Read Online Soul of the World by Christopher Dewdney - Free Book Online
Authors: Christopher Dewdney
Ads: Link
forty-five feet. But what if there’s a big boulder embedded on the shore of this bay? We measure it and it adds another five feet. Do we include that?”
“Why not?” asks the philosophy student.
“Okay,” says the lead surveyor. “What if there’s an indentation in that boulder, a crack that measures a foot and a half on each side. Do we include those three feet?”
“Why not?” the philosophy student asks again.
“All right,” says the lead surveyor. “What if, in that crevice, there were a smaller crevice? Would we measure that?”
The philosophy student realizes where this is going.
“You’ve got me there,” she says. “Obviously there is no end.”
“That’s right,” says the lead surveyor. “If you measure ever smallerfeatures on a shoreline, going from feet to inches to hundreths of an inch, you’ll soon discover that this nation’s coastline is infinitely long!”
Our little survey crew stumbled on a fact that has a profound implication for measuring time. One of the paradoxes of Zeno’s Arrow was that it could never reach its target because the distance it had to travel could be infinitely halved. Nearly three thousand years later, in the early half of the twentieth century, a British scientist by the name of Lewis F. Richardson continued Zeno’s quest. Coastlines and borders fascinated Richardson. Visiting countries that shared a common, zigzagging border, such as Holland and Belgium or Spain and Portugal, he found that the encyclopedias in each of these countries had estimates of their common borders that varied by as much as 20 percent. The discrepancy could be blamed on bad surveying, but Richardson didn’t think so. He thought there was something more profound going on, and he was right. But it wasn’t until years later that the French mathematician and physicist Benoît Mandelbrot, the father of chaos theory, picked up on Richardson’s interest in borders and coastlines and took it to its logical conclusion. Like our imaginary surveyors, he discovered that any irregular, natural coastline is endless.
You’d think that there would be a limit to this measurement. After all, coastlines exist in the real world. They are fixed, measurable. They don’t wiggle around or fade in and out of existence. But Mandelbrot discovered otherwise. Certainly if you were measuring something like a perfect rectangle lying on the ground, there would be a final value, an ultimate, fixed distance, but he found that with an irregular, natural shoreline there was no end to the bays and peninsulas. They simply got smaller and smaller until finally you were measuring them on themolecular and then the atomic scale. Perhaps on the atomic scale there might be an end to the measurement, a final length of the coastline. But that’s where, maddeningly, everything becomes fuzzy, because the quantum world is indeterminate.
Time, it appears, is the same. Like a shoreline, time is composed of ever smaller, divisible units of itself. A second then, at least hypothetically, ought to contain an eternity, and with the burgeoning pace of ever more accurate clocks, the second is indeed opening up into a new universe of time. After Harrison’s No. 4 Chronometer set a precedent for accuracy, it was inevitable that an even more accurate clock would be built. It happened in 1889. Siegmund Riefler of Germany constructed a clock that worked inside a partial vacuum to reduce the influence of air pressure on the moving parts. His device had an accuracy within a tenth of a second a day and could easily measure milliseconds, or thousandths of a second. It was at this point that clocks became capable of measuring actions that are beyond our ability to see…a housefly flapping its wings once every three milliseconds. But even Riefler’s preeminence was short-lived.
In the 1920s, William H. Shortt, an English railroad engineer, built the first electromechanical clock. It was based on two clocks: a “master” and a
“Why not?” asks the philosophy student.
“Okay,” says the lead surveyor. “What if there’s an indentation in that boulder, a crack that measures a foot and a half on each side. Do we include those three feet?”
“Why not?” the philosophy student asks again.
“All right,” says the lead surveyor. “What if, in that crevice, there were a smaller crevice? Would we measure that?”
The philosophy student realizes where this is going.
“You’ve got me there,” she says. “Obviously there is no end.”
“That’s right,” says the lead surveyor. “If you measure ever smallerfeatures on a shoreline, going from feet to inches to hundreths of an inch, you’ll soon discover that this nation’s coastline is infinitely long!”
Our little survey crew stumbled on a fact that has a profound implication for measuring time. One of the paradoxes of Zeno’s Arrow was that it could never reach its target because the distance it had to travel could be infinitely halved. Nearly three thousand years later, in the early half of the twentieth century, a British scientist by the name of Lewis F. Richardson continued Zeno’s quest. Coastlines and borders fascinated Richardson. Visiting countries that shared a common, zigzagging border, such as Holland and Belgium or Spain and Portugal, he found that the encyclopedias in each of these countries had estimates of their common borders that varied by as much as 20 percent. The discrepancy could be blamed on bad surveying, but Richardson didn’t think so. He thought there was something more profound going on, and he was right. But it wasn’t until years later that the French mathematician and physicist Benoît Mandelbrot, the father of chaos theory, picked up on Richardson’s interest in borders and coastlines and took it to its logical conclusion. Like our imaginary surveyors, he discovered that any irregular, natural coastline is endless.
You’d think that there would be a limit to this measurement. After all, coastlines exist in the real world. They are fixed, measurable. They don’t wiggle around or fade in and out of existence. But Mandelbrot discovered otherwise. Certainly if you were measuring something like a perfect rectangle lying on the ground, there would be a final value, an ultimate, fixed distance, but he found that with an irregular, natural shoreline there was no end to the bays and peninsulas. They simply got smaller and smaller until finally you were measuring them on themolecular and then the atomic scale. Perhaps on the atomic scale there might be an end to the measurement, a final length of the coastline. But that’s where, maddeningly, everything becomes fuzzy, because the quantum world is indeterminate.
Time, it appears, is the same. Like a shoreline, time is composed of ever smaller, divisible units of itself. A second then, at least hypothetically, ought to contain an eternity, and with the burgeoning pace of ever more accurate clocks, the second is indeed opening up into a new universe of time. After Harrison’s No. 4 Chronometer set a precedent for accuracy, it was inevitable that an even more accurate clock would be built. It happened in 1889. Siegmund Riefler of Germany constructed a clock that worked inside a partial vacuum to reduce the influence of air pressure on the moving parts. His device had an accuracy within a tenth of a second a day and could easily measure milliseconds, or thousandths of a second. It was at this point that clocks became capable of measuring actions that are beyond our ability to see…a housefly flapping its wings once every three milliseconds. But even Riefler’s preeminence was short-lived.
In the 1920s, William H. Shortt, an English railroad engineer, built the first electromechanical clock. It was based on two clocks: a “master” and a
Similar Books
