AMUSEMENTS IN WINTER AMONG THE MOUNTAINS OF WALES. No. IV. THREE-NINE-AND ELEVEN. The winds from off Old Snowdon blow, YES-winter has set in with violence indeed. Dark clouds hover on the summits of the mountains; the winds whistle along the valley; the sea roars at a distance; and it is more dark than Dante describes the progress to the lower regions. I have heaped my fire, trimmed my lamp, and purpose to devote one hour to the science of numbers. There are three numbers so very peculiar, that I cannot express my admiration of them. These are the numbers THREE, NINE, and ELEVEN. Some attribute letters to Moses; but that they were invented before his time, is evident from the thirteenth and fourteenth verses of the twenty-first chapter of Numbers : "From thence they removed, and pitched in the valley of Zared. From thence they removed, and pitched on the other side of Arnon, which is in the wilderness that cometh out of the coasts of the Amorites : for Arnon is the border of Moab, between Moab and the Amorites; wherefore it is said in the Book of the Wars of the Lord, what he did in the Red Sea, and in the brooks of Arnon." The Syriac and Chaldaic characters have been attributed to ABRAHAM; the Hebrew, to MOSES; the Egyptian, to Isis; the Greek, to the PHOENICIANS; the Latin, to NICOSTRATA; and the Gothic, to ULPHILAS. For the NUMERALS we now employ, and without which, neither logarithms nor fluxions could, perhaps, ever have been invented, we are doubtless indebted to the Arabians; as we are for the use of gunpowder, and a multitude of other inventions. EUCLID, by connecting the elementary parts of geometry, as it were, in one circular chain, established the only perfect part of human knowledge. NAPIER invented logarithms; and so perfect did they emanate, that only one material improvement has been invented since : and of that improvement he had the honour of inventing a part. TAYLOR, in one analytical formula, compressed a whole science into a single proposition, from which almost every method and truth of the new analysis may be deduced. These instances appear to me to afford greater examples of the intellectual unity of power, than any others with which we are acquainted, save one; for though NEWTON's discovery of fluxions might seem to bear as great an analogy to intellectual unity as either of these; yet the simple circumstance of LEIBNITZ having, nearly at the same time, made the same discovery, proves that the road leading towards the invention had been so sufficiently opened, that two persons, to use a homely expression, could walk a-breast. Gun *The history of the discovery of gunpowder by a German, is idle enough. powder was known in the eleventh century; and he can be little acquainted with the history of Spain, who does not know that it was employed by the Moors in their Spanish wars, during the thirteenth century. But there is yet a greater instance of intellectual unity, than even all these combined. JOHANNES, well known in Trinity College, Dublin, was nearly blind; and yet he could answer the question, relative to the name of the day of the week, on which any day of the month fell in any year, whether in the new or the old style, instanter ;-and BUXTON, the calculating peasant, could give the product of any arithmetical question, by the simple operation of his mind, as the best calculator could with his pen; and this, too, after employing a circuitous* method. These are extraordinary instances; but that of BIDDER, the calculating boy, amounts so much to the wonderful, that to me he is the greatest phenomenon that has ever exercised the faculties of the intellectual world. The most wonderful things have been recorded of this boy's arithmetical genius; but he has never yet been able to explain the method by which he is enabled to solve the various questions that have been proposed to him. In reference to these, one would imagine (says a modern writer) that, by some peculiar organization of his brain, a ray of omniscience had shot athwart it, giving us a simple glimpse of its divine origin; as when the clouds are opened by lightning, we appear to get a momentary peep into the glories of the innermost heaven. All these operations are performed through the medium of the brain. The brain is generally admitted to be a gland of a peculiar kind. Its sensorial communication with all the other parts of the body, is through the medium of the nerves. Hence, the brain may be styled the instrument of general sympathy; but of its connexion with the mind, we are altogether ignorant. Few steps have been made towards detecting its actual seat. Neither the heart nor the brain are essential to all animal life; though they appear to be so in the human anatomy, The seat of intellect is supposed to be the brain; but the nicest skill of the anatomist has not only not been able to detect its actual residence, but has not been able to ascertain the reason, why the brain is divided into three compartments. Nor, indeed, has it been positively determined, whether the spinal marrow is a continuation of the brain, extended through the chain of the back-bone; or whether the nervous system is the spinal marrow itself: which, instead of issuing from the brain, may give birth to it. Most English physicians, and, I believe, most foreign ones, adhere to the former opinion; though the sense of touch in animals is almost universally believed to flow from the spinal marrow; from the chord of which Le Gallois supposes the heart to derive its principle of life and motion: though Phillip insists, that the brain and spinal marrow of animals may be destroyed, and yet the heart continue to act forcibly and speedily, provided the lungs be exercised by the artificial breath of a pair of bellows. We ought, however, to speak with great caution, relative to results of anatomical, and indeed all physical experiments; they often leading to such immediately opposite conclusions. Thus Pitcairn calculates the force, with which the heart contracts, in order to To find what sum, for instance, 740, would amount to, if multiplied by a hundred; instead of adding two ciphers to the figure, he first multiplied 740 by five, and the product by twenty. ensure the due circulation of the blood, to be equal to 117,088lbs. at each contraction; and Borelli, at 180,000lbs. ; whereas Monro calculates it at not more than five ounces. But great errors sometimes lead to great truths.-What preserved chymistry? The search after the philosopher's stone. And as NEWTON's merit in the discovery of the powers of gravitation, consisted in giving the evidence of demonstration to that which a few preceding philosophers had only conjectured: so it is to be hoped that some Newton in metaphysics will so improve the hints that Locke and other philosophers have thrown out, as to furnish us with data on which to found some correct conclusions. Actual demonstration it were unreasonable to expect; though some have supposed, that there exists one single principle, into which the entire science of mind may be resolved. This, however, I think, we shall never be able to discover, any more than we can remember the hour of our birth, or calculate, when in health, the day of our death. He who discovers truth in philosophy, is not to be valued more than he who first teaches the method by which it may be discovered. But how slowly truth travels is sufficiently demonstrated by the fact stated by Voltaire, that though Newton survived the publication of his "Principia" forty years; yet, at his death, he had not twenty followers out of England. Newton says, towards the conclusion of his Optics, that if natural philosophy should continue to be improved in its various branches, the bounds of moral philosophy will be enlarged also. Some of the clergy, however, think otherwise. But to return to the subject on which we set out-NUMBERS: The number THREE is remarkable, since it has been in all ages a number, that has recommended itself to theologians of almost every creed. The CHALDEANS, for instance, respected it has being illustrative of figure, light, and motion;-the EGYPTIANS-of matter, form, and motion; the PERSIANS-of past, present, and future ;ORPHEUS—of life, light, and wisdom;-the GREEKS of the God of Heaven, the God of Earth, and the God of the Sea;-the early CRETANS-of life, cause, and energy;-and the HINDOOS-of power, understanding, and love. With CHRISTIANS this number is illustrative of the Trinity-" three persons in one God." 66 12. The number ELEVEN is remarkable, inasmuch as it is entirely unknown in BOTANY :-botanical arrangements are compelled to leave the number entirely out :-thus 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Perhaps, this is the most wonderful circumstance connected with Botany. Square numbers," says Taylor in his additional notes on the TIMEUS of PLATO, "are beautiful images of self-subsistence. For that which produces itself, effects this by hyparxis or summit. But the root of a number is evidently analogous to hyparxis; and, consequently, an even square number will be an image of a nature which produces itself; and hence, self-production is nothing more than an involution of hyparxis." I confess, I do not fully understand this argument; but that here are wonderful mysteries in the science of numbers is beyond all question. Thus, CUVIER assures us, that in an insect which he dissected, not one inch long, there were 494 muscles, 494 pair of nerves, and 40,000 antennæ ! The number NINE is so wonderful a number, that it may be safely employed as an emblem of the Divinity; for multiply it in whatever shape we will, it has the astonishing property of resolving all the other numbers into itself: thus, The number nine, too-so much reverenced by the Tartars, has the remarkable quality of resolving other numbers, when joined with itself, into themselves also: thus, Pythagoras might well say, that the knowledge of numbers was the knowledge of the Deity! A Babylonian writer was also accustomed to say, that he who could number to perfection, knows all things. * Yet Gibbon asserts of the mathematics, that they harden the mind by the habit of rigid demonstration; so destructive of the finer feelings of moral evidence, which must determine the actions and opinions of our lives. Surely no one thoroughly initiated into the evidences of mathematical science, will allow a position so entirely at war with example and experience as this! Who does not know, on the contrary, that Euclid, Archimedes, Euler, Newton, and Napier, were not only in the first order of mathematicians, but in the first order of excellent men? IMPROMPTU, Written on a blank page of "Colton's Lacon." SINCE the days of Lord Bacon, There's nothing like Lacon; So strange, yet so true, The substance of sense, Each truth has been lit By the spirit of wit, So brief and so bright, They're the essence of light! *See also Wisdom of Solomon, ii. 17; Ecclesiasticus, i. 2, &c. |