Readers whose mathematical faculty is weak or undeveloped and who like something concrete with “human interest” in it will find what they want in “Flatland by A Square,” a book published in Boston in 1891. The author, who turned out to be the Reverend Edwin Abbott, tells of a land in only two dimensions. The ruling class consisted of polygons, the bourgeoisie of squares and equilateral triangles, the lower class of isosceles triangles of narrow base, while the criminals had more irregular forms and the women were mere needles. Since all were confined to a surface, four lines set in a square made a tight prison. The inhabitants of Flatland, even the aristocratic and intellectual individuals who had so many sides as to be almost circular, could not conceive of a third dimension from which a person like ourselves could look down and see at a glance the insides of their houses, their safes and their bodies just as a being in the fourth dimension could see the insides of ours. The narrator, that is, A Square of Flatland, visits as a missionary the land of two dimensions where all the people lie in a line and refuse to believe in anything outside it and finally he encounters and endeavors to convert a solitary point of no dimensions but finds him, as we should expect, an incorrigible solipsist. We should all of us have been familiar with the fourth dimension for years if Slade had not turned out a trickster. Slade was an American medium--the original of Browning’s “Mr. Sludge”--who fooled Professor Zöllner by giving him what purported to be experimental evidence of the fourth dimension. Zöllner was a distinguished German physicist, Professor of Astronomy in the University of Leipzig, old, near-sighted, pre-disposed to spiritualism, and unskilled in legerdemain. Any proofs that Zöllner asked for, Slade was usually able at the next séance to produce. All the things that one might do in four dimensions but could not do in three were forthcoming by the obliging spirits whom Slade had at call. [Illustration: In space of one dimension (a straight line) there could be neither bend, loop nor knot in a string.] [Illustration: In space of two dimensions (a flat surface) a double bend could be made in the string but no loop or knot could be made.] [Illustration: But if we raise one string (into the third dimension) and lay it over the other like this:] [Illustration: We get a loop but cannot form a knot without using the ends.] [Illustration: A knot like this cannot be made in a string so long as the ends are held by the hands. But if we could use a fourth dimension we could tie such a knot as easily as we made a bend by the use of the second dimension and a loop by the use of the third. If such a knot could be tied in a string so held it would be experimental evidence of the existence of four-dimensional space.]