Dr. Muir, already well known by many investigations into determinants and continued fractions, and by a charming little introduction to determinants, has thoroughly studied the history of this subject, and has arranged his account of it with remarkable clearness. Each writer’s results are stated in his own language, followed by a luminous commentary. An ingenious table shows the history of forty-four theorems, and at the same time serves as an index to the first half of this volume, which, it is to be presumed, is one-half of the first part, and not more than one-fourth of the whole work.
Perhaps Dr. Muir attaches a little too much importance to theorems, as contradistinguished from methods and ideas. Thus, he speaks rather unfavorably of Bézout’s work (1779), although it contains the idea of polar multiplication; but because this is not made a theorem, Dr. Muir hardly notices it. The first paper analyzed in the book is by Leibnitz, and contains the umbral notation, which is the quintessential idea of the theories of determinants as well as that of matrices, to which the theory of determinants is but an appendage.
We have already mentioned that the last number of the American Journal of Mathematics contains an admirable memoir upon matrices by Dr. Henry Taber of Clark University.
10
Review of Fraser’s Locke
| 25 September 1890 | The Nation |
Locke. By Alexander Campbell Fraser. [Philosophical Classics for English Readers.] Edinburgh: Wm. Blackwood & Sons; Philadelphia: J. B. Lippincott Co. 1890.
Mr. Galton’s researches have set us to asking of every distinguished personality, what were the traits of his family; although in respect, not to Mr. Galton’s eminent persons, but to the truly great—those men who, in their various directions of action, thought, and feeling, make such an impression of power that we cannot name from all history more than three hundred such—in respect to these men it has not been shown that talented families are more likely than dull families to produce them. The gifts of fortune, however, are of importance even to these. It is not true that they rise above other men as a man above a race of intelligent dogs. In the judgment of Palissy the potter (and what better witness could be asked?), the majority of geniuses are crushed under adverse circumstances. John Locke, whose biography by Berkeleyan Professor Fraser is at our hand, came of a family of small gentry, his mother being a tradesman’s daughter. The family had shown good, but no distinguished ability, and no remarkable vitality. The philosopher, John, the eldest child of his parents, was born (1632) two years after their marriage; there was one other child five years later. John Locke himself never contemplated marriage.
He resembled not in the least a genius of the regulation pattern—a great beast, incapable of self-control, self-indulgent, not paying his debts, subject to hallucinations, half-mad, absent-minded. He did not even, like the popular hero, attribute all that distinguished him to his mother’s influence. He called her “pious and affectionate,” but rarely mentioned her. On the other hand, he often spoke of his father with strong love, with respect for his character, and with admiration for his “parts.” That father gave him all his instruction up to the age of fourteen years; and since he alone of Locke’s teachers escaped the bitter maledictions of his later life for their pedantry and “verbal learning,” the father it doubtless was who first taught our philosopher to think for himself.
“I no sooner perceived myself in the world,” says Locke, “but I found myself in a storm.” When he was ten years old, the Civil War broke out, and the house was near Bristol, one of the centres of operations. His father at first joined the Parliamentary army, but returned within two years. Such events made food for reflection and doubtless suggested toleration.
At fourteen he was put to Westminster school, under stern Dr. Busby, whose pedantry he detested; at twenty sent to peripatetic Oxford, and was still thoroughly discontented. He had not been a precocious boy, and was quite unconscious of superior power. At first he only read romances, and probably never studied very hard. He was awakened by the books of Descartes, whose system he did not embrace, but whose lucidity encouraged him to believe himself not a fool. “This same John Locke,” says Anthony à Wood, “was a man of turbulent spirit, clamorous and discontented; while the rest of our club took notes deferentially from the mouth of the master, the said Locke scorned to do so, but was ever prating and troublesome.” But this is the distortion of hatred, such as that which later prompted the lie that caused Charles II to order Locke’s expulsion from his studentship. The envious tribe said to infest colleges must take everlasting comfort in the reflection that efforts like theirs expelled John Locke from Oxford, and almost stifled the Essay Concerning Human Understanding.
Two years before the Restoration, he took his master’s degree, and was afterwards appointed to that life studentship, to lectureships in Greek and rhetoric, and to a censorship in moral philosophy. At a later date, he took the degree of Bachelor in Medicine. His father and brother died in 1661, leaving him about half enough to live upon. In 1666, being thirty-four years old, he made the acquaintance of Lord Ashley, afterwards Earl of Shaftesbury, grandfather of the author of the Characteristics. This nobleman took up Locke and formed him into a man of business, a man of the world, and a politician, fit to become, as he did become, the philosophical champion of the Glorious Revolution.
Locke falsifies the maxim that he who has done nothing great at twenty-seven years of age never will. His first publication (barring a few early verses) at double that age consisted of two anonymous articles in an encyclopædia. He never learned to write a good style. His great Essay appeared three years later, May, 1689, though he had been at work upon it for nearly twenty years. He only lived fifteen years more, during which he was much engaged in public business, so that the time of his active authorship was brief.
Locke’s was a frail and diminutive figure, with sloping shoulders, a gracefully set head, a forehead appearing low because cut off below by strong eyebrows rising to an angle over a nose long, pointed, and highridged. His eyes were prominent, his mouth well-formed, his chin strong. He must have resembled a little the late E. H. Palmer. His health was always delicate; he was a great sufferer from asthma.
That great observer, Sydenham, many years before Locke became famous, wrote of him as “a man whom, in the acuteness of his judgment and in the simplicity—that is, the excellence—of his manners, I confidently declare to have amongst the men of our own time few equals and no superiors.” That Locke’s manners should have made so powerful an impression upon Sydenham bespeaks magnetism if not greatness. A fascinating companion, gay, witty, observant, shrewd, thoroughly in earnest in his convictions, he added to his good fellowship the air of meaning to get himself all the happiness out of life he could, and to impart it to those about him. He maintained he had the sanction of Scripture in living for enjoyment, and the great pleasures he pursued were, he tells us, these five: health, reputation, knowledge, the luxury of doing good to others, and the hope of heaven. Few men have had so many warm friends; and to these friends he was devoted with a passion strong as a lover’s.
At the same time he was no mean diplomatist, knew well enough how to play upon weaknesses, and no one more than he possessed the art of turning men inside out. Many little maxims on this head are scattered through his writings. He himself was impenetrable. “I believe there is not in the world,” said one who had tried a lance with him, “such a master of taciturnity and passion.” He confesses himself to be choleric, though soon appeased; but, in fact, self-control is the characteristic mark of his thoroughly well-regulated life. His personal economy was strict. He was methodical in business to a fault. His prudence was carried to the point of excessive caution. He was moderate