The work of the Embryo Geometry Lab presents a model solution to major issues confronting science:
How does Nature form the animal and plant body?
By what quasi-miraculous means is a single egg cell transformed in a few hours to the embryo of mind-boggling complexity?
What is consciousness?
How can the claim to decoding the very secret of life be expressed without the taint of braggadocio? Indeed, many investigators have hitherto laid claim to the same mystery only to disappoint science with the failure to complete the train of logic that must constitute proof of principle. These include Darwin, Thompson, Turing, Watson and Crick, who have each presented a possible, not implausible system that could account for living form. Yet, none of these scientists substantiate their claim. Biological science has conquered the mysteries of the DNA molecule and commands the understanding of the physiology and pathologies of the living body yet is at a loss to account for the origin of the structure of the living organism beyond the declaration that we are enlargement of our embryo.
While simple microscopy permits embryologists the clear observation of the successive cleavages of the egg cell to form a ball of cells called the blastula, Nature contrives to veil the succeeding step called gastrulation from prying eyes. The hundreds of transparent cells comprising the blastula are seen to erupt in chaotic motion, as incomprehensible as a dog fight inside a burlap sack. After a few days, the embryo, ancestor of the fetus appears suddenly, fully formed, much as the photographic image occurs suddenly in the exposed plate in the tray of developing chemicals. While the photographer understands what is happening, biological scientists today have no idea what is directing the quasi-miracle of gastrulation. Consequently, science offers no explanation for the structure of our bodies. Our work shows, in a set of mechanical drawings, how the body structures and surface patterning of virtually all plant and animal life are formed.
Plant and animal life occurs and persists based on the curious universal property of living tissue to reproduce itself. Wounds heal, broken bones repair, amphibians can regrow lost limbs. Stick a twig into the earth and a whole tree will eventually appear. The property of regeneration generally claims that a sample of tissue, however small, from any part of the living complex organism, can reproduce the entire body. The single egg cell knows how to produce any one of the millions of species.
The life story begins with these simple acts: the egg cell bisects three times to create a cube of eight cells. Whereupon each of the eight repeats the drill, forming a cube of cubes, and then a cube of cubes of cubes–an archetypally perfect fractal. With this axiomatic given the following pages spin out the corollary consequences that provide working blueprints for virtually all living phenomena of form.
The elegantly simple account of this mystery is based on elementary principles of geometry and mechanics that govern the stacking of spheres, i.e., the sequence of 1, 2, 4, 8, 16, 32, 64, 128, 256…culminating in the embryo. Embryonic geometrical order derives from the mechanical law that cells cleave in a plane 90 degrees from the previous cleavage, hence three cleavages make a cube, and the next three cleavages make a cube of cubes.
What makes the story interesting is biodiversity which ensues because the cells do not split equally nor split completely, remaining connected by microtubules. Inequalities in the first three cell cleavages create vast deformations down the line. This thesis demonstrates how the stacking of cells by these givens generates the initial complex structure called the blastula, a hollow ball of cells comprising a multicell membrane bristling with rows of periscope-like extrusions from the inner layers, each bearing a simulacrum of a video camera that can project images of the environment onto the inner walls. The balloon-form blastula will burst and shrivel into the embryo. We therefore descend directly from a mechanical device. We lay claim to this predecessor of the embryo as the consciousness machine.
How is it that the simple model described by our lab cannot be directly observed by embryologists? Contrary to the initial events presented in the model, the first dividing cells are observed to assume no structure until they are in their hundreds. This embarrassment can provide grounds for the skeptical reader to doubt the entire premise, rightly proclaiming what they see is nothing like what I describe.
The answer lies in the remarkable phenomenon called heterochrony, that guides the progress of evolution, claiming that over eons the events of embryological development change the order in which they occur. Events that occur twice a day for a hundred million years learn the drill so well that complex structures can be self-assembled in the absence of preceding causes. Language is an example of this process. We don’t think of grammar when we speak.
So it is that the blastula, a ball comprising a thousand cells, can suddenly repeat the form of a cube in remembrance of the first three cleavages. Heterochrony uses the ample asset of vast periods of time to encode the forms of the first few cell subdivisions to be expressed later in the development of the embryo.
We Do Not Know How We Are Made
Human curiosity demands an account for everything. Indeed, historians and scientists have come to explain how every material artifact on earth and in the universe has come to be, but for one notable exception–human beings: we do not know how we are made.
The complex structure of the human body and the rest of the forms of nature are taken for granted. When asked how we are made, biologists sheepishly refer to the DNA molecule, saying it makes structures randomly, and paraphrasing Darwin, some, by chance, survive because they are useful at some tasks.
Natural selection has given way to mechano-biology, which holds that shapes and forms of nature arise from patterns that occur during the formation of the embryo. The embryo is formed in the event called gastrulation, but the transparency of the microscopic membranes makes it frustratingly impossible to observe what is going on, comparable to manufacturers who hide secret processes.
The Principles of Embryo Geometry
Embryo Geometry is the mathematical/biological discipline that seeks to account for the shapes and forms of the complex plant and animal body forms. The premise of Embryo Geometry is that the path from the single cell to the complex animal and plant body is predictable by the study of the patterns emerging from the geometrical consequences of the splitting of the egg cell. The phenomenon can be called scalar self-same enlargement, claiming that the complex adult body is an enlargement of the configurations assumed by the first few cell divisions. Each side of the bilaterally symmetrical animal body is the parallel enlargement of the two halves of the first cell division. Similarly, the head/abdomen, back/belly configuration results from the next two divisions.
The geometrical given of cell division dictates that cleavages occur in a plane ninety degrees from the previous cleavage. We instinctively follow this rule in cutting an orange by alternating the axis of the resulting halves, quarters and eighths. The principles of embryo geometry derive from these simple axioms.
Buildings are constructed from pictures called blueprints, depicting the sequence of stages in the construction. Embryo geometry is likewise pictorial, comprising animated sequential drawings from a single cell to the complex structure, each stage depending on and caused by the previous stage, in the process called epigenesis.
If, as demonstrated above, my embryo is a mechanically derived contraption, then I must be a machine of the AI species, programmed by eons of human cultural information.
Embryo Geometry
The basic elements of the geometry of Euclid are the point and the line, from which axioms are set forth which logically predict the complex forms useful to architects and engineers. The fundamental element of embryo geometry is the cell–a microscopic bubble consisting of a membrane made of molecules called lipids.
LIPID UNIVERSE
The cell is a bubble possessed of the property of alternating growth and bisection, thanks to the properties of the lipid molecule that makes up the membrane of all plant and animal cells.
Carbon, element number six in Mendeleev's periodic table, is possessed of the unique property of forming chains, for which it is granted its own study called organic chemistry. A chain of eight carbons is octane, or gasoline. The lipid molecule is a chain of nine carbon atoms with a greasy end and a watery end bearing an oxygen atom. This configuration results in the property of lipid molecules to line up like matchsticks in mats that expand by intercalation, i.e., all over, at once, by the insertion of new molecules into the sheet, like cards in a deck. When sheets of lipids form a bubble, the bubble will grow all over at once until it reaches a certain size when it will split in two–voila–the cell, and life. Life is the crystallography of lipid molecules. Lipids are to life as water is to snowflakes.
GASTRULATION LAID BARE
Upon fertilization the oversize egg cell undergoes the process called reduction-division where sequential bisections result in a ball of microscopic cells called the blastula, which will shrivel into the structure called the embryo. The transparency of the cell membranes makes it impossible for the microscope to resolve one layer from the next in the process of embryogenesis called gastrulation, which therefore cannot be directly observed and remains unknown to science.
PREDICTIVENESS OF EMBRYO GEOMETRY
Embryo Geometry is the discipline that purports to provide a model solution to the mystery by proposing a plausible account of gastrulation based upon Euclidian-style logic. Embryo geometry lays claim to the go-to explanation of virtually all phenomena regarding shape, form and structure of the living body, including, to begin with, the reason plants grow vertically while animals grow horizontally, why birds' eggs are so perfectly egg-shaped, why both vertebrates and insects alike have a head, body, and jointed segmented limbs, why turtles and armadillos have shells, why snakes have no limbs but can swallow an egg, why life surfaces bear gorgeous patterns of stripes and spots.
CELL CLEAVAGE
The fundamental active force of embryo geometry is cell cleavage, the alternating growth and bisection of the cell, seen as a property of space, in the consecutive bisections each ninety degrees from the previous. Since space is three dimensional the three bisections literally return to square one. Cell bisections are quantified in rounds of three, each creating a cube of eight cells. The living body is a cube of cubes of cubes etc. NB: this structure is, by definition a fractal–more about which is to follow.
CUBISM
For the first few billion years, cells divided completely, each daughter cell going its own way, the primeval pond inhabited by one-cell creatures like bacteria and amoebas. Later the anomaly of incomplete cell division occurred where the two daughter cells remained connected by a thin capillary tube and served to conduct fluid between them, creating complex structures as they subdivide. Pressed together the daughter cells are flat on one side, causing the next cleavage to bisect in a plane at right angles to the last. Three cleavages make an eight-cell cube. The eight-cell cube becomes the fundamental crystal that guides the construction of the subsequent massive complex body form.
MORPHOGENESIS
The proposed model provides the path from the single cell to the complex animal and plant body is predictable by the study of the patterns emerging from the mechanical and geometrical consequences of the initial sequential splitting of the egg cell.
The cubical geometry shared by the vertebrates and insects can be resolved as a pair of symmetrical mirror images of two sides, the front pair the head, the rear pair the body, top and bottom, the back and belly.
SUBDUCTIVE GASTRULATION, SPHERES WITHIN SPHERES
The primary embryological foundational event in plant and animal body form is called subductive gastrulation wherein in unequal cell cleavage the smaller daughter cell may shrink and be resorbed within the larger daughter creating concentric spheres. The expanding inner sphere is constrained to expand internally, beginning in plants with an incursion at the top, and in animals with an incursion at the bottom. In both cases the body plan is established by the simple predictable forms occurring with the expansion of sphere within sphere. This critical process is described rigorously in the succeeding pages. It will account, for example, for the diminishing sequence of our limb-bone length leading to grasping and walking.
GROWTH AXIS DIRECTION
The plausible conjecture of embryo geometry can provide an account for this fundamental morphological phenomenon of nature: Plants grow vertically, animals grow horizontally.
The geometrical given of cell division dictates that cleavages occur in a plane ninety degrees from the previous cleavage. The initial bisection the egg cell may be either horizontal or vertical. Three bisections generate an eight-cell cube, in a sequence that is either horizontal-vertical-horizontal or vertical-horizontal-vertical. In either case, one direction will outnumber the other direction, two-to-one, causing either a dominant horizontal or a vertical growth pattern.
Humans are born crawling because the first cleavage of our fertilized egg cell was vertical, laying down a horizontal body axis. Plants start with a sideways cleavage creating a vertical axis for trees, flowers and fruits. The spherical egg cell grows by the predominance of horizontal growth rewarding us with the stunningly perfect ovoidal egg for breakfast.
BIODIVERSITY
Cell divisions are not necessarily equal. The slightest inequality in cell division produces a lopsided cube. Repetition of unequal cell division in subsequent divisions magnifies the departure from the perfect cubical form resulting in the extremes of biodiversity. Biodiversity is encoded in the degree of inequality in unequal cell cleavage.
THE ROLE OF THE GENES
DNA is the recorder of body building rather than the guide. Emmanuel Farge's work at the Curie Institute concludes that cell division is the cause rather than the result of cell division.
EXTRA-TERRESTRIAL LIFE
If body form is geometrical in origin, then is it not probable that alien beings may assume humanoid shapes?