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Efeito Borboleta e reações em cadeia

CAPÍTULO 4 – VERIFICAÇÃO DA POSSIBILIDADE DE UTILIZAÇÃO DA TEORIA DO CAOS NA ANÁLISE DA APLICAÇÃO DOS

4.1. SOBRE O CAOS

4.1.1. Efeito Borboleta e reações em cadeia

O “Efeito Borboleta” é o fenômeno criado a partir de mínimas condições iniciais que reagem em cadeia. A pergunta que se faz é: pode o bater das asas de uma borboleta, em um determinado ponto do globo, como o Japão, influenciar nas condições atmosféricas a ponto de colaborar na criação de um furacão em outro local, mesmo distante, como o Caribe?141

Contribuindo para o aprofundamento das realidades de reação caótica em cadeia, outro escritor, o americano Gary William Flake142 esclarece que, no reino físico ou da natureza, o “movimento” mais comum é o “não-linear”, devido ao caos gerado por pequenas condições iniciais que atuam sobre a gênese de um processo de construção ou crescimento natural, tanto de minerais e plantas, como em formas peculiares encontradas em seres vivos.143

São características do caos físico-natural, como confirma Flake:

determinístico – o sistema produzido pela ação do caos é determinado pelas condições iniciais; sensitivo – sensível às condições iniciais, como no Efeito Borboleta; ergódico – a trajetória espacial estabelecida num sistema caótico sempre irá retornar para a região local de

141 Assim, James Gleick (nota de rodapé anterior) prossegue: “A razão disso era o Efeito Borboleta. Para

pequenas condições meteorológicas – e para um meteorologista global, pequeno pode significar tempestades e nevascas -, qualquer previsão perde o valor rapidamente. Os erros e as incertezas se multiplicam, formando um efeito de cascata ascendente através de uma cadeia de aspectos turbulentos, que vão dos demônios da poeira e tormentas até redemoinhos continentais que só os satélites conseguem ver.

[...]. Se tivesse ficado apenas no Efeito Borboleta, uma imagem da previsibilidade substituída pelo simples acaso, Lorenz teria produzido apenas uma notícia muito ruim. Mas ele viu algo mais do que aleatoriedade, em seu modelo de tempo. Percebeu nele uma bela estrutura geométrica, a ordem mascarada de aleatoriedade. [...].O Efeito Borboleta não era um acidente: era necessário. [...]. Para produzir o rico repertório do tempo real da terra, a sua bela multiplicidade, dificilmente poderíamos desejar alguma coisa melhor do que um Efeito Borboleta.

O Efeito Borboleta recebeu um nome técnico: dependência sensível das condições iniciais. [...]. Sabe-se muito bem, tanto na ciência como na vida, que uma cadeia de acontecimentos pode ter um ponto de crise que aumente pequenas mudanças. Mas o caos significava que tais pontos estavam por toda parte. Eram generalizados. Em sistemas como o tempo, a dependência sensível das condições iniciais era conseqüência inevitável da maneira pela qual as pequenas escalas se combinavam com as grandes”.

142

“Simple motion is rare in nature. It is more common to find highly complicated non-linear motion due to chaos. Chaotic systems can easily be mistaken for randomness despite the fact that they are always deterministic. Part of the confusion is due to the fact that the future of chaotic systems can be predicted only on very short-term time scales. Chaotic systems possess a form of functional self-similarity that shows itself in fractal strange attractors. This fractal functionality, combined with chaotic unpredictability, is reminiscent of the uncertainty found in computing systems”.

143 The computational beauty of nature: computer exploratios of fractals, chaos, complex systems and adaptation. Bradford Book, Mit Press. Cambridge, Massachusetts; London, England, 1999, pp. 148/156.

um ponto prévio específico dessa mesma trajetória, ou em outras palavras, há uma beleza matemática e visual no caos que surge no mundo físico ou natural, representada por desenhos marcados por um tipo peculiar de padrão; e encaixado144 – os sistemas caóticos estão encaixados a um número infinito de órbitas periódicas instáveis (ou outros entes sujeitos ao caos)145.

Outro estudioso do caos, Bonting146, ao investigar a ocorrência do caos no mundo, traz mais uma importante constatação: a de que o homem pode controlar o caos.147

144 Tradução livre para embedded.

145“Deterministic. Chaotic systems are completely deterministic and not random. Given a previous history of a

chaotic system, the future of the system will be completely determined; however, this does not mean that we can compute what the future looks like.

[…]. Sensitive. Chaotic systems are extremely sensitive to initial conditions, since any perturbation, no matter how minute, will forever alter the future of a chaotic system. This fact has sometimes been referred to as the ‘butterfly effect’, which comes from Edward Lorenz’s story of how a butterfly flapping its wings can alter global weather patterns. In his book Chance and Chaos, David Ruelle gives an even better example of sensitivity to initial conditions, which I will paraphrase here. Suppose that by some miracle the attractive effect of a single electron located at the limit of the known universe could b suspended momentarily. How long do you think it would take for this slight perturbation to change the future on a macroscopic scale? Since the motion of air causes individual molecules to collide with one another, it would be interesting to know how long it would take for these collisions to be altered. Amazingly, after only about fifty collisions the molecules in Earth’s atmosphere will have collided in a different manner that they would have originally. If we wait another minute or two, the motion in a turbulent portion of the atmosphere will be altered at the macroscopic level. And, if we wait another week or month, the motion of the entire weather system will be measurably altered.

[…]. Ergodic. Chaotic motion is ergodic, which means that the state space trajectory of a chaotic system will always return to the local region of a previous point in the trajectory. For example, we can define a local region of interest by a single point in a state space an a distance measure. Every point in the state space that is within the specified distance from the point will be considered to be in the local region of the point. If a system is ergodic, then no matter how small we make the local region, as long as it’s nonzero, we are guaranteed that the system will eventually return to this local region. Using the weather as an example, ergodicity means that it is very likely that someday in the future you will experience weather almost – but not exactly – identical to today’s weather.

Embedded. Chaotic attractors are embedded with an infinite number of unstable periodic orbits”.

146 BONTING, Sjoerd Lieuwe. Creation and double chaos: science and theology in discussion. Minneapolis:

Fortress Press, 2005, pp. 117/118.

147 “Do chaos events really happen in the natural world? […]. Celestial systems with more than two objects are

subject to nonlinear dynamics. For our solar system, this had been worked out by means of a computer simulation. The current distance between the sun and Earth has been determined to be 150 million kilometers with an uncertainty of only 1 kilometer. The computer simulation shows that this uncertainty of 1 kilometer will increase in the astronomically short time of 95 million years to 150 million kilometers. This is not due to a change in orbital radius, but to variation in eccentricity of an elliptical orbit. Therefore, at this moment, we cannot predict whether 95 million years from now, Earth will collide with the sun, be twice as far away from it as at present, or be somewhere in between. Neither extreme may ever come about, but the point is that we cannot predict the distance between the sun and Earth after 95 million years from now.

Another example is the weather: With all our advances in observation and computation, we are still unable to predict the weather for more than a week ahead. After that, it becomes unpredictable through chaos events. As John Stanford says, ‘the forecast is extremely sensitive to the starting conditions, so much so that it may not even prove possible to predict weather accurately beyond a week or two, due to the fundamental complexities of chaotic dynamics’. Therefore, chaos theory is now commonly used to improve medium – and long - term

Através dessa verificação, o horizonte da comunicação entre o ser humano e os fenômenos caóticos alargou-se, na medida em que o primeiro pode interferir na dinâmica das reações físicas.

Assim, com as experiências científicas de Bonting, ficou mais uma vez provado que o homem pode, se quiser, tornar-se um agente transformador da realidade, suscitando o desencadeamento e mesmo o refreamento do caos.

As formas naturais geradas pela interferência das condições mínimas estão ao nosso redor, como o microscópico design do floco de neve, o formato de algumas plantas, a espiral de uma concha ou mesmo de uma galáxia.

weather forecasts and is used in hurricane modeling for forecasting and, hopefully, finding ways to divert hurricanes from population centers.

Chaos events may also be operating in cases of so-called chance events in evolution. An example is the Cambrian evolutionary explosion, when, after 3 billion years of evolution of unicellular life, there arose 540 million years ago in a mere 5 million years the ancestors of all currently existing life-forms. Peter Smith acknowledges that random mutation in evolution may involve chaos events: ‘If similar environmental triggers always produced the same mutation, then evolution would be even slower that it is’.

Smith also suggests that our brain may well be among the chaotic systems to be found in the world: ‘The mathematical analysis of signal propagation in neural nets together with some suggestive experimental work indicates that certain states of the brain may well evolve with a non-linear, chaos-prone, dynamics’. From experiments involving the balancing of a stick on a finger, scientists have concluded that the rapid, involuntary movements of the stick (faster than a conscious reflex reaction) result from electric noise in the nervous system, which has a chaotic component.

In two cases, human control of chaotic behavior has been found possible. The first case involves turbulent flow. When helium is cooled to 0.001ºK (above the absolute zero of -273ºC), there is no friction, and rotating the vessel in which the helium is contained will not make the fluid rotate. But when the temperature is lowered to between 0.0008ºK and 0.0004ºK, turbulence occurs, indicating chaotic behavior. This condition may also describe the behavior of the rotating neutron ‘fluid’ inside neutron stars.

The other case involves the movement of electrons through a semi-conductor device by means of an applied voltage. At certain discrete voltages, the diffusion of the electrons becomes chaotic, as indicated by a large increase in the current flow. The chaotic diffusion can be switched on an off abruptly by manipulating the voltage. The extreme sensitivity of the phenomenon may provide a new switching method for electronic and photonic devices, permitting the development of novel devices.

These examples lend support to the idea that chaos events are real and have a wide occurrence on a cosmic scale, on our scale, and possibly even on a quantum scale. They make the universe unpredictable and at the same time flexible and open to novelty. The last two examples show that chaos events are open to human control once the right parameter has been found and is set to the right values (such as temperature in the helium experiment and voltage in the electron diffusion experiment)”.