"This american-guided missile destroyer is a perfect example of how we in the modern world take for granted we know where we're going all the time." "In this case, we've built a ship with sophisticated electronic warfare technology, antisubmarine attack systems, surface-to-surface and surface-to-air search-and-destroy capability, and awesome firepower, and none of it could hit a barn door, so to speak," "if the crew did not know at every moment where on the surface of the Earth-- to within feet-- they are, but they do, thanks to their satellite navigation systems." "This information is passed down to the electronic brain of the ship and used there to enable it to do its job with deadly accuracy." "Here's what they do with it." "Here in what's called the command information center, the data from the satellites plus data from one land-based and one ship-based navigational system tell the main computer where it is every second." "You see the point." "If you're moving and the sea's moving and the wind's moving and the enemy's moving, going "bang" successfully can be extremely complicated." "But this system will make it a bit easier, because it will do practically everything except say, "hands up."" "Look." "This is us at the center of the display." "I'll ask the system to say something about that subject." "Here's the interrogator." "I'll lock it onto us." "And... there, our identity, course, and speed and our position in latitude and longitude besides." "And it will do that for us or for any enemy who is foolish to be in the area and attract our attention." "Flying, floating, or submerged, it will tell us where he is, what he is, whose side he's on, and what he's up to, and when we deem the moment to be right," "it will go bang successfully, and it'll do a lot more besides that it won't tell us about." "This entire room makes the business of hitting landfall or the bull's-eye a piece of cake, because the system knows where we are." "And curiously enough, that confident ability of ours in the modern world to know where we are and where we're going, so powerfully expressed in this floating crisis management center, began over 500 years ago with a fellow" "who himself could only be called a floating crisis management center, only virtually all the navigation aid he had was this." "In the summer of 1394, a small ship headed out of Constantinople for Italy on a crisis mission." "The Byzantine empire was under attack by the Turks." "Without immediate western military aid," "Constantinople might fall." "So here's the crisis team facing their first crisis, getting there, which they wouldn't if they ever lost sight of the coastline." "The reason you kept land in sight was because only idiots didn't." "You were the navigator;" "you got far out to sea;" "you stayed far out to sea." "I mean, you knew some things, like the time, and if you dropped a trawl overboard, as it floated away and pulled out the line with regularly spaced knots in it, you could count how many "knots" you were going at." "And you had a thing called a Portolan chart showing the headlands along the coast if you weren't too far offshore to see them." "On your Portolan, you measured distance and bearing to the next headland and hoped the boat would go on sailing in that direction." "You also had a compass, but with only a square sail, your boat only went the way the wind blew, and if that was the wrong way, tough luck." "Why, if they blew out to sea, they'd blow the mission was because any atlas showing further out than inshore was total guesswork, but by the strangest quirk of fate," "Manuel Chrysoloras, who was heading this mission, was to turn out to be the key to one of the greatest discoveries ever made about what the world looked like, one that would scrap this old medieval view of three continents" "with Jerusalem center of everything." "You'll gather that Chrysoloras did reach Italy and save greek culture, though not the way he expected." "Chrysoloras and the Pope just didn't hit it off, so the mission to save the Byzantine empire sank without trace, and Chrysoloras found himself out of work but not for long." "In 1397, here in Florence, they asked him to start a university course in greek." "With nothing else in the offing, Chrysoloras jumped at it." "And for the florentines," "Chrysoloras was the answer to a maiden's prayer." "He had the breeding;" "they had the money." "And when I say "money," I mean the place was loaded." "Florence was a kind of crossroads bang in the middle of Italy, the ideal spot for a successful commercial set:" "the wine and grain and leather of northern Europe traded for the silks and spices and cottons of the Middle East in Florence, with the florentines creaming off the middleman profit, which in turn they used to set up" "their own woolen industry and make even more profit." "And the same year Chrysoloras arrived, the Medici family had started an international bank to lend all that spare florentine cash and really rake it in thanks to double-figure interest rates, a kind of florentine express with branches all over Europe." "Worked like a charm, thanks to a new financial secret weapon nobody outside Florence could get their hands on:" "double-entry bookkeeping, the system everybody still uses today to balance their accounts." "So money ran Florence." "The place was full of accountants, merchants, and, more than anywhere else in Europe, bureaucrats." "And in spite of the way it looks, there was no aristocracy." "Anybody with power and position in Florence had bought it out of the profits." "They'd have hated the description, but they were what we'd call nouveau riche." "This was a dynamic republican, capitalist, no-holds-barred company town, where if you had the wherewithal, there was nowhere money would take you but up." "Trouble was, there comes a time when you run out of "up,"" "and that's where Chrysoloras came in." "His classes in the greek classics became a kind of "where the elite meet" thing." "He got all the top people." "You see, his exposition of the glory that was Greece had tremendous snob appeal because it was pre-christian, so it had none of that" ""life and the world are worthless;" "moneymaking is evil;" "only the hereafter matters"" "that the Church was always on about." "Evidently, Ancient Rome and Greece had been places where a fellow with a bit of money who took his public responsibility seriously was looked up to, which was just what the florentines wanted:" "decorum, dignity, a touch of class." "So when Chrysoloras suggested a package tour to Greece, the home of the highfalutin, well, everybody who was anybody was on the trip." "And like all package tours, they bought the town, anything the locals would sell, including a rather curious atlas by a fellow called Claudius Ptolemy the like of which nobody had ever seen before, with the whole world and grid lines." "The main thing was, they came back with a real thirst for anything that would teach them to live like heroes, so they went looking for their own classical past." "Fortunately, lying forgotten around the monasteries of Europe was the latin literature they were looking for, kind of ancient roman Rotary Club handbook stuff:" "after-dinner speaking, etiquette, how to be a pillar of the community, and so on." "Of course, all this mania for moldy manuscripts did us a favor, too, when they rescued the only surviving copies of great latin classics from the effects of the mildew and the rats." "Well, the more they read of these stacks of poetry and rhetoric and history and civics and good living, the more it made them feel great, because this stuff, being pre-christian, was all about getting your reward on earth" "never mind waiting for hereafters-- that humans could live in human ways with or without heavenly help, which gave the bookworm brigade a really terrific idea." "They'd call themselves "humanists,"" "which left only one rather uncomfortable problem:" "did any of this lot say how to make your home actually look classical?" "In other words, how to turn Florence into a place that would look like ancient Rome." "Most unfortunately, no." "Well, there was only once place to come to get the real McCoy, and that was Rome, where, at the time, there was also somebody else who was interested in moving upmarket too, the Pope." "See, after years of hard times and no money and living in tin-pot brick churches and fighting off the competition from the Antipopes in France, by 1417, the roman papacy was dead keen to use all that trouble with the Turks" "back in Constantinople to its own advantage, the military aid for the Greeks, money, even, in return for recognition that the Pope was in charge of, well, the world." "If they could pull that off, well, for Rome, it was gonna be like old times, capital of the universe, all that." "Unfortunately, the local romans hadn't exactly kept the place in good nick." "The glory that was Rome was as likely as not doubling as a flowerpot stand." "What had once been the envy of the world, the Eternal City, looked like a bomb site..." "Trees and bushes in the Forum now used as city dump, marble long since stripped from the brickwork and burnt for lime." "At night, two things moved:" "wolves and muggers." "Still, our social climbers from Florence were not to be put off by a mere thousand years of neglect and decay lying around in bits." "I mean, this was not any ordinary rubbish." "These were genuine roman fragments to be studied with care and copied back home, so they descended on the place with measuring rods and bits of string and paper and scribbled furiously." "They found what they were looking for, all right, not much, but what they did almost made them wish they hadn't." "Look at it." "Everywhere they looked, they saw things they couldn't do:" "triumphal arches, pediments, coffered ceilings, barrel-vaulting giant columns." "There were never, ever going to rise to class like this." "The question was how to get hold of the know-how that would tell them enough to build like the Romans." "The answer was to come from here," "Padua in northern Italy, because this sleepy little market town was the M.I.T. of the 15th century." "If you wanted in on the latest scientific breakthrough, this was the place." "There were more researchers per square foot here than anywhere else in Europe, and they worked and taught in little rooms all over town... like this one here." "Ironically, this one's now a drawing office." "I say "ironically" because back then, the red-hot subject was very much all this:" "visuals, optics." "Above all, how do you see what you see?" "And they used medieval high tech to teach it with." "Now, the guru in optics was an arab called al-Hassan, who, back in the 11th century, had taken a look at the subject and written the definitive textbook." "First he demolished all the old theories:" "one, that somehow your eyes sent out rays of light to illuminate everything you looked at." ""Garbage," said al-Hassan." "If that were true, why would bright light hurt your eyes?" "And if you did send out rays, you'd have to light up that every time you blinked." "Another theory that said objects gave out color and that changed the color of your eye, well, why didn't this make my eye multicolored?" "No, the only theory that was any good for what al-Hassan was interested in, like reflection, refraction, rainbows, why the Sun got big at sunset, was a theory that said light did come into your eye" "from all the objects around you." ""True," said al-Hassan." "And the reason it doesn't confuse your eye is because the rays act selectively." "Objects do send off rays, but only the ones going straight into your eye, the so-called centric rays, make you see." "The ones that come in at an angle get bent, refracted, so you don't see them, and big near objects make more of those rays than little distant ones, so you end up overall with a visual pyramid of rays" "coming in from everything out there and converging on your eye." "Blindingly obvious to you, knockout theoretical physics to the 15th-century students here, including one from Florence, a fellow called Paolo Toscanelli, who thought the sun rose and set on al-Hassan." "Sometime around 1424, Toscanelli-- on the right-- was out to dinner back in Florence when he met an architect called Brunelleschi, who was one of those people trying to do bigger and better than the ancient Romans, so he had a problem." "Toscanelli, with his theoretical science background, was a godsend." "Toscanelli had ideas based on all that optical theory he'd learned in Padua that might give architects the help they all needed." "You remember that Ptolemy atlas the florentines had brought back from Greece with grids all over it?" "Toscanelli came across things in the atlas that were right up Brunelleschi's street, like how Ptolemy had used grids as a standard unit of measure and how he must have used optical theory to get the foreshortening effect of the grids" "that would re-create the Earth's curving surface, the same optical theory that al-Hassan had developed, you will recall, about the way rays of light came into the from outside and how the way you saw things was something" "that could be handled with geometry and maths." "You can guess what must have been going through Brunelleschi's mind as he watched Toscanelli." "If he could understand enough of this fancy geometry to produce some kind of blueprint, his troubles might be over, because he could get a proper scientific grip on things he was trying to build, including a crazy scheme he had taken on" "to give the florentines something even bigger than the Romans had managed..." "To put the biggest dome ever built on their unfinished cathedral." "He had this imaginative way of doing it." "Toscanelli had the math to help." "The florentines got their huge status symbol from Brunelleschi, all right, but it was what he got up to in 1425 down at the front door of the same church that would put Florence on the map, literally." "It came out of that dinner table conversation with Toscanelli about how you saw things." "Brunelleschi set up his equipment exactly 6 feet inside the church door opposite the Baptistery building in the square outside." "On one easel, he put a square wooden tablet, and on the other, a mirror with a handle on it set to give him a reflection of the Baptistery as he stood with his back to it and then began to outline on the wooden tablet" "the view of the Baptistery as he saw it in the mirror." "He was using a mirror because it would exaggerate any off-center positioning, so Brunelleschi knew he had an absolutely symmetrical view on which to draw the optical geometry lines that Toscanelli had told him about." "Brunelleschi had planned it all like an architect would." "The Baptistery was exactly as high and as wide as the distance between it and the spot he was painting it from, so he had a simple spatial relationship to deal with." "Now, you may feel, like this passing churchman, that what Brunelleschi was up to was no great shakes." "Certainly didn't look like the world's greatest painter." "But dismiss it as you might," "Brunelleschi's little effort was a lot more than 15th-century painting by numbers." "It was to change everything." "Now, in order to appreciate fully the totally knockout effect of what Brunelleschi was about to produce, permit me a brief interruption to give you a quick bash of Aristotle and the medieval Church, a mixture of which kind of dictated" "how people saw things before Brunelleschi, which was not the way you or I do." "Number one, the Church view:" "all that matters about this life is getting ready for the next one, so the visible world around you isn't worth bothering about." "Number two, Aristotle:" "since the Almighty handcrafted every object in existence himself, each object is unique." "The universe is filled with these individual, separate, unrelated objects, and all that matters about their position is where they stand in relation to the center of the universe." "Weird, no?" "However, when you were using your extremely expensive artist, say, to paint this wall, you got things painted from god's point of view, big if they were good and important like those cardinals and bishops up there" "and small if they were unimportant and bad like those dancers there." "Those were their theological sizes, the only sizes that mattered." "See the church there?" "It's big, but it's only three times bigger than the bishops and cardinals." "And look at the heavenly gates, big angels welcoming in tiny people into Paradise, where the blessed souls are big because they are blessed." "And right at the top, Jesus on his throne is gigantic, the biggest thing in the picture." "Now, our reaction to that is that it's all very simple and unrealistic and childish, but that's not because they were stupid." "They just had different priorities when it came to splashing paint around, and, of course, this was done before Brunelleschi did what he did." "Speaking of which, back to the action." "When Brunelleschi had finished his painting, the first based on the geometry that Toscanelli had studied, the effect on anybody who saw it was electrifying." "Nothing like it had ever been done before, not only a perfect reproduction of exactly what you saw when you looked across the square at the baptistery but much more." "When you looked through a hole in the back of the painting, you saw the real Baptistery until the mirror came up, when you saw a reflection of the painting of it." "Between the real thing and the reflection of the painting, there just wasn't any difference." "When the florentines got their first sight of the new kind of painting, they couldn't get enough of it." "What they were looking at gave them an entirely new perspective on art, because it gave them just that, perspective." "And in keeping with their sense of style and savoir faire," "Brunelleschi's fellow citizens went, elegantly, bananas." "Well, no wonder they all went wild about it." "Brunelleschi had come up with a way of measuring the whole universe." "You could examine any distant object's characteristics without ever having to go near it, because you knew its relative size and distance from you and all other objects because of perspective geometry." "Well, that knocked Aristotle for six for a start, or it would have if Brunelleschi had been up to the theoretical maths, which he wasn't." "Fortunately, an amateur painter and ex-letter writer for the Pope called Alberti was." "And he knew all that al-Hassan stuff about optics and Ptolemy's gridding system because he'd been to college, so he put it all together in a book called How to paint, two versions: one in latin for the coffee-table crowd" "and one in italian for the hoi polloi." "Lesson one, he says:" "take a gridded frame and plunk it in front of your scene like that." "The grid of threads on the frame helps you to get the size of any object in the scene relative to all other objects, wherever they may be, with great accuracy." "For instance, that church is almost one frame tall." "That clump of trees is just over two." "My hand is bigger than the church, see?" "Because it's close to you than the church is." "What you get with this grid is a kind of slice through that visual pyramid al-Hassan was on about of all the light coming from a scene to your eyes, remember?" "So this was a way of copying a view square by square with everything in proportion, which was okay for copying." "What if you wanted to invent a scene for yourself?" "Well, in Alberti's book, that was lesson two, how to draw a perspective framework:" "at eye level, a horizon line, a center point, and floor lines." "Then, from a point where a viewer of the painting would be standing, lines from the viewer's eye to the end of each floor line and, from where they cut the frame, horizontals, giving you a checkerboard perspective effect" "for the painted figures to stand on." "Add roof lines, like floor lines, for everything above head height, and there's the framework on which you paint your painting, which isn't a painting; it's a church, designed by Brunelleschi according to the rules of perspective," "where everything converges on the center point, the altar." "Clever, isn't it?" "Perspective lets you copy reality with mathematical precision or build your own to exact specifications." "So that's what started happening." "Architects built stuff that looked like paintings." "Painters painted stuff that looked like buildings, like the first one by a young friend of Brunelleschi's called Masaccio." "In 1326, his Trinità was so realistic, it looked like a hole through a wall into a chapel." "Watch how the way the painting is structured on those perspective lines converging at the viewer's own head height forces you to feel you're at the foot of the cross looking up." "The new perspective framework was copied immediately." "Look how Christ, on the left, is the center point for a perspective structure centering on him and how your horizon line is at his eye level too." "As this new realistic view of life caught on, scenes were still taken from the Bible, but they used subjects whose clothes and faces were taken from individuals in everyday life." "Of course, it was too good to last." "If perspective gave you the ability to control things from a distance, you could bet it wouldn't be long before the things being controlled became people." "But in the brief interval before that happened, in the interval we call the Renaissance, perspective meant what it said:" "getting things in proportion in every sense." "And nowhere was that more true in terms of what it did to people's lives than here, a little town in central Italy called "Little town," Urbino." "It's a warm higgledy-piggledy place, and in the 15th century, it belonged to a Duke called Federico, whose ducal palace was a new departure from the usual fortified monstrosities." "It's somebody's home, posh but comfortable, to be lived in, and with Federico and his home, you get everything the Renaissance began... all that confident individualism up there on the wall." "It says, "I am Federico, and I built this place."" "Harmony, balance, classical style:" "this courtyard is the best example there is, the three original levels in proportion" "3 to 2 to 1-- straight lines, geometrical spacing, roman columns, just like the paintings the Duke commissioned." "They show the ideal world the renaissance man wanted to live in." "The paintings are full of urban views and gracious squares, and even in the paintings on religious subjects, like the flagellation of Christ, the painter gives equal attention to the architecture the Duke had." "In the Duke's study, you can see what he was like." "He loved novelty." "All this is the latest 3-d perspective trick stuff in marquetry, some of it looking like windows opening onto the newly fashionable natural landscapes." "Federico had the classics read to him at dinner." "He played his own music." "Science fascinated him, and he loved books." "His library here was said to be better than Oxford's." "Oh, and the little reading seat, even that was a trick." "And all these illusions worked particularly well for Federico because he was one-eyed." "He had two organists, a room for keeping snow in summer, and a pet giraffe, and these were his heroes:" "writers, scholars, philosophers." "And when he added his portrait to theirs, it showed him in armor but reading." "And from his new palace, Federico looked out on a world that people like him felt they could now explain rationally for the first time." "Man had become the measure of all." "In the nicest possible way, the mathematical view the florentines had always had because of their trade moved out and took over the world they lived in:" "delicate, beautiful, regimented." "You get a feel for how the florentine state really operated, the iron hand in the velvet glove." "Now, it's not fashionable to say this about the florentine love affair with balance and symmetry and such, but I wonder what it was like to live with the rules of proportion shoved down your throat everywhere you looked," "like the florentine church of Santa Maria Novella." "The whole facade is an exercise in ratios, this lot all 2 to 1 to each other and the rest in a 3-to-1 ratio, and there's only one way that kind of obsession leads you." "You start, like they did, to design groups of buildings by numbers and then streets and finally, whole geometrically balanced ideal cities." "They actually built some of those ideal cities." "This is one, called Palmanova, a garrison town near Venice, and in Palmanova, you see where, ultimately, mathematics can lead you, because you can now plan and build an entire city to fit one purpose," "in this case, defense against artillery, and everything inside the walls is subordinate to that purpose, including, of course, the now strictly planned life of the citizen." "Have a look at how they did it." "The central square is really a command and control post." "6 main streets radiate out from the central square to the gun emplacements on the walls, the streets built for only on purpose:" "to move men and ammunition." "And see how everything is in straight lines or circles?" "Life designed for maximum efficiency, soulless, the beginnings of town planning and the social manipulation it offers:" "wide streets for parades, narrow streets to bottle up the mob." "You know exactly where you are, and you can pinpoint where everybody else is." "The whole town is a set of controlled coordinates." "Meanwhile, as the paramilitary potential of perspective was gladdening the hearts of repressive governments everywhere, it was about to have exactly the opposite effect because of what knowing where you were meant to a lot of seafaring gents here at Sagres," "a small community stuck out at the end of Europe, literally, on Cape Saint Vincent, the headland down at the bottom left-hand corner of Portugal." "From 1419, this had been the site of a navigation school set up by Prince Henry of Portugal, well-known exploration freak." "Now, as ruler of a particularly penniless part of Europe," "Henry had two things in mind:" "money and money, the first to be gained by going down the coast of Africa to get to the gold and slaves and such he'd heard they practically gave away, the other from going on down the coast of Africa" "and round the bottom to get to the Far East, thus avoiding the Turks, who were charging an arm and a leg for the Red Sea route, to get at that license to print money:" "pepper, the new rave gourmet delight and apparently falling off the trees out east." "Now, to be fair to Henry, he did also plan to hand out christianity with the beads." "Well, he had one minor problem." "Nobody had the faintest idea how to go down the coast of Africa." "Of course, you had compasses and hourglasses and maps with oodles of coastline detail for the stuff you knew, like Spain on this Portolan chart with lines of bearing and direction that you measured with your measurers." "Down here beyond the Church's domain inland, it was anybody's guess." "Looking at this map as you are, you will have already seen Henry's little problem." "Even after 10 years of sending brave lads down here to explore, it was always brick wall time at this bit," "Cape Bojador." "Let me explain." "In those days, if you came across a place that had fog, vicious currents, shifting sands, lousy weather, and, above all, a wind blowing strongly the wrong way for a fellow who wanted to get home, well," "such a spot was a complication devoutly to be missed, and Bojador was that in spades." "Beyond it, the Arabs said, "darkness and death."" "Aristotle said, "regions of fire."" "Henry said, "money," so they kept at it." "In 1434, some daredevil called Eannes went and did it and limped home saying," ""Oh, gee, fellas, it was nothing,"" "and gave Henry a real problem:" "how do you sail what the philosophical and theological authorities call "off the edge"?" "Fortunately for Henry, they had recently taken advice from the florentine expert on long-range problems." "Yes, you've recognized him, Toscanelli, busy chatting up the portuguese Prince Pedro in Florence to see the latest in mapping techniques." "Something else you'll recognize:" "the Ptolemy atlas with its grid, but more to the point, what it said about where the Portuguese were trying to find a route down Africa to the Far East, and then, it was the only remotely accurate map" "of the world." "You could see Ptolemy was trustworthy when he dealt with the real faraway stuff by checking the way he'd used his cartographic techniques to draw maps of parts of the world a good deal closer to home." "His charts of the country, say, in the northern Mediterranean were terrific." "Toscanelli told Pedro enough to send him back to Portugal convinced they were doing the right thing," ""A", because Toscanelli had realized that Ptolemy was using perspective geometry to get an extremely exact view of the world because of the way it could reproduce the shape of a sphere on a flat surface, and, "B", because of these magic words:" "Terra incognita, "Unknown territory."" "Ptolemy wasn't saying, like everybody else, that there was nothing south of the equator." "He was saying there might be something." "Well, there was only one way to find out." "Encouraged by Toscanelli's say-so, by 1455, the Portuguese were getting their first glimpse of the native cultures of West Africa, setting up their trading posts, making their own coastline maps as they went along, getting closer and closer to the equator," "and getting more and more worried the closer they got." "Because now it really did begin to look as if they were gonna sail off the edge, in navigational terms, anyway." "Look what they were doing." "Here they go with their Portolan charts further and further south, mapping as they go, until they get to where I am, here, Sierra Leone, which, incidentally, they named." "And what is dreadfully wrong with this lovely spot?" "I'll tell you." "See this?" "Portuguese quadrant, 15th-century high tech, tells you the position in the night sky of the Pole Star, which you navigate by because while you may move, it never does." "Portuguese idea, that." "Anyway, you line up the sight on the star and read off how high up it is so many degrees there." "Now, here's the Earth," "Pole Star, you." "As you head north up the Atlantic heading for home, that angle gets bigger and bigger, and when it gets to 39°, you turn east, and sooner or later, you'll hit Lisbon, because 39° is Lisbon's angle of latitude." "Going south, of course, the angle gets smaller and smaller." "And here in Sierra Leone, the Pole Star is only 8° above the northern horizon, there." "So you see why they were getting worried." "A few miles further south over the equator, and the Pole Star wouldn't be there, and then how do you get home?" "And the worst thing was," "This place was really starting to look up." "The people were friendly and so generous." "You gave them a few pots and pans, and in their marketplaces, they'd hand over all the slaves you wanted, silver, ivory, copper, and a knockout substitute for pepper called Angel Dust that would blow your head off." "But above all, they had a casual help-yourself attitude to the gold they seemed to have too much of." "All in all, West Africa was money for old rope." "So the Portuguese weren't about to quit." "Besides, they still had to get to the Far East for the spices, remember?" "So they set up a troubleshooting committee back in Lisbon, and its chairman, a fellow called Martins, got in touch with Toscanelli." "Now, our italian friend had recently sat in on an Ecumenical Council in Florence attended by bigwigs from everywhere, and he'd picked their brains about what it was like back home where they came from, and then he put it all together." "Europe, he knew about and this much of Africa, and the chinese ambassador told him about this bit and this bit." "And a really weird italian called Conti, who had traveled for 25 years in places where no european had ever been before, filled in the rest." "India, Sri Lanka, Siam," "Malaysia, Sumatra," "Cippangu, "Japan"-- names, distances, and, above all, where the money was to be had." "Well, all this was good stuff, but the Portuguese still didn't know how to get there." "This place Africa was great, but press on regardless as they might, nobody was getting any further east going down here." "Toscanelli took another look at this map." "First, he laid a Ptolemy grid on it, each square 5° or 250 miles." "This grid gave you the first-ever mapping coordinates, even for places you'd never been to, and it was a scale you could use to measure distances from anywhere to anywhere else, but how is that gonna help the Portuguese?" "And then it hit him like a ton of bricks." "Conti had said that out here beyond Japan, there was a great ocean." "Well, because Toscanelli had got Asia 5,000 miles longer than it really was, he reckoned this ocean couldn't be that big, and he must have reckoned he knew what ocean it was." "On the 24th of June, 1474, Toscanelli sent one of those letters that changes history to Martins about his map." ""Dear sir," it said, "here is my chart," ""gridded to make navigation easier." ""Count the squares, and you'll get the distances." ""This is you." ""This is Japan, a long haul, unless, of course, you go this way."" "Stupefied portuguese amazement?" "Uh-uh." "They hemmed and hawed." "They argued about the mileage." "And then one of their lads got around the tip of Africa, and it was, "Thanks, but no, thanks,"" "which is exactly what they said to an ex-pirate, ex-bookseller with white hair and a smooth line of talk who, some years later, had picked up Toscanelli's map and made it an even better sell by cutting the circumference of the Earth by 25%." "The figure was anybody's guess in those days, thus making the atlantic route to Japan a very attractive 2,400 miles," ""a mere bagatelle," he said," ""for a fellow who's already been to Iceland."" "Think about it." "Well, as I said, this sales pitch went over with the Portuguese like a lead balloon, and when he tried it on the Spanish, all he got was, "Mañana"." "Still, that did leave the French, so he was on his way here at the lonely and otherwise unimportant little monastery of La Rabida on the southwestern coast of Spain, also visiting his son in the school here" "and winding up his spiel for Paris, when the spanish backers changed their minds, and suddenly, the trip was on." "They gave him two ships, and he borrowed from the locals here to charter a third." "And at 5:15 a.m. on a Friday, August the 3rd, it was, they upped anchor at the port of Palos upstream from here and floated down the river, kneeling bareheaded on the deck as they passed the monastery out there." "And in the captain's book, he had stuck Toscanelli's chart and the letter containing that extraordinary phrase," ""Go east by going west."" "By 8:00, they had crossed the bar into the Gulf of Cadiz here and headed out across open sea, bound at last for Japan." "They never made it." "Almost exactly where he had predicted Japan would be," "Columbus found America." "Columbus went into the unknown with the new, boundless confidence of the time of men who, thanks to perspective, could measure and predict that unknown, men for whom nothing was impossible, unhindered by superstition and ignorance," "free, rational individuals, typical of the modern Americans who make the return journey today from a land where that individualism is more strongly expressed than anywhere else in the world, a land prepared, if need be," "to fight for the freedom of the individual." "But it's one of history's great ironies that the power al-Hassan, Toscanelli, and Ptolemy gave us to grid the world and to go anywhere our ships can sail should, in the long run, turn back on us." "This ship can go anywhere, and thanks to the other ships, the ones we send into space, she can never get lost." "She knows her position, just like Columbus did, by knowing where a star should be at a certain time, but her satellite star is man-made." "But the other side of the coin is this." "Look." "Here's southern Spain from space," "Strait of Gibraltar, La Rabida, the U.S. naval base at Rota, and here is a better shot of the base from 300 miles up in space." "Pilot's off the ship." "And when they slip anchor and head out into the anonymity of the trackless ocean like Columbus did, that's what they look like from another satellite:" "ships' wakes from 400 miles up at night." "That's the irony." "The very ability to measure and control the universe at a distance means that we, too, can be measured and controlled in the same way." "In gridding the world, we have gridded ourselves." "There's nowhere to go and hide anymore." "But, then, today who would want to?"