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?

Perhaps music is in the Fourth Dimension. Time may be in two dimensions. Heraclitus before Bergson compared Time to a river always flowing, yet a permanent river: if we emerged from this stream at a certain moment and entered it an hour later, would it not signify that Time has two dimensions. And where does music stand in the eternal scheme of things? Are not harmony with its vertical structure and melody with its horizontal flow proof that music is another dimension in Time? Miss Williams's notion of the Fourth Spatial Dimension is a spiritual one. Creative Involution is to supersede the Darwinian evolution. Again, the interior revolution described for our salvation in the epistles of the Apostle Paul. All roads lead to religion. Expel religion forcibly and it returns under strange disguises, usually as debasing superstitions. Yet religion without dogma is like a body without a skeleton—it can't be made to stand upright.

Mathematicians are poets, and religion is the poetry of the poor, just as philosophy is the diversion of professors. Modern science, said Mallock, put out the footlights of life's stage when it denied religion. But matter, in the light of recent experiment, is become spirit, energy, anything but gross matter. Tyndall might have to revise the conclusions of his once famous Belfast address in the presence of radium. Remy de Gourmont said that the essential thing is to search the eternal in the diverse and fleeting movements of form. From a macrocosmic monster our gods are become microcosmic; god may be a molecule, a cell. A god to put in a phial; thus far has the zigzag caprice of theory attained. And religion is "a sum of scruples which impede the free exercise of our faculties," says Salomon Reinach in Orpheus. Bossuet did not write his Variations in vain. All is vanity, even doctrinal fluctuations. Goethe has warned us that "Man is not born to solve the mystery of Existence; but he must nevertheless attempt it, in order that he may learn how to keep within the limits of the Knowable." Goethe detested all "thinking about thought." Spinoza was his only philosophical recreation.

Man must no longer be egocentric. The collective soul is born. The psychology of the mob, according to Professor Le Bon, is different from the psychology of the individual. We know this from the mental workings of a jury. Twelve otherwise intelligent men put in a jury-box contaminate each other's will so that their united judgment is, as a rule, that of a full-fledged imbecile. Mark Twain noted this in his accustomed humorous (a mordant humour) fashion, adding that trial by jury was all very well in the time of Alfred the Great, candle-clocks, and small communities. Miss Williams, who sees salvation for the single soul in the collective soul—not necessarily socialistic—nevertheless warns parents against the dangers in our public-school system, where the individuality of the child is so often disturbed, if not destroyed, by class teaching. Mob psychology is always false psychology. The crowd obliterates the ego. Yet to collective consciousness may belong the future. It is all very well for Mallock to call war the glorification, the result, and the prop of limited class interests. (This was years ago.) Stately, sedate, stable is the class that won't tolerate war; a class of moral lollipops. War we must have; it is one of the prime conditions of struggling existence. As belief in some totem, fetich, taboo is the basis of all superstitions, so the superstition of yesterday builds the cathedrals of faith to-day. (Read Frazer's Golden Bough—James Frazer, who is the Darwin of Social Anthropology.) Happiness requires limitations, as a wine needs a glass to hold it; and if patriotism is a crime of lÈse-majesty against mankind, then be it so. But like the poor, war and patriotism are precious essences in the scheme of life, and we shall always have them with us. However, the warning of Miss Williams is a timely one. At school our children's souls are clogged with bricks and mortar, instead of being buoyant and individual.

She quotes—and her little volume contains a mosaic of apt quotations—with evident approbation from Some Neglected Factors in Evolution, by the late H. M. Bernard, an English thinker: "Organic life is thus seen advancing out of the dim past upon a series of waves, each of which can be scanned in detail until we come to that one on which we ourselves, the organisms of to-day, and the human societies to which we belong, are swept onward. Here we must necessarily pause, but can we doubt that the great organic rhythm which has brought life so far will carry it on to still greater heights in the unknown future?" Rhythm, measured flow, is the shibboleth. Zarathustra tells us that man is a discord and hybrid of plant and ghost. "I teach you Beyond-Man (superman); Man is something that will be surpassed ... once man was ape, and is ape in a higher degree than any ape.... Man is a rope connecting animal and Beyond-Man." "Believe that which thou seest not," cries Flaubert in his marvellous masque of mythologies ancient and modern, The Temptation of St. Anthony. Tertullian said the same centuries before the Frenchman: Believe what is impossible. We all do. Perhaps it is the price we pay for cognition.

Miss Williams is not a Bergsonian, though she appreciates his plastic theories. She has a receptive mind. Henri Bergson is a mystagogue, and all mystagogues are mythomaniacs. He has yet to answer Professor Hugh S. R. Elliott's three questions: "1. Bergson says, 'Time is a stuff both resistant and substantial.' Where is the specimen on which this allegation is founded? 2. Consciousness is to some extent independent of cerebral structure. Professor Bergson thinks he is disproving a crude theory of localisation of mental qualities. Will he furnish evidence of its existence apart from local structure? 3. Instinct leads us to a comprehension of life that intellect can never give. Will Professor Bergson furnish instances of the successes of instinct in biological inquiries where intellect has failed?" (From Modern Science and the Illusions of Professor Bergson, 1912.) These "metaphysical curiosities," as they are rather contemptuously called by Sir Ray Lankester in his preface to this solidly reasoned confutation, are the pabulum of numerous persons, dilettantes, with a craving for an embellished theory of the Grand Perhaps. Miss Williams is not the dupe of such silken sophistries, and while her divagations are sometimes in the air—which, like the earth, hath bubbles, as was observed by the greatest of poets—she plants her feet on tangible affirmations. And to have faith we must admit the Illative sense of John Henry Newman. Thus "the wheel is come full circle." Creative Involution will please mystics and mathematicians alike. The author somersaults in the vasty blue, but safely volplanes to mother earth.