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linked by invisible webs of pressure and tension to every other grain. So the full dynamics of sand physics grew in complexity
a millionfold every second. New grain of sand? Okay, you had to remap
everything.
No computer could work that fast. The nature of this expanding complexity demolished the concept of prediction. “As one attempts
to make predictions further and further into the future,” Bak had speculated, “the amount of information one needs to gather
about the initial conditions increases exponentially.” And this is exactly what Held saw inside that Plexiglas case. While
you might be able to predict how one or two or even a hundred grains would interact, by the time you got to a thousand grains,
it was impossible to measure every little detail you’d need to even try to guess what was going to happen next. Such a world
was beyond the scope of even the most complex forms of Newtonian physics. In Bak’s mind there was almost no limit to how far
you might extend this logic. Any complex system likely expressed the same dynamics: the earth’s crust, ecosystems, stock markets,
international politics. Past a certain point, the internal dynamics of these systems were simply, bewilderingly unknowable.
Held tried making piles on larger and larger plates and found that, after a certain size, even the power-law distribution
of avalanches disappeared. The systems became so complex that no rules offered even a general sense of how often a grain of
sand would lead to catastrophe. You just had to sit there and watch, grain by grain, and wait. And while you sat there, you
could think about this: nothing in the history of physics or mathematics could tell you what was going to happen next.
Bak’s world wasn’t stable or well ordered. The chaos, the random, hectic shifting and shuffling of Held’s microscopic beach
particles, was an expression of energy of a sort, energy just as likely to create as to destroy. The sandpile was in a continuous
state of change; it never stood still long enough for any one set of equations to describe it fully. If Bak was right about
his theory, it should be as true outside the lab as inside — and that would demand nothing less than a complete revolution
in how the scientists around him thought. There was something profound and amazing in the dynamics of the piles, he thought:
their ability not only to translate order into chaos, but also to translate chaos into order. Sand grains, stocks, pieces
of the earth’s crust — these moved not according to some simple input and output formula but rather because of a complex logic,
where dense internal forces were as important as any outside forces. Avalanches and earthquakes expressed that logic, but
what got Bak excited was that the same physics was also at work when the sandpiles produced California from pebbles, or great
fortunes from the movement of markets. The sandpile seemed to
make
things, maybe even most of the world.
Bak liked to pass along a quote from the nineteenth-century French novelist Victor Hugo as a prescient summary of the idea:
“How do we know that the creations of worlds are not determined by falling grains of sand?” What if the real world was like
this, precariously unbalanced between stability and chaos? Bak wondered. If the logic of such a complex system could be penetrated,
even a little bit, there might be no limit to what you could create. The world wasn’t a slew of senseless randomness; it just
required new and different ways of calculating. If you could manage to discover those new ways, even the most difficult problems
would open up. This had happened before — repeatedly — in science. But if the system remained opaque? If the logic stayed
buried in those shifting sand grains? Well, then, science would continue chasing the phantoms that had undone every model
for the universe ever created. The logic of the world, even while expressing an immense inner
a millionfold every second. New grain of sand? Okay, you had to remap
everything.
No computer could work that fast. The nature of this expanding complexity demolished the concept of prediction. “As one attempts
to make predictions further and further into the future,” Bak had speculated, “the amount of information one needs to gather
about the initial conditions increases exponentially.” And this is exactly what Held saw inside that Plexiglas case. While
you might be able to predict how one or two or even a hundred grains would interact, by the time you got to a thousand grains,
it was impossible to measure every little detail you’d need to even try to guess what was going to happen next. Such a world
was beyond the scope of even the most complex forms of Newtonian physics. In Bak’s mind there was almost no limit to how far
you might extend this logic. Any complex system likely expressed the same dynamics: the earth’s crust, ecosystems, stock markets,
international politics. Past a certain point, the internal dynamics of these systems were simply, bewilderingly unknowable.
Held tried making piles on larger and larger plates and found that, after a certain size, even the power-law distribution
of avalanches disappeared. The systems became so complex that no rules offered even a general sense of how often a grain of
sand would lead to catastrophe. You just had to sit there and watch, grain by grain, and wait. And while you sat there, you
could think about this: nothing in the history of physics or mathematics could tell you what was going to happen next.
Bak’s world wasn’t stable or well ordered. The chaos, the random, hectic shifting and shuffling of Held’s microscopic beach
particles, was an expression of energy of a sort, energy just as likely to create as to destroy. The sandpile was in a continuous
state of change; it never stood still long enough for any one set of equations to describe it fully. If Bak was right about
his theory, it should be as true outside the lab as inside — and that would demand nothing less than a complete revolution
in how the scientists around him thought. There was something profound and amazing in the dynamics of the piles, he thought:
their ability not only to translate order into chaos, but also to translate chaos into order. Sand grains, stocks, pieces
of the earth’s crust — these moved not according to some simple input and output formula but rather because of a complex logic,
where dense internal forces were as important as any outside forces. Avalanches and earthquakes expressed that logic, but
what got Bak excited was that the same physics was also at work when the sandpiles produced California from pebbles, or great
fortunes from the movement of markets. The sandpile seemed to
make
things, maybe even most of the world.
Bak liked to pass along a quote from the nineteenth-century French novelist Victor Hugo as a prescient summary of the idea:
“How do we know that the creations of worlds are not determined by falling grains of sand?” What if the real world was like
this, precariously unbalanced between stability and chaos? Bak wondered. If the logic of such a complex system could be penetrated,
even a little bit, there might be no limit to what you could create. The world wasn’t a slew of senseless randomness; it just
required new and different ways of calculating. If you could manage to discover those new ways, even the most difficult problems
would open up. This had happened before — repeatedly — in science. But if the system remained opaque? If the logic stayed
buried in those shifting sand grains? Well, then, science would continue chasing the phantoms that had undone every model
for the universe ever created. The logic of the world, even while expressing an immense inner
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