The Fourth Dimension Simply Explained

Almost all of the essayists explored analogies for constructing a four-dimensional geometry that extended our understanding of ordinary three-dimensional space, and almost all of them debunked the spiritist claims. Manning explains that there is a great deal of repetition in the essays, although there are differences in emphasis that justify their selection.

The Dimensional Analogy
For several years after his graduation from Brown University in 1883, Manning taught in secondary schools, so he was aware of the importance of the dimensional analogy in the curriculum. He starts his introduction “The geometry studied in the schools is divided into two parts, Plane Geometry, or Geometry of Two Dimensions, and Solid Geometry, or Geometry of Three Dimensions, and the study of these geometries suggests an extension to geometry of four or more dimensions.” Unfortunately a good deal of solid geometry has disappeared from the secondary-school curriculum, so the power of the dimensional analogy is no longer so strong. This may be one of the most important reasons to republish these essays, reflecting as they do a common appreciation of the geometrical background of the average reader of Scientific American nearly a century ago.