Saturday, February 18, 2023

Chaos




The question is not Can they reason?, nor Can they talk?, but Can they suffer? -Jeremy Bentham, jurist and philosopher

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Arms dealing.
Indian Prime Minister Narendra Modi announced that India aims to more than triple its annual defense exports to $5 billion over the next two years. While India aspires to become a manufacturer of sophisticated defense equipment in collaboration with global giants, first to meet its own needs and eventually to export, it will have to depend on arms imports until then. Their usual supplier is Russia--and India has declined to criticize Russia's invasion of Ukraine.
But the U.S. is in India displaying their new Lockheed Martin F-35s.

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The district earlier this school year replaced the honors classes at Culver City High School with uniform courses that officials say will ensure students of all races receive an equal, rigorous education.

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Chaos

On a winter day 50 years ago, Edward Lorenz, SM ‘43, ScD ‘48, a mild-mannered meteorology professor at MIT, entered some numbers into a computer program simulating weather patterns and then left his office to get a cup of coffee while the machine ran. When he returned, he noticed a result that would change the course of science.

The computer model was based on 12 variables, representing things like temperature and wind speed, whose values could be depicted on graphs as lines rising and falling over time. On this day, Lorenz was repeating a simulation he’d run earlier—but he had rounded off one variable from .506127 to .506. To his surprise, that tiny alteration drastically transformed the whole pattern his program produced, over two months of simulated weather.

The unexpected result led Lorenz to a powerful insight about the way nature works: small changes can have large consequences. The idea came to be known as the “butterfly effect” after Lorenz suggested that the flap of a butterfly’s wings might ultimately cause a tornado. And the butterfly effect, also known as “sensitive dependence on initial conditions,” has a profound corollary: forecasting the future can be nearly impossible.

Like the results of a wing’s flutter, the influence of Lorenz’s work was nearly imperceptible at first but would resonate widely. In 1963, Lorenz condensed his findings into a paper, “Deterministic Nonperiodic Flow,” which was cited exactly three times by researchers outside meteorology in the next decade. Yet his insight turned into the founding principle of chaos theory, which expanded rapidly during the 1970s and 1980s into fields as diverse as meteorology, geology, and biology. “It became a wonderful instance of a seemingly esoteric piece of mathematics that had experimentally verifiable applications in the real world,” says Daniel Rothman, a professor of geophysics at MIT. (from MIT Technology Review)

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