Fractal Evolution
Copyright 1995 - Leading Edge Research Group
"A decade after Mandelbrot published his physiological speculations,
some theoretical biologists began to find fractal organization controlling
structures all through the body. The standard 'exponential' description
of a bronchial branching proved to be quite wrong; a fractal description
turned out to fit the data...." --James Gleick
In the view of the Darwinists, the endlessly exquisite designs of nature
are the result of an interplay of two factors--random genetic mutation
and Natural Selection. Genetic mutation proposes, Natural Selection
disposes.
The question of "design" in nature was one that troubled
Charles Darwin all his professional life. In the year following the
publication of the Origin, he writes to Asa Gray: "I am conscious
that I am in an utterly hopeless muddle. I cannot think that the world,
as we see it, is the result of chance; and yet I cannot look at each
separate thing as the result of design."
Darwinist Ernst Mayr, for one, is well aware of the design dilemma.
"No consequence of Darwin's theory of natural selection was a source
of greater dismay to his opponents than the elimination of design from
nature. Those who studied the countless superb adaptations of animals
and plants had been most gratified by the explanation that such perfection
was clearly the result of design by the maker of this world." In
fact, Darwin did not eliminate design from nature, as he himself indicates
in his letter to Gray. Darwin and his followers succeeded only in challenging
the traditional idea that the source of all design is God.
After citing many examples of fantastic design in nature, Mayr goes
on to say, "But when we ask how this perfection is brought about,
we seem to find only arbitrariness, planlessness, randomness, and accident...."
If Mayr and his fellow Darwinists find in nature only "arbitrariness,
planlessness, randomness, and accident" that is a reflection on
their ability, not on the capability of nature.
Today, any graduate student asked to develop a paper on the subject
of design in nature would invariably wind up looking into fractal geometry
and mathematics. Fractal geometry, as its name implies, is a geometry
focusing on the description of geometrical structures, and structuring,
in fract[ion]al space.
Until 1975, we didn't have a fractal geometry. Our only geometry was
the familiar Euclidean geometry, which goes back over two thousand years.
The Elements of Euclid (circa 300 B.C.) summarized in thirteen volumes
the mathematical knowledge of ancient Greece. Up into our own century,
Euclid's books of geometry were taken as the final, authoritative word
on the subject. Euclidean geometry deals with whole rather than fractional
realities. Plane geometry concerns planar (one- and two-dimensional)
structures, and solid geometry describes volumetric (three-dimensional)
structures.
"New geometry's always begin," writes James Gleick, "when
someone changes a fundamental rule." Fundamental supposition would
be a better term than rule. Gleick continues: "Suppose space can
be curved instead of flat, a geometer says, and the result is a weird
curved parody of Euclid that provides precisely the right framework
for the general theory of relativity. Suppose space can have four dimensions,
or five, or six. Suppose the number expressing dimension can be a fraction....
suppose shapes are defined, not by solving an equation once, but by
iterating it [repeating it] in a feedback loop."
French mathematician Benoit Mandelbrot made a number of the above suppositions,
and the result was the birth in 1975 of "fractal" (fractional)
geometry and mathematics (Les Objets Fractal). The original stimulus
behind Mandelbrot's work was an interest in irregular (seemingly "chaotic")
patterns. Cotton prices over a long period of time, frequency of earthquakes,
flooding conditions.... all seemed to occur with a regular irregularity.
What was the principle of order within the chaos?
Mandelbrot's "studies of irregular patterns," Gleick indicates,
"and his exploration of infinitely complex shapes had an intellectual
intersection: a quality of self-similarity. Above all, fractal meant
self-similar."
"Self-similarity is symmetry across scale. It implies recursion,
pattern inside of pattern. Mandelbrot's price charts and river charts
displayed self-similarity, because not only did they produce detail
at finer and finer scales, they also produced detail with certain constant
measurements...."
The physical world, the explicate realm, is structured along the lines
of fractal geometry. The basic underlying idea is the idea of repetition
of structure in different scales of magnitude. The common example is
a coastline. A photograph of a section of coastline from a blimp will
show the same ragged contours as a photograph of the whole coast taken
from a space station. A photograph of a one-foot-long section of the
same coast will also show the same contours. The various coastlines
are "self-similar," each similar to the others in shape, but
different in magnitude.
Mandelbrot and those who took up the tools he provided found endless
evidence of the fact that the creation, the explicate realm, is designed
via fractal mathematics. In light of these findings, the idea of Mayr
and other Darwinists that the perfections of nature are the result of
"planlessness" is simply ludicrous. The physical realm is
structured like "Chinese eggs," eggs nested within eggs.
"A decade after Mandelbrot published his physiological speculations,"
Gleick writes, "some theoretical biologists began to find fractal
organization controlling structures all through the body. The standard
'exponential' description of bronchial branching proved to be quite
wrong; a fractal description turned out to fit the data. The urinary
collecting system proved fractal. The biliary duct in the liver. The
network of special fibers in the heart that carry pulses of electric
current to the contracting muscles...."
"How did nature manage to evolve such complicated architecture?"
Gleick asks, rhetorically. "Mandelbrot's point is that the complications
exist only in the context of traditional Euclidean geometry. As fractals,
branching structures can be described with transparent simplicity, with
just a few bits of information...." "Fractal mathematics"
is comprised of the simple formulas by which conversions are made--fractal
to fractal.
The seemingly infinite complexity of the Mandelbrot set is based on
the simple formula z = z2 + c. Take a number, multiply it by itself,
and add the original number.
"By the 1980s," Gleick writes, "a home computer could
handle arithmetic precise enough to make colorful pictures of the [Mandelbrot]
set, and hobbyists quickly found that exploring these pictures at ever-greater
magnification gave a vivid sense of expanding scale. If the set were
thought of as a planet-sized object, a personal computer could show
the whole object, or features the size of cities, or the size of buildings,
or the size of rooms, or the size of books, or the size of letters,
or the size of bacteria, or the size of atoms. The people who looked
at such pictures saw that all the scales had similar patterns, yet every
scale was different. And all these microscopic landscapes were generated
by the same few lines of computer code."
A decade or so after the publication of Les Objets Fractal, as Gleick
observes, a number of biologists (and not just "theoretical biologists")
began the work of re-understanding the body in terms of fractal engineering.
Today, the fractal approach is being used to better understanding every
component of the human body. Neuroscientist Ary Freeman, for instance,
maintains that a kind of "ordered unpredictability" lies at
the heart of the brain's ability to perceive the world. "Studying
the electrical activity of the brains of rabbits trained to recognize
various smells, Freeman finds that the animals' brain waves shift to
a different pattern of chaotic activity as each smell is inhaled."
"Paul Rapp of the University of Pennsylvania has found similar
results in humans. When his subjects were asked to count backward from
100 by sevens, their brain-wave patterns suddenly shifted into a chaotic
state that marked intense concentration...."
The Freeman and Rapp references are from a recent article titled "The
Mathematics of Human Life," by William F. Allman. We sense Allman's
excitement as he comes to realize the full dimensions of the fractal
phenomenon: "The body's overall structure bears the signature of
the chaotic processes that shape it--right down to the DNA molecule
that serves as its genetic blueprint.... The fractal nature of DNA appears
to play a role in its ability to pass on biological information that
controls development of the various parts of the body. Because fractals
represent a midway point between randomness and predictability, DNA's
fractal structure may represent a compromise between encoding the maximum
amount of information, while still being extremely resilient to damage...."
The Work of Dr. Bruce Lipton
In the early eighties, the Darwinian orthodoxy still reigned supreme,
and consequently it was assumed that the secrets of biological evolution
would be discovered as the result of research in genetics. Most biologists
interested in evolutionary process were guided (or misguided as it were)
by the doctrine of the primacy of the DNA. For these researchers, fractal
geometry was of interest as it might apply to understanding the nature
and workings of the DNA. The above reference to the "fractal nature
of DNA" suggests the sort of conclusions that came from the orthodoxy.
Among the more unorthodox biologists interested in fractal mathematics
was University of Virginia-trained anatomist and cell biologist Dr.
Bruce H. Lipton. As indicated in earlier chapters, improvements in electron-microscopy
during the fifties had made it possible for researchers to get a really
look at the cellular membrane. Lipton's career as evolutionist began
when he realized that consciousness is not something encoded in the
genes (the position of the orthodoxy) but something that is "transduced"
by the IMP system of the cell membrane.
The biological basis of consciousness, Lipton maintains, is the IMP
(integral membrane protein) unit, a stimulus-response mechanism in which
the "receptor" is the stimulus receiver and the "effector"
the response activator. "So," Lipton says, "we get into
a really interesting understanding of consciousness here. The fundamental
unit of consciousness happens to be a protein receptor and protein effector
in combination. If you separate either of these two proteins from each
other, then the unit of that perception is not made. If you cut the
receptor off, no signals come in, or if you cut the effector out then
there's no response to the signal. In either case, you break the perception
pathway."
The biological primacy of the membrane over the DNA is demonstrated,
Lipton indicates, by the simple fact that if the IMP receptors are cut
off, then the cell goes comatose and dies, whereas if the nucleus is
taken out of the cell, the cell continues to operate normally, until
such time as it requires new parts. New parts are supplied by the cell's
Parts Department--the genome. Consciousness does not originate in the
genome (the "ghosts in the machine" hypothesis of the Darwinists),
it originates in the environment; it is transduced (processed) by the
cellular membrane, and various of the signals that are so processed
activate creative processes in the genome. If we view the cell as itself
a stimulus-response mechanism, a kind of super IMP, then the cellular
membrane would be the stimulus-receiver component and the genome the
bottom-line response component.
By consciousness, we refer to a process that occurs in any organism,
from the prokaryotic cell to the human being--the process of receiving
signals (from outer environment and inner domain) and translating those
signals into appropriate biological responses. Clearly, as Lipton indicates,
there is a wide spectrum of awareness, "from the hypothetical organism
that can see one percept--meaning it would have just one receptor and
effector, so it can see only one thing, to a human being, who has an
enormous range of awareness and enormous versatility in terms of response."
In keeping with orthodox doctrine, many biologists define consciousness
as a strictly human phenomenon. That is not our definition here. There
are great differences between the signal reception-response expressed
by a unicellular organism and the signal reception-response expressed
by the human being, but these differences do not justify the hypothesis
that there is no relationship between awareness at the cellular level
and awareness at the human level. Indeed, from the point of view of
methodology, such an hypothesis--a "negative hypothesis"--is
invalid. It's possible to prove that which is, but how is it possible
to find evidence for the non-existence of something? "God does
not exist, and here's the proof...."
If Darwinism should have taught us anything, it is the fact that evolution
expresses continuity with change. First there is a something, and then
the something becomes something else. The exact nature of the something
else is determined by the nature of the something and by certain other
factors that come into play to modify the something. By the standard
of continuity with change, so convincingly expressed by Darwinism, we
would suppose not that human consciousness is a "special phenomenon"
(an idea which "smacks of" the Biblical doctrine that man
is a special creation), but that human consciousness is an evolved form
of lower consciousness.
Our presumption is that human consciousness is an evolved expression
of cellular consciousness. That presumption is a starting point, and
not necessarily the best possible starting point. It may be that Itzhak
Bentov is correct in his understanding that we humans operate via two
distinct consciousnesses--the rudimentary consciousness (the collective
cell consciousness) and the higher consciousness, an emanation of our
higher selves. In our present context, however, the main focus is on
specific means by which organisms became "smarter."
Means of Cellular Consciousness Expansion
Lipton identifies three primary means by which consciousness evolved,
from unicellular consciousness to human consciousness. The first means
was increase of cellular membrane surface area. Nature had to figure
out how to make the prototype cell (the prokaryote) into a smarter cell--a
cell with greater consciousness capability. Again, the cellular mechanism
of perception is the IMP network. IMPs require access to the external
environment and to the inner domain, and thus they cannot be stacked.
The cell membrane contains only one layer of IMPs. This means that if
the IMP (consciousness) capability of the cell is to be increased, then
the surface area of the membrane must be increased.
Expansion of cell membrane surface area was accomplished in two ways,
through the development of an internal skeleton (the prokaryotic cell
has an exo[outside]skeleton) and through the internalization of all
systems not requiring a face-to-face contact with the external environment.
In the case of the prokaryote, all systems (including the DNA) are on
the membrane surface; in the case of the eukaryote (final stage cell),
only the "nervous system" is on the surface. The other systems
are internalized as organelles.
How are organelles formed? Lipton: "In evolution, functional groupings
of plasmalemmal [membrane] IMPs invaginated and detached from the cell
surface. These internalized portions of the plasmalemma provided for
the formation of discrete membranous organelles, including the nucleus.
Organization, functional integration, and mobility of the organelles
was provided by the cytoskeletal matrix."
The Integration of Outputs
What the evolution of consciousness next requires, as part of what we
might call the "membrane expansion program," is the development
of the optimal program for the integration of inputs. The IMP receptors
receive signals (inputs) and the effectors activate the output functions
that transduce the signals into behavior. In addition to receptors and
effectors there is an intermediate protein called a processor protein,
or "G protein," Processor proteins interface between receptors
and effectors, and given their positions they have great potential for
directing and re-directing incoming frequencies. In the words of Bruce
Lipton: "A processor can hook a receptor to one output, and another
processor can hook the same receptor to a different output--so that
one incoming signal can be split by the processor into multiple functions.
Over evolution the processor proteins are co-ordinated, or co-ordinate
themselves, in such a way that the processor sub-system has tremendous
versatility in terms of its ability to 'get the most' out of incoming
signals. The sub-system might be able, for instance, to use just one
incoming signal to provide a wide variety of biological functions."
What the processor protein sub-system represents, Lipton says, is "a
mechanism of expanding the consciousness not just by increasing the
numbers of receptors and effectors, but by integrating them into functional
biological repertoires."
The Fractal Ladder
Once nature perfected the cell, which is to say maximized its capability
for receiving and processing signals, then there was, according to Lipton,
a momentary pause in the evolutionary process. If nature was to continue
with the work of building greater and greater consciousness capabilities
into the biological realm, she had to come up a new format. The cell
format had been completed. What would be the next step? What was the
solution that nature came up with?
Dr. Lipton recalls the moment in 1983 when he discovered the answer
to that question: "I was sitting in my laboratory looking at a
eukaryotic cell through an electron microscope. I was reiterating in
my mind the common understanding that all the physiologic systems that
can be found in the human being are in the eukaryotic cell when it really
struck me.... the cell I was looking at was a fractal of the human being.
Alternatively, the human being is a fractal of the cell--a version on
a greater order of magnitude." From that moment, Lipton the anatomist
and cell biologist became Lipton the evolutionist.
"Evolutionary process is not that very very long uninterrupted
upward inclined plane that the Darwinists suppose it is," Lipton
says. "In terms of simple structures, evolution is more like a
ladder--a fractal ladder which takes us, 'us' being the material realm,
into higher and higher consciousness. The single cell--from prokaryote
to eukaryote--is one rung of the ladder. After this rung was completed,
nature took a bunch of state-of-the-art [eukaryotic] cells and combined
them into the first multicellular organism. That first organism was
the beginning of a new fractal rung, a rung that is completed with the
completion of the human being. We humans are the eukaryotes of our fractal
level."
In the years following his realization, Lipton accumulated more and
more information supportive of the hypothesis that fractal mathematics
and geometry are at the formative heart of biology and evolution. "The
story of evolution at the level of the single cell is largely the story
of cell membrane expansion," Lipton says. "The more membrane
surface, the more IMPs can be packed in. At the level of the multicellular
organism, the maximizing of cellular membrane surface area is achieved
through 'fractal packing.' The way to get the most surface area into
any given three-dimensional space is by means of fractal structuring."
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The third primary means of consciousness expansion, Lipton reasons,
is the combination of fractal rung end products into the proto-products
of the next fractal step. The eukaryote is the end product of the single
cell fractal rung. When it was completed, the next step was the combination
of eukaryotic cells into the first multicellular organism. Human beings
are the end-products of the multicellular rung. What marks the completion
of this rung? Level of consciousness is the measure. Probably, the key
marker of completion is the development of "creator consciousness,"
the understanding that we "create our own realities."
Currently, we (humans) are very much in the process of discovering
the facts of our "creation consciousness," all that to do
with the various programs (paradigms) on which we run. The book you
are reading at this moment participates is this discovery process. What
we call Darwinism is a basal paradigmatic program, one on which Western
civilization has operated on for over a hundred years. It is not so
much scientific program as a political program. If the masses are convinced
that existence is without purpose or plan, that "anything goes"
and "anything can happen," then of course what's needed is
strict top-down controls. Thus we have the so-called "New World
Order," which is understood by many as an elitist conspiracy to
control the world through control of economics, politics, and ultimately
genetics and thought.
In endeavoring to explain the origins of New World Orderism, critics
invariably point to secret societies, some of which have been around
for a very long time. The bottom-line source of whatever problems we
might have as a civilization is the basal paradigm(s) we operate upon.
Look at the paradigm, not at the people.
People are in a real sense merely puppets of their paradigms. At least,
this has been the case until recently. Now, we as a civilization seem
to be really getting the idea that we and the creator energy are in
some sense synonymous. Yes, we are fractals of the Creator. This is
the meaning of the idea that man is made "in the image" of
God. This is the message of Christ (and of other great spiritual leaders)--a
message that humankind was not ready to receive, not until now.
Embracing the understanding that what we call physical existence is,
as it were, computer modeled by means of fractal mathematics is a key
to the reconciliation of Western religion and science--of metaphysics
and physics. Whatever label we might care to give the implicate order
doesn't really matter, so long as we have a reasonably accurate understanding
of "the way it all works." The Christ message and the New
Physics message point in the same direction, toward "participatory
Creatorism."
Another important implication of fractal biology and evolution is that
at long last, we have solid support for the Gaia hypothesis that the
planet is one organism. The human being is a fractal of the single cell,
the planet is a fractal of the human being. If existence is structured
along fractal lines, then it is very difficult to avoid the conclusion
that Earth is a single organism.
If our planet is a single organism, then what is Homo sapiens? What
is the role of humans? As suggested earlier, the probable role of humans
with regard to the planet is akin to the role of immunity cells in the
body--"to serve and protect." The Biblical idea that humans
are meant to be the "stewards" of the planet is an early (and
very correct) expression of the understanding that humans are immunity
cell equivalents.
It's important to note that immunity cells are not simply the cops
of the body. They are, in the words of Bruce Lipton, "the cells
of evolution." They have the ability to embrace the new things--the
unknown--to learn those new things. They are the experts -- the Sherlock
Holmeses. Further, they are little creators .... the creators of genetic
blueprints for organisms that can protect the body against antigens.
If we are the protectors, it is certainly incumbent on us to complete
our training soon. We may already be in the process of being tested.
Not long ago, I attended a lecture by a most colorful and gifted Hopi
by the name of Robert Morning Sky. Morning Sky claims that his grandfather
and five other young men were the rescuers of an extraterrestrial whose
ship crashed in August of 1947, not long after the famous Roswell crash.
From this alien, Morning Sky says, much information was learned as to
the true history of this solar system and this our planet.
"Star Elder" told the young men who rescued him (all from
different tribes), that the gods of old, the "olden gods"
of Sirius and Orion, are coming back to renew their claim of ownership
of Earth (Terra), and to renew their claim of mastery over humankind.
If we humans do not know who and what we are, then we will continue
to be what we've always been--farm animals. An interesting story....
incredible perhaps, but interesting in its timing. Just as we humans
are coming to realize who and what we are, we are going to be tested
by the appearance of some very interesting extraterrestrial "antigens."
What will these antigens say when we as a civilization have gone beyond
master-slave games into the realization that we are the planet? In the
words of a popular song, "we are the world." Probably, what
they will say is, "We're certainly glad you had the smarts to figure
that out. In that you're evolving quite nicely now, we won't have to
re-cycle you and start all over. Welcome to the association of gods
[biological entities that understand they are creators of their reality].
Do you think you might have a bit of space here or there so we could
set up a liaison office?"
