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We are now in the middle of a long process of transition in the nature of the image which man has of himself and his environment. Primitive men, and to a large extent also men of the early civilizations, imagined themselves to be living on a virtually illimitable plane. There was almost always somewhere beyond the known limits of human habitation, and over a very large part of the time that man has been on earth, there has been something like a frontier...
Gradually, however, man has been accustoming himself to the notion of the spherical earth and a closed sphere of human activity. A few unusual spirits among the ancient Greeks perceived that the earth was a sphere. It was only with the circumnavigations and the geographical explorations of the fifteenth and sixteenth centuries, however, that the fact that the earth was a sphere became at all widely known and accepted. Even in the thirteenth century, the commonest map was Mercator's projection, which visualizes the earth as an illimitable cylinder, essentially a plane wrapped around the globe, and it was not until the Second World War and the development of the air age that the global nature of tile planet really entered the popular imagination. Even now we are very far from having made the moral, political, and psychological adjustments which are implied in this transition from the illimitable plane to the closed sphere.
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p.3

 

Kenneth Boulding

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In the imagination of those who are sensitive to the realities of our era, the earth has become a space ship, and this, perhaps, is the most important single fact of our day. For millennia, the earth in men's minds was flat and illimitable. Today, as a result of exploration, speed, and the explosion of scientific knowledge, earth has become a tiny sphere, closed, limited, crowded, and hurtling through space to unknown destinations. This change in man's image of his home affects his behaviour in many ways, and is likely to affect it much more in the future.

 

Kenneth Boulding

 

...the stereographic projection of the spherical surface. From the north pole P we draw radial lines to project every point of the surface of the sphere upon the horizontal plane [below, perpendicular to a line joining it to P and the sphere's center]. In general this transformation is unique and continuous , although the metrical relations are distorted; for the point P, however, it shows a singularity. Point P is mapped upon the infinite; i.e., no finitely located point of the plane corresponds to it. It can be shown that every transformation possesses a singularity in at least one point. The surface of the sphere is therefore called topologically different from the plane. Only a "sphere without a north pole" [point] would be topologically equivalent to a plane. ...such a sphere has a point-shaped hole without a boundary and is no longer a closed surface.

 

Hans Reichenbach

 

The surfaces of three-dimensional space are distinguished from each other not only by their curvature but also by certain more general properties. A spherical surface, for instance, differs from a plane not only by its roundness but also by its finiteness. Finiteness is a holistic property. The sphere as a whole has a character different from that of a plane. A spherical surface made from rubber, such as a balloon, can be twisted so that its geometry changes. ...but it cannot be distorted in such a way as that it will cover a plane. All surfaces obtained by distortion of the rubber sphere possess the same holistic properties; they are closed and finite. The plane as a whole has the property of being open; its straight lines are not closed. This feature is mathematically expressed as follows. Every surface can be mapped upon another one by the coordination of each point of one surface to a point of the other surface, as illustrated by the projection of a shadow picture by light rays. For surfaces with the same holistic properties it is possible to carry through this transformation uniquely and continuously in all points. Uniquely means: one and only one point of one surface corresponds to a given point of the other surface, and vice versa. Continuously means: neighborhood relations in infinitesimal domains are preserved; no tearing of the surface or shifting of relative positions of points occur at any place. For surfaces with different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface.

 

Hans Reichenbach

 

The Earth is cylindrical, three times as wide as it is deep, and only the upper part is inhabited. But this Earth is isolated in space, and the sky is a complete sphere in the center of which is located, unsupported, our cylinder, the Earth, situated at an equal distance from all the points of the sky.

 

Anaximander

 

The earth is the sphere, the measure of all; round it describe a dodecahedron; the sphere including this will be Mars. Round Mars describe a tetrahedron; the sphere including this will be Jupiter. Describe a cube round Jupiter; the sphere including this will be Saturn. Now, inscribe in the earth an icosahedron, the sphere inscribed in it will be Venus: inscribe an octahedron in Venus: the circle inscribed in it will be Mercury.

 

Johannes Kepler