2 SPHERICAL INTEGRITY FOR A FLAT MAP OF THE ROUND WORLD
2‘‘I think I have found something pretty exciting.’’ Buckminster Fuller was warming up to the prospect of explaining a new concept to his patent lawyer. From the restrained eagerness in the soft voice and the sparkle in the inventor’s eye, you could tell that it was going to be well worth the listening. When Bucky opened a conversation that way, you knew you had to listen hard. Good chance that your powers of concentration and imagining were going to be stressed to their tensile limits. But if you could hold fast to the tumbling torrent of thought, you were certain to be rewarded with some deep insight that would indeed be ‘‘pretty exciting,’’ as Bucky had promised.
3 More often than not, such a session would see a mealtime or bedtime fly past unheeded. As the inventors story unfolded, and some new world of scientific and philosophic revelation was breaking through the mists of imperfect understanding, you almost could become a little giddy. Ideas can achieve a richness that possesses an inebriating quality, and the fresh thrusts of Bucky’s unfettered imagination made a heady potion.
4 Celestial bodies responding to immutable laws of gravity and motion whirl in stately procession inexorably through time. Their movements within the symmetry of orbital flight are forever curving, oblivious to man’s unreal world of arbitrary straight lines and ‘‘immovable’’ objects. He, plodding with ant-like persistence along the enticing thin, straight lines of Euclidean thought, responds to a system of statics which in turn almost is oblivious to the whirling universe which his eyes cannot see. His habitual thought process, inwardly directed, so blurs the focus of his imaginative power as only to increase his difficulty in perceiving the more comprehensive truths of the world in which he lives and has his being.
5 How strange it now seems that in olden times men conceived that the world was flat. Yet such a view is only one manifestation of man’s seeming insistence that the whole of mathematics, science and architecture must be generated from beginning concepts of straight lines and flat planes. Ultimately, through development of these concepts with the use of more straight lines as radial generators, his ancient geometry brings him to the cylinder and the sphere, but it has been a long way round red robin’s barn. When beginning Euclid, he was taught that, ‘‘A straight line is the shortest distance between two points.’’ Later on, if ever he was called upon to work out an ordinary problem of ‘‘the sailings’’ in navigation, he found to his chagrin that in order to sail the shortest distance between two points, he must pursue a ‘‘great circle’’ course which on his chart isn’t a straight line but a curved one!
6 And now, brought into crisp focus by a mind swept clear of the limitations of old geometry, the idea which the inventor thought ‘‘pretty exciting’’ began to unfold. ‘‘The problem of the navigator is how to sail (or fly) the shortest course, which on a conventional chart will be a curved line.’’ Bucky paused, studying his listener’s face for sign of full attention, then continued. ‘‘I simply design an unconventional chart which is so constructed that all future navigators can find their courses as straight lines. This means that I will need a new kind of map projection in which all great circles of a sphere will be seen as straight lines.’’ It will be noticed that in Fuller’s eyes the first step would be to break away altogether from existing concepts so that he could start afresh in hope of reaching a more comprehensive solution. No thought of simply trying to improve on the older systems of map projection. Begin again from the very beginning. Let no old thought intrude, however hallowed by time.
7 Strange as it may now seem for pre-Copernicus man to have imagined that the world was flat, it can be thought even stranger that once having discovered that his flat-ish notion was foolish and unreal, he still persisted in holding tenaciously to the equally foolish notion that the parallels of latitude must appear as straight lines on a chart poorly suited to the navigator’s needs in sailing a course about his new round world! Knowing it was round was comforting, as he would not sail off the edge of it. But he still had to contend with the awkwardness of a chart which in a most arbitrary fashion retained so peculiar a use of the seemingly indispensable straight line. So peculiar, in fact, as to represent what is not the shortest distance between two points, and which has no validity as a scale of distance. Only along the Equator or by following a great circle meridian could the sailor find true distance, or plot the shortest course as a straight line. These were special cases not often to be encountered in the realm of practical navigation. What was needed, reasoned Fuller, was a solution that somehow could bring greater spherical integrity to a flat map of the round world.
8 ‘‘As the Earth is a spherical body, so the only true cartographic representation of its surface must be spherical,’’ said Fuller, adding, ‘‘All flat surface maps are compromises with truth.’’ Mercator’s projection, we know, is true to scale only along the Equator, so that Alaska, Greenland and all far northern lands are stretched beyond any semblance of reality. Azimuthal projection is limited to conversion of the meridians at one pole at a time. Other systems of projection known before Fuller’s cartography came into being in 1943--44, could be made to give uniform scale along parallels, or to yield other fragments of spherical integrity. Any comprehensive verity in a world map was still lacking, and it remained for Fuller to point the way to flat-mapping the world with a new kind of world-around integrity of scale.
9 Fuller’s fresh approach to this age-old problem of the map makers was to resolve the Earth’s surface into sections which are entirely bounded by projections of great circles. To begin with, this could be made to give the complete truth, and nothing but the truth, along the boundary of every section of the map. The navigator would need only to measure the distance along these great circle boundaries to know his answer in true nautical miles. It was like Equator or meridian sailings multiplied to cover the earth in a comprehensive network of true-distance lines.
10 Next, while maintaining all these ‘‘truth boundaries,’’ the projection of land and water features from the spherical to the flat surfaces according to the inventor’s cartography, brought the ‘‘subsidence’’ distortion, that is the distortion enforced by translation from sphere to plane, to an irreducible minimum. This might be explained by thinking of an orange peel section squeezed flat without stretching or breaking its edges as compared with another orange peel section which is perhaps more tender and splays out at the edge when pushed flat. 1116 first orange peel, flattened, continues to portray true edge measurements of its section; the second has lost all capacity to give any true measurements except that at its unbroken center, there is a single point remaining as it was in the orange. But only a point, not a line. Nothing that could be measured to show true scale or distance. What Fuller did, then, was to discover how to use a grid of intersecting great circles for geometric translation of a sphere into a plane. These were his great circles of truth, a concept neatly fitting the intuitive dynamics of the man, circles being inherently representative of energy and motion as opposed to statics.
11 Logic, progressing with measured steps of unerring dignity in a straight line from premise to conclusion, is deceptive. Turtle-like, it moves slowly and commendably to a short-sighted goal. An imagination such as Fuller’s whirls without restraint, encompassing whole new galaxies of thought. One can almost literally see Fuller’s whirling pattern of thought within the geometrically wound ball of yam wrapped into its overall maze of great circles. Unwrapped, they become a map of greater truth than any before.
12 Here, then, we perceive the meaning and worth of Fuller’s habitual exercise of comprehensive thought. There is first the whole, consisting of a network of intersecting great circles, the open mesh of the net filled again with great circle gridding, and only after that the resolution, or taking apart, into the pieces which are to be assembled, puzzle-wise, into a map. At first the whole; comprehensiveness. The result of the comprehensive thought procedure in this instance brought into being a world map1, which gives a truer overall picture of areas, boundaries, directions and distances than had been provided before by any known system of map projection.