The Biology of Belief - Bruce H. Lipton [88]
The mathematics of fractals is amazingly simple because you need only one equation, using only simple multiplication and addition. The same equation is then repeated ad infinitum. For example, the “Mandelbrot set” is based on the simple formula of taking a number, multiplying it by itself and then adding the original number. The result of that equation is then used as the input of the subsequent equation; the result of that equation is then used as the input for the next equation and so on. The challenge is that even though each equation follows the same formula, these equations must be repeated millions of times to actually visualize a fractal pattern. The manual labor and time needed to complete millions of equations prevented early mathematicians from recognizing the value of fractal geometry. With the advent of powerful computers Mandelbrot was able to define this new math.
Inherent in the geometry of fractals is the creation of ever-repeating, “self-similar” patterns nested within one another. You can get a rough idea of the repeating shapes by picturing the eternally popular toy, hand-painted Russian nesting dolls. Each smaller structure is a miniature, but not necessarily an exact version of the larger form. Fractal geometry emphasizes the relationship between the patterns in a whole structure and the patterns seen in parts of a structure. For example, the pattern of twigs on a branch resembles the pattern of limbs branching off the trunk. The pattern of a major river looks like the patterns of its smaller tributaries. In the human lung, the fractal pattern of branching along the bronchus repeats in the smaller bronchioles. The arterial and venous blood vessels and the peripheral nervous system also display similar repeating patterns.
Are the repetitive images observed in nature simply coincidence? I believe the answer is definitely “no.” To explain why I believe fractal geometry defines the structure of life, let’s revisit two points.
First, the story of evolution is, as I’ve emphasized many times in this book, the story of ascension to higher awareness. Second, in our study of the membrane, we defined the receptor-effector protein complex (IMPs) as the fundamental unit of awareness/ intelligence. Consequently, the more receptor-effector proteins (the olives in our bread and butter sandwich model) an organism possesses, the more awareness it can have and the higher it is on the evolutionary ladder.
However, there are physical restrictions for increasing the number of receptor-effector proteins that can be packed into the cell’s membrane. The cell membrane’s thickness measures seven to eight nanometers, the diameter of its phospholipid bilayer. The average diameter of the receptor-effector “awareness” proteins is approximately the same as the phospholipids in which they are embedded. Because the membrane’s thickness is so tightly defined, you can’t cram in lots of IMPs by stacking them on top of one another. You’re stuck with a one-protein-thick layer. Consequently, the only option for increasing the number of awareness proteins is to increase the surface area of the membrane.
Let’s go back to our membrane “sandwich” model. More olives mean more awareness—the more olives you can layer in the sandwich, the smarter the sandwich. Which has more intelligence capacity, a slice of cocktail rye or a large slab of sour dough? The answer is simple: the larger the surface area of the bread, the greater the number of olives that can fit into the sandwich. Relating this analogy to biological awareness, the more membrane surface area the cell has, the more protein “olives” it can manage. Evolution, the expansion of awareness, can then be physically defined by the increase of membrane surface area. Mathematical studies have found that fractal geometry is the best way to get the most surface area (membrane) within a three-dimensional space (cell). Therefore, evolution becomes