Where in the world am I?

Jim McMahon got hooked on geography in fifth grade. "My teacher was a geography goon," he says. "When the class got unruly, he'd line us up against the walls, take his big floor map-puzzle of the United States, and throw it across the room. Then he'd call out someone's name and that kid had five minutes to put the map back together."

That was the beginning of Mr. McMahon's fascination with place. Today he's the resident "Mapman" for Scholastic magazines. He says he thinks everyone is born with the impulse to know how we're connected to our space. Whether we're lost in a new school or just rearranging our furniture, we all like to make sense of our surroundings. That's how maps begin, McMahon says.

Maps are attempts to answer the questions, Where am I? and Where is everything else? The first mapmakers had to do a lot of guessing sometimes. Their maps of the earth were pictures of how they thought places in the world were arranged. Remember, no one had a bird's-eye view (except from mountaintops) until the first manned hot-air balloon lifted off from Paris on Nov. 21, 1783.

A map dating from about 500 BC shows a flat earth surrounded by a ring of ocean. A circular map of the earth in an AD 1250 English Book of Psalms shows East at the top, with Adam and Eve looking out from the Garden of Eden. To the right is the Red Sea, and Jerusalem is at the center. It's not the kind of map to help you find your way around the world. The magnetic compass had appeared in Europe in the 1100s and was being used for navigation. (The Chinese may have been using compasses since 100 BC.)

In the 1400s, Europeans began to explore lands far from home. They needed maps based on fact. Familiar places, such as the boot of Italy, are drawn very accurately on the maps of these times. But mapmakers sketched in unfamiliar places using legends, travelers' tales, and their imaginations.

These explorers had a major problem: At sea, away from land, there were no landmarks. They could find their latitude (their north-south position) by measuring the angle of the sun to the horizon at noon. They could also determine this by the angle of Polaris (the North Star) in the night sky. But figuring out longitude (their east-west position), was a lot trickier.

The earth turns 360 degrees every 24 hours. That's 15 degrees every hour. So for every 15 degrees east or west you travel from your starting point, it's an hour earlier or later than it is where you began. If you know what time it is where you started and what time it is where you are, you can figure out how many degrees east or west you've traveled. You don't need a clock to determine the local time, since noon is easy to figure out. What explorers needed was a clock that kept time well enough so they would know what time it was at home. By comparing local time (noon) to the time on the clock, they could figure out how far east or west they had traveled.

On land, it was pretty easy. All clocks were pendulum clocks, and although land transport was pretty jarring, it wasn't so jarring that it threw off the clocks.

But the waves at sea messed up pendulum clocks. What to do? Have a contest. In 1714 the British Parliament offered a prize of £20,000 (that's the equivalent of $12 million today!) for a practical way to calculate longitude at sea.

A poor village carpenter named John Harrison spent most of his life inventing a clock that didn't need a pendulum but used a spring instead. Finally in 1760, his silver "watch" made a stormy, two-month journey from England to Jamaica and lost only five seconds. On the way the ship ran out of fresh water and badly needed to find the islands of Madeira, off the coast of northwest Africa. Using the new clock, John Harrison's son, William, correctly calculated the ship's longitude and helped the captain find the islands. The elder Harrison, however, had to fight for years to claim the entire prize for having solved "the longitude problem."

Have you ever hiked to the summit of a mountain and found a brass plate drilled into the rock that says "USGS"? That's where a surveyor set up his tripod and measured the height of the land above sea level and the distances to other nearby features of the landscape. Beginning in 1927, the United States Geologic Survey collected these "benchmarks" and made topographic maps of every town and city in the United States.

Today we have very sophisticated ways to measure where we are on the earth. You've probably heard of GPS (Global Positioning System) receivers. They used to be top secret and used only by the American military forces. Now anyone can hold a GPS receiver in his or her hand and it can tell their latitude and longitude to within 25 feet or less. Twenty-four satellites send signals back to earth continuously. By reading at least three of these signals at once, a GPS receiver can determine your location. There's a fun, new sport that uses GPS called "geocaching."

David Smith, a professor of geography at Ohio Northern University, says the Internet has revolutionized mapmaking. Because so much mapped information is stored in databases, maps can be produced very quickly and cheaply. Professor Smith teaches students how to make maps using Geographic Information System (GIS).

"It's a marriage of a 'paint' program and a data base," he says. Cartographers can click out maps showing whatever they want, such as where wildfires are raging.

Mapmaking has become so high-tech! But not everything is as exact as you might think. For instance, there's more than one system of map coordinates (latitude and longitude numbers) for GPS receivers. How can there be more than one right answer to the question, Where am I? David Smith says it's because scientists haven't determined the exact size and shape of the earth yet. Or at least they haven't all agreed. Different groups have come up with different measurements.

The "people" side of geography can cause trouble, as it did a few years ago. The Pacific island nations of Tonga and Kiribati were preparing for tourists as the new millennium approached. Tonga was just west of the International Date Line. Developers began building hotels in Tonga for those who wanted to be the first to ring in the 21st century. Kiribati, a new nation just east of the Date Line, didn't want to miss out. So in 1997 Kiribati passed a resolution to move the Date Line so that tourists in their country could celebrate first. Tongans were very upset, but couldn't do anything about it. There's no international law governing it. (Time zones don't always show much logic, either.)

Even with the latest technology, "Where in the world am I?" doesn't always have a straightforward answer. For that matter, feeling "at home" doesn't depend on being located at a certain set of coordinates. either.

It was like a treasure hunt. We knew from a website that someone had hidden a cache near Malakoff Diggins, an old mining village in a California State Historic Park. The geocache site gave us another clue, written in code. "Ybpngrq nobhg 30 sg. bss gur genvy va n ebggvat gva gho," it said. Using the key, my daughter Bronwyn wrote out, "Located about 30 ft. off the trail in a rotting tin tub."

But the most important clue was that the cache was hidden on the spot of earth that was precisely 39 degrees, 22.058 minutes north of the equator and 120 degrees, 54.158 minutes west of the prime meridian that runs through the Royal Observatory in Greenwich, England.

We entered those numbers, or map coordinates, into our GPS (Global Positioning System) receiver. We were counting on the little device, which looks like a cellphone, to help us find the treasure.

We drove to the site. The GPS receiver said we were 232 feet away from the cache. I handed the GPS unit to Bronwyn's friend, Kristin, and the two of them headed down an unmarked trail covered with pine needles.

"Ninety-two feet!" Kristin shouted. We were getting closer. The girls ran and skipped, hooting with excitement. But GPS has its limitations.

"We've got a weak signal," Kristin called. The screen showed only one satellite symbol. That meant that our GPS unit was receiving radio signals from only one of the 24 satellites put into orbit (at a cost of $12 billion) by the United States Department of Defense to help with military navigation. Signals from at least three satellites are needed for the GPS to calculate our location more precisely.

We headed back into a clearing. Now our receiver had a good "view" of the sky. Soon Kristin shouted, "You guys! I'm at 27 feet!" We fanned out, looking behind pine trees and between cedar seedlings.

"Nine feet!" was the last report. Then Kristin spotted it - a rusted tub lying on its side behind a big tree.

Bronwyn opened the plastic container inside the tub. A note read, "Congratulations! You've found it!" And there was the treasure: a variety of trinkets. Bronwyn chose a small penknife, Kristin a key-clip. We put in two Christmas ornaments and signed the log book.

"Look for an article about this on www.csmonitor.com," I wrote.

If you'd like to look for one of more than 58,000 caches in 180 countries around the world (as of Nov. 3), log onto www.navicache.com or www.geocaching.com. GPS receivers are available at sporting-goods stores and begin at about $100.