays
served the Eucharist, the corporal presence of our Lord at Communion, wearing no
trousers or underpants beneath his robes. A sudden change in a stock index in
response to the “shock” of a terrorist attack takes much longer to settle down if a
cataclysmically bigger change is in the neighborhood. This extension of the
system’s usual relaxation time is sometimes called critical slowing. In the bifurcation
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regime of a schizophrenic break down, critical slowing can be both global and literal
as the patient freezes in catatonic postures.
In the neighborhood of the bifurcation set, big jumps in the stock index, up or
down, are possible under almost the same surrounding conditions. This stock
analyst-humbling phenomenon is called bimodality. Jimmy Swaggert’s Saturdays
were often spent watching the show at naked dance parlors and buying videos at
the pornography shops of Metairie Highway near Schwegmann’s Grocery outside
New Orleans. Sundays found him on national television engaged with infectiously
real, transcendent experiences in the public arena of the pulpit. The ecstatic
congregation was deeply moved by his eloquent and tearful sermons about sin and
salvation. Counter to most suspicions, this is less conscious fakery than the
genuinely felt alternating states intrinsic to the bimodality in neighborhoods of
spiritually unstable, born again transitions.
Similarly, beginning with nearly the same initial values near the boundary of
the bifurcation set, very similar motions lead to dramatically different results. This
counter-intuitive behavior has been called divergence. At UCLA’s Neuropsychiatric
Institute, I interviewed a pair of lively teenage, genetically identical male twins raised
by a loving family in Los Angeles’s Valley. One was president of his high school
class, a Sunday school nursery school volunteer and a Saturday soup server to the
poor. The other twin sold pot and cocaine to support his habit. Deep and potentially
dark mysteries live in these spiritual bifurcation sets. They leave us pondering child
sexual abuse by deeply religious clergy and the massacre by mass suicide of a
New Christian congregation by James Jones. We wonder why it is that
fundamentalists (Jewish, Christian and Muslim) have the most ecstatic and direct
validating experiences of God and do the most shooting and bombing of other
people. In Burt Lancaster’s portrayal of bifurcation set dweller, Elmer Gantry,
charismatic believer and exploitative psychopath, were simultaneous and both
credibly real.
Another feature of the occupancy of this bifurcation region in control space is
that the values producing a sudden jump that occur passing through going one way
along the “normal” dimension usually jump back much further along when moving
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the other way. Theorists call this characteristic sign of bifurcation land, hysteresis. It
is generally known that sudden healing changes of the first born again experience
can arrive magically fast whereas a run at it a second time, another born again state
after the loss of the first one, comes, if at all, with much more effort and difficulty.
Members of Alcoholic’s Anonymous know that getting on the AA wagon the first
time may be quick, joyful and easy. Getting back on this wagon after a fall is much
more painfully slow and demanding, analogous to the Carmalite monk; St. John’s
lost faith engendered suffering of the Dark Night of the Soul.
Viewing the instabilities and extremes near the boundary of a bifurcation
brings inquiries and advice about why a rational compromise, some form of
disciplined moderation, would not be more desirable. It turns out that in this
parameter regime, the in-between state is intrinsically inaccessible. The pocket in
the S shaped fold of the upper manifold cannot be attained, at least for very long, by
varying the values of the two parameters. However, if one increases the number of
controls, it might be possible to stabilize a small island in a parametric sea of
instabilities. In an application of this strategy, Smith College and Harvard Professors
James Callahan and Jerome Sashin used a geometric representation of the difficult
to stabilize region of normal weight on a double cusp manifold representing the
behaviors of patients with eating disorders with both anorexia nervosa and bulimia.
They varied five controls to stabilize a very small result area representing normal
eating by varying the control values for ability to verbalize feelings, to imagine
solutions, to defend against anxiety with unconscious forgetting called repression, to
make contact with realistic rationality and to modulate feelings with say exercise,
meditative practice or psychopharmaceuticals.
My experiences with the so-called borderline personality, with the tendency
toward sudden and global personality change, from Sunday school teacher to Harlot
in the space of a breath, has been both sexually exciting and personally ruinous for
me in my life. I could feel the instabilities in these dwellers of the bifurcation pockets
and my heart raced at the promise of mutually unconsidered impulses, the blurring
of orificial identities, the experiments with sexual roles and modes and the
incipiency of collapse into regressive mud play. Most of all, I anticipated that their
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screaming orgasms, potentiated by a natural inclination to bifurcate, would be so
messianic as to carry me along to a transcendentally erotic new place.
Unfortunately, paranoid rages, bursts of promiscuity and hopeless inconsistency of
goals and efforts dominated the remainder of our living days.
Further Readings for TRANSMOGRIFICATIONS OF ENERGIES
Religions in Four Dimensions; Existential, Aesthetic, Historical, Comparative, Walter
Kaufman, Reader’s Digest Press, 1976
Religious and Spiritual Groups in Modern America, Robert S. Ellwood, Prentice-
Hall, Englewood Cliffs, 1973.
The Evangelicals, What They Believe, Who They Are, Where They are Changing,
David F. Wells and John D. Woodbridge, Abington Press, Nashville, 1975
A Nation of Believers, Martin Marty, Univ. Chicago Press, Chicago, 1976
Conversion: Christian and Non-Christian, Alfred C. Underwood, George Allen,
Unwin Ltd., London, 1925
Eros and the Sacred, Paul Avis, SPCK, London, 1989
Mukteshwari, The Way of Muktananda, SYDA Foundation, Ganeshpuri, India, 1972
Godtalk, Travels in Spiritual America, Brad Gooch, Knopf, N.Y. 2002
The Beat of a Different Drum; The Life and Science of Richard Feynman, Jadish
Mehra, Clarendon Press, Oxford, 1994
62
The Shape of Space, Jeffrey Weeks, Dekker, NY, 1985
The Topological Picture Book, George K. Francis, Springer-Verlag, NY 1988
Mathematical Models of Morphogenesis, Rene Thom, Wiley, NY 1983
Catastrophe Theory, Selected Papers, 1972-1977, Christopher Zeeman, Addison-
Wesley Reading, MA 1977
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CHAPTER 4:
SENSUAL IN-BETWEEN ENTROPIES
Since the early teens, I’ve been beguiled by girls and women that have what
might be regarded as exquisite sensibility, perhaps more precisely, exquisite self
sensibility. These inhabitants of the near transformational neighborhoods of
bifurcation sets, are grandly responsive receivers of emotionally significant
information arising from their insides and the world. They are the canaries in the
deep mines of human experience. Not the usual one lively-eye, one sober-eye,
binocular difference of most of us, both their eyes sparkle, their feeling antennae
await a happening and each is regarded as new. I spot these brains in a crowd
within minutes and am compulsively drawn to know them better, to become part of
them, to vicariously experience and serve them. They seem to have little inhibitory
control of even weak sensory information on its way to their strong, global feelings.
Near ecstasy and excruciating pain await. They feel their anticipations with their
body, down to their painted toes. Their receptivity brings me lower abdominal
warmth in remembrance.
At sixteen in my Dad-purchased second hand Ford convertible, I was parked
with my new girl friend on Sarasota’s Lido Beach, hearing and seeing dark shadows
of the Gulf of Mexico’s waves hit white sand against the night sky. I took her flat
party shoes off to message her feet. When I kissed her left foot and sucked gently
on her toes, she gasped and became faint. She told me that a strong electric shock
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had run up her back. The passionate licking and sucking of her musky, moist, pink
labial lips brought what she said were explosions of pink and blue lights. She had
several ecstatic multicolored crises in a row, sometimes without pause. She begged
me to stop. I was as pleased as a sexually inexperienced young man in love could
have possibly been.
Bowled over by what seemed to be the uniquely sensual properties of her
brain, I began to wonder if her sensitivity was more general when she asked me to
keep the windows open or top down, even in the cool of a Florida January, because
the exhaust smell in my car was suffocating, though I couldn’t smell it. The car had
been checked and registered negative for abnormal fumes and leaks by Anderson
Ford. She asked me never to wear any kind of after-shave lotion because it choked
her. Jazz music on the car radio had to be played quietly. On-coming headlights
gave her headaches. Her mother, sometimes desperate, called me for help during
her daughter’s episodes of premenstrual emotionality and early menstrual
discomfort. During these times, we would drive together for hours as she explained
the many different colors of lower abdominal pain and how this particular kind
yawned darkly before it cramped. It was more purple then any of the others. I tried
to explain what I intuited but didn’t understand to her mother about the her gift of
unfiltered information coming through her nerve endings, her ever readiness for
surprise and her brain’s unwillingness or inability dampen or ignore what it didn’t
like. She saw things in art, heard things in music that I only saw, and heard after her
telling. She had tearful smiles listening to Debussy’s Afternoon of a Fawn. The
flatted fifths of Charley Parker and the laconic riffs of Miles Davis made her anxious.
Since then and for all these many years, the same sensually susceptible
brains showed up in my life carrying a variety of woman’s names and I never lost
my fascination for them. I learned that their heightened awareness extended to the
spiritual realm with unusually strong metaphysical inclinations and readiness for
transcendent experience. They seemed to live closer to the direct experience of
God. Attending Assembly of God and other Pentecostal midweek service, I found
that praying in tongues and dying in the Lord came as easily and dramatically to
them as their orgasmic experiences. At the same time, distant bad news could
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suddenly become immediate and loud in a litany of threatening thoughts that
hooked and persisted through sleepless nights. They taught me to see genuinely
the delicate beauty of flowers and to know in my stomach that some forms of
sadness felt hollow like homesickness. In medical school I found that that many of
them were the clinic patients, women and men, with unusual sensitivity to chemical
odors, think Gulf War Syndrome, and fibromyalgia, which I heard as unusually
sensitive awareness of normal sensory information about posture and position
coming in from the bones and muscles of the body but experienced as pain. This
background of odorific and somatic information is usually repressed from
consciousness by the rest of us. Their medical histories contained detailed accounts
about how each of their organs was feeling at the time, sensations that the
textbooks say we are incapable of consciously knowing. Internists and psychiatrists
often dismissed their accounts as signs of somatoform disorder, psychological
conflicts expressed in the language of body feelings.
In the psychophysiological laboratory, I learned these brains tended not to
habituate. Each of a series of noises continued to elicit startle responses that could
be picked up in brain wave recordings or in the running record of a
psychophysiological, lie detector, machine. In psychoanalytic training, I learned that
these brains remembered their dreams more richly than the rest of us and that
treatment with over twice a week analytic sessions was potentially dangerous. The
psychoanalytical situation-engendered fantasies and feelings could get too strong
and exaggerated, too real.
Professor Iris Bell of University of Arizona’s Alternative Medicine Research
Program has, studying these brains, found slower reaction times, defects in divided
attention psychological tasks, longer latencies to the first dream, and unusual
patterns of odor reception called cacosmia or dysosmia. Using brain wave and
cardiac interbeat interval data as markers, Bell reports the increase in the amount of
alpha awake brain waves and decreases in cardiac interbeat interval variation
associated with increasing sensitivity, rather than habituation, with repeated
exposure to a variety of smells over time.
In spite of these brains usually requiring what is known as high maintenance
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in relationships, I continue to be erotically spellbound, in love with them in all their
forms. Questions about how to think about these exquisitely sensitive women, Bell’s
Syndrome exists but is rarer in men, continue to drive aspects of my scientific
research. It has been variegated quest, which began with trying to find a general
conceptual framework that would help my understanding of this unique capacity to
be aware and process large amounts of internal and external information that
escape the awareness of most of us. As one might guess, this search led to
fundamental ideas about information and its inverse, the entropy indicating the
amount of information transport capacity, with respect to their characterization,
quantification and measurement.
To get to the end from close to the beginning, we recall that it was Claude
Shannon and his followers who both mathematically proved and experimentally
verified that a receiver must have more entropy, less already fixed knowledge and
more wondering, than the sending source, in order for the message to be sensitively
and reliably received and encoded. Sensibility seems to have something to do with
the readiness for information transmission afforded by the brain’s high entropy,
minimal fixed information states, in its resting dynamics. Their remarkable
receptivity derives from a baseline brain state like the formless emptiness of the
bodhisattva’s “…no form, no sound, no feelings, no perceptions, no
consciousness…” of transcendent Tibetan Buddhism as described in the Heart
Sutra of The Dalai Lama.
In Chinese Medicine, xu, meaning emptiness, contrasts with shi, the word for
fullness, both of these complementary opposites having multiple specific meanings.
Most metaphysically relevant is the characterization of xu as the emptiness of the
deepest reality of being and the highest state of human spirituality. Like that aspect
of Lao-Tsu’s ineffable Dao, The Way that is empty, xu indicates a mind devoid of
desire, being lucid and serene. In the context of dynamical form, xu shares the
structureless, non-imagery of maximal entropy systems and shi the lower dynamical
entropy of fixations on form, desires and beliefs. Shigehisa Kuriyama’s The
Expressiveness of the Body, elucidating historical and conceptual divergences of
Greek and Chinese Medicine, notes that xu was the supreme end of self-cultivation
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and the secret to vigor and longevity. “…to achieve fullness of life one had to abide
in empty nothingness, xuwu.” In Lao-Tsu’s Tao-Te-Ching, “…the Way is gained by
daily loss, loss upon loss until…by letting go, it all gets done…”
William James, in The Principles of Psychology, tried to capture the subjective
dynamics of the brain as an on-going preconscious stream of statistical wave
processes. He envisioned autonomously increasing and decreasing coherence
emerging spontaneously and from sensorial evoked thoughts via the confluence
and disaggregation of statistical wave processes, “…wave crests and hollows…”
that achieved temporary statistical stability by “…feelings of relation, consubstantial
with our feelings or thoughts of the terms between which they (only temporarily)
obtain.” In the more receptive, higher entropy brain systems, fleeting forms change
without continuity, jumping from one to another with “magical rapidity,” but being not
already engaged, are available for use for self-organized structure evoked by new
information. Without ordered, low entropy, preconceived ideational defects in the
resting random brain field, the full attentional statistical machine is available to
sensitively respond in self-organized, quasi-stable states of cognitive, conative and
affective integration. They then disappear; this brain relaxes quickly, ready for new
experience. This contrasts with those brains that are dominated by islands of order
composed of personality fixations and rigid belief systems, low entropy defects,
which interfere with sensorially responsive self-organization.
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As in most systems of authoritarian premises, precise definitions and what
appears to be strict logical continuity, as in discussions of Torah among Orthodox
Jews and Canon Law by Catholic bishops, classical equilibrium thermodynamic
ideas that are borrowed for use out of the context of their origins, risk the calumny
of their physicist practitioners. We have probably already earned more than a little
distain from those quarters with our use of none-minimal or none-maximal but inbetween
entropies. This phrase cannot be found in the literature of physics or, as
such, in the writings of communication and information theory. In the modern theory
of nonlinear motion called dynamical systems, in-between entropies can be
generated by chaotic systems that are non-uniform in their rates of separation of
near by points and convergence of far-away points in dynamics that have been
previously described as nonuniformly hyperbolic.
The energies and their transformations that fuel and support karmic escape
from the personality fixations of samsara and accession to unmanifest Divine Life
can occur without the loss of the richness and multiplicity of apparent reality. Big
internal changes without external sign can occur in the arrangements of the
ineffable and mysterious formless silence within which we have associated with
states of high, but not maximal, in-between entropy. For examples, the Indian Saint,
Sri Aurobindo, in the early 20 th Century, the Catholic metaphysical anthropologist,
Teilhard de Chardin and currently American pandits (spiritual seekers with
intellectual and academic inclinations) such as Ken Wilber, among many others
over the millennia, direct us toward the goal of Nirvanically changeless emptiness
without the properties of space or time. At the same time, we maintain an astute
and effective yet distantiated appreciation for existential realities. The non-dual
enlightenment of Integral Being or Yoga involves realizing emptiness through the
world of form. There is a way of thinking about and even computing that “nothing
within” and its changes.
As John R. Pierce suggested in the 1981 revision of his book that made the
theorems of the father of communication theory, Claude Shannon, so accessible,
“…if we want to understand information-related entropies, it is perhaps best to clear
our minds of any (physical) ideas associated with the entropy of physics.”
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Nonetheless, historical comments about what the classical thermodynamic term,
entropy, is and is not about are in order.
We recall that Richard Feynmann, in his well-known 1962 class notes,
Lectures on Physics, said that the subject of thermodynamics is the study of
relationships among the heat, energetic and organizational properties of materials,
without knowing their internal structure. Historically, the relational formalisms of
equilibrium thermodynamics emerged before our knowledge of the internal structure
of matter. For examples, the pressure in an insulated container of gas is due to
molecular bombardment of the container walls, which increases with heat or
compression of its volume. Compression of its volume increases its temperature
and expansion of its volume leads to cooling. Note that these relationships hold
without specifying the constituents and the specifics of a particular gas or solid.
In his lectures, Feynman’s intuitively accessible examples of reversible
thermodynamic properties are reminiscent of his on camera performance at the
Senatorial hearings about the Challenger disaster. Recall that he dropped an O-ring
in a glass of iced water demonstrating cold-induced rigidification of the rubber ring,
which he postulated to be the cause of the fuel leak and resulting explosion. In his
Lectures, he said that if one holds a rubber band between ones lips as a crude
thermometer, stretching a rubber band heats up the lips and relaxing it cools them.
Working the same system in reverse, and equilibrium thermodynamic systems are
classically reversible, we find that heating a rubber band makes it contract. These
changes involve complicated alterations in the internal arrangements of the
polymeric strands of rubber, their structural properties, the details of which, for the
purpose of global thermodynamic characterization, need not be known. The
relationships between physical state, energy and temperature in this material were
predictable from thermodynamic laws even without specific knowledge of the
complex internal structure and physical dynamics of rubber.
Thermodynamic theory, which makes deep conceptual connections between
quantitatively measurable primitives such as heat, hotness and work and the
invisible in the form of derived ideas such as energy and entropy, yielded an
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enormously rich and logically consistent intellectual framework from within which to
characterize macroscopic behavior composed of unknown molecular mechanisms.
Ideas about entropy grew out of William Thomson's (a.k.a Lord Kelvin)
thermodynamic laws about energy conservation and its allowable transformations.
Later Clausius decomposed the energy into that which was available for mechanical
work, called work-content, and that which was not, called transformation content.
He referred to the transformation content, a reflection of what changes in the
internal order properties of the system that occurred as a concomitant of changes in
energy and heat, as the entropy.
Rudolph Clausius added the word entropy as a thermodynamic property to
the conceptual armamentarium of theoretical physics in about 1865. This followed
the earlier work of the French engineer, Nicolas Leonard Sadi Carnot, who was
trying to develop a theoretical framework within which efficiencies in heatgenerating
engines might be understood. It implicated positive, > 0, changes, d, in
entropy, S, with changes in time, t, i.e. dS
dt
> 0, entropy is increasing in time, as a
concomitant of the inevitable mechanical inefficiencies in an energy driven system.
The resulting losses in the form of wasted energy show up as increases in
molecular motion, which could be estimated from the increases in heat. Wasted
energy dissipated as heat increases the amount of random motion and volume
occupied by the surrounding molecules in physical processes involving heat,
pressure, vaporization, condensation and work; all elements of that era’s dominant
physical metaphor, the steam engine.
The highly developed, multifaceted, often quite abstract formal
characteristics of the inferred property, entropy, prevent glib definitions and
generalizations. In the context of Kelvin-Clausius theory, the entropy of a closed
system will remain the same if it is isolated from any matter or energy exchanges
with the environment. If heating a system such that the change, d, in heat, Q, is
positive, i.e. dQ > 0, it experiences a rearrangement in its microstructural motions,
but the temperature is left unchanged. The (inferred) entropy, S, increases (i.e., dS
> 0) as the ratio of change in added heat, dQ, over the unchanging, absolute
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temperature, T. Thus, one definition of entropy change is dS = dQ/T. In classical
contexts, dS is expressed in units of heat called Joules per degree of absolute
temperature in units Kelvin, the temperature in Centigrade plus 273.16 o . The bestknown
physical image involves the heat-energy transfer to and from heat baths
called reservoirs as intermediate actions of the work of the heat driven engine
executing what has come to be known as the Carnot Cycle. The same formulation
emerges in this more concrete context: the heat, Q, transfer, dQ, at a particular
absolute temperature, T, dQ/T, has been used to define an entropy change, dS =
dQ/T related to some not-need-to-know-about specific alteration(s) in a system’s
internal physical properties.
If one allows some loose thinking about heat-induced increases in the
statistical randomness of molecular motion in the above reservoir that is associated
with the loss of useable energy, the positive entropy change, dS > 0, is vaguely
relatable to the kinds of information entropies to be discussed below. If a gas
trapped in an insulated, physically isolated, closed cylinder is allowed to expand
infinitely slowly, reversibly, called adiabatically, pushing up the piston that closed off
its end, the gas will become cooler, energy having been expended doing the work of
lifting the piston. Defined as an isolated system (of course no where in the real, nonlaboratory,
world can this condition of absent exchanges of energy or matter with
the environment be found), it is a reversible process, because returning the energy
of the work by, again, infinitely slowly pushing down on the piston and compressing
the gas to its original volume, returns it to its former temperature-defined energy
state. In this historically prominent thought-toy of physics, there has been a
reversible change in energy but no changes in the entropy, dS = 0. The gas’s heat,
temperature (and energy and volume) can be completely restored in this
metaphysically mythic classical thermodynmical tale of an entropy-conserving,
reversible process.
While fixed entropy and independence of the specific path is the case for the
above noted abstract reversible cycle, in the real, irreversible orbits of most physical
and all biological systems, entropy increases, dS > 0. Walter Nernst’s 1907 heat
theorem yields a zero point from which to determine a difference measure in the
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postulated, real physical world of ever-increasing entropy. He showed that at an
absolute temperature of zero, entropy is zero. We can illustrate an approach to this
singular state by placing a heated metal rod in ice water which would result in a
decrease in the entropy of the rod’s molecular motions by dQ/ T 1 < 0, the cooling
reducing the complexity of molecular motion in the metal bar and an increase in the
entropy of the water by dQ/T 2 > 0 indicating an increase in the amount and
complexity of the surrounding water’s molecular motions. Of course the heat moves
from metal rod to the water as T 1 →T 2 making dQ > 0 positive and the entropy
change, dS = dQ/ T 2 - dQ/ T 1 , also positive. In another simple example, producing
friction by rubbing a surface generates heat, dQ > 0, at a temperature T. This
induces a positive change in entropy, dQ/ T > 0, in the form of increasing amount
and complexity of the patterns of molecular motion in the air surrounding the rubbed
surface.
Using another related and well-known thermodynamic thought toy, the
original isolated, insulated body of gas in the cylinder is partitioned by a membrane
into two chambers, one containing all the gas with its temperature, pressure and
ability to do mechanical work and the other a vacuum without these properties. This
equilibrium state is changed into another equilibrium state by suddenly removing the
membrane, filling both chambers with gas and, while increasing its entropy
irreversibly, dS > 0, removes at least some of the gas’s ability to do piston raising
work. In the context of classical thermodynamics, it is in this way that irreversibility
can be defined by its associated increase in entropy. Though there has been no
change in total energy in this insulated closed system, an increase in entropy
means a decrease of the energy available for work. The increased disorder in the
gas is associated with the loss of ability to convert heat, thermal energy, into
mechanical energy. Historically important and still available elementary texts by
Enrico Fermi (1936), Mark Zemansky (1957) and Herbert Callen (1985), among
many others, explicate clearly the formal, but far from biologically relevant, classical
theory of the physical entropy of closed equilibrium thermodynamic systems.
Growing in part out of the formal thermodynamics of physics, statistical
mechanics offers yet another set of intuitions about the not-necessarily-known
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molecular details associated with changes in entropy. These ideas are closer to
applicability in problems of making measures on the behavior of biological systems.
Very generally, in the statistical mechanical context, an increase in entropy means a
decrease in the order, which can be a quantitative observable reflecting a decrease
in predictability and/or knowledge about the system. For example, we can locate the
molecules of the gas more accurately when they are all on one side of the
membrane-partitioned cylinder compared with the situation when the membrane is
suddenly removed. This accompanying increase in ambiguity and decrease in
knowledge in locating a set of gas particles reflects a statistical mechanical view of
increases in entropy. Can anything general be said about the bounds on an
increase in entropy? The statistical developments of the Yale mathematical
physicist, Josiah Willard Gibbs (about 1875), consonant with the logical arguments
of the Greek mathematician, Constantin Caratheodory (about 1910), conclude that
the entropy increase goes to the maximum allowed by the constraints imposed by
or upon the system. A change in likelihood as a probability is a characteristic way to
quantify the entropy change, reflecting an alteration in knowledge or its reciprocal
complement, uncertainty. The system’s entropic uncertainty said more colloquially,
and relevant to the Bell Syndrome’s women of my life, is its capacity for surprise.
A statistical mechanical approach to the total entropy of a bounded set of
molecules in motion involves summing this property across all the participating
molecules. We let N be the number of particles involved. As a problem in Newtonian
mechanics, each of the N particles is represented in 6N dimensional phase space.
That means that each point represents one of the N molecules in the three
dimensions of location space plus three dimensions of motion space as its velocity,
more specifically, the product of mass times velocity called momentum. This adds
up to 6 dimensions of measurement. This so called phase space reconstruction of
the molecules of a gas as individual particles are a daunting task, though fast
computers and new algorithms are making computations from first principles more
generally attainable. Those based on the first principles of short-range repulsion
and long-range weak attraction among particles and the bumper-car collision
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dynamics between them can now be implemented if the system of particles being
simulated is sufficiently small and the computer simulation is for very short times.
To transform the entropy into something more statistical and global, we
return to the theoretical work of Ludwig Boltzmann whose formalism was used
previously to quantitate pathological developmental simplification. He assumed that
given a set of constraints, say the closed volume, V, of a box, B, of a fixed size, V
(B), the orbit of each particle would eventually explore all the space in the box that
was available to it. Boltzmann’s entropy became a constraint dependent, n-
dimensional volume measure, with the assumption that the entropy, S, equals the
logarithm of this volume measure, S = ln V (B). To calculate a value for the entropy,
compute the volume of the molecular motion as determined by the invariant
constraints of the system, such as the volume, temperature, pressure and/or its total
number of molecules. We may partition, discretize, the volume up to some limit of
resolution such that it is divided into Ω small boxes, each containing the
representation of a particular state.
Making the same assumptions of closed system, equilibrium
thermodynamics, such a system is completely isolated from outside sources of
matter and energy, it spends equal time in each of its Ω available states. In such a
case, the characteristic occupancy time of any state is inverse to the number of
states available, e.g. 1/Ω, and the system’s entropy is maximal for that set of states.
Under these conditions, S = k ln(Ω), where the k term is the Boltzmann constant
that contributes to the numeric units of entropy, as above, in Joules of heat /degrees
Kelvin of the temperature. If the system is in contact with a heat bath, but cannot
exchange matter with its environment, it is called diathermally isolated. The
distribution of times spent in the available states of a classical diathermally isolated
system of gas molecules can be represented by what is called a Boltzmann
distribution of probabilities of state occupancies, ρ (as a function of their energy
level, more measurably, their responsiveness, susceptibility, to heat). Here the
characteristic time of the system spent in each state varies as the particular state’s
probability.
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Leaving the framework of physical thermodynamic entropies entirely, the
entropy of information was introduced in the context of communication engineering
in electrical and electronic devices. The metaphorical machine for the current age of
entropy, analogous to the role of heat and steam engines in classical
thermodynamics, is the computer. Energy in this context is a relatively trivial
property. Ammeters and other monitors of load are unable to discriminate between
a computer actively engaged in encoding and computation or one simply
maintaining its dynamic memory while resting in computational readiness. This
situation is very analogous to the results of early work discussed previously on the
metabolic rates and sources of the whole brain’s energy, oxygen and glucose
metabolism, by National Institutes of Mental Heath’s Seymore Kety and Louis
Sokoloff and the State of Illinois Thudicum Laboratory’s Harold Himwich. Using
whole head arterial-venous, energy-in, energy-out, differences, they could not
demonstrate differences in rates of whole brain metabolism between states in which
the human subjects were engaged in solving mathematical problems or deeply
sleep. In today’s brain imaging research, using a variety of physical reflections of
the brain’s metabolic activity, it is the differences in regional distributions of
metabolic activity that are relatable to subjective and behavioral states, not
differences in total amount of energy expended. In graphically coded
representations of the regional metabolism of the brain in action, one or another or
many areas “light up” and others “grow dark” in correlation with changes in thinking,
feeling and action.
The entropy first developed by Claude Shannon was formalized for use in
1948 in what was then called communication theory and now information theory. It
represented a measure of the ambiguity and uncertainty that had the potential for
being resolved by new knowledge. In this context, entropy and information were
obviously complementary descriptors. A message that informs us about which of
ten possibilities should be chosen contains less information than one that informs us
about the proper choice to be made from among a thousand possibilities. The
entropy of communication theory is a measure that is computed on uncertainty. The
information reception capacity of a system is dependent upon the amount of
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uncertainty in the receiver that pre-existed the receipt of the message. In the binary
coding scheme of digital electronic operations, the unit of information is the bit, a
choice made between 0 or 1 in the resolution of a two state ambiguity at each place
of some power of two number of places. Our relatively common computers these
days have 32 or 64 bit processors. If these 0,1 choices are made in a random
sequence in which each step is independent of the previous one, the sequential
probabilities,  � ��  � are multiplicative: e.g. the probability of getting two 1’s (heads
in a fair coin) in a row are the product of each 0.5 probability: ρ 1 = 0.5 × ρ 2 =�0.5 =
ρ 1 ρ 2 = 0.25. Using the common base ten system of logarithms to demonstrate the
algebraic fact that multiplicative probabilities are logarithmically additive (and
ignoring the minus sign that comes with making logarithms of the decimal fractions
of probability), we notice that log 10 (0.5) = 0.693147 and log 10 (0.25) = 1.386294 and
that 0.693147 + 0.693147 = 1.386294.
The dot-dash choices of Morse code machines, the go, no-go gates of
transistors, the open versus closed ion channel-mediated neuronal membrane
discharge and the left, right spins of the single electrons of today’s quantum
computers lead naturally to an information encoding of multiplicative sequences as
the sum of logarithms in base (equal to the number of available states) two, each ρ�=
0.5 choice called, log 2 (0.5) = 1, a bit. Shannon’s 1938 master’s thesis mapped
George Boole’s algebraic scheme for doing yes-no, either-or computation onto
current switching devices such that circuit closed was “true” and circuit open was
“false.” Using Boole’s laws such as “Not(A and B)” always equals “(Not A) or (Not
B)” led to schemes for circuit routing through electronic gates which also serve for
information storage in gadgets ranging from cell phone directories to computer hard
disks.
Following Claude Shannon, each logarithmically additive entropy term is
expressed as the sums, Σ ι � of its probability, ρ ι , times the probability’s logarithm,
Σ ι (ρ ι �× log 2 ) (ρ ι ��in base two. A logarithm is an exponent of its relevant base such that,
for example, the logarithm, base two, of 2 × 2 × 2, 2 3 , = 3 and 3 bits can encode
eight binary (0,1) numbers: (000, 001, 010,011,100,101,110, and 111). Shannon
used a hill-like, called convex, entropy function S (ρ)= -Σ(ρ ln (ρ)). The amount of
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information required to gain knowledge of an event is dependent upon the
probability of its occurrence. log 2 (0.5) = 1 is the maximal entropy when modeling the
equilibrium entropy of an independent random 0,1, (heads or tails) series of
informational states as might result from flipping a fair coin a large number of times.
This value would be maximal when the coin was fair, ρ(heads, tails) = 0.5, and the
entropy would be 2(number of allowed states)×0.5(probability of occupying each
state)×log 10 (0.5) = 0.693147...or in bits, log 2 (0.5) = 1.
More generally, if system’s behavior is distributed equally among its possible
states, the Shannon entropy is maximal and equal to the logarithm of the number of
defined states, for example, log 2 (2) = 1. Shannon’s classical equation about
information content says the amount of information, I = -ρ log 2 ρ, measured in bits.
The minus sign in this reciprocal relation indicates that the information content of
data, I, goes up as the probability of occurrence of the observed data, ρ, goes
down. Since soon we will be talking about brains and their various styles of
information encoded content as well as its transmission, we note the other famous
Shannon theorem dealing with limits on the channel capacity, C, for information
transport is C = Wlog 2 (1+S/N) where W is bandwidth, the range of frequencies
available for information transport, S is the strength of the signal and N is the
strength of the noise. Recall that the log 2 (1) = 0 so only the signal-to-noise ratio,
S/N contributes to the value of the product of the multiplication by bandwidth, W.
Transparent clinical examples come from studies of the perceptual and cognitive
decline in normal geriatric patients in which the range of aural frequencies (W)
heard without augmentation decreases with age as does the frequency range (W)
observed in their resting brain waves. The inattentiveness of the obsessively
worried ruminator can be used as an example of brain channel capacity being
reduced by the amount of on going head noise, an increase N, which, of course,
reduces the value of S/N and therefore C.
Measures of the informational complexity of systems in motion, in contrast
with the information content of a static equilibrium state, are of dynamical entropy.
Dynamical entropy is often called H, in contrast with thermodynamic and/or
informational entropy, S. One can begin with a representational image of the
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location, velocity and directional tendency of every point generated by a dynamical
system by an arrow on the surface of action, the manifold, of a dynamical system.
This field of arrows indicating directional and strength of motional tendencies is
called a vector field. A vector represents its location at the base of the arrow, its
velocity by the length of the arrow (called the modulus) and the direction of the
motion by the direction of the arrow. If we regard all moduli as equal to one, every
vector on the surface has the same length. The resulting graphs are called direction
fields. Looking at a stop-action photograph of any point on this surface, its
associated vector informs about where the system would take it over the next unit of
time. The whole surface can be marked by initial points, which the dynamical
systems move as they generate patterns of orbits of moving arrows in time. The
following two brain and behavioral experimental circumstances make this depiction
and its relevance to dynamical entropy more concrete.
We review in more detail the concrete and visualizable findings from
experiments requiring the quantification of characteristic patterns of motion in
animals and man. They can be embedded into a similar surface-like setting, which
might be called a behavioral manifold. For examples, my students from the past,
Martin Paulus and Mark Geyer, now Professors at the Medical School of the La
Jolla branch of the University of California studied the effects of psychotropic drugs
on the patterns made on the floor by rats of various genetic strains while they
wandered about, in exploratory behavior in a bounded space. Monitored by a video
camera placed above the ceiling less cages, the patterns made by the paths taken
by the rats over time were reconstructed as vectorial orbits on a behavioral
manifold. This manifold was then repeatedly partitioned, covered with, from just a
few large, in graded progression, to many smaller boxes, each partition composed
of rectangular lattices of a particular size. Units of time were also partitioned into
range of units from larger to smaller durations of observation. Differences in the
rat’s genetic strain as well as injections of stimulants, antidepressants or
antipsychotic drugs resulted in characteristic and discriminable path geometries
mapped onto the behavioral manifold as orbital patterns. Each path was encoded
as a sequence of size-dependent numbered boxes that were entered and occupied
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or left. The new information being generated by the pattern of spatial orbits took the
form of sequences of numbers or symbols representing the sequence of labeled
boxes. The complexity of these numeric or symbol sequences was then quantified
in a variety of ways including the use of two fundamental measures of dynamical
entropy.
One measure reflects how many new, previously unexplored boxes were
entered by the rat per unit of time. This rate represents a percent of the possible.
The second measure reflects how much of the time did the rat in each box visited
as a distribution of the probable. The rate of expansion of the possible and the
relative time in occupancy of these possibles, the probables, form the bases for the
computation of these two kinds of entropies. For example, the work of Paulus and
Geyer showed that the administration of a very small amount of stimulant drug,
compared with a salt water control, led to an increase in the first measure of the
number of new, previously unexplored, boxes entered per unit time. With respect to
the second measure, the stimulant drug augmented exploratory activity was also
more uniformly distributed over the possible boxes, making for more uniform
probability. Administration of higher doses of stimulant drugs, at a critical dose, led
suddenly to more spatially and temporally restricted and stereotyped patterns of
motion of the rats, compulsive circling alternating with frozen sniffing. Both
contributed to a decrease in the possible and nonuniformity in the distribution of the
probabilities. In man, low doses of amphetamine tend to increase the rate and
creativity of thought streams and high doses generate fixed ideas and paranoid
delusions. In the statistical approach to nonlinear dynamical systems, timedependent
generation of new possibilities is called topological entropy, H T and the
entropy associated with the distribution of probabilities is called the metric entropy,
H M. These kinds of entropies have also been used to quantitate characteristic
patterns of in human behavior as well.
We have previously mentioned these measures as used in human
experiments by Karen Selz, a Research Professor of Psychiatry at Emory University
in Atlanta. Recall that she devised a set of experiments leading to unobtrusive
measures made on human subjects by asking them to remove, as many as they
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could, the dots in a lattice, one by one, from the computer screen, by clicking on
each point with a mouse. In some experiments, after removal, the dot reappeared in
fifty milliseconds, in the “fast return condition”, or after one-second delay in the
“slow return condition.” Unbeknown to the subject, the path made by the motions of
their mouse on the computer screen over time while removing dots were
reconstructed as a path on a fine to coarse grained box-partitioned behavioral
manifold. Entropic indices of the rate of expansion of the possible, number of new
boxes entered, reflecting H T , and the relative occupancy of the partition of the
possible, reflecting H M , the distribution of probabilities with respect to the boxes,
could then be computed. For examples, Selz found that the spatial and temporal
patterns of computer mouse motions made in this dot search and destroy task
correlated highly with the subjects’ age, sex and personality types as defined by
profiles from the Minnesota Multiphasic Personality Inventory, MMPI, and the
Structured Clinical Interview, SCI, associated with the standard Diagnostic and
Statistical Manual, DSM IV. She found that subjects whose personalities were like
my high self-sensibility girlfriends demonstrated high indices of both H T and H M .
The actions of nonintegrable nonlinear differential equations, not solvable by
the usual techniques of integration, can be transformed into graphical images by
plotting their orbits in abstract phase spaces with the three physically measurable
coordinates of location x (or some other temporarily fixed value), velocity y (the rate
of change in the location or measured value) and z acceleration (the rate of change
of the rate of change in location or value) in x, y, z space. Graphical representations
of the system in action in phase space can serve in place of analytic solutions to the
equations. This idea was one of Henri Poincare’s major contributions to
mathematics and physics, and has come to be the centerpiece of the qualitative
theory of differential equations. The often point-to-point unpredictable but globally
and qualitatively characteristic geometric shapes of the orbital patterns in abstract
phase space are the objects of interest. There are visualizable representations such
as cycles as circles and statistical measures made on these objects such as the H T
and H M entropies and the in-betweenness (neither maximal nor minimal) of their
difference.
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A global statistical context for these qualitative differential systems was
inspired by the Russian mathematician, Andrei Nikolaevic Kolmogorov. In his now
famous foundational talk about the stability of classical mechanical systems in the
final session of the 1954 International Congress of Mathematics, he gave public
birth to, among other ideas, what has come to be called the ergodic or statistical,
measure theory of dynamical systems. Here, ergodic means the existence of an
invariant statistical measure on the phase space attractor of the system that can be
obtained using a variety of equivalent methods and beginning the count at any of its
points. Two phase space objects generated by a dynamical system may look
different in phase space but their statistical measures may all be the same, i.e.
invariant. These qualitative orbits in a box-partitioned space can be visualized as
Paulus and Geyer’s rats exploring a space and Selz’s path sequences of computer
screen dot quenches produced by clicking on them with a computer mouse.
A precursor of Kolmogorov’s ergodicity was the earlier ergodicity of Ludwig
Boltzmann. This describes a suitably partitioned system such that equivalent values
come from quantitating the behavior of one single orbit exploring the space of the
lattice of boxes over very long times time as those obtained from a single aggregate
photograph of all orbits run from all possible starting places simultaneously. The
ergodicity of gas-like molecular randomness implicates systems being in one of only
two possible equilibrium statistical states: measure zero (at most occupying a single
point, zero, minimal entropy) or its “complement,” full measure one (occupying all
available space in a state of maximal entropy). Joseph Goldstein, a well known
teacher of meditation, giving advice recorded in Daniel Goleman’s 1977 book on the
subject said that all methods of nirvana directed meditation amounted to “…simple
mathematics …all systems aiming for One or Zero—union with God or emptiness.”
In place of the maximal or minimal values for the H T and H M entropies of these
states of transcendence, we in the world of samsara are stuck in states of inbetween
entropy which invariant statistical measures of on phase space shapes
help quantify.
To generalize measures made on rat and computer mouse paths to more
general and idealized systems, after plotting an orbital path in a phase space, we
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may partition the space of values taken by the journey of the orbital action
generated by the equation over time with rectangular grids of increasing fineness.
The result is an equipartition of phase space such that there is at most one orbital
point in each rectangle of the grid, with, of course, many rectangles in the finer grids
being empty. This final grid partition is called a generating partition. The proportion
of the available boxes of the partition occupied by points is called its area or volume
measure. This measure has been given a variety of names including Liouville, Haar
and Lesbegue measures. If every box is occupied, it has measure one. If at most
one box, it has measure zero. If we allow partitions to be non-uniform and/or not
fine enough to be generating and apply probability weightings for how many points
fall into each particular box of the grid, the method is called the Sinai-Ruelle-Bowen
or SRB measure after Kolmogorov’s students and followers, the Russian, Ya Sinai,
the Belgian Frenchmen, David Ruelle and the American, Rufus Bowen.
Similar to the SRB measure, the distribution of box occupancy probabilities
multiplied by their logarithms and summed over all cells of the partition yields a
statistical measure that is close to the informational entropy of Claude Shannon as
described above. It is called the metric entropy ( H M = -Σ(ρ i ln(ρ i )), where H means
entropy and ρ i is the proportion of the total observations that occupy cell i of the
phase space or state space partition. It was the above noted Russian father of
modern dynamical systems, Kolmogorov, who in 1956 proved that the Shannon
metric entropy is a quantifiable invariant of systems even in very complicated
motion. Stanford University's Donald Ornstein won a Field’s Medal (the under forty
year old mathematician’s Nobel Prize) for his late 1960’s work proving that the
Shannon metric entropy, H M , was the only invariant for a large class of appropriately
defined, expansive (near by points separating in time) dynamical systems. Recall
that we refer to metric entropy reflecting the relative occupancy as probability
among the possible boxes (or states) as H M . H M is maximal when the percentage
occupancy of all occupied boxes is uniform.
IBM’s Roy Adler in New York and Brian Marcus in California, Hebrew
University’s Benjamin Weiss, Warwick University’s English mathematicians, William
Parry, Peter Walters, Mark Pollicott and others developed and proved the relevance
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of a related measure of the rapidity of dynamical expansion, the generation of new
information seen as the rate of entering new boxes of the partition, a logarithmic
rate of expansion of the possible. Counting the number of previously unoccupied
squares entered by the dynamical systems orbit per unit time over the generating
partition, for instance, yields an estimate of entropy that, as in the rat and computer
mouse examples above, is called the topological entropy, H T . H T , is about how
much new information is being generated by the system per unit time. Theorems
have been proven that H T is a maximal estimate of the global dynamical entropy
with H M proven to be a minimum estimate. Monitoring single or aggregate molecular
motion in a system with the maximum randomness of a space filling gas, we find
that, on the average, every box is entered and occupied uniformly such that H T = H M
or said another way, H T – H M = 0.
As evidenced by the above described experiments in rats and people, the
same entropic relations (but usually not with maximal or minimal measure) can be
found in biological systems. We have previously described the manifold geometry of
a generic (typical, idealized) nonlinear dynamical systems as hyperbolic defined by
the presence of simultaneous but decomposable components of the motion
including the straight ahead and round and round actions on the center manifold,
the new possibility generating, expansive, away from the center manifold motions
along unstable manifolds and the back to the center manifold, contracting motions,
along the stable manifolds. Uniform expansive and contractive influences in the flow
leads to mixing of the order of the initial sequence of the values inscribed by the
orbits. This results in maximization of the entropies and satisfaction of a
concomitant of the uniformly hyperbolic condition, H T – H M = 0.
These clean and mathematically proven findings do not hold for the quasimess
that is human neuropsychobiology. Enmeshed as most of us are in only
intermittently random or nonuniformly hyperbolic systems with the in-between
entropies of the only apparently real world of maya, H T – H M ≠ 0. How the H T – H M
= 0 of uniform hyperbolicity fails, H T – H M ≠ 0, and along with it the dispassionate
detachment of entropic emptiness and fullness, becomes a problem not unrelated to
the existence and quantitative qualities of personality styles and their dissolution
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with return toward but not reaching the maximally entropic openness, flexibility and
naïve credulousness of the in Jesus and Holy Ghost occupying transcendent
dynamical states. We are all stuck somewhere in the range of measures indicating
in-between entropies.
Further Readings for Sensual In-Between Entropies
Ecstasy in Secular and Religious Experience, Marghanita Laski, Tarcher, Los
Angeles, 1961.
The Role of Neural Plasticity in Chemical Intolerance, Barbara A. Sorg and Iris R.
Bell, Ann. N.Y. Acad. Sci. Vol. 933, 2001
The neuropsychiatric and somatic characteristics of young adults with and without
self-reported chemical odor intolerance and chemical sensitivity, I.D. Bell, C.S.
Miller, G.E. Schwartz, Arch. Environ. Health 51:9-21, 1996.
Application of entropy measures derived from the ergodic theory of dynamical
systems to rat locomotor behavior, M. Paulus, M. Geyer, L. Gold, A. Mandell, Proc.
Natl. Acad. Sci. (USA) 87:723-727, 1990.
Long-range interactions in sequences of human behavior, Martin Paulus, Phys.
Rev. E. 55:3249-3256,1997.
Mixing properties in human behavioral style and time dependencies in behavior
identification: The modeling and application of a universal dynamical law. Karen A.
Selz, UMI, Ann Arbor, 1992.
A family of autocorrelation graph equivalence classes on symbolic dynamics as
models of individual differences in human behavioral style, Karen A. Selz and
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Arnold J. Mandell, In (ed. R.R. Vallacher and A.J. Nowak), Dynamical Systems in
Social Psychology, Academic Press, San Diego, 1994.
Toward a neuropsychopharmacologicy of habituation: a vertical integration. Arnold
J. Mandell, Math. Modeling 7:809-888,1986.
Thermodynamics, Enrico Fermi, Dover, N.Y. 1956.
Thermodynamics and Statistical Mechanics, Peter T. Landsberg, Dover, N.Y. 1978.
Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, T. Bedford, M. Keane
and C. Series, Oxford, Oxford, 1991.
The Mathematical Theory of Communication, Claude E. Shannon and Warren
Weaver, U. of Illinois Press, Urbana, 1963.
Science and Information Theory, Leon Brillouin, Academic Press, N.Y. 1962.
Brain Metabolism and Cerebral Disorders, Harold E. Himwich, Williams and Wilkins,
Baltimore, 1951.
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CHAPTER 5:
SOME ENTHEOGENIC ENTROPIES
In the spring of 1968, members of my laboratory team were looking for new
brain metabolic pathways of the essential amino acid tryptophan, the dietary
precursor of the human mood, sleep and libidinal neurotransmitter, serotonin. After
struggling for several months to identify an apparently new compound, which turned
out not to be new but only new in the brain, we collected evidence for a human
brain enzyme that could catalyze the production of an LSD-like hallucinogen,
dimethyltryptamine, DMT. Tracing its metabolic origins, we found that DMT was
derived from tryptamine, a common metabolite of the essential and omnipresent
amino acid, tryptophan. This enzyme and its metabolic product were located in
highest concentrations in brain stem systems that influence the neural regulation of
the heart, blood pressure, temperature, breathing, vomiting and primitive approachavoidance
behavior. It was also found in limbic brain nuclei thought to modulate the
emotional coloring of perception and thought. Richard Wyatt, working at the
National Institutes of Mental Health found DMT in the urine of schizophrenic
humans. He also showed that DMT increased significantly if tryptamine’s normal
pathway for degradation was blocked by monoamine oxidase inhibitors, such as
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Nardil, Marplan, Eutony, Parnate and others of a then common family of
antidepressant drugs.
The presence of a DMT-generating enzyme in human brain was particularly
exciting because we knew from the work of Harvard botanist, Richard Shultes and
others, that DMT and the monoamine oxidase inhibitor, beta carboline, are
combined in a mixture of the leaves of a shrub and the bark of a vine, both
Amazonian plants, used together by the shaman of Peru, Colombia and Ecuador for
thousands of years to evoke mystical experiences in themselves. In their state of
chemically-facilitated, spiritual transformation, they were better able to engage in
healing and divination of others. More recently this and other similarly acting
biochemicals have been called entheogenic, “connecting to the sacred within.”
Consistent with our neurochemical findings in human brain, the shamanic
concoction, called by many names including ayahuasca and yage, combined the
DMT containing plant, Psychotria viridis, with an extract of a vine with the powerful
monoamine oxidase inhibitor properties of the beta carbolines found in
Banisteriospsis caapi. In 1975, working with a graduate student, Louise Hsu, we
found that the mammalian brain could also synthesize beta carbolines. This family
of compounds from the vine protects the tryptamine substrate as well as DMT from
metabolic degradation such that it could circulate in the blood long enough after oral
ingestion for enough to cross the blood brain barrier to induced prolonged and
dramatic alterations in perceptions, feelings and thoughts. In addition, the
carbolines of the Benisteriospsis component extended the time of action of DMT
beyond the 15-30 minutes of effect of DMT when injected alone in human subjects.
We found it fascinating that the human brain made combinations of DMT and beta
carbolines similar to the blend that indigenous shamamic chemists discovered as an
entheogenic from plant sources.
Ralph Metzner, in the introduction to his 1999 collection of papers called
Ayahuasca concluded that “…it is widely recognized by anthropologists as
being…the most powerful and most widespread of the shamanic hallucinogens.”
William Burrough in a 1953 City Lights published book written with Allen Ginsberg,
The Yage Letters, said that yage “…gave entrance to a city where all human
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potential is spread out in a silent market…” It was generally believed that with
adequate spiritual preparation, ayahuasca could generate transcendent states that
allowed access to ones inner being and the beings of other worlds that could serve
as sources of mystical knowledge and healing. The Shams dervish of the 13 th
Century, wandering the Turkish portion of the Silk Road, used the word sohbet to
describe the inner land of mystical conversations about mystical subjects that their
turning meditation, whirling, and the shaman’s entheogenic compounds such as
DMT give entrance.
The question was whether our finding of DMT and its human brain enzyme
had been an artifact, an accidental laboratory fluke. Members of my neurochemical
research teams at the University of California Medical Schools in Irvine and La
Jolla, notably Dr. Lee Poth, now a professor of pediatric endocrinology at the
Uniform Services Medical School in Washington D.C., demonstrated that the DMT
synthesizing enzyme existed in the brains of recent accident victims that as far as
we were able to learn from their family and social histories, had been completely
psychologically normal. More than a little bit startled by this finding and worried
about making a sensational scientific mistake, we repeated the experiments with a
variety of controls with the same findings. Though our original estimates of the
human brain enzyme concentration were on the high side, we confirmed the general
finding and published them in Science in 1969 and Nature in 1970. Our carboline
work was published in the Journal of Neurochemistry in 1975. A year or so after our
Nature paper was published, the Nobel Prize winning neuropharmacologist at the
National Institutes of Mental Health, Julius Axelrod, confirmed the presence of the
DMT biosynthetic enzyme that converted the tryptophan product, tryptamine, to
DMT in mammalian brain tissue. We were both delighted and relieved.
We speculate, perhaps too grandly, that this finding, along with the beta
carboline human brain synthesizing capacity, supplies one of many possible
neurobiological and neurochemical mechanisms for the claims of the cross-cultural
universality of mystical experience. We all had human brains with these enzymes.
The idea that the phenomena accompanying primary religious experience were
common to all cultures was a major theme of the life’s work of the philosopher-
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psychologist, William James, and was studied using fieldwork by anthropologists
such as Bronislaw Malinolowki as described in his classic book, Magic, Science and
Religion. Was this neurochemical-behavioral organization an evolutionarily adaptive
mechanism selected so that some spiritually gifted individuals self-selected from a
severely stressed population could escape and then lead the rest of us out of a
sense world that had become intolerable? Could this be an antidote for the
hopeless, without materialistic solutions and trapped in a belief system of spiritual
nihilism? Was this a brain chemical transcendence escape and spiritual delivery
system for the suprapsychological survival of those in dire need? As the 13 th
Century Islamic mystic, Jelaluddin Rumi, has written, “If a tree could fly off, it
wouldn’t suffer the saw…” and more concretely, “…if you can’t go somewhere,
move into the passageways of the self…,” a spiritual escape via a neurobiological
road to the God-space within.
What followed were a few years of occasional exploration of an “inside out”
understanding of the mystical states evoked by the entheogenic family of chemicals.
There were varieties of settings for these personal experiments. I found myself
LSD-lost, circling endlessly in the tall silence of a Northern California redwood
forest. I tried on Hunter Thompson’s mescaline lenses for the experience of Las
Vegas unfiltered. I was expertly mentored in these quests by a distinguished
collection of guides: Cultural anthropologist Michael Harner who taught me about
the yage and datura use among the shaman of the Jivaro; Social anthropologist,
Barbara Meyerhoff introduced me to the personal renewal rituals of the peyote
cactus-using Huichol Indians of the Southwestern Sonora Desert; Neurochemically
sophisticated Sidney Cohen, founding director of the National Institutes of Health’s
Institute on Drug Abuse, told me stories of his involvement with Aldous Huxley and
Barbara Brown in the Los Angeles covey of early American LSD explorers; organic
chemist Albert Hoffman, Sandoz’s designer of a series of ergot alkaloids including
LSD, told me stories of his accidental post-sniff hallucinations while returning home
on a bicycle; An anonymous group of us conducted personal experiments with
Sacha Shulgin, the University of California at Berkeley professor who first
synthesized and tested the mescaline-derived, Ecstasy series of compounds; We
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did some work with the dissociated anesthesias (producing wide awake but not
there states) having consulted with John Lilly, a brain scientist who used these
agents as a courageous self-medicating explorer of sensory isolation tanks; I met
several native shamanic practitioners including the Huichol Indian that was the
model for Don Juan in Carlos Castanada’s five volumes of pseudoethnography
written up in my essay “Is Don Juan Alive and Well?” in The Pushcart Prize of 1977.
Issues of culture and brain chemistry came together in several accounts about
entheogenic, mescaline-containing peyote use among the Huichol Indians in a book
edited by Kathleen Berrin and Thomas Seligman of the San Francisco Art Museum
called Art of the Huichol Indians.
Over these years I collected many nauseating, upper and lower bowel
wrenching and ecstatically transcendent and exhausting day-long episodes of the
angular geometries of visual pattern-generating DMT, the animistic breathing of
bush and flower breathing peyote cactus, the darkly forbidding shadows of the
psylocybin-containing mushrooms, the irreversible rocket launches into the
electrically buzzing, kaleidoscopic circus of LSD-containing vials from Sandoz and
the optimistic, trust engendering, expansively warm rush of six of Sacha Shulgin’s
gregarious, rave dancing, chlorinated, methoxylated and ethoxylated
phenylethylamines which he had, years before, synthesized for “an undisclosed
purpose” for the Dow Chemical Corporation under contract with the U.S. Army
Chemical Corps. The best known of the latter group remains part of the rave culture
as Ecstasy.
These agent’s peaks are flooded with exaggerated, caricaturizing images of
people’s faces and a belief in the mindedness of animals and even the embodiment
of inanimate things. Evoked are simultaneous and diametrically conflicting
interpretations of the same social context, heteromodal sensory fusion called
synesthesia so that sound bespoke color and smells induced music, habitual
thoughts rearranged as new ideas in what is experienced as exciting new insights,
and, most of all, that which Louis Lewin, Berlin’s early 20 th Century Freud of
psychotropic drugs in his book Fantastica, called gladness of the soul. Timothy
Leary wrote of entheogenic escape from the habitual human brain’s mental-
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manipulative and socio-sexual circuits gaining access to the rapture and ecstasy
brain pathways on the way to the new planet within.
What is seldom written about is the aftermath of chemical entheogenic
agents. After the several hours of fireworks, all of these entheogenic agents, some
more than others, gifted me with weeks to months of more self-sufficient, emotional
fullness and ease in the conduct of living that was less contaminated by narcissistic
preoccupation or defensive distantiation. I was left with increased interpersonal
sensitivity and a noticeable repair of my deficiencies in aesthetic sensibility,
particularly for the visual arts and landscapes. What were once two dimensional,
trivial, beside-the-point, scattered copses of trees and apparently casual arrays of
plant life in the Boboli Gardens behind the Palazzo Pitti in Florence, became the
grandly structured, botanical wonder of increased dimension, communicating awe
filled new perceptions of its previously unseen beauty. For the first time, I found
myself walking slowly and stopping for several minutes, wordless, spellbound, in
front of the modern art pieces of New York’s Guggenheim Museum. Lost in the
experience, I found myself exclaiming to no one in particular, “I can see!”
The delicacy and deliciousness of post-entheogenic agent’s new and
beautiful everything made me tiptoe watchfully so as not to injure an ant. Feelings of
omnipersonal kindness and generous compassion were without prideful selfreflection.
This state of grace felt like an invasion of a shimmering presence that
made contact with my other, generally unknown to me, life. It brought new
perceptions, feelings and ideas for which I was moved to give thanks. I began to
think I understood a little bit about what was meant by living in the Spirit and
merging with God. Mircea Eliade, the French, University of Chicago Professor of the
History of Religions, in his classic The Sacred and Profane, calls the revelation of
the sacred in ordinary objects, people and events an hierophany. In the state that
this requires, “…all nature is capable of revealing itself as cosmic sacrality….” The
entire world can become a hierophany with what Abraham Abulafia called an
activated mind, the Jewish soul of emergent properties called the Nefesh.
This entirely new world, Rudolf Otto in his 1917 Das Helige (The Sacred)