been an ordinary fool, the exposure of him would have been a useless task, but the follies of the learned are sometimes worth recording as lessons to mankind. Warburton was always violent and self-willed. As an illustration of his temper, I may remind you of what Spence tells us, that this arrogant and ferocious priest was originally an attorney, and "got into orders. by spitting in a nobleman's face at an election." Churchill says of him He was so proud, that should he meet He'd turn his nose up at them all, And shove his Saviour from the wall. No. X. SIR ISAAC NEWTON-PASCAL-MATHEMATICS-ANCIENT PHILOSOPHY-UTILITARIANISM. H.-I saw some very good remarks the other day in Blackwood's Magazine on the subject of imagination. A man, says the writer, (either Wilson or Lockhart, I suppose) may have high intellect, with little or no imagination, but he cannot have a high imagination with little or no intellect. The intellect of Dante, Milton, and Shakspeare was higher, he thinks, than that of Aristotle, Newton, and Bacon. A. Both Wilson and Lockhart are poets; and poets have always been disposed to overrate the value of the faculties required for the production of excellence in their favorite art. Such partiality is a very natural weakness. You talk as if only great poets and artists were largely gifted with high imagination. It is a gross mistake. All great inventions and discoveries are first suggested by the imaginative faculty and completed by deep thought and study. H.-I am glad to find you take this turn; because scientific men in general speak with great contempt of the imagination, and do not acknowledge the utility of the divinest of our faculties. But you go almost as far as Wordsworth, who says that poetry is the breath and finer spirit of all knowledge. What poetry there is in Lord Bacon's Essays! His thoughts often involuntarily move harmonious numbers. As the book is at hand let me call your attention to a passage in the Essay on Gardens "For the heath, which was the third part of our plot, I wished it to be framed as much as may be to a natural wildness. Trees I would have none in it, but some thickets made only of sweet-briar and honey-suckle, and some wild vine amongst; and the ground set with violets, strawberries, and primroses; for these are sweet and prosper in the shade." Now observe how naturally this passage takes the form of blank-verse : For the heath, which was the third part of our plot, I wished it to be framed As much as may be to a natural wildness. Trees I'd have none in it, but some thickets made Only of sweet-briar and honey-suckle, And some wild vine amongst; and the ground set With violets, strawberries and primroses; For these are sweet and prosper in the shade. How poetical is the remark in the same Essay that the breath of flowers is far sweeter in the hand than in the air, where it comes and goes like the warbling of music! A. Yes there is poetry in Lord Bacon's prose; but if there were not something besides and better, he would not rank quite so highly amongst the benefactors of mankind. H.-You would not say so, if you had a due sense of the real claims of poetry, and had not been in the habit of regarding it as nothing more than an elegant accomplishment. "Newton is a great man," said Coleridge, "but excuse me if I think it would take many Newtons to make a Milton." A. This sort of arithmetical criticism applied to intellectual qualities of totally different natures is supremely absurd and unjust. He might as well have said it would take many turnips to make a tulip. And why thus multiply your poetical authori ties? On matters of science they have not the weight of a straw, except with poets themselves. H.-There is an excellent article in the Edinburgh Review on the subject of mathematics, in which the writer produces a host of high authorities against the study of them as a mental exercise. He brings forward some of the most eminent mathematicians as evidence against their own sciences. He shows that even mathematicians themselves have felt that too close a study of mathematics contracts and freezes the intellect. A.-Oh, nothing is easier than to collect the opinions of celebrated men for or against any branch of human learning. From Solomon, who tells us that all is vanity and vexation of spirit, down to our own days, there is perhaps no eminent personage to be found who has not, at some time or other, under the weariness of labour or disappointment, expressed his disgust at his own peculiar occupation. H.-Pascal, a profound genius and an eminent mathematician, was amongst those who have avowed their contempt for mathematics. A.-Pascal died a devotee at thirty-nine, and expressed his contempt for all human learning, and abandoned all studies, as he himself says, in order to apply himself solely to what our Saviour calls the one thing needful. H.-If you will look into Bayle's Philosophical Dictionary you will find it there stated that Pascal despised mathematics before he gave himself up to devotion. You observe that it is easy to collect authorities for or against any branch of human knowledge. This is true with respect to the opinions of men on those arts and sciences in which they have not themselves excelled; but it would give you some little trouble, I suspect, to show that eminent historians, philosophers, poets, painters, and musicians have spoken with that unqualified contempt of the subject of their studies with which eminent mathematicians have spoken of their own sciences. A. You are much too fond of settling all questions by the authority of great names. The American Franklin tells us that Plato has somewhere said that any one who does not understand the 117th proposition of the 13th Book of Euclid ought not to be ranked amongst rational creatures. If the authority of a great name were a great argument this ought to settle our dispute. I do not attribute so much importance as you do to the decision of individuals, however eminent, respecting any particular branch of knowledge. All true knowledge is more or less valuable, and perhaps nothing would be more easy than to prove that of all knowledge mathematical knowledge is the most practically useful. H.-How can you talk in this extravagant way? Why, a knowledge of mathematics is of so little use in daily life that you may know a man intimately for half a century without discovering whether he has mastered the first proposition in Euclid. But ignorance in the elements of a literary education cannot be concealed for a day-not for an hour-not indeed for five minutes, if the ignoramus will only attempt to speak or write. Are there not hundreds of ladies and of gentlemen, too, (eminent authors amongst them-teachers of mankind) whose conversation is in the highest degree elegant, instructive, and delightful, who know absolutely nothing of the first elements of mathematics? Bayle, says D'Israeli, knew nothing of Geometry, and, as LeClere informs us, acknowledged that he could not comprehend the first problem in Euclid-and yet what a subtle reasoner he was! What would be the mental character of that man or woman who should know absolutely nothing of the first elements of literature? Could he or she be otherwise than coarse and vulgar? Which student would have the best chance of acquiring a refinement and elevation of soul-he who should confine himself to literature or he who should confine himself to mathematics? Pope in his Dunciad has a couplet against mathematics. Do Full in the midst of Euclid dip at once, And petrify a genius to a dunce. you think that the name of Shakspeare or Milton could be put in the place of Euclid, in this couplet, without turning the meaning into downright nonsense? A. I am sick of your poetical authorities. I laugh at your poets who laugh at mathematics; they talk as if the great business of life was to write and read verses, and they affect a superiority over every art or science that happens to be beyond their comprehension. H.-Beyond their comprehension! Dugald Stewart was no poet, and yet you must remember his remark-"How small is the number of individuals who are qualified to think justly on metaphysical, moral, or political subjects, in comparison with those, who may be trained by practice to follow the longest processes of mathematical reasoning." It is notorious that little boys at school, and very dull ones, too, often acquire, in a wonderfully short time, a marvellous amount of mathematical knowledge. There was a calculating boy," exhibited in London some years ago, who was almost an idiot, but who exhibited an amazing aptitude for the most difficult mathematical calculations. Idiotic boys do not shine in literature. The Journal of Education (for October 1832) quotes from a Sicilian Journal an account of three mathematical children. One of them, who was only seven years old, gave off-hand answers to problems which usually require tedious arithmetical calculations. He would listen to a question and give his solution while pursuing his pastimes. Montaigne, in one of his Essays, tells us that the "Tunny-fish is well acquainted with mathematics." I have known many human mathematicians who seemed to be very little elevated above the Tunny-fish. A man's wisdom, or utility, or moral worth depends very little upon the propositions in Euclid. A. You might add with equal truth that they depend as little on as in presenti or propria quæ maribus. H.-Well, then, let me have an explanation of the utility of the science of mathematics. A.—It builds our houses and our bridges; fortifies them and defends them when fortified-constructs our ships and takes them safely across the pathless ocean-frames every kind of machinery, from the watch, which is our constant guide and companion, to the steam-engine, which is uniting the opposite ends of the earth in an intercourse more intimate than ever neigh |