Biological system based on a wave function

In summary, Christopher Humphrey discusses the disparity in the formation of complex body plans in the fossil record and how science is attempting to explain this through genomic constraints. His discovery reveals that a wave function and microbial substrate played a crucial role in the formation of the first complex animal life and subsequent phyla. He also discusses the gaps in our understanding of morphological origins and genetic controls in the context of the fossil record. In addition, David Wilcox raises questions about the origin of life, the first animals, and species stasis, and argues that these phenomena cannot be fully explained by current models of genetic organization. Maxson McDowell adds to this argument by highlighting the concept of self-organization in dynamic systems and how it contributes to the emergence of
  • #36
This whole model is based on a fossil artifact.
Physics news on
  • #37
Monique said:
How do you go from an energetic "stepping stone" to needing a circulatory system.

And what is that artifact you are talking about.

The macro-environment of oolitic spheres and cyanobactia combined with the overall torus shape or dissipative structure, Allows for the optimum energetic boost to a higher organized state. {For the eukaryote}
Last edited by a moderator:
  • #38
This photo and photo-shop rendering is all I have at the moment. What I really need is a photo shop animation of the dynamic.

The fossil has a opening all the way though the center just as the photo-shop rendering.

This representation is what I think this embryo would have looked like when it was alive. The right intake aperture became dominant over the left, resulting in an asymmetrical growth of extruding mineralization around the left aperture.

This particular vesica attractor would have resulted in a conch, or gastropod design.
The dominant right intake would develop a gill while the left developed a spiraling shell and central axis of the [columella.]

This would keep spiraling until the shell enclosed the left aperture complexly. This left spiraling point then became what most would assume as the front. Myself included.

If both chambers keep a symmetrical flow, which would have been very rare, the result would be a symmetrical body plan and two gills.

If the attractor retained the shell and a symmetrical flow though the apertures, the result would be a cephalopod. This shell is not a genetic adaptation but more precisely the a receipt from paying {Schrödinger entropy debt}

{The oolitic mass would shrink [dissipate] during this pulse into a higher ordered state.}

A fish’s body plan is the most perfect of all the possible out comes, and looks as though it only occurred once. All the myriad shell designs now appear to me as beautiful attempts at a fish’s body plan. Even natures screw up’s are geometrical marvels.

The fossil came from a creek bed cutting down though early Cambrian strata This strata is made up of dolomite limestone. The strata this originated from developed layers of a microbial mats in fine silty mud, that is devoid of any particles that would induce the growth of stromatalites, so instead you just find layers of cyanobacteia. When fine quartz particles our introduced, oolites are formed.
Last edited by a moderator:
  • #39
This vesica attractor represents an emerging eukaryote system that crystallizes though successive stages from higher to lower order iteration matrices, while being shaped by an internal and external fluid dynamics.
An attractor in the form of a mobile circular mass of cyanobacterail filaments and oolites capture and contain a circular flow of sea water after it comes to rest.
This internalized flow inside the micro-environment is then captured a second time, and further ordered by Eukaryote cells as they reproduce in this layered internal system. The eukaryote growth appears to radiate out from these flow channels, creating a recursive symmetrical circulatory system.

To visualize this layered pattern take a pencil, tape the end of a ribbon around the pencil now wrap the ribbon tightly three or four times in a clockwise direction. Now reverse the direction counterclockwise do this about 7-8 times. Now tape down the outside all the way around tightly. now wrap your thumb and forefinger around the ribbon in a circle. take the end of the pencil and turn in a ratcheting motion. You will get a rough idea of the internal dynamic of the vesica attractor. A central paisley turning in unison with the surrounding layers resembling a circulating toaist Mandela , contained in a torus or bagel structure.
I believe this recursive concentric system is the bases for most, if not all the complex body plans of the higher taxon that emerged during the Cambrian. This particular scenario reflects one of a fish, the most perfect of all the emerging vesica attractors. differing body plans would result from differing perturbations of separately emerging attractors. As the eukaryote system develops, the layered structure begins to differentiate as the oolitic matrix shrinks. A tension emerges throughout the system and starts to divide into three main domains. The still open heart cavity, the outer layers conforming around external dynamics. The domain of loosely bound middle layers that will form into some of the internal organs, but at the moment only contain a developing symmetrical circulatory system powered by external forces.

As the oolites shrink the domains begin to differentiate even further. This ever increasing tension crystallizes the form in an descending order of smaller domains of connectives, until the oolites have completely dissolved leaving in there place a vast patterned array of flexible geodesic scaffolding. called the extra-cellular matrix, at this phase the connectives is on a very fine cellular level, also at this stage the central heart tissue forms by coiling connected cells inward like a watch spring, separating from the outer right and left apertures that have now become subject to their own domain of connectives, a few layers of this heart tissue will be taken by the apertures as they differentiate from the central chamber. Two very critical steps take place at this stage. A connection is maintained though this tissue between the chamber and apertures while the heart chamber is enclosed as apertures shift and redirect and access an second outer layer. The sea water is redirected into this new layer opening a second cavity. This new chamber forms the, mouth, digestive system and anus and the apertures form the gill slits. A flow is maintain throughout this process but now blood cells begin to circulate though the enclosed internal circulatory system. The yet unformed mouth acts as an placental attachment to the oolitic bed which provides a nursery food of mineral spheres and algae. This substance begins to help form the developing digestive track.

The developing cellular matrix begins to respond to, and is further ordered by a finer flow of information now passing from the cellular microcosm to the macrocosm of the environment.
A cognitive system forms around this flow of light, sound and movement between these two worlds. This connecting flow of information is the key to an understanding the evolutionary roll of cognition in a biological system. Once this synergetic vortex is opened and set in motion it becomes a self-sustaining system. These original connecting points have been the central circulating force of information in evolution ever since.
  • #40
Metatron said:
The simple animals before the Cambrian such as a jellyfish and worms did not have the genetic diversity to form complex cellular networks and formed around differing dynamics.
You're saying jellyfish and worms don't have complex cellular networks? How are you definining a cellular "network"?

The jellyfish for instance relates to the environment in cycles that move up and down with the sun, and still posses a symbiosis with the photosynthetic cells.

Relates to the environment? In what way? What cycles are you referring to? And what up and down movement? This sentence says nothing, much like the rest of the posts in this thread. Symbiosis has a very specific biological definition, and I don't see how it relates to your above sentence. Jellyfish do not have photosynthetic cells. They are animals, not plants!

I'm in agreement with Monique that you are using a lot of fancy words to say absolutely nothing. There is no coherent argument here.
  • #41
jelly fish that contain a photosynthitic relationship move up and down in cycles following the sun I have observed this first hand when I was in the south china sea stationed on a destroyer.

quote"BIOLOGICAL EVOLUTION: As rising oceans and incoming tides carried percolating sea water into the lakes, they also allowed microscopic organisms to flow through the small limestone pores. Among those microscopic organisms were the larva of a variety of invertebrate organisms and fish. One of those larval organisms was a jellyfish of the genus Mastigias. These jellyfish feed by capturing small zooplankton with their cnematocysts (stinging cells). Once trapped inside the lake, Mastigias found that there were too few plankton to support their predatory habits. Luckily, for this versatile creature it was armed with a more creative method of feeding. Mastigias jellyfish (along with hard corals and giant clams), harbor an interesting group of algae cells in their tissues called zooxanthellae. The algae cells collect sunlight and photosynthesize creating an excess of sugars and proteins. The Mastigias release an enzyme which forces the zooxanthellae to give up this valauble resource. In exchange for this free meal the jellyfish carry the algae cells throughout the day, to the areas of the lake with the highest concentration of sunlight. Their migrations are not only horizontal but vertical as well. When the sun sets, the Mastigias sink down to the bottom of the lake to collect nitrates and phosphates to fertilize their algae cells. Thus the jellyfish have made a fascinating evolutionary transition from aggressive predators to passive farmers. The relationship between the jellyfish and algae cells is known as mutualism. Most animal populations are constrained by their food supply. As the Mastigias population in this lake is limited only by sunlight and nutrients the numbers of individuals will be staggering.

As the Mastigias began to rely only on sunlight for their food supply they no longer had the need to produce metabolically expensive tentacles and stinging cells. The slow elimination of these structures through evolutionary time is a classic example of regressive evolution."
Last edited:
  • #42
I now see your point though, the word symbiosis is not in this text instead it is "mutualism" I'm not sure what the difference is?
  • #43
Okay, so now you've managed to demonstrate there is a single species of jellyfish that has formed a mutualistic relationship with algae, thus must exhibit behavioral patterns that allow them to maximize this relationship by utilizing energy from the sun during daylight hours and nutrients from deeper waters during the night.

Circadian rhythms are well-known to exist across phyla. So none of this is surprising.

So, now let's take the next small step; how does this example specifically relate to your overall hypothesis? Actually, I'm not even sure what your overall hypothesis is yet. Could you explicitly state it in just a few sentences?
  • #44
This is the best I can do for now.

The fossil record shows a disparity in the formation of complex body plans.
The individual eukaryote cannot build these structures. They do not carry within themselves a blue print for an overall structure.
Science today is attempting to answer these questions, [ via, systems science] though genomic constraints. My discovery shows the missing information in the original body design was provided by a wave function, acting on a mass of oolitic spheres bound by a microbial substrate.{ a dissipative structure}
This substrate crystallized into an archetypal pattern. The first complex animal life. [source of a body plan pattern] that then spawn an entire phyla.
This central archetype then becomes a sustained, central information bank for the phyla.
Releasing new genetic information in pulses over time.
This model not only accounts for the original forms, but also genetic control patterns of punctuated equilibrium. This is what this fossil is showing, in the context of the fossil record.
Last edited:
  • #45
This may be a solution to some lose ends in our present understanding the development of complex morphology. The answer it appears is the architectural framework formed first, from wave dynamics working from the outside inward, while the interior design of genetics, worked from the inside out. Presently most research is focused solely on genomic controls in the formation of complex morphology. The answer it appears is that nature hired its architect first {wave dynamics} its interior designer second, {genetic probabilities} Just as we would in building a structure.
  • #46
I think I get you now. You are saying that life had no organizing ability when it evolved, so it relied on the environment to shape it.

You are saying that there are flow currents that direct an organism to 'crystallize' in a certain way.

Do you know Jean-Baptiste Lamarck? He hypothesized that acquired traits can be inherited, this Lamarckian inheritance is in conflict with the findings of genetics and has now been largely abandoned.

Take the example of giraffes. Giraffes have long necks, how do they get those. Does the tree shape the giraffe's neck and does the giraffe then pass down that information to further generations, or does the giraffe successively grow longer necks because it has a survival advantage when it can reach higher.

Environmental information can not be coded into genes, the genes adapt themselves to environmental information.

Have you ever read any books on genetics and development? I don't think so. You say:
The individual eukaryote cannot build these structures. They do not carry within themselves a blue print for an overall structure.
Then how does a human being grow from a zygote. There are a number of genetic mechanisms known that causes a multicellular organism to grow in such amazing symmetry. You can have a very simple mechanism of two interacting molecules and grow a complex pattern from that.
  • #47
Monique said:
I think I get you now. You are saying that life had no organizing ability when it evolved, so it relied on the environment to shape it.

You are saying that there are flow currents that direct an organism to 'crystallize' in a certain way.

Do you know Jean-Baptiste Lamarck? He hypothesized that acquired traits can be inherited, this Lamarckian inheritance is in conflict with the findings of genetics and has now been largely abandoned.

Take the example of giraffes. Giraffes have long necks, how do they get those. Does the tree shape the giraffe's neck and does the giraffe then pass down that information to further generations, or does the giraffe successively grow longer necks because it has a survival advantage when it can reach higher.

Environmental information can not be coded into genes, the genes adapt themselves to environmental information.

Have you ever read any books on genetics and development? I don't think so. You say: Then how does a human being grow from a zygote. There are a number of genetic mechanisms known that causes a multicellular organism to grow in such amazing symmetry. You can have a very simple mechanism of two interacting molecules and grow a complex pattern from that.

The problem is not lack of knowledge on ether side….. except in regards to my communicating an Idea based on the fossil.

Eukaryote cells carry within an animal a blue print of the body plan, of course this is a given, I am not arguing that.

What I am suggesting is, the first animals of complex form arrived directly from a microbial substrate. Though an attractor.

All the material I presented was showing the process.

Long long ago, in a land of single celled eukaryote,cyanobacteria,and oolites...Just prior to the cambrian explosion.

The architecture was being formed in this very special dissipative structure {an attractor} the cells will crystallize into alleles or genotypes.

This happens as the “ attractor” bonds with the environment.

Now the “archetype” can code in each cell a blue print, For the entire body plan.

Imagine a tornado in reverse;

In the tornado are microscopic pieces of a house,{single cell eukaryote} all these cells are just probabilities.{genetic potential}{stem cells} The tornados has special kind of construction energy{wave function-phi} {underlying geometrical probabilities} and is directing these scattered probabilities into a cohesive whole. Once the house is brought together an "architect" can emerge, make blue prints and start building the neighborhood.

Yes I know this is not what the present text says but it does work.

Thanks for unlocking this post. I live!
Last edited:
  • #48
There are a number of genetic mechanisms known that causes a multicellular organism to grow in such amazing symmetry. You can have a very simple mechanism of two interacting molecules and grow a complex pattern from that.[/QUOTE said:
This symmetry Is a pre-existing structure in the universe. This is what the model is showing that complex heart based body plans, not only form from an attractor{source of symmetry} but are still sustained by this embeded wave pattern [refer to post 9\10]

This is why DNA is shaped the way it is. Its an efficient way for energy, or information, to flow.

"Such an object is stable, and so can be recognized, only when the corresponding attractor is structurally stable." ... Rene Thom, [Post 19]
Last edited:
  • #49

I just found this very abreviated but really well written intro to chaos theory, this should help anyone that is having trouble understanding this post.

Chaos and Complexity

One of the themes straddling both biological and physical sciences is the quest for a mathematical model of phenomena of emergence (spontaneous creation of order), and in particular adaptation, and a physical justification of their dynamics (which seems to violate physical laws).

The physicist Sadi Carnot, one of the founding fathers of Thermodynamics, realized that the statistical behavior of a complex system can be predicted if its parts were all identical and their interactions weak. At the beginning of the century, another French physicist, Henri Poincare`, realizing that the behavior of a complex system can become unpredictable if it consists of few parts that interact strongly, invented "chaos" theory. A system is said to exhibit the property of chaos if a slight change in the initial conditions results in large-scale differences in the result. Later, Bernard Derrida will show that a system goes through a transition from order to chaos if the strength of the interactions among its parts is gradually increased. But then very "disordered" systems spontaneously "crystallize" into a higher degree of order.

First of all, the subject is "complexity", because a system must be complex enough for any property to "emerge" out of it. Complexity can be formally defined as nonlinearity.

The world is mostly nonlinear. The science of nonlinear dynamics was originally christened "chaos theory" because from nonlinear equations unpredictable solutions emerge.

A very useful abstraction to describe the evolution of a system in time is that of a "phase space". Our ordinary space has only three dimensions (width, height, depth) but in theory we can think of spaces with any number of dimensions. A useful abstraction is that of a space with six dimensions, three of which are the usual spatial dimentions. The other three are the components of velocity along those spatial dimensions. In ordinary 3-dimensional space, a "point" can only represent the position of a system. In 6-dimensional phase space, a point represents both the position and the motion of the system. The evolution of a system is represented by some sort of shape in phase space.

The shapes that chaotic systems produce in phase space are called "strange attractors" because the system will tend towards the kinds of state described by the points in the phase space that lie within them.

The program then becomes that of applying the theory of nonlinear dynamic systems to Biology.

Inevitably, this implies that the processes that govern human development are the same that act on the simplest organisms (and even some nonliving systems). They are processes of emergent order and complexity, of how structure arises from the interaction of many independent units. The same processes recurr at every level, from morphology to behavior.

Darwin's vision of natural selection as a creator of order is probably not sufficient to explain all the spontaneous order exhibited by both living and dead matter. At every level of science (including the brain and life) the spontaneous emergence of order, or self-organization of complex systems, is a common theme.

Koestler and Salthe have shown how complexity entails hierarchical organization. Von Bertalanffi's general systems theory, Haken's synergetics, and Prigogine's non-equilibrium Thermodynamics belong to the class of mathematical disciplines that are trying to extend Physics to dynamic systems.

These theories have in common the fact that they deal with self-organization (how collections of parts can produce structures) and attempt at providing a unifying view of the universe at different levels of organization (from living organisms to physical systems to societies).


The Hungarian writer and philosopher Arthur Koestler first brought together a wealth of biological, physical, anthropological and philosophical notions to construct a unified theory of open hierarchical systems.

Langauge has to do with a hierarchical process of spelling out implicit ideas in explicit terms by means of rules and feedbacks. Organisms and societies also exhibit the same hierarchical structure. In these hierarchies, each intermediary entity ("holon") functions as a self-contained whole relative to its subordinates and as one of the dependent parts of its superordinates. Each holon tends to persist and assert its pattern of activity.

Wherever there is life, it must be hierarchically organized. Life exhibits an integrative property (that manifests itself as symbiosis) that enables the gradual construction of complex hierarchies out of simple holons. In nature there are no separated, indivisible, self-contained units. An "individual" is an oxymoron. An organism is a hierarchy of self-regulating holons (a "holarchy") that work in coordination with their environment. Holons at the higher levels of the hierarchy enjoy progressively more degrees of freedom and holons at the lower levels of the hierarchy have progressively less degrees of freedom. Moving up the hierarchy, we encounter more and more complex, flexible and creative patterns of activity. Moving down the hierarchy behavior becomes more and more mechanized.

A hierarchical process is also involved in perception and memorization: it gradually reduces the percept to its fundamental elements. A dual hierarchical processis involved in recalling: it gradually reconstructs the percept.

Hierarchical processes of the same nature can be found in the development of the embryo, in the evolution of species and in consciousness itself (which should be analyzed not in the context of the mind/body dichotomy but in the context of a multi-levelled hierarchy and of degrees of consciousness).

They all share common themes: a tendency towards integration (a force that is inherent in the concept of hierarchic order, even if it seems to challenge the second law of Thermodynamics as it increases order), an openess at the top of the hierarchy (towards higher and higher levels of complexity) and the possibility of infinite regression.

Hierarchies from Complexity

Stanley Salthe, by combining the metaphysics of Justus Buchler and Michael Conrad's "statistical state model" of the evolutionary process, has developed what amounts to a theory of everything: an ontology of the world, a formal theory of hierarchies and a model of the evolution of the world.

The world is viewed as a determinate machine of unlimited complexity. Within complexity, discontinuities arise. The basic structure of this world must allow for complexity that is spontaneously stable and that can be broken down in things divided by boundaries. The most natural way for the world to satisfy this requirement is to employ a hierarchical structure, which is also implied by Buchler's principle of ordinality: Nature (i.e., our representation of the world) is a hierarchy of entities existing at different levels of organization. Hierarchical structure turns out to be a consequence of complexity.

Entities are defined by four criteria: boundaries, scale, integration, continuity. An entity has size, is limited by boundaries, and consists of an integrated system which varies continuously in time.

Entities at different levels interact through mutual constraints, each constraint carrying information for the level it operates upon. A process can be described by a triad of contiguous levels: the one it occurs at, its context (what the philosopher Mario Bunge calls "environment") and its causes (Bunge's "structure"). In general, a lower level provides initiating conditions for a process and an upper level provides boundary conditions. Representing a dynamic system hierarchically requires a triadic structure.

Aggregation occurs upon differentiation. Differentiation interpolates levels between the original two and the new entities aggregate in such a way that affects the structure of the upper levels: every time a new level emerges, the entire hierarchy must reorganize itself.

Salthe also recalls a view of complexity due to the physicist Howard Hunt Pattee: complexity as the result of interactions between physical and symbolic systems. A physical system is dependent on the rates at which processes occur, whereas a symbolic system is not. Symbolic systems frequently serve as constraints applied to the operation of physical systems, and frequently appear as products of the activity of physical systems (e.g., the genome in a cell). A physical system can be said to be "complex" when a part of it functions as a symbolic system (as a representation, and therefore as an observer) for another part of it.

These abstract principles can then be applied to organic evolution. Over time, Nature generates entities of gradually more limited scope and more precise form and behavior. This process populates the hierarchy of intermediate levels of organization as the hierarchy spontaneously reorganizes itself. The same model applies to all open systems, whether organisms or ecosystems or planets.

By applying principles of complex systems to biological and social phenomena, Salthe attempts to reformulate Biology on development rather than on evolution. His approach is non-Darwinian to the extent that development, and not evolution, is the fundamental process in self-organization. Evolution is merely the result of a margin of error. His theory rests on a bold fusion of hierarchy theory, Information Theory and Semiotics.

Salthe is looking for a grand theory of nature, which turns out to be essentially a theory of change, which turns out to be essentially a theory of emergence.

Dissipative Systems

By far, though, the most influential school of thought has been the one related to Ilya Prigogine's non-equilibrium Thermodynamics, which redefined the way scientists approach natural phenomena and brought self-organizing processes to the forefront of the study of complex systems. His theory found a stunning number and variety of fields of application, from Chemistry to Sociology. In his framework, the most difficult problems of Biology, from morphogenesis to evolution, found a natural model.

Classical Physics describes the world as a static and reversible system that undergoes no evolution, whose information is constant in time. Classical Physics is the science of being. Thermodynamics, instead, describes an evolving world in which irreversible processes occurs. Thermodynamics is the science of becoming.

The second law of Thermodynamics, in particular, describes the world as evolving from order to disorder, while biological evolution is about the complex emerging from the simple (i.e. order arising from disorder). While apparently contradictory, these two views show that irreversible processes are an essential part of the universe.

Furthermore, conditions far from equilibrium foster phenomena such as life that classical Physics does not cover at all.

Irreversible processes and non-equilibrium states turn out to be fundamental features of the real world.

Prigogine distinguishes between "conservative" systems (which are governed by the three conservation laws for energy, translational momentum and angular momentum, and which give rise to reversible processes) and "dissipative" systems (subject to fluxes of energy and/or matter). The latter give rise to irreversible processes.

The theme of science is order. Order can come either from equilibrium systems or from non-equilibrium systems that are sustained by a constant source (or, dually, by a persistent dissipation) of matter/energy. In the latter systems, order is generated by the flux of matter/energy. All living organisms (as well as systems such as the biosphere) are non-equilibrium systems.

Prigogine proved that, under special circumstances, the distance from equilibrium and the nonlinearity of a system drive the system to ordered configurations, i.e. create order. The science of being and the science of becoming describe dual aspects of Nature.

What is needed is a combination of factors that are exactly the ones found in living matter: a system made of a large collection of independent units which are interacting with each other, a flow of energy through the system that drives the system away from equilibrium, and nonlinearity. Nonlinearity expresses the fact that a perturbation of the system may reverberate and have disproportionate effects.

Non-equilibrium and nonlinearity favor the spontaneous development of self-organizing systems, which maintain their internal organization, regardless of the general increase in entropy, by expelling matter and energy in the environment.

When such a system is driven away from equilibrium, local fluctuations appear. This means that in places the system gets very unstable. Localized tendencies to deviate from equilibrium are amplified. When a threshold of instability is reached, one of these runaway fluctuations is so amplified that it takes over as a macroscopic pattern. Order appears from disorder through what are initially small fluctuations within the system. Most fluctuations die along the way, but some survive the instability and carry the system beyond the threshold: those fluctuations "create" new form for the system. Fluctuations become sources of innovation and diversification.

The potentialities of nonlinearity are dormant at equilibrium but are revelead by non-equilibrium: multiple solutions appear and therefore diversification of behavior becomes possible.

Technically speaking, nonlinear systems driven away from equilibrium can generate instabilities that lead to bifurcations (and symmetry breaking beyond bifurcation). When the system reaches the bifurcation point, it is impossible to determine which path it will take next. Chance rules. Once the path is chosen, determinism resumes.

The multiplicity of solutions in nonlinear systems can even be interpreted as a process of gradual "emancipation" from the environment.

Most of Nature is made of such "dissipative" systems, of systems subject to fluxes of energy and/or matter. Dissipative systems conserve their identity thanks to the interaction with the external world. In dissipative structures, non-equilibrium becomes a source of order.

These considerations apply very much to living organisms, which are prime examples of dissipative structures in non-equilibrium. Prigogine's theory explains how life can exist and evolution work towards higher and higher forms of life. A "minimum entropy principle" characterizes living organisms: stable near-equilibrium dissipative systems minimize their rate of entropy production.

From non-equilibrium Thermodynamics a wealth of concepts has originated: invariant manifolds, attractors, fractals, stability, bifurcation analysis, normal forms, chaos, Lyapunov exponents, entropies. Catastrophe and chaos theories turn out to be merely special cases of nonlinear non-equilibrium systems.

In concluding, self-organization is the spontaneous emergence of ordered structure and behavior in open systems that are in a state far from equilibrium described mathematically by nonlinear equations.

Catastrophe Theory

Rene' Thom's catastrophe theory, originally formulated in 1967 and popularized ten years later by the work of the British mathematician Erich Zeeman, became a widely used tool for classifying the solutions of nonlinear systems in the neighborhood of stability breakdown.

In the beginning, Thom, a French mathematician, was interested in structural stability in topology (stability of topological form) and was convinced of the possibility of finding general laws of form evolution regardless of the underlying substance of form, as already stated at the beginning of the century by D'Arcy Thompson.

Thom's goal was to explain the "succession of form". Our universe presents us with forms (that we can perceive and name). A form is defined, first and foremost, by its stability: a form lasts in space and time. Forms change. The history of the universe, insofar as we are concerned, is a ceaseless creation, destruction and transformation of form. Life itself is, ultimately, creation, growth and decaying of form.

Every physical form is represented by a mathematical quantity called "attractor" in a space of internal variables. If the attractor satisfies the mathematical property of being "structurally stable", then the physical form is the stable form of an object. Changes in form, or morphogenesis, are due to the capture of the attractors of the old form by the attractors of the new form. All morphogenesis is due to the conflict between attractors. What catastrophe theory does is to "geometrize" the concept of "conflict".

The universe of objects can be divided into domains of different attractors. Such domains are separated by shock waves. Shock wave surfaces are singularities called "catastrophes". A catastrophe is a state beyond which the system is detroyed in an irreversible manner. Technically speaking, the "ensembles de catastrophes" are hypersurfaces that divide the parameter space in regions of completely different dynamics.

The bottom line is that dynamics and form become dual properties of nonlinear systems.

This is a purely geometric theory of morphogenesis, His laws are independent of the substance, structure and internal forces of the system.

Thom proves that in a 4-dimensional space there exist only 7 types of elementary catastrophes. Elementary catastrophes include: "fold", destruction of an attractor which is captured by a lesser potential; "cusp", bufurcation of an attractor into two attractors; etc. From these singularities, more and more complex catastrophes unfold, until the final catastrophe. Elementary catastrophes are "local accidents". The form of an object is due to the accumulation of many of these "accidents".

Similar threads

  • Sci-Fi Writing and World Building
  • Biology and Medical
  • General Discussion
  • Sci-Fi Writing and World Building
  • Other Physics Topics
  • Biology and Chemistry Homework Help