Israel Zangwill, in the papers he contributed once upon a time to the _Strand Magazine_ and later reunited in a book bearing the happy title Without Prejudice, spoke of women writers as being significant chiefly in their self-revelation. What they tell of themselves is of more value than what they write about. Whether Mr. Zangwill now believes this matters little in the discussion of an unusual book by a woman. Perhaps to-day he would open both eyes widely after reading Creative Involution, by Cora L. Williams, M. S., with an apposite introduction by Edwin Markham. Miss Williams deals with no less a bagatelle than the Fourth Dimension of Space (what we do not know we fear, and fear is always capitalised). Speculative as is her work, she is not a New-Thoughter, a Christian Scientist, or a member of any of the other queer rag-tag and bobtail beliefs and superstitions--fortune-telling, astrology, selling "futures" in the next life, table-rapping, and such like. Cora Lenore Williams is an authority in mathematics, as was the brilliant, unhappy Sonya Kovalevska. Her ideas, then, are not verbal wind-pudding, but have a basis of mathematics and the investigations of the laboratory, where "chemists and physicists are finding that the conduct of certain molecules and crystals is best explained as a fourth-dimensional activity."
We have always enjoyed the idea of the Fourth Spatial Dimension. The fact that it is an _x_ in the plotting of mathematicians in general does not hinder it from being a fascinating theme. J. K. F. Zoellner, of Leipsic, proved to his own satisfaction the existence of a Fourth Dimension when he turned an india-rubber ball inside out without tearing it. Later he became a victim to incurable melancholy. No wonder. If you have read Cayley, or Abbot's Flatland, or the ingenious speculations of Simon Newcomb and W. K. Clifford, you will learn the attractions of the subject. Perpetual motion, squaring the circle, are only variants of the alchemical pursuit of the philosopher's stone, the transmutation of the baser metals, the cabalistic Abracadabra, the quest of the absolute. Man can't live on machinery alone, and the underfed soul of the past period of positivism craves more spiritual nourishment to-day. Hasn't the remarkable mathematician Henri Poincaré (author of Science and Hypothesis, The Value of Science, Science and Method) declared that between the construction of the spirit and the absolute of truth there is an abysm caused by free choice and the voluntary elimination which have necessitated such inferences? Note the word "free"; free-will is restored to its old and honourable estate in the hierarchy of thought. The cast-iron determinism of the seventies and eighties has gone to join the materialistic ideas of Büchner and Clifford. It is a pluralistic world now, and lordly Intuition--a dangerous vocable--rules over mere mental processes. (There is, as George Henry Lewes asserted, profound truth in the Cullen paradox: _i. e._, there are more false facts than false theories current.) Science only attains the knowledge of the correspondence and relativity of things--no mean intellectual feat, by the way--but not of the things themselves; one must join, adds Poincaré, to the faculty of reasoning the gift of direct sympathy. In a word, Intuition. Even mathematics as an exact science is not immutable, and the geometries of Lebatchevsky and Riemann are as legitimate as Euclid's. And at this point the earth beneath us begins to tremble and the stars to totter in their spheres. Is the age of miracles now?