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Fantascience Digest, v. 1, issue 1, November-December 1937
Page 16
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Page 16 FANTASCIENCE DIGEST [[?]] a four dimensional sphere covered by a three dimensional surface which is curved around in the fourth dimension. Or rather don't try to imagine it. Just consider it. Now, the universe is this three dimensional surface. It is not the sphere itself, but the surface, and everything on it has the [[?]] properties of lines on the surface of a sphere, just expanded one dimension further. On the surface of a sphere there are no such things as straight lines. You have, instead, great circles, which are the circumferences of sections which go through the center of the sphere. Just like "parallels" of longitude on the earth. And incidentally, the term "parallel" is not so bad, because although the lines meet at the poles, spherical geometry is different from plane geometry and on the surface of a sphere these lines actually are parallel. It is obvious that on a surface of a sphere a point which moves in a straight line (along a great circle) will come back to its starting point. No matter in what direction it moves, it will come back to the place it started from. The same is true of the universe. Since it is to be considered the surface of a sphere, all straight lines on it are sections of great circles, and an object which sets out in any direction at all will return to the starting point.It will seem to have traveled in a straight line, according to all the tests you can impose upon it but lo and behold it is back from where it started. An objection can be raised here. When an object travels around the world its curve can be obscured[[?]]. Why not in space? this is because [[?]] we occur[[?]] a two dimensional [[?]]
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Page 16 FANTASCIENCE DIGEST [[?]] a four dimensional sphere covered by a three dimensional surface which is curved around in the fourth dimension. Or rather don't try to imagine it. Just consider it. Now, the universe is this three dimensional surface. It is not the sphere itself, but the surface, and everything on it has the [[?]] properties of lines on the surface of a sphere, just expanded one dimension further. On the surface of a sphere there are no such things as straight lines. You have, instead, great circles, which are the circumferences of sections which go through the center of the sphere. Just like "parallels" of longitude on the earth. And incidentally, the term "parallel" is not so bad, because although the lines meet at the poles, spherical geometry is different from plane geometry and on the surface of a sphere these lines actually are parallel. It is obvious that on a surface of a sphere a point which moves in a straight line (along a great circle) will come back to its starting point. No matter in what direction it moves, it will come back to the place it started from. The same is true of the universe. Since it is to be considered the surface of a sphere, all straight lines on it are sections of great circles, and an object which sets out in any direction at all will return to the starting point.It will seem to have traveled in a straight line, according to all the tests you can impose upon it but lo and behold it is back from where it started. An objection can be raised here. When an object travels around the world its curve can be obscured[[?]]. Why not in space? this is because [[?]] we occur[[?]] a two dimensional [[?]]
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