“TWO BILLION DIGITS OF PI? Where do they keep them?” Samuel Eilenberg said scornfully. Eilenberg was a distinguished topologist and emeritus professor of mathematics at Columbia University.
“I think they store the digits on a hard drive,” I answered.
Eilenberg snorted. He didn’t care about some spinning piece of metal covered with pi. He was one of the reasons why the Chudnovskys would never get permanent jobs at Columbia; he made it pretty clear that he would see to it that they were denied tenure. “In the academic world, we have to be careful who our colleagues are,” he told me. “David is a nudnik! You can spend all your life computing digits. What for? It’s about as interesting as going to the beach and counting sand. I wouldn’t be caught dead doing that kind of work.”
In his view, there was something unclean about doing mathematics with a machine. Samuel Eilenberg was a member of the famous Bourbaki group. This group, a sort of secret society of mathematicians that was founded in 1935, consisted mostly of French members (though Eilenberg was originally Polish) who published collectively under the fictitious name Nicolas Bourbaki; they were referred to as “the Bourbaki.” In a quite French way, the Bourbaki were purists who insisted on rigor and logic and formalism. Some members of the Bourbaki group looked down on applied mathematics—that is, they seemed to scorn the use of mathematics to solve real-world problems, even in physics. The Bourbaki especially seemed to dislike the use of machinery in pursuit of truth. Samuel Eilenberg appeared to loathe the Chudnovskys’ supercomputer and what they were doing with it. “To calculate the two billionth digit of pi is to me abhorrent,” he said.
“‘Abhorrent’? Yes, most mathematicians would probably agree with that,” said Dale Brownawell, a respected number theorist at Penn State. “Tastes change, though. To see the Chudnovskys carrying on science at such a high level with such meager support is awe-inspiring.”
Richard Askey, a prominent mathematician at the University of Wisconsin at Madison, would occasionally fly to New York to sit at the foot of Gregory Chudnovsky’s bed and talk about mathematics. “David Chudnovsky is a very good mathematician,” Askey said to me. “Gregory is a great mathematician. The brothers’ pi stuff is just a small part of their work. They are really trying to find out what the word ‘random’ means. I’ve heard some people say that the brothers are wasting their time with that machine, but Gregory Chudnovsky is a very intelligent man who has his head screwed on straight, and I wouldn’t begin to question his priorities. Gregory Chudnovsky’s situation is a national problem.”
“IT LOOKS LIKE KVETCHING,” Gregory said from his bed. “It looks cheap, and it is cheap. I don’t think we were somehow wronged. I really can’t teach. So what does one do about it? We barely have time to do the things we want to do. What is life, and where does the money come from?” He shrugged.
At the end of the summer, the brothers halted their probe into pi. They had other things they wanted to do with their supercomputer, and it was time to move on. They had surveyed pi to 2,260,321,336 digits. It was a world record, doubling their previous world record. If the digits were printed in type, they would stretch from New York to Los Angeles.
In Japan, their competitor Yasumasa Kanada reacted gracefully. He told Science News that he might be able to get a billion and a half digits if he could rent enough time on the Hitachi—the half-megawatt monster.
“You see the advantage of being truly poor,” Gregory said to me. “We had to build our machine, but now we own it.”
M zero had spent most of its time checking the answer to make sure it was correct. “We have done our tests for patterns, and there is nothing,” Gregory said. He was nonchalant about it. “It would be rather stupid if there were a pattern in a few billion digits. There are the usual things. The digit three is repeated nine times in a row, and we didn’t see that before. Unfortunately, we still don’t have enough computer power to see anything in pi.”
And yet…and yet…the brothers felt that they might have noticed something in pi. It hovered out of reach, but seemed a little closer now. It was a slight change in pi that seemed to rise and fall like a tide, as if a distant moon were passing over the sea of digits. It was something random, probably. The brothers felt that they might only have glimpsed the human desire for order. Or was it a wave rippling through pi? Would the wave, if it was there, be the first thread in a tapestry of worlds blossoming in pi? “We need a trillion digits,” David said. Maybe one day they would run the calculation into a trillion digits. Or maybe not. A trillion digits of pi printed in ordinary type would stretch from here to the moon and back, twice. Maybe one day, if they lived and if their machines held together, they would orbit the moon in digits, and would head for Alpha Centauri, seeking pi.
Gregory is lying on his bed in the junkyard, now. He offers to show me the last digits the supercomputer found. He types a command, and suddenly the whole screen fills with pi. It’s the raw Ludolphian number, pouring across the screen like Niagara Falls:
72891 51567 97145 46268 92720 56914 19491 70799 30612 27184
95997 75819 61414 47296 81115 92768 25023 87974 42024 32465
81816 25413 12164 96683 83188 86493 16114 55018 80584 26203
71989 99024 98835 10467 22124 63734 94382 70510 64281 32133
84515 75884 47736 80693 93435 69959 13571 88057 62592 60719
58508 38025 73050 11862 43946 99422 06487 07264 08095 58354
41083 43437 83790 00353 73416 69273 76820 40100 54718 28029
00958 45404 09196 25724 40953 10724 75287 88238 71194 22897
36462 82455 69706 19364 35459 84229 95107 39973 54996 68154
14759 50184 95343 60383 37189 76295 12572 70965 58816 94729
09508 25947 06150 01226 73434 26496 86070 41411 62634 95296
69333 80436 51116 81295 92670 33384 07650 40965 11979 85185
50164 21984 40980 27554 25619 05834 95554 34498 43497 55136
88999 51731 69029 01197 60153 45399 73782 80898 99826 36229
28846 77788 04108 11793 89363 51922 14801 13183 14735 68818
49953 27420 48050 19186 07391 11248 22845 78059 61348 96790
18820 54573 01261 27678 17413 87779 66981 15311 24707 34258
41235 99801 92693 52561 92393 53870 24377 10069 16106 22971
02523 30027 49528 06378 64067 12852 77857 42344 28836 88521
72435 85924 57786 36741 32845 66266 96498 68308 59920 06168
63376 85976 35341 52906 04621 44710 52106 99079 33563 54625
71001 37490 77872 43403 57690 01699 82447 20059 93533 82919
46119 87044 02125 12329 11964 10087 41341 42633 88249 48948
31198 27787 03802 08989 05316 75375 43242 20100 43326 74069
33751 86349 40467 52687 79749 68922 29914 46047 47109 31678
05219 48702 00877 32383 87446 91871 49136 90837 88525 51575
35790 83982 20710 59298 41193 81740 92975 31
We observe pi in silence.
A Death in the Forest
IN 1911, A WOMAN NAMED SALLIE DOOLEY established a Japanese garden at Maymont, her estate in Richmond, Virginia. She planted bamboo, built a gazebo and a waterfall, and, according to her husband, James Dooley, a financier, “purchased the most costly evergreens from all parts of the world.” She died in 1925, leaving Maymont to the city of Richmond. It became a park, and the Japanese garden went untended. In 1951, an entomologist with the Virginia Department of Agriculture discovered a species of Asian insect known as the hemlock woolly adelgid infesting an eastern hemlock—a tree native to North America—on property near Maymont Park. The hemlock woolly adelgid is a tiny brown bug similar to an aphid; the body of an adult is covered with a protective white fluff that makes it look like a fleck of cotton. It is a parasite, and it feeds on several species of hemlock and spruce trees in Asia. This was its first known appearance in eastern North America. The suspicion was that it had come from Sallie Dooley’s languishing evergreens, though no one could be sure. Experts considered it a curiosity.
After hatching from an eg
g, the woolly adelgid goes through a crawler stage, when it moves around. The crawlers are almost invisible to the naked eye. They can drift in the air from tree to tree, and they can cling to the legs and feathers of migrating birds. The insect eventually settles down among the needles of a host tree. It inserts a bundle of mouthparts at the base of a needle and spends the rest of its life—a few months—sucking nutrients out of the tree. A female can lay eggs without being fertilized by a male. The offspring are clones of their mother—genetically identical to her. As it has turned out, the population of woolly adelgids in North America seems to consist entirely of female clones. Males still hatch occasionally, but they breed and live in spruce trees, and American spruces lack certain nutrients they need, so they die—a further indication that the adelgids are transplants. It hardly matters: a single female clone can generate as many as ninety thousand copies of herself in a year.
In Asia, many kinds of natural predators, especially beetles, eat the woolly adelgid, and the host trees have developed resistance to it. In North America, though, there are no natural predators of the adelgid, and eastern hemlocks have virtually no resistance to it. In coming to America, the Asian insect escaped its predators. When millions of woolly adelgids cover the branches of an eastern hemlock, it turns a dirty whitish color, as if it had been flocked with artificial snow. Many of its needles fall off. The tree puts out a new crop of needles the following spring, but the crawlers attach themselves to the new needles, the tree goes into shock, and the needles fall off again. The cycle of shock and defoliation continues until the tree dies, usually in two to six years.
There weren’t many eastern hemlocks in Richmond. The tree doesn’t occur naturally in the area, but it had been planted in some people’s yards, and specimens were scattered sparsely through the city. (Hemlocks are often trimmed into hedges.) For thirty years after its discovery near Maymont Park, the insect gradually moved around the hemlocks of Richmond, and over time many of the the hemlocks in the city lost their needles and died. However, gardeners found that if they sprayed an infested hemlock once a year with pesticides or an oil spray, the bugs would be suppressed.
In the 1980s, an entomologist with the Virginia Department of Forestry named Tim Tigner began tracking the woolly adelgid around Richmond. “We advised people not to worry about it,” Tigner said to me recently. “It didn’t seem to be doing anything.” Then, in the late eighties, Tigner learned that the insect had made its way into a natural stand of ancient hemlocks on the York River, forty miles east of the city, and he went to have a look. He got a shock: 90 percent of the hemlocks were dead. The woolly adelgid had turned the grove into a sun-bleached ruin.
BOTANISTS SOMETIMES REFER to the eastern hemlock as the redwood of the East. It is a tall, long-lived conifer with soft, flat needles and feathery foliage. It has a massive, straight trunk that rises to an impressive height, flaring into a dark, mysterious-looking crown, which is filled with all sorts of living things. The eastern hemlock’s species name is Tsuga canadensis. It occurs naturally in the Appalachian Mountains from Georgia to New Brunswick and Nova Scotia, with a range that runs westward through Michigan into Wisconsin. The tallest eastern hemlocks are somewhat more than 170 feet high, and the largest ones (measured by volume of wood) can be more than six feet in diameter. The oldest living specimens may be more than six hundred years old. Hemlocks and redwoods are extremely shade tolerant—they can grow in dark places where no other trees can survive. Both kinds of trees do especially well in moist valleys filled with temperate rain forest. It seems that few people know that there are rain forests in California. Possibly even fewer people realize that there are also rain forests in the East.
Hemlocks thrive in the temperate rain forest found in the southern Appalachian Mountains. In simple terms, a temperate rain forest is a cool forest that receives at least 80 inches of rainfall a year. Some parts of the southern Appalachians receive up to 130 inches of rainfall a year, with very little snow—more rain than in many parts of the Amazon basin. In the temperate rain forests of the southern Appalachians, hemlocks grow in moist, cool valleys and on mountain slopes, and they form dense stands in the upland valleys called coves.
Hemlocks cast deep shade, and they cover the ground with beds of needles, altering the temperature, moisture, and chemistry of the soil around them. This creates a distinctive habitat for certain animals and plants. An old-growth forest is a forest that’s survived for many centuries without being changed by logging or fire. Only small fragments of old-growth forests remain in the East. Many of them are in Great Smoky Mountains National Park, which lies along the mountainous divide between Tennessee and North Carolina. The national park covers half a million acres; about a fifth of the park has apparently never been logged. Loggers haven’t bothered to go into many coves to cut hemlocks, because the tree is practically worthless for lumber: the wood is full of knots, and often fractures when the tree falls. Some ecologists believe that the hemlock coves of the southern Appalachians contain, or until recently contained, the last examples of primeval rain forest in eastern North America—pockets of rain-forest habitat that seem to have remained unchanged for thousands of years.
In 1988, around the time Tim Tigner saw how the woolly adelgid had destroyed a grove of old hemlocks by the York River, the insect was discovered in Shenandoah National Park, in northern Virginia. It seems to have arrived there when crawlers clung to the legs and feathers of migrating birds that visit or nest in hemlock trees—the black-throated green warbler, the solitary vireo. In Shenandoah, the insect got into stands of old hemlocks packed tightly together in coves, and it multiplied with explosive speed. By 1992, most of the hemlocks in the park were infested, and three years later the majority of them were dead. Today, stands of eastern hemlock have essentially disappeared from Shenandoah National Park.
The crawlers spread rapidly northward. They moved southward only slowly, though, possibly because there were few crawlers around in the autumn when birds flew south. By 1998, many of the hemlock groves in the Delaware Water Gap National Recreation Area, which lies between Pennsylvania and New Jersey, were infested and had begun to die. From eastern Pennsylvania to Connecticut, hemlocks were being turned into skeletons. The insect got to Massachusetts. There, stands of old hemlocks were defoliated. However, a spell of intensely cold weather during the winter of 1996, when temperatures in parts of the Northeast fell to as low as twenty degrees below zero, seemed to kill many adelgids. “The hemlocks looked okay after that cold winter,” James Akerson, an ecologist with Shenandoah National Park, said. “It may have given us a false sense of hope.”
INVASIVE SPECIES OF MICROBES, plants, and animals are changing ecosystems all over the planet in a biological upheaval that may affect almost everything that lives. The cause of the upheaval is the human species. Life on the planet is being homogenized by the expanding human population and the frequent and rapid movement of people and goods, which carry invasive organisms with them. These invasives often flourish in their new ecosystems because, like the woolly adelgid, they have escaped their predators. A fungal disease called chestnut blight, from Asia, first appeared in North America in 1904. Spread by wind, rain, and birds, it killed almost every American chestnut tree. Chestnuts had once saturated vast stretches of forest in the Appalachians. They essentially vanished from the ecosystem. The term biologists use for this is “functional extinction.”
Since the 1930s, the American elm has gone almost extinct in the wild, pushed into oblivion by an invasive Asian fungus spread by an invading beetle from Europe. In the 1960s and ’70s, the balsam woolly adelgid (from northern Asia) got into the Fraser fir, a native American species growing on the higher ridges and peaks of the southern Appalachian Mountains; this parasite killed from 70 to 90 percent of the mature wild Fraser firs, making the mountains look as if they were covered with driftwood. (Today the wild Fraser firs in the Appalachians often don’t get much taller than a person before they die from adelgid infestation.) A fungal di
sease of unknown origin has killed off the vast majority of the wild flowering dogwoods in North America. Another disease, sudden oak death, has killed hundreds of thousands of oaks in California and may get into Eastern oaks. A European insect carrying a European fungus has lately caused a mass dying of the American beech tree, and the American beech’s future as a species in the wild is uncertain. An Asian beetle called the emerald ash borer arrived in Michigan in 2001 in packing wood from China. It is devastating to a number of species of American ash trees. Despite strong efforts to control it, the emerald ash borer keeps appearing in different places, and it seems capable of not only wiping out the ash but threatening the classic major-league baseball bat (which is commonly made of ash). Another invader, the Asian long-horned beetle, had its North American debut in Brooklyn, where it showed up in a park near warehouses that held large amounts of packing wood from China. The Asian long-horned beetle has infested tens of thousands of trees in New Jersey and Long Island, and it has shown up Sacramento. It could take out the sugar maple. In effect, the trees of North America have been hit with all sorts of Ebolas of their own.
When a parasite moves to a new habitat, it can find new hosts through a process called the trans-species jump. Often the new host has no resistance; the host and the parasite haven’t had time to adjust to each other through natural selection. (It is frequently not in the best interest of a parasite to kill its host quickly.) One example is the human immunodeficiency virus, HIV. It appears to have once lived in chimpanzees, though it doesn’t make them sick—the chimp’s immune system is well acquainted with the virus and has learned how to deal with it. In Africa, at various times and places in the twentieth century, HIV made trans-species jumps into humans—probably through hunters who killed and butchered chimps, and so were exposed to infected chimp blood. Once the virus had escaped the chimpanzee’s immune system, it amplified itself freely in its new hosts.