Butterfly effect

A) “Small causes may have large effects…”

1. Although such an idea may have a significant influence on how we perceive the natural laws and the way we behave towards nature and ourselves, it is not sufficient that we set for example a tree on fire in order to burn down a forest. But if we repeatedly set separate trees on fire, finally the forest will lose its defenses, so that the fire will become more and more widespread and devastating. This is exactly what is happening to the forests right now. If the people had been more aware of this problem 50-100 years ago, the environment may have been saved. The truth however is that as physical systems have no memory, so do we often forget about our past mistakes and repeat them again and again. When the same mistake is made repeatedly then it becomes too bad a habit and too great a burden to get rid of.

B) The butterfly effect

2. The sensitive dependence of physical systems (the effects) on the initial conditions (the causes) is called the butterfly effect in chaos theory. The term, coined by Edward Lorenz, is derived from the metaphorical example of the details of a tornado being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that was rounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome. [1]

C) Fractals

3. The chaotic behavior of physical systems in mathematics is often described by fractals. A fractal is a detailed, recursive, and infinitely self-similar mathematical set which is encountered ubiquitously in nature. Fractals exhibit similar patterns at increasingly small scales, also known as expanding symmetry or evolving symmetry. [2]

D) The strange attractor

(No matter how much you deviate, you eventually return to the average value)

4. What is significant about chaotic systems, such as fractal structures, is that they tend to be organized and evolve around a certain and central point, which is called strange attractor. An attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. An attractor is called strange if it has a fractal structure. [3]

5. Thus chaotic systems are not so random after all. Not only do they appear as a set of miniscule but similar patterns of shapes and behavior, but they also tend to evolve toward a certain point (the strange attractor).

E) A mathematical butterfly

6. How would a butterfly look like to the eyes of a computer? Hofstadter’s butterfly is a mathematical object describing the theorized behavior of electrons in a magnetic field. It takes its name from its visual resemblance to a butterfly. It is a fractal structure and as such it shows self-similarity, meaning that small fragments of the structure contain a (distorted) copy of the entire structure. [4]

F) The real thing (A real butterfly)

7. Butterflies are insects in the clade which also includes moths. Adult butterflies have large, often brightly colored wings, and conspicuous, fluttering flight. Butterfly fossils date to the Paleocene, which was about 56 million years ago. Butterflies are often polymorphic, and many species make use of camouflage, mimicry and aposematism (e.g. warning coloration) to evade their predators. Some, like the monarch and the painted lady, migrate over long distances. Culturally, butterflies are a popular motif in the visual and literary arts. [5]

8. ‘Polymorphism, mimicry, aposematism (i.e. deceitfulness)…’ This is the art of camouflage. I was thus wondering: What is hidden beneath a butterfly’s appearance and whereabouts? In the case of Hofstadter’s digital butterfly what is hidden is a pattern according to which electrons move in a magnetic field. Incidentally the magnetic field looks like a spider in many cases. A butterfly captured in a spider’s web… But if the next move of a butterfly cannot be predetermined then how is it possible that a butterfly escapes from a spider’s web? How is it possible that a spider knows how to construct a web? How come a butterfly can move at all?

G) The archetype of the butterfly

9. My personal view is that a butterfly is the materialization of an archetype which has a certain shape and follows a certain pattern of behavior. While I don’t know how exactly one could illustrate an archetype with a mathematical function, I believe that one should start from the overall shape and then move toward the details. Thus one should follow the direction opposite  to fractals. The key point here is that one cannot delve into the details if one has no idea of the general pattern in the first place. Take for example a beach which is made of sand. While all the grains of sand put together compose the beach, grains of sand have no meaning without any reference to the beach as the overall picture. In the same sense fractal structure (or any kind of structure) cannot be organized if there isn’t any model of construction in the first place.

H) The aspect of symmetry

10. Does nature look like a fractal, or does a fractal look like nature? The question is symmetrical, and about symmetry is the question. Whenever we speak of symmetry we refer to harmony. Harmony means the composition of opposites. If we only have one thing then we have to cut it into two in order to compare one half with respect to the other half, on both sides of some reference axis of symmetry. But how does a butterfly know what disguise it must wear to deceive its hunters? It doesn’t need to- it is sufficient that nature itself knows how. But how come nature knows how to create butterflies or any other species if there aren’t any pre-established patterns according to which species take a physical form and evolve? How come such patterns emerged in the first place?

I) Spontaneous symmetry breaking

11. Spontaneous symmetry breaking is a way symmetry breaks in a physical system. The underlying laws do not change, but the system as a whole changes. Symmetry breaking in physics occurs when a system is crossing a critical point. Small fluctuations decide the system’s fate, by determining which branch is taken. [6]

J) Spontaneous generation

12. How was the world created? How come flowers had been producing nectar before insects appeared? Had they known that bees were going to come about? How does a chameleon know which camouflage to use, according to the surroundings? How come octopuses change color in relation to how they feel? How come people are able to imagine things which do not exist?

13. This is what Aristotle said about such an aspect of spontaneous generation:

“Now there is one property that animals are found to have in common with plants. For some plants are generated from the seed of plants, whilst other plants are self-generated through the formation of some elemental principle similar to a seed; and of these latter plants some derive their nutriment from the ground, whilst others grow inside other plants... So with animals, some spring from parent animals according to their kind, whilst others grow spontaneously and not from kindred stock; and of these instances of spontaneous generation some come from putrefying earth or vegetable matter, as is the case with a number of insects, while others are spontaneously generated in the inside of animals out of the secretions of their several organs.” [7]

14. Even though Aristotle didn’t know about the atomic theory (the ‘elemental principle similar to a seed’), the atomic theory knows nothing about the different qualities of elementary particles. For example, given that the position or momentum of a particle is known, as well as the kind of field to which this particle belongs, is this information sufficient so that, after we collect all necessary such particles of different kinds, we reconstruct a living human being- not as a ‘lump of mass,’ but as a living entity with thoughts and feelings? Such thoughts and feelings are based on the repetitive and elusive patterns (the archetypes), which are spontaneously generated in the universe, and intermingle with each other in order to produce the living organisms. Everything in nature is produced and evolves according to the same hidden patterns of symmetry.

K) The chiral vacuum

15. The ultimate background from which these patterns of form and behavior spontaneously emerge could be the vacuum itself:

“There is something about the vacuum- empty space itself- which knows the difference between an up quark and a down quark, and it’s the influence of the vacuum on these particles that makes them look different to us.” [8]

16. Thus even the vacuum itself may be inhomogeneous, exposing such a fundamental asymmetry that a couple of quarks, or any other elementary particle, knows where is ‘up’ and ‘down’ or ‘left’ and ‘right’ beforehand. Such an inhomogeneity suggests that the vacuum is not composed of similar ‘blocks’ of empty spacetime, but of discrete regions of different elementary patterns. How many such patterns may be is not the most significant aspect. The important thing is that patterns are pre- existent and pre- differentiated, they come in different shapes and functions, they rise spontaneously in the vacuum and they are organized in ways which create all inanimate objects and animate beings.

L) Fractal universe

17. According to a point of view, the universe consists of a series of spiral bodies of diminishing size, each made in turn by plasma ejection and molded by a spatial Coriolis effect: a rotating fractal universe. [9]

18. If we look at everyday objects very closely then even their slightest movement will seem too fast to us. If on the other hand we look at the stars in the sky, they will look immovable like any distant object. If the distance on its own determines the motion of objects then spacetime seems to be non- isotropic. A similar observation may have been the inspiration of Laurent Nottale, who was led to conclude that the whole universe has a fractal structure. [10]

19. Indeed, looking at the distant fixed stars through telescopes, we will see that the galaxies have a spiral structure, beginning from the center and unfolding in a repetitive manner to form the arms. Such a self- replicating pattern from the smallest to the largest is characteristic of fractals. In fact our own universe could be a small fraction of a much larger multiverse, repeating itself to infinity and for eternity.

M) The holographic principle

(The whole is greater than the sum of its parts) 

20. Even if the universe can be modeled as a giant fractal, there will still be something missing in that. Besides the aspect of self- replication, which is characteristic of fractals, another equally important and more general aspect is what we might call hologeneity (i.e. wholeness). Apart from the fact that the universe may consist of discrete parts (e.g. galaxies) like a fractal, it has also the property of organizing the parts into a consistent and coherent sum. Although a fractal has the property of blindly replicating itself, a hologram has the additional property of containing the information about its whole structure.

21. Holography is the science and practice of making holograms. Typically, a hologram is a photographic recording of a light field, used to display a fully three-dimensional image of the holographed subject. The hologram itself is an encoding of the light field as an interference pattern on the surface profile of the photographic medium. When suitably lit, the interference pattern diffracts the light into a reproduction of the original light field and the objects that were in it appear to still be there. [11]

22. It has been suggested that our own brain works like a hologram. The holonomic brain theory, developed by neuroscientist Karl Pribram, initially in collaboration with physicist David Bohm, is a model of human cognition that describes the brain as a holographic storage network... In a hologram, any part of the hologram with sufficient size contains the whole of the stored information. [12]

23. In fact this is not only how the brain but also more generally how the mind works. It consists of individual thoughts, but all these thoughts are organized into a coherent sum which we call the mind. This aspect of wholeness is what distinguishes us from ‘blind worms,’ instinctual organisms which keep on living unaware of their own existence. Thus wholeness, or hologeneity on the large scale, can also explain the rise of consciousness.

24. It has even been proposed that the universe itself is a gigantic hologram. Key to understanding the worldview that cosmometry is founded upon is the idea that the universe is both fractal (the same pattern of wholeness is found at every scale) and holographic (the wholeness is present everywhere and within every entity), as well as synergetic (the whole is greater than and unpredictable from the sum of the parts). [13]

N) Consciousness is the whole plus the sum of the parts

25. This way the whole universe becomes a unity conscious about the parts of which it consists. A proof of this is that we are aware about the existence of both the universe and ourselves at the same time. Would it be possible that we have awareness if consciousness had not been a property of the universe? Apparently not.

26. Small repetitive changes in a system cannot be organized into a coherent pattern and lead toward a certain direction if there isn’t any knowledge of the overall system beforehand. This is the basic aspect of holograms. A fractal is based on a function which replicates its variables one at a time, while the hologram reproduces its variables all at once. In fact the parts need not know about the whole structure, but there has to be a connecting principle in the structure to take care of the parts, as well as to have some idea about its own entity.

27. Such an awareness is what seems to be missing from humans unfortunately. We behave as if we as the part were the whole of the world. Even if a butterfly seems to be unaware of its actions, it lives in harmony with nature. Such a lack of harmony in modern society reflects our own inability to perceive the world as a unity. Physics and mathematics in fact imitate nature. In that sense all our science is the result of our failure as a species to be indistinguishable from nature (like bees, ants or butterflies are).

O) Redefining the ‘small causes…’

28. Small disturbances in a system can lead to the chaotic behavior of the system, if these changes are repetitive and systematic (towards the same result). If the flight of a butterfly over Asia may cause a hurricane in America, imagine what the destruction of the forests can do to the global climate. Is nature chaotic and destructive on its own after all? Should we simply become a civilization fully integrated with nature, simply letting nature have its own way? Or should we, as part of nature, become more aware of our role in the world as a whole, so that our own cause will finally make the whole universe a better place to be?

[1]: [https://en.wikipedia.org/wiki/Butterfly_effect]
[2]: [https://en.wikipedia.org/wiki/Fractal]
[3]: [https://en.wikipedia.org/wiki/Attractor#Strange_attractor]
[4]: [https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly]
[5]: [https://en.wikipedia.org/wiki/Butterfly]
[6]: [https://simple.wikipedia.org/wiki/Spontaneous_symmetry_breaking]
[7]: [https://en.wikipedia.org/wiki/Spontaneous_generation]
[8]:[http://blogs.discovermagazine.com/cosmicvariance/2005/10/24/hidden-symmetries/#.W47EzegzbIU]
[9]: [http://www.fractaluniverse.org/v2/?page_id=2]
[10]: [https://en.wikipedia.org/wiki/Scale_relativity]
[11]: [https://en.wikipedia.org/wiki/Holography]
[12]: [https://en.wikipedia.org/wiki/Holonomic_brain_theory]
[13]: [http://www.cosmometry.net/fractal-holographic-synergetic-universe]

9/5/2018

Picture: [https://fineartamerica.com/featured/butterfly-fractal-christy-hodgin.html]