. . Darwin's theory of evolution is based on his study of speciation, the appearance of new species. If he had had at his disposal an electron microscope, undoubtedly he would have based his theory on study of the simplest organisms -—the unicellulars. Currently, it is the cell biologists who stand at the leading edge of evolutionary science. Two, in particular, are worthy of very close attention: Dr. Lynn Margulis, whose theory of cellular evolution by means of serial endosymbiosis has successfully run the gamut of peer protest and won recognition as most certainly true; and Dr. Bruce Lipton, whose theory of cellular evolution by means of membrane expansion, is known to thousands through articles and lectures and is about to make its debut in book format.
. . As Margulis has already been discussed, we go directly to the "fractal evolution" of Lipton. The term fractal, a contraction of fractional, derives from the "fractal geometry and mathematics" gifted the world in 1975 by Benoit Mandelbrot. Prior to 1975, our one and only geometry was Eucidean, which dates back to 300 B.C. . Euclid's geometry is a geometry of whole integers; Mandelbrot's is a geometry of fractional space --the space between whole integers.
. . Whether you're conscious of it or not, you are quite familiar with fractals and have been ever since you were a child. Remember a time or two when you tossed a stone into a pond? When you did this, you observed that when the stone plunged into the water, "ripples" were created. Each ripple had the very same shape as the other ripples, but a different magnitude, right? Each was thus a fractional version of the other ripples, or "fractal." Ripples are water-fractals. Altogether, the ripples formed what is called a "set."
. . Fractal mathematics is comprised of simple formulas by which conversions are made -—fractal to fractal. The seemingly infinite complexity of the famous Mandelbrot set is based on the simple formula z [arrow pointing right] z2 + c. Take a number, multiply it by itself, then add the original number. (Gleick, 227)
. . Fractal mathematics made possible the art of computer modeling. It also made possible the new science called Chaos theory, the science of finding regularity in irregular, seemingly chaotic patterns.
. . In 1982, Mandelbrot published his second book on the subject of fractal design --The Fractal Geometry of Nature. This book demonstrates that the physical world is modeled by means of fractal geometry and mathematics. The modeling involves the endless repetition of self-similar structures in different scales of magnitude. For example, consider a coastline, any coastline. A photograph of a section of this coastline taken from a blimp will show the very same ragged contours as a photograph of the whole coastline from a satellite. What's more, a photograph of a one-foot section of the coastline will show the same contours shown by the other photographs!
. . Soon after publication of The Fractal Geometry of Nature, many biologists, including Bruce Lipton, began looking for evidence of fractal design in their specific fields of interest. "Some theoretical biologists", writes Gleick, "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...." (Gleick, 109) By 1993, fractal mathematics was being called "the mathematics of human life." (Allman, 84-85).

I’ve written about and discussed Lipton’s fractal evolution for nearly ten years. In discussion, every time I pop the phrase “fractal evolution”, I get blank stares.
. . In times past, I found myself having follow up with a briefing on fractal geometry and mathematics, much like the one above, and then launch into a mini-dissertation on bio-construction that went something like this: “The DNA strands are one-dimensional, okay? They are strings coding design patterns; strings are considered lines, lines are considered one-dimensional. Now … how does nature manage to convert one-dimensional design patterns into full-blown three-dimensional structures? Answer: By employing fractal geometry and mathematics -—the same mathematics used in computer modeling.”
. . “Okay”, the listener would say, “but what the heck does that have to do with evolution?”
. . I would then begin another dissertation … until, one day, it occurred to me that I could simplify, and clarify, my presentation, greatly, by describing the Lipton theory as “evolution by means of intelligence expansion”. That seems to make instant sense to people, no doubt because it’s in accord with what most people (Darwinists excepted) believe: Evolution is all about increasing intelligence.
. . “How is this expansion accomplished?”
. . “In Lipton’s theory”, I now explain, “the basic physiologic units of perception, or intelligence, are protein complexes embedded in the cellular membrane. These protein complexes are about seven nanometers in length; the complexes are about seven nanometers long, which is quite fortunate, as in order to do their thing, they need to interface with both the external environment and the inner domain of the cell. The story of the expansion of intelligence, at the cellular level, is the story of membrane expansion….”

The very first unicellular to appear on Earth is called the prokaryote, which means "without a nucleus." Many millions of years after the prokaryote appeared, the eukaryote arrived on the scene. The most apparent difference between the prokaryote and eukaryote is size. The eukaryote is thousands of time larger. The evolutionary significance of this difference has nothing to so with size per se, and everything to do with extent of membrane surface area. Why is membrane surface area such an important factor?
. . "The greater the membrane surface area", Dr. Lipton states, "the smarter the organism." In order to fully appreciate this statement, we need to look at the reasoning behind it....

(1) "Consciousness", Lipton writes, "is an intangible conceptualization of awareness and as such it is very difficult to define. Usually, the term conjures up the idea of human consciousness. However, human consciousness, in all its various degrees, would have to be considered at the upper end of the evolutionary biological awareness spectrum. To understand consciousness, the best starting point would be at the simple end of the spectrum -—the study of cellular consciousness. As physics tells us that frequencies are the 'stuff' that life is made out of, and that everything existing has its own specific signature vibration, the question becomes... how does a unicellular perceive frequencies? -—and how does it grasp frequencies? Consciousness implies grasping something."

(2) "Embedded in the basic membrane is a vast network of integral membrane protein complexes, or IMPs. This network is the neurological system, or brain, of the cell. Its job is to go shopping in the Environmental Supermarket and to acquire all of the groceries et cetera that the cell needs for survival and reproduction."

(3) "The standard IMP complex contains two components --a receptor and an effector. The receptor looks something like an antenna. If you were a microscopic observer standing on the surface of a cell, you would see around you a forest of strange antennas. These are the receptors. Each of them is tuned to identify a specific frequency in the environment. When a receptor identifies its target-frequency, it reconfigures itself so that it can grasp --capture-- the frequency. The reconfiguration process mechanically activates the effector component of the complex, the job of which is to get the captured frequency into the inner domain of the cell, a process called transduction. The receptor gets the goods, and the effector puts them in the cupboard."
. . "In short, the IMP complex is the biological basis of consciousness, defined here as awareness of the environment. By environment, I mean both external environment and inner domain—invironment. There are some IMPs which read invironment."

(4) In order to do their jobs, the IMP complexes must have access to both the environment and the invironment. Thus, they cannot be stacked. Thus... any given section of membrane surface can contain only a specific number of IMPs complexes. Thus, if Mother Nature wants to make a unicellular into a smarter unicellular, she has two options --utilize the outer membrane surface more efficiently, or increase membrane size."
. . "In the evolution of the prokaryote into the eukaryote, both options are employed. The prokaryote carries its organelles and genetic strands on the surface; in the case of the eukaryote, however, organelles and genome are internalized, and so all exterior membrane surface is available for IMPs."
. . "The prokaryote has an external skeleton, exoskeleton as it is called. In designing the eukaryote, Mother Nature devised an internal skeleton (endoskeleton), which meant the unicellular was no longer restricted by a hard encasement. The eukaryote is thousands of times bigger than the prokaryote, and that means a tremendous increase in membrane surface area, i.e., there's a whole lot more room for IMPs. And that means, of course, a much smarter unicellular. If the prokaryote is John Doe, the eukaryote is R. Buckminster Fuller."

What about endosymbiotic merger? This would be a third option --a fast-track means of cellular intelligence increase. The Lipton and Margulis theories appear to me to be quite complementary.

In sum: "A unit of perception in a biological membrane processor is represented by a single gate/channel complex --the IMP complex. In computer processes, a single gate/channel complex is referred to as a bit, which coincidently represents a fundamental unit of computer information (awareness). Consequently, a biological unit of perception is structurally and functionally equivalent to a computational bit.
. . "The information handling power of a processor, be it a biological membrane or computer chip, is in large part determined by the quantity of receptor/channel complexes (IMPs and bits, respectively). Evolution, concerned with increasing awareness, reflects a greater ability to read and appropriately respond to environmental information. By definition, evolution would then entail the accumulation and integration of perception units. IMPs are discrete measurable elements limited to a monolayer within a two-dimensional plane of the membrane. Consequently, awareness, related to the quantity of IMPs complexes, becomes directly proportional to membrane surface area. Evolution is physically linked to an increase in membrane surface area."

Strange as it might sound, Dr. Lipton is the first modern evolutionist to validate the common belief that evolution is synonymous with the increasing of intelligence. Darwinists never made this equation. For Darwin, all that evolution meant was "descent with modification." As Stephen Jay Gould remarks, "Darwin explicitly rejected the common sense equation of what we now call evolution with any notion of progress." (Gould, 36) Indeed, Darwin "maintained that evolution has no direction; it does not lead mentally to higher things. Organisms become better adapted to their local environments, and that is all...." (Gould, 13) The rejection of the equation of evolution with greater intelligence was continued by the neo-Darwinists.

One day in 1983, Dr. Lipton was in his lab viewing a unicellular through an electron microscope, when lightning, of the cognitive kind, struck. "The familiar fact that the unicellular has all the physiologic systems that a human body has crossed my mind, when, suddenly, it hit me... the cell is a fractal of the human body!"
. . A geometrical fractal is described by the formula "same shape, different magnitude." What Lipton discovered may be termed "biological fractals." The formula for a biological fractal: Same bio-system, different level of complexity. The importance of Lipton's insight becomes clear when we recognize, as he did, that the cell-human body fractal set can be expanded to include the planet itself. The single cell, the human body, and planet Earth form a bio-fractal group that may be called "the Gaia set." Lipton had come up with a proof of the Gaia hypothesis, or Gaia theory as it is now called.
. . The characteristics of any given fractal are exhibited by all the other fractals in the set. Thus if we say that the human being is singular and conscious, we would have to conclude that the single cell and planet are also singular and conscious. What are human beings within the greater body Earth? Lipton's suggestion is that they are the planetary equivalents of IMPs.

Let us back up a bit, to 1994…. Dr. Lipton and I are discussing the fractal nature of nature. As an historian, I’m always interested in the political implications of theories, especially theories of biology and evolution, which serve as base references for the life sciences (medicine, psychology, etc.) and for the social sciences. I ask Lipton to comment on the social implications of fractalism, and his response runs to some twenty transcribed pages. The following are excerpts from that response:

* “Fractal geometry is very interesting in that by looking at any one particular level of the nesting, you can identify information in regard to the structure or appearance of levels in orders of magnitude much greater or orders of magnitude much smaller than that you are looking at. The repetition is very important because it provides information as to precursor nests and, actually, nests that will come in the future!”

* Understanding the fractal design of nature is critically important. By understanding, for example, the structure of the cell membrane and how it works, I can understand the structure and function of what we call in biology an epithelium. That’s a community of cells which form a membrane. Their functions are exactly the same. Their structures are not exactly identical, but they are closely similar. And if we can talk about how a cell is mirrored in a multi-cellular organism, we can also employ the fractal understanding to perceive how human society represents a fractal image of the cell or body, and, using the precursor models of cell and body, we could suggest how societal organizations could be maximized in terms of efficiency and in terms of goal fulfillment, the primary goal of all life being to increase intelligence…. Therefore, with the understanding of fractal evolution, we will be able to move more quickly in the direction of growth and go to our next evolutionary leap without a lot of side-stepping and back-stepping. Fractal evolution offers real guidance, in other words. Darwinism, which is based on randomness, does not.”

* “Randomness is why we are in so much trouble now. Our standard theory of evolution, based on randomness, offers us no ability to predict. Evolution based on fractal geometry is, of course, predictive because the structures of the nests [in the fractal set] are all self-similar.”

* “Fractal geometry lies somewhere between two-dimensional and three-dimensional geometry. Well, this is really very significant because if you understand the fact that awareness begins in the two-dimensional realm [cell membrane] and then gives birth to three-dimensional structures, you can grasp more easily the understanding that everything comes from consciousness. Consciousness drives biology, not the other way around.”

It was Itzhak Bentov would first suggested, I believe, that the universe itself might be a humongous single cell within a much larger organism. Can the Gaia set be expanded to include the entire universe? If so, we then have a proof of the holographic theory of universe. "Holon" is a word coined by Arthur Koestler to describe a microcosmic piece of a macrocosmic whole. What is a holon but another name for fractal?
. . If the universe is a gigantic cell, then it, too, has a membrane loaded with the universal equivalents of IMPs. As we know from the astrophysicists, the universe is continually expanding. As we know from Dr. Lipton, membrane expansion means increasing intelligence. Our universe is becoming, moment by moment, more and more intelligent.
. . What about us? Are we holons of the universe growing in wisdom? -—which is the mark of successful consciousness processing. Or are we failing to measure up to the evolutionary work at hand? --and thus losing our "fitness" to survive.

Time will tell.

Copyright TD Hall 2003
. . This essay is extracted from a soon-to-be-published book by the title Over the Bones of the Dead —A New Look at Evolutionary Science.

Direct comments and inquiries to halltheodore(at)hotmail.com