XKCD relevant to current news about the stock market.

"Do mathematicians believe in intuition?"

"Absolutely. Very important, intuition. Actually, I was thinking of fractals," Malcolm said. "You know about fractals?" 

Grant shook his head. "Not really, no." 

"Fractals are a kind of geometry, associated with a man named Mandelbrot. Unlike ordinary Euclidean geometry that everybody learns in school-squares and cubes and spheres-fractal geometry appears to describe real objects in the natural world. Mountains and clouds are fractal shapes. So fractals are probably related to reality. Somehow. 

"Well, Mandelbrot found a remarkable thing with his geometric tools. He found that things looked almost identical at different scales." 

"At different scales?" Grant said. 

"For example," Malcolm said, "a big mountain, seen from far away, has a certain rugged mountain shape. If you get closer, and examine a small peak of the big mountain, it will have the same mountain shape. In fact, you can go all the way down the scale to a tiny speck of rock, seen under a microscope-it will have the same basic fractal shape as the big mountain." 

"I don't really see why this is worrying you," Grant said. He yawned. He smelled the sulfur fumes of the volcanic steam. They were coming now to the section of road that ran near the coastline, overlooking the beach and the ocean.

"It's a way of looking at things," Malcolm said. "Mandelbrot found a sameness from the smallest to the largest. And this sameness of scale also occurs for events."

"Events?"

"Consider cotton prices," Malcolm said. "There are good records of cotton prices going back more than a hundred years. When you study fluctuations in cotton prices, you find that the graph of price fluctuations in the course of a day looks basically like the graph for a week, which looks basically like the graph for a year, or for ten years. And that's how things are. A day is like a whole life. You start out doing one thing, but end up doing something else, plan to run an errand, but never get there. . . . And at the end of your life, your whole existence has that same haphazard quality, too. Your whole life has the same shape as a single day."

"I guess it's one way to look at things," Grant said.

"No," Malcolm said. "It's the only way to look at things. At least, the only way that is true to reality. You see, the fractal idea of sameness carries within it an aspect of recursion, a kind of doubling back on itself, which means that events are unpredictable. That they can change suddenly, and without warning."

"Okay . . ." 

"But we have soothed ourselves into imagining sudden change as something that happens outside the normal order of things. An accident, like a car crash. Or beyond our control, like a fatal illness. We do not conceive of sudden, radical, irrational change as built into the very fabric of existence. Yet it is. And chaos theory teaches us," Malcolm said, "that straight linearity, which we have come to take for granted in everything from physics to fiction, simply does not exist. Linearity is an artificial way of viewing the world. Real life isn't a series of interconnected events occurring one after another like beads strung on a necklace. Life is actually a series of encounters in which one event may change those that follow in a wholly unpredictable, even devastating way." Malcolm sat back in his seat, looking toward the other Land Cruiser, a few yards ahead. "That's a deep truth about the structure of our universe. But, for some reason, we insist on behaving as if it were not true."

At that moment, the cars jolted to a stop, "What's happened?" Grant said.

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