The Collapse of Chaos: Discovering Simplicity in a Complex World by Ian Stewart & Jack Cohen

Author:Ian Stewart & Jack Cohen [Stewart, Ian & Cohen, Jack]
Language: eng
Format: epub
Tags: Science, Chaotic Behavior in Systems, General
ISBN: 9780141938288
Google: Pyvsn1ul4awC
Amazon: B00IGZ09WA
Publisher: Penguin UK
Published: 2000-03-01T16:00:00+00:00

8 THE NATURE OF LAWS

Ivan and Pyotr were watching the installation of the Omsk telephone exchange. “These modern gadgets,” sighed Pyotr. “I can never understand how they work.”

“But it is easy,” replied Ivan. “It is like a very long dachshund. You twist his tail, and he barks in the middle of the city.”

“Ah,” said Pyotr. “That explains telephones. But what about radio?”

“Radio is exactly the same,” said Ivan, “but without the dachshund.”

Our exploration of the influence of context upon the behavior of the universe begins with physics and chemistry. At first it might seem strange that such things as contextual physics and chemistry could have any meaning; but that's because reductionism attains its fullest development in those areas, where we are so accustomed to the reductionist view that we tend to ask only questions that have reductionist answers. In fact, most of the “big picture” questions in physics and chemistry—the arrow of time, the interpretation of quantum mechanics, the nature of the physical universe—depend at least as much upon context as upon content. So do many questions about common patterns that arise within systems whose insides are extremely different (for example, both galaxies and bathwater follow spirals).

Scientists get themselves enormously confused about big questions. The reason is that they try to tackle them in the same way that they tackle the small questions. When trying to understand the gas laws, they come across principles such as the second law of thermodynamics, whose usual interpretation is that the amount of disorder in the universe steadily increases. This principle works brilliantly when applied to the behavior of gases, but it sits uneasily with the rich complexities of life on our planet. In a similar manner, the linearity of quantum mechanics—the fact that any two quantum states can be superposed to yield another—works brilliantly for electrons but leads to the paradoxical plight of Schrödinger's cat, which seems to make no sense whatsoever.

Both cases have a lot in common. Each rests on a single, rather simple mathematical law—irreversibility in one, linearity in the other. Each law is exceedingly general in scope: Every mechanical system is time-reversible; every set of quantum states can be superposed. Each runs into conflict with our senses when it is applied to the complex systems that make up the world on the human scale. To a physicist, an atom is simple, but a cat is an enormously complicated system of around 1026 atoms. To a child pouring out a saucer of milk, a cat is simple but an atom is incomprehensibly complicated.

We shall argue that the apparent paradoxes inherent in these problems rest upon an inadequate understanding of the role of context. The simple laws of physics answer particular, simple questions in their own appropriate contexts: gases; electrons. They seem to answer similar questions in much wider contexts, such as cats. So why do they also seem to give wrong answers, answers in conflict with everyday experience? Because in the context of everyday experience they are addressing quite different questions from those they appear to be addressing.

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