On the Origin of Form

On the Origin of Form, Evolution by Self-Organization, provides a mathematical solution to the twin problems that have faced science since Aristotle:

• How the complex body is formed from a single cell;

• How the first single-cell creatures evolved into complex multi-cellular animal and plant life.

Ten years of research by dozens of participants have yielded the discovery of a simple, mathematical algorithm which provides a complete account of the origin of complex biological forms.

It has been discovered that the forms predictably assumed by the expanding surfaces of a spherical bilayer simulate the shapes of the phyletic body forms of animals and plants.

This theory is a geometric, topological solution to the problem. It postulates that the origin of form is the double-walled bubble that self-assembles out of certain chemicals called lipids, widely accepted as the origin of the first cells.

The model illustrates the predictable shapes which the lipid bilayer sphere must assume as both of its two contiguous surfaces expand.

The following states the theorem.

The Premise:

The form of the complex multi-cellular body is the predictable result of the expansion of a spherical bilayer.

The body shapes of the animal and plant phyla may be simulated by the expansion of the surfaces of a double-walled sphere.

Demonstration:

Constrained by an outer inelastic sphere, called the vitelline sphere, the expansion of the surfaces of the bilayer sphere is directed inwardly. Opposite poles grow toward each other internally, meeting within, forming thereby two elongated toruses, one within the other.

The toroidal surface, newly formed from the inner sphere, generates a highly regular star-shaped pattern in the cross-section of its interior surface. This pattern is congruent with the pattern you see when you slice a tomato or a pepper. The body plans of flowers and animals may be simulated accurately by simple topological deformations of this structure.

1. Compression of the anterior-posterior axis simulates the bodies of the radial animals and flowers.

2. Bending the axis generates internal transverse creases that fold out, simulating limbs in bilateral animals.

Comment:

The primeval seas swarmed with self-organized phospholipid bilayer vesicles. As they expanded, several different phyletic forms developed (none have developed since). The differences among them are the topological consequence of small, chemically-induced variants in the stiffness of the surfaces that may influence the way the surface bends and folds. The later introduction of genes serves to maintain, and occasionally change, the proportions of the otherwise immutable phyletic form.

Conclusion:

The complex multi-cellular body is the predictable result of the expansion of a spherical bilayer.

In sixty illustrative plates, the "blueprints" are presented, showing the steps from spherical bilayer to torus to multi-torus to the main forms of nature. The theorem is the discovery that the expansion of a spherical bilayer can accurately simulate the forms of complex animals and plants.

To attempt to explain why this process is invisible to the observing embryologist, two well-known phenomena are suggested---Embryological Condensation and Morphogenetic Fields. Condensation. A fundamental principle in embryology states that as the species becomes more “evolved” the first stages in the development of the embryo disappear as stages are added at the end. This is the reason that the images illustrated do not correspond with the observed stages of embryology, representing, instead, the reconstitution of the missing first stages, much as a detective re-enacts the steps of a crime. On the Origin of Form suggests that the mechanism by which the forms are encoded from generation to generation is the phenomenon called Morphogenetic Fields. The egg is cleaved into a thousand cells, each of which "remembers" its former neighbors, and proceeds to reassemble the whole during embryogenesis.

Does this model constitute proof? The model is a system, like the Periodic Table of the Elements, or the Linnaean system of biological classification. These organize a body of existing data, demonstrating a pattern in the relationship of the parts, conferring rationale to the whole. These systems are corroborated by the rational placement of each individual into the pattern of the whole. Only in math is there proof. The purported solution in On the Origin of Form is a hypothetical sequence of past events which can account for what we now see. This common form of every-day reasoning is the basis of astronomy, geology, and any discipline based on historical evidence. To succeed, the model must account for all observed phenomena in the field it claims to explain. Is nature a mathematical problem to be solved? Natural forms possess universal characteristics by which we easily recognize the living from the inorganic. The ancients used the expression, “God the Geometer.”

Seventeenth century botanists presumed a mathematical origin of the shapes of flowers. Goethe sought the Urform, geometric mother of all form. This model demonstrates that the gamut of complex life can be derived directly from the forms that naturally occur when confined concentric spheres expand. Since life is widely believed to have begun by the self-organization of lipid bilayer spheres, there is good reason to suspect that the proposed model is what nature is secretly using.

The two main current theories on evolution are the natural selection of random genetic mutants and creationism. By the late nineteenth century embryologists provided detailed descriptive drawings of the stages of embryo development. This model is causative, the first such to be published. It is an epigenetic, mechanically coherent, non-metaphoric account of evolution. It presents a plausible scientific alternative to the theory of evolution by natural selection.

Stuart Pivar
September 2009