Cathedral of the World Sailing Notes for a Blue Planet

Charts and Other Fiction Some of my earliest memories are of games I used to play with my father on long winter evenings, the two of us hunched over a table in our living room studying the charts for the next sailing trip he was always planning for the family during his upcoming holiday. Armed with a pencil and a set of parallel rules, we would set sail on imaginary voyages across the bays of summer, marking off distances and estimated times of arrival, checking depths and the location of buoys, poking into coves, making plans. The thing I remember most about my father's charts was the way they set us free. They were like novels without characters: settings in which we were the actors and the creators of our own episodes. They contained fabulous worlds, and we lived in them like supermen, traveling through their benign geography as if we were invincible. There seemed no reason, then, to worry about the dangers that might have been lurking somewhere within the games we played. The games themselves seemed harmless enough. In fact, they seemed a perfect way for a little boy and his father to share a few pleasant hours together. I wasn't concerned at the time about the inconsistencies between the charts and the actual geography they were intended to represent. I wasn't thinking about the real bays of summer: the ones with uncharted ledges and misplaced buoys and currents that flowed in opposite directions to the ones predicted by the cartographers. As a child I learned to roam across the worlds of my father's charts careless and free. But I didn't learn about their limitations. I didn't realize that nautical charts, like all maps, are only guidebooks: fictitious renderings of a world perceived by imperfect human beings, never identical with the actual places they describe. I learned about the wealth of information the charts contained. But I didn't learn that they were also filled with oversights and half-truths and miscalculations. This realization has taken many years to learn--years of trial and error, summers of close calls, winters of near catastrophe when I've made the mistake of trusting the chart spread out before me, only to discover that the cartographer must have been half asleep the day he drew this line or marked that shoal or measured such and such a distance. Nautical charts suffer from a basic flaw: the flaw of scale. They are complicated, often powerful abstractions of the actual world, but they are not--cannot be--identical with that world. The terrain they attempt to map is too large and too complex. To be useful at all, they must reduce and simplify. The Polish-American mathematician Benoit Mandelbrot once asked an odd question whose implications may have forever changed the face of modern mathematics: "How long is the coast of Britain?" The answer, he argued, is not to be found on any chart. In fact, the answer is not to be found in any conclusive way at all, at least not with the tools of measurement that we have presently available to us. The reason for this apparent dilemma has to do with scale. Imagine a cartographer armed with a measuring device one meter in length. He paces off the coastline in question one meter at a time, traveling in and out of bays, across rocky headlands, over river deltas, until he comes up with a total number of meters. Now imagine the same cartographer with a much shorter measuring device, say one centimeter in length. This time as he remeasures the distance, his total will include more detail. His new "coastline" will include pebbles and rocks that were ignored in his first calculation, and the resulting answer will be somewhat greater. What Mandelbrot discovered was that there seemed to be no limit to the length of the coastline, providing only that the scale of measurement could be made smaller each time. A microscopic measuring stick would reveal as yet undetected bays and promontories tArms, Myron is the author of 'Cathedral of the World Sailing Notes for a Blue Planet' with ISBN 9780385494762 and ISBN 0385494769.