little fuel left, but its crew was able to fly over Kokura on the way back to Tinian, and taking advantage of a break in the clouds, they dropped the bomb there. Ninety thousand people died in Kokura. The
On August 11th, 1945, a child named Ai Matsui was born in Hiroshima. In 1960 she began to speak in local meetings on many topics, including Hiroshima’s special position in the world. Its citizens had escaped annihilation, she said, as if protected by some covering angel (or law); they had a responsibility to the dead of Kokura and Nagasaki, to represent them in the world of the living, to change the world for the good. The Hiroshima Peace Party quickly grew to become the dominant political movement in Hiroshima, and then, in revulsion at the violence of the 1960s in Vietnam and elsewhere, all over Japan. In the 1970s the party became a worldwide movement, gaining the enthusiastic support of ex-President Kennedy, and President Babbitt. Young people from every country joined it as if experiencing a religious conversion. In 1983 Japan began its Asian Assistance League. One of its health care programs saved the life of a young woman in India, sick with malaria. The next year she had a child, a woman destined to become India’s greatest leader. In 1987, the nation of Palestine raised its flag over the West Bank and parts of Jordan and Lebanon; a generation of camp children moved into homes. A child was born in Galilee. In 1990 Japan started its African Assistance League. The Hiroshima Peace Party had a billion members.
And so on; so that by July 29th, 2045, no human on Earth was the same as those who would have lived if the nomad in Kirgiz had not stepped on the butterfly a century before.
This phenomenon is known as the butterfly effect, and it is a serious problem for all other models of historical explanation; meaning trouble for you and for me. The scientific term for it is “sensitive dependence on initial conditions.” It is an aspect of chaos theory first studied by the meteorologist Edward Lorenz, who, while running computer simulations of weather patterns, discovered that the slightest change in the initial conditions of the simulation would quickly lead to completely different weather.
So the strong covering law model said that historical explanation should equal the rigor of scientific explanation. Then its defenders, bringing the model into the quantum world, conceded that predictions can never be anything but probabilistic at best. The explanandum was no longer deducible from the explanans; one could only suggest probabilities.
Now chaos theory has added new problems. And yet consider: Captain Frank January chose to miss Hiroshima. Ten years later, nuclear weapons were universally banned. Eleven years later, local conflicts in the Middle East erupted into general war, and nuclear weapons were quickly reassembled and used. For it is not easy to forget knowledge, once it is learned; symmetry T, which says that physical laws are the same no matter which way the time arrow is pointed, does not actually exist in nature. There is no going back.
And so by 1990, in this particular world, the bombed cities were rebuilt. The Western industrial nations were rich, the southern developing nations were poor. Multinational corporations ruled the world’s economy. The Soviet bloc was falling apart. Gigantic sums of money were spent on armaments. By the year 2056, there was very little to distinguish this world from the one in which January had dropped the bomb, in which Tibbetts had bombed Hiroshima, in which Tibbetts had made a demonstration, in which Tibbetts bombed Kokura.
Perhaps a sum over histories had bunched the probabilities. Is this likely? We don’t know. We are particles, moving in a wave. The wave breaks. No math can predict which bubbles will appear where. But there is a sum over histories. Chaotic systems fall into patterns, following the pull of strange attractors. Linear chaotic figures look completely non-repetitive, but slice them into Poincare sections and they reveal the simplest kinds of patterns. There is a tide, and we float in it; perhaps it is the flux of the cosmos itself; swim this way or that, the tide still carries us to the same destination. Perhaps.
So the covering law model is amended yet again. Explanations still require laws, but there are not laws for every event. The task of historical explanation becomes the act of making distinctions, between those parts of an event that can be explained by laws, and those that cannot. The component events that combine to create an explanandum are analyzed each in turn, and the historian then concentrates on the explicable components.
Paul Tibbetts flies toward Hiroshima. The nomad steps out of his yurt.
Lyapunov exponents are numbers that measure the conflicting effects of stretching, contracting, and folding in the phase space of an attractor. They set the topological parameters of unpredictability. An exponent greater than zero means stretching, so that each alternative history moves farther and farther apart as time passes. An exponent smaller than zero means contraction, so that alternatives tend to come back together. When the exponent equals zero, a periodic orbit results.
What is history’s Lyapunov exponent? This is the law that no one can know.
Frank January flies toward Hiroshima. The nomad stops in his yurt.
It is said that the historian’s task requires an imaginative reconstruction of the thinking of people who acted in the past, and of the circumstances in which they acted. “An explanation is said to be successful when the historian gets the sense of reliving the past which he is trying to explain.”
You are flying toward Hiroshima. You are the bombardier. You have been given the assignment two days before. You know what the bomb will do. You do not know what you will do. You have to decide.
There are a hundred billion neurons in the brain. Some of the neurons have as many as eighty thousand synaptic endings. During thought, neurotransmitter chemicals flow across the synaptic clefts between one neuron’s synaptic knobs and another’s dendritic spines, reversing a slight electric charge, which passes on a signal. The passage of a signal often leaves changes in the synapses and dendrites along the way, forever altering the structure of the brain. This plasticity makes memory and learning possible. Brains are always growing; intensely in the first five years, then steadily thereafter.
At the moment of choice, then, signals fly through a neural network that has been shaped over a lifetime into a particular and unique structure. Some signals are conscious, others are not. According to Roger Penrose, during the process of decision quantum effects in the brain take over, allowing a great number of parallel and simultaneous computations to take place; the number could be extraordinarily large, 10 to the 21st power or more. Only at the intrusion of the “observation,” that is to say a decision, do the parallel computations resolve back into a single conscious thought.
And in the act of deciding, the mind attempts the work of the historian: breaking the potential events down into their component parts, enumerating conditions, seeking covering laws that will allow a prediction of what will follow from the variety of possible choices. Alternative futures branch like dendrites away from the present moment, shifting chaotically, pulled this way and that by attractors dimly perceived. Probable outcomes emerge from those less likely.
And then, in the myriad clefts of the quantum mind, a mystery: the choice is made. We have to choose, that is life in time. Some powerful selection process, perhaps aesthetic, perhaps moral, perhaps practical (survival of the thinker), shoves to consciousness those plans that seem safest, or most right, or most beautiful, we do not know; and the choice is made. And at the moment of this observation the great majority of alternatives disappear without trace, leaving us in our asymptotic freedom to act, uncertainly, in time’s asymmetrical flow.
There are few covering laws. Initial conditions are never fully known. The butterfly may be on the wing, it may be crushed underfoot. You are flying toward Hiroshima.
“A REAL JOY TO BE HAD”
Kim Stanley Robinson Interviewed by Terry Bisson
I didn’t know science fiction existed until I was eighteen; then I fell in pretty deeply. The first book I remember reading was
