The Cardinal Numbers

Abstract

UNLIKE Hudibras, who could, as we are told, “extract numbers out of matter,” Mr. Hopkins proposes in the essay before us to extract matter from numbers, or, as he says in the preface, “to show that every-day things—numbers being one of them—possess in themselves materials worth investigation, and connections with other subjects of thought and study.” Our author does not attempt any systematic investigation of the properties of numbers: to do so would far transcend the modest limits to which he confines himself. He prefers to consider numbers in their relation to such subjects as religion, music, poetry, mythology, and superstition. Some purely numerical facts are, however, given, which either are, or else ought to be, found in every text-book of arithmetic—for instance, the rules (given on p. 75, at the beginning of the appendix) for determining when a number is divisible by any of the first twelve numbers, 7 only excepted. The cardinal numbers from 1 to 10 inclusive are treated separately in ten distinct chapters. These, with the introductory chapter and an appendix, the principal portion of which is taken up with magic squares, form the whole of the work.

The Cardinal Numbers, with an Introductory Chapter on Numbers Generally.

By Manley Hopkins. (London: Sampson Low, 1887.)