SOURCE: Garnett, William. Introduction to Flatland: A Romance of Many Dimensions, pp. vii-x. New York: Barnes and Noble, Inc.: 1963.

In the following introduction to the 1963 edition of Flatland, Garnett discusses thoughts on the fourth dimension illuminated by Abbott's novel.

In an address to the Committee of the Cayley Portrait Fund in 1874 Clerk Maxwell, after referring in humorous terms to the work of Arthur Cayley in higher algebra and algebraical geometry, concluded his eulogium with the lines—

March on, symbolic host! with step sublime, Up to the flaming bounds of Space and Time! There pause, until by Dickenson depicted, In two dimensions, we the form may trace Of him whose soul, too large for vulgar space In n dimensions flourished unrestricted. 

In those days any conception of “dimensions” beyond length, breadth and height was confined to advanced mathematicians; and even among them, with very few exceptions, the fourth and...