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IntroductionREEF, CITY, WEBas imagination bodies forth The forms of things unknown, the poets pen Turns them to shapes and gives to airy nothing A local habitation and a name SHAKESPEARE, A Midsummer Nights Dream, Vi Darwins ParadoxApril ,Over the eastern expanse of the Indian Ocean, the reliable northeast winds of monsoon season have begun to give way to the serene days of summer On the Keeling Islands, two small atolls composed of twenty seven coral islands six hundred miles west of Sumatra, the emerald waters are invitingly placid and warm, their hue enhanced by the brilliant white sand of disintegrated coral On one stretch of shore usually guarded by stronger surf, the water is so calm that Charles Darwin wades out, under the vast blue sky of the tropics, to the edge of the live coral reef that rings the islandFor hours he stands and paddles among the crowded pageantry of the reef Twenty seven years old, seven thousand miles from London, Darwin is on the precipice, standing on an underwater peak ascending over an unfathomable sea He is on the edge of an idea about the forces that built that peak, an idea that will prove to be the first great scientific insight of his career And he has just begun exploring another hunch, still hazy and unformed, that will eventually lead to the intellectual summit of the nineteenth centuryAround him, the crowds of the coral ecosystem dart and shimmer The sheer variety dazzles butterflyfish, damselfish, parrotfish, Napoleon fish, angelfish golden anthias feeding on plankton above the cauliflower blooms of the coral the spikes and tentacles of sea urchins and anemones The tableau delights Darwins eye, but already his mind is reaching behind the surface display to aprofound mystery In his account of the Beagles voyage, published four years later, Darwin would write It is excusable to grow enthusiastic over the infinite numbers of organic beings with which the sea of the tropics, so prodigal of life, teems yet I must confess I think those naturalists who have described, in well known words, the submarine grottoes decked with a thousand beauties, have indulged in rather exuberant languageWhat lingers in the back of Darwins mind, in the days and weeks to come, is not the beauty of the submarine grotto but rather the infinite numbers of organic beings On land, the flora and fauna of the Keeling Islands are paltry at best Among the plants, there is little but cocoa nut trees, lichen, and weeds The list of land animals, he writes, is even poorer than that of the plants a handful of lizards, almost no true land birds, and those recent immigrants from European ships, rats The island has no domestic quadruped excepting the pig, Darwin notes with disdainYet just a few feet away from this desolate habitat, in the coral reef waters, an epic diversity, rivaled only by that of the rain forests, thrives This is a true mystery Why should the waters at the edge of an atoll support so many different livelihoods Extract ten thousand cubic feet of water from just about anywhere in the Indian Ocean and do a full inventory on the life you find there the list would be about as poor as Darwins account of the land animals of the Keelings You might find a dozen fish if you were lucky On the reef, you would be guaranteed a thousand In Darwins own words, stumbling across the ecosystem of a coral reef in the middle of an ocean was like encountering a swarming oasis in the middle of a desert We now call this phenomenon Darwins Paradox so many different life forms, occupying such a vast array of ecological niches, inhabiting waters that are otherwise remarkably nutrient poor Coral reefs make up about one tenth of one percent of the earths surface, and yet roughly a quarter of the known species of marine life make their homes there Darwin doesnt have those statistics available to him, standing in the lagoon in , but he has seen enough of the world over the preceding four years on the Beagle to know there is something peculiar in the crowded waters of the reefThe next day, Darwin ventures to the windward side of the atoll with the Beagles captain, Vice Admiral James FitzRoy, and there they watch massive waves crash against the corals white barrier An ordinary European spectator, accustomed to the calmer waters of the English Channel or the Mediterranean, would be naturally drawn to the impressive crest of the surf The breakers, Darwin observes, are almost equal in force to those during a gale of wind in the temperate regions, and never cease to rage But Darwin has his eye on something elsenot the violent surge of water but the force that resists it the tiny organisms that have built the reef itselfThe ocean throwing its waters over the broad reef appears an invincible, all powerful enemy yet we see it resisted, and even conquered, by means which at first seem most weak and inefficient It is not that the ocean spares the rock of coral the great fragments scattered over the reef, and heaped on the beach, whence the tall cocoa nut springs, plainly bespeak the unrelenting power of the wavesYet these low, insignificant coral islets stand and are victorious for here another power, as an antagonist, takes part in the contest The organic forces separate the atoms of carbonate of lime, one by one, from the foaming breakers, and unite them into a symmetrical structure Let the hurricane tear up its thousand huge fragments yet what will that tell against the accumulated labour of myriads of architects at work night and day, month after month Darwin is drawn to those minuscule architects because he believes they are the key to solving the mystery that has brought the Beagle to the Keeling Islands In the Admiraltys memorandum authorizing the ships five year journey, one of the principal scientific directives is the investigation of atoll formation Darwins mentor, the brilliant geologist Charles Lyell, had recently proposed that atolls are created by undersea volcanoes that have been driven upward by powerful movements in the earths crust In Lyells theory, the distinctive circular shape of an atoll emerges as coral colonies construct reefs along the circumference of the volcanic crater Darwins mind had been profoundly shaped by Lyells understanding of the deep time of geological transformation, but standing on the beach, watching the breakers crash against the coral, he knows that his mentor is wrong about the origin of the atolls It is not a story of simple geology, he realizes It is a story about the innovative persistence of life And as he mulls the thought, there is a hint of something else in his mind, a larger,encompassing theory that might account for the vast scope of lifes innovations The forms of things unknown are turning, slowly, into shapesDays later, back on the Beagle, Darwin pulls out his journal and reflects on that mesmerizing clash between surf and coral Presaging a line he would publish thirty years later in the most famous passage from On the Origin of Species, Darwin writes, I can hardly explain the reason, but there is to my mind much grandeur in the view of the outer shores of these lagoon islands In time, the reason would come to himThe Superlinear CityFrom an early age, the Swiss scientist Max Kleiber had a knack for testing the edges of convention As an undergraduate in Zurich in the s, he roamed the streets dressed in sandals and an open collar, shocking attire for the day During his tenure in the Swiss army, he discovered that his superiors had been trading information with the Germans, despite the official Swiss position of neutrality in World War I Appalled, he simply failed to appear at his next call up, and was ultimately jailed for several months By the time he had settled on a career in agricultural science, he had had enough of the restrictions of Zurich society And so Max Kleiber charted a path that would be followed by countless sandal wearing, nonconformist war protesters in the decades to come He moved to CaliforniaKleiber set up shop at the agricultural college run by the University of California at Davis, in the heart of the fertile Central Valley His research initially focused on cattle, measuring the impact body size had on their metabolic rates, the speed with which an organism burns through energy Estimating metabolic rates had great practical value for the cattle industry, because it enabled farmers to predict with reasonable accuracy both how much food their livestock would require, and how much meat they would ultimately produce after slaughter Shortly after his arrival at Davis, Kleiber stumbled across a mysterious pattern in his research, a mathematical oddity that soon brought a muchdiverse array of creatures to be measured in his lab rats, ring doves, pigeons, dogs, even humansScientists and animal lovers had long observed that as life gets bigger, it slows down Flies live for hours or days elephants live for half centuries The hearts of birds and small mammals pump blood much faster than those of giraffes and blue whales But the relationship between size and speed didnt seem to be a linear one A horse might be five hundred times heavier than a rabbit, yet its pulse certainly wasnt five hundred times slower than the rabbits After a formidable series of measurements in his Davis lab, Kleiber discovered that this scaling phenomenon stuck to an unvarying mathematical script called negative quarter power scaling If you plotted mass versus metabolism on a logarithmic grid, the result was a perfectly straight line that led from rats and pigeons all the way up to bulls and hippopotamiPhysicists were used to discovering beautiful equations like this lurking in the phenomena they studied, but mathematical elegance was a rarity in the comparatively messy world of biology But thespecies Kleiber and his peers analyzed, the clearer the equation became metabolism scales to mass to the negative quarter power The math is simple enough you take the square root of ,, which is approximately , and then take the square root of , which is again, approximatelyThis means that a cow, which is roughly a thousand times heavier than a woodchuck, will, on average, livetimes longer, and have a heart rate that istimes slower than the woodchucks As the science writer George Johnson once observed, one lovely consequence of Kleibers law is that the number of heartbeats per lifetime tends to be stable from species to species Bigger animals just take longer to use up their quotaOver the ensuing decades, Kleibers law was extended down to the microscopic scale of bacteria and cell metabolism even plants were found to obey negative quarter power scaling in their patterns of growth Wherever life appeared, whenever an organism had to figure out a way to consume and distribute energy through a body, negative quarter power scaling governed the patterns of its developmentSeveral years ago, the theoretical physicist Geoffrey West decided to investigate whether Kleibers law applied to one of lifes largest creations the superorganisms of human built cities Did the metabolism of urban life slow down as cities grew in size Was there an underlying pattern to the growth and pace of life of metropolitan systems Working out of the legendary Santa Fe Institute, where he served as president until , West assembled an international team of researchers and advisers to collect data on dozens of cities around the world, measuring everything from crime to household electrical consumption, from new patents to gasoline salesWhen they finally crunched the numbers, West and his team were delighted to discover that Kleibers negative quarter power scaling governed the energy and transportation growth of city living The number of gasoline stations, gasoline sales, road surface area, the length of electrical cables all these factors follow the exact same power law that governs the speed with which energy is expended in biological organisms If an elephant was just a scaled up mouse, then, from an energy perspective, a city was just a scaled up elephantBut the most fascinating discovery in Wests research came from the data that didnt turn out to obey Kleibers law West and his team discovered another power law lurking in their immense database of urban statistics Every datapoint that involved creativity and innovationpatents, RD budgets, supercreative professions, inventorsalso followed a quarter power law, in a way that was every bit as predictable as Kleibers law But there was one fundamental difference the quarter power law governing innovation was positive, not negative A city that was ten times larger than its neighbor wasnt ten timesinnovative it was seventeen timesinnovative A metropolis fifty times bigger than a town wastimesinnovativeKleibers law proved that as life gets bigger, it slows down But Wests model demonstrated one crucial way in which human built cities broke from the patterns of biological life as cities get bigger, they generate ideas at a faster clip This is what we call superlinear scaling if creativity scaled with size in a straight, linear fashion, you would of course findpatents and inventions in a larger city, but the number of patents and inventions per capita would be stable Wests power laws suggested something farprovocative that despite all the noise and crowding and distraction, the average resident of a metropolis with a population of five million people was almost three timescreative than the average resident of a town of a hundred thousand Great cities are not like towns only larger, Jane Jacobs wrote nearly fifty years ago Wests positive quarter power law gave that insight a mathematical foundation Something about the environment of a big city was making its residents significantlyinnovative than residents of smaller towns But what was it The RuleThe first national broadcast of a color television program took place on January when NBC aired an hour long telecast of the Tournament of Roses parade, and distributed it to twenty two cities across the country For those lucky enough to see the program, the effect of a moving color image on a small screen seems to have been mesmerizing The New York Times, in typical language, called it a veritable bevy of hues and depth To concentrate so much color information within the frame of a small screen, the Times wrote, would be difficult for even the most gifted artist doing a still painting To do it with constantly moving pictures seemed pure wizardry Alas, the Rose Parade broadcast turned out to be not all that broad, given that it was visible only on prototype televisions in RCA showrooms Color programming would not become standard on prime time shows until the late s After the advent of color, the basic conventions that defined the television image would go unchanged for decades The delivery mechanisms began to diversify with the introduction of VCRs and cable in the late s But the image remained the sameIn the mid s, a number of influential media and technology executives, along with a few visionary politicians, had the eminently good idea that it was time to upgrade the video quality of broadcast television Speeches were delivered, committees formed, experimental prototypes built, but it wasnt until July that a Raleigh, North Carolina, CBS affiliate initiated the first public transmission of an HDTV signal Like the Tournament of Roses footage, though, there were no ordinary consumers with sets capable of displaying its wizardry A handful of broadcasters began transmitting HDTV signals in , but HD television didnt become a mainstream consumer phenomenon for another five years Even after the FCC mandated that all television stations cease broadcasting the old analog standard on June thanpercent of US households had televisions that went dark that dayIt is one of the great truisms of our time that we live in an age of technological acceleration the new paradigms keep rolling in, and the intervals between them keep shortening This acceleration reflects not only the flood of new products, but also our growing willingness to embrace these strange new devices, and put them to use The waves roll in at ever increasing frequencies, andandof us are becoming trained surfers, paddling out to meet them the second they start to crest But the HDTV story suggests that this acceleration is hardly a universal law If you measure how quickly a new technology progresses from an original idea to mass adoption, then it turns out that HDTV was traveling at the exact same speed that color television had traveled four decades earlier It took ten years for color TV to go from the fringes to the mainstream two generations later, it took HDTV just as long to achieve mass successIn fact, if you look at the entirety of the twentieth century, the most important developments in mass, one to many communications clock in at the same social innovation rate with an eerie regularity Call it the rule a decade to build the new platform, and a decade for it to find a mass audience The technology standard of amplitude modulated radiowhat we now call AM radioevolved in the first decade of the twentieth century The first commercial AM station began broadcasting in , but it wasnt until the late s that radios became a fixture in American households Sony inaugurated research into the first consumer videocassette recorder in , but didnt ship its first Betamax for another seven years, and VCRs didnt become a household necessity until the mid eighties The DVD player didnt statistically replace the VCR in American households until , nine years after the first players went on the market Cell phones, personal computers, GPS navigation devicesall took a similar time frame to go from innovation to mass adoptionConsider, as an alternate scenario, the story of Chad Hurley, Steve Chen, and Jawed Karim, three former employees of the online payment site PayPal, who decided in earlythat the Web was ripe for an upgrade in the way it handled video and sound Video, of course, was not native to the Web, which had begun its life fifteen years before as a platform for academics to share hypertext documents But over the years, video clips had begun to trickle their way online, thanks to new video standards that emerged, such as Quick Time, Flash, or Windows Media Player But the mechanisms that allowed people to upload and share their own videos were too challenging for most ordinary users So Hurley, Chen, and Karim cobbled together a rough beta for a service that would correct these deficiencies, raised less thanmillion in venture capital, hired about two dozen people, and launched YouTube, a website that utterly transformed the way video information is shared online Within sixteen months of the companys founding, the service was streamingthanmillion videos a day Within two years, YouTube was one of the top ten most visited sites on the Web Before Hurley, Chen, and Karim hit upon their idea for a start up, video on the Web was as common as subtitles on television The Web was about doing things with text, and uploading the occasional photo YouTube brought Web video into the mainstreamNow compare the way these two ideasHDTV and YouTube changed the basic rules of engagement for their respective platforms Going from analog television to HDTV is a change in degree, not in kind there arepixels the sound isimmersive the colors are sharper But consumers watch HDTV the exact same way they watched old fashioned analog TV They choose a channel, and sit back and watch YouTube, on the other hand, radically altered the basic rules of the medium For starters, it made watching video on the Web a mass phenomenon But with YouTube you werent limited to sitting and watching a show, television style you could also upload your own clips, recommend or rate other clips, get into a conversation about them With just a few easy keystrokes, you could take a clip running on someone elses site, and drop a copy of it onto your own site The technology allowed ordinary enthusiasts to effectively program their own private television networks, stitching together video clips from all across the planetSome will say that this is merely a matter of software, which is intrinsicallyadaptable than hardware like televisions or cellular phones But before the Web became mainstream in the mid s, the pace of software innovation followed the exact same pattern of development that we saw in the spread of other twentieth century technologies The graphical user interface, for instance, dates back to a famous technology demo given by pioneering computer scientist Doug Engelbart inDuring the s, many of its core elementslike the now ubiquitous desktop metaphorwere developed by researchers at Xerox PARC But the first commercial product with a fully realized graphical user interface didnt ship until , in the form of the Xerox Star workstation, followed by the Macintosh in , the first graphical user interface to reach a mainstream, if niche, audience But it wasnt until the release of Windowsin almost exactly ten years after the Xerox Star hit the marketthat graphical user interfaces became the norm The same pattern occurs in the developmental history of other software genres, such as word processors, spreadsheets, or e mail clients They were all built out of bits, not atoms, but they took just as long to go from idea to mass success as HDTV didThere are many ways to measure innovation, but perhaps the most elemental yardstick, at least where technology is concerned, revolves around the job that the technology in question lets you do All other things being equal, a breakthrough that lets you execute two jobs that were impossible before is twice as innovative as a breakthrough that lets you do only one new thing By that measure, YouTube was significantlyinnovative than HDTV, despite the fact that HDTV was acomplicated technical problem YouTube let you publish, share, rate, discuss, and watch videoefficiently than ever before HDTV let you watchpixels than ever before But even with all those extra layers of innovation, YouTube went from idea to mass adoption in less than two years Something about the Web environment had enabled Hurley, Chen, and Karim to unleash a good idea on the world with astonishing speed They took the rule and made it From the Trade Paperback editionStimulating and insightful like one of the reefs that initially baffled Darwin and are so admired by Johnson a huge diversity of bright ideas co exist happily without destroying or spoiling each other John Gapper FT