To offer some perspective, he retrieved, from a vault within the vault, one of the library’s oldest and most precious maps, a so-called Portolan chart of the Mediterranean, dating to 1456. It showed the sea’s entire coastline, with hundreds of ports labelled in the manner of stations on a railroad map, the names neatly lined up parallel to one another, in the order in which one would encounter them if one were sailing along the coast.

“The tension between these two modes of navigating goes back to these maps,” he said. “The itinerary represents space as one experiences it on the ground. A map like this has that element, but it starts to introduce the notion that you can conceive of it as a larger unit. It’s a God’s-eye view, which puts you in charge of navigating through space. This is the origin of the notion that you can pull yourself away from the world and see it from above.”

The irony is that centuries later, when we have perfected the God’s-eye map and become conversant with it, we have, in the thrall of technology, turned back to the ancient way: the itinerary and the strip map. OnStar and MapQuest zero in on the information that’s relevant to reaching your destination. “They close down your choices and give you a route,” Akerman said.

It can be amusing to see what MapQuest and its ilk come up with. They don’t always work. For example, I recently looked to see how MapQuest would get me from East Ninety-sixth Street in Manhattan to the North Shore of Long Island, an hour-long trip that I and countless other drivers have honed (with variations for personal preference, traffic avoidance, and monotony-breakage) over the years. Triborough Bridge to the Grand Central Parkway to the Whitestone Expressway to the Cross Island Parkway to the Long Island Expressway. Bing-bang-boom. MapQuest had an unprecedented suggestion: take the Triborough Bridge to the Bruckner Expressway and then to the Throgs Neck Bridge. From the Upper West Side, a few traffic lights west, MapQuest, snickering, guides you to the Cross Bronx Expressway and then to the Throgs Neck. The Cross Bronx? It would seem that the algorithms are new to the area. These directions involve a disconcerting degree of noncontiguousness. Why cross a body of water at its widest possible point? Why even mess with the Bronx? You may as well stick a sandwich in your ear before putting it into your mouth.

Generally, MapQuest and OnStar choose a road based on their calculations of which will get you there fastest. The criterion is time, a function both of speed and of distance. They do not, as some people suspect, simply pick the shortest route; otherwise, you might spend all your time on side streets, stuck at traffic lights or goat crossings. The algorithms consider the length of a road segment and the expected speed of the road and calculate the time it will take you to pass along it. Every road segment has a “costing,” a sum of the features that can slow a driver down. Turns, merges, exits, toll plazas, stoplights, speed zones: they all carry a cost. (Navteq has five “functional classes” of road, ranked according to connectivity and speed. An interstate highway is a one; a local street is a five.) These systems do not yet take into consideration traffic, construction, weather, time of day, or one’s tendency, on certain roads, to go faster than the speed limit.

There are features that we associate with maps or navigation which have little bearing on the kind of road directions favored by MapQuest and OnStar. Traditional visual landmarks—flagpole, river bend, stone church—are hardly recognized. And a road that traverses water (i.e., a bridge) is no different from one that cuts through a golf course or a drug-free school zone if the speed limit is the same. This is why the Throgs Neck looks more reasonable to an algorithm, even if to a driver that extra water crossing may mean another toll and greater potential for bottleneck traffic.

With MapQuest, you can either look at a map, presented in a manner that makes your route the center of the world, or you can get an itinerary. But, since MapQuest’s directions are derived from looking at a route on a map, the advice it gives is based mostly on map reality, not driver reality. Traditionally, verbal directions capture the experience of driving on the road, much as the McNally Photo-Auto Guide did; MapQuest captures that of plotting the route, from a God’s-eye view. This is why, for instance, MapQuest will identify a short stretch of road—an off-ramp, a connector—that to the traveller would normally be negligible (without mentioning that you should keep the river or the graveyard on your right). Whether a segment is 0.1 or two thousand miles long, it is given equal billing. This sometimes has a ludicrous effect. For example, Google’s directions for leaving Spokane, Washington: “Head north from N. Lincoln St., go 33 feet. Turn left at W. Main Ave., go 0.1 mi. Turn left at W. Spokane Falls Blvd., go 127 feet.” Certainly, once someone following this kind of itinerary loses his way he has no idea where he is, because he has no sense of how the directions he’s following fit into the larger picture.

Most navigation devices in cars display your route on a small dashboard screen; the settings can be altered, but more often than not the top of the display represents the direction in which you are moving. The onscreen map, in other words, is not oriented north-south, like a paper map. The map constantly readjusts itself, so that the road ahead is up. This is a boon to people who may be disinclined to see the ground in terms of north-south—people who when standing on a street corner will hold a paper map and turn it so that what is in front of them on the ground is also in front of them (above them) on the map. As to the age-old and oft-debated question of whether women are more apt to do this than men—of whether geographic proficiency correlates to one gender or the other—there is a great deal of straight-faced academic research. Suffice it to say that the scholarship is inconclusive, though it does tend to find that men and women, whether by nature or by nurture, perceive space differently.

At any rate, the in-car map displays generally represent small swatches of land, your immediate surroundings. You can zoom in and zoom out, but the area you’re passing through is a disembodied square, free of the context of the larger landmass. For example, as you pass along the Bruckner, on your way to the Throgs Neck, you see a web of lines, and words like “Port Morris” and “Hunts Point.” What you tend not to see is where the Bruckner and the Bronx fit into the bigger picture—the Bronx poised like a catcher’s mitt between the legs of Manhattan and Long Island, the southernmost wedge of New York State mainland breaking up into an archipelago. You do not see, in other words, how taking the Throgs Neck might appear, on a standard map, to be a detour.

In the spirit of fair-mindedness, I tried this route one Saturday morning, when there would likely be little traffic to corrupt the results of the experiment. The affront to both habit and the inner compass—every fibre crying out, “Turn east, east!”—was especially acute as, per MapQuest, I followed signs directing me to New England, instead of to Long Island. So was the unpleasant prospect of paying the additional toll of four-fifty that the Throgs Neck would require: a deal-breaker, especially if you’re one of those people who plot routes primarily on the basis of toll avoidance. (You know the type: he loves the Macombs Dam Bridge.) Still, I stayed with it. The road was clear and fast, the prospect—Rikers Island, from the north!—refreshing. As the Throgs Neck Bridge conveyed me onto Long Island, and I rejoined the usual route, on the Cross Island Parkway, I noted, on the digital clock on the dash, that I’d made great time. Perhaps this way was a minute or two longer. Hardly more. Over the years, those minutes, not to mention the toll payments, could add up, but still: MapQuest’s algorithms had apparently opened an iconoclastic alternate route, a Long Island commuter’s Northwest Passage.

Chicago, you might say, is the Sagres of the American imperium, a hub of geographic and cartographic expertise. This is due mainly to Chicago’s role, in the nineteenth century, as a major railroad center. Rand McNally (“to maps what Jell-O is to gelatine,” as Akerman said) was based there (it is now just up the pike, in Skokie), as were many other prominent map publishers. The University of Chicago had, until recently, one of the best geography departments, and is still a leading publisher of scholarly books on geography and cartography.

Navteq (the name is a contraction of Navigation Technologies) started life in 1985, in Silicon Valley, and moved to Chicago in 1997. Its revenues have tripled since 2002, amid the digital mapping boom. It occupies an ever-expanding suite of offices on an immense floor of the Merchandise Mart, one of the largest commercial buildings in the world. It would be wise, when visiting Navteq, to bring bread crumbs or a handheld G.P.S. to keep from getting lost. One morning this fall, in a conference room I’m sure I could never find again, I met Judson Green, the company’s C.E.O., and Salahuddin Khan, a senior vice-president, who supervises the complicated task of converting raw data, including the observations of analysts like Arcari and Singh, into lefts and rights. Navteq is as much a collator of information as a collector of it. The raw information comes from a variety of sources, including the government—for example, from what are known as TIGER files, prepared by the Census Bureau. This information is in the public domain. A lot of it is out of date, idiosyncratic, incompatible, and, at the very least, requires cleaning up. Digital aerial photography is used as well.

The existing data, from the government and other sources, had not been collected with way-finding in mind, so it was necessary to look at the world again through the eyes of a driver, instead of those of a tax collector or a land surveyor—“to add all the attributes no one ever thought to add because they weren’t thinking of navigation in the first place,” Khan said. “Guidance, one-way systems, no left turns. Does something go under or over when you have two lines that cross a map?”

Khan, who was born in Pakistan, is placid and precise, with a neatly trimmed beard and a slight burr, a vestige of more than three decades in Britain. He happened to be heading out himself the following day to do a little ground-truthing in Wyoming.

“It’s like news reporting,” Khan said. “You could not do it all from Washington. You need to have stations and field offices in order to get that local knowledge.”

Khan has three cars and a single-engine plane; being a pilot (and, by training, an aeronautical engineer) got him interested, years ago, in moving maps, in which the map centers on your present location—a kind of predecessor to the devices employed in cars these days. He began using navigational systems well before he came to Navteq, in 1998, and finds it strange that in this day and age someone would have a road atlas in the car. “Maybe that’s a guy thing,” he said. He is a self-professed “map nut,” but really more of a gearhead. “Historically, I had what I would call ‘lost anxiety’—anxiety about being lost,” he said. “I then got to experience navigation systems. And I feel that I have effectively diluted lost anxiety out of my system. In other words, I’ve been conditioned not to be anxious when lost, even when I am in a vehicle that does not have a navigation system.”

As he calmly summoned a world in which technology would do away with the experience of going astray, I began reassessing, in the rearview mirror of my mind, all the times I’d been lost or confused, angry at the map or the person next to me who couldn’t make sense of it. Panic in a New Jersey rotary; despair in the pitch black of the Poconos at night; the shame, after you’ve got on the wrong highway, of hurtling past a sign saying “NEXT EXIT 13 MILES.” All the rash U-turns and frantic attempts to get the attention of the driver in the next car—you give him the now quaint but still widely recognized “roll down your window” signal and shout helplessly across the gulf, “Where can I find Route 17?” Yours for the violent ward, straight and sure. For the first time, I began to think that one of those devices might not be such a bad idea. Even map nuts get lost.