Mathematicians From England

"The errors which arise from the absence of facts are far more numerous and more durable than those which result from unsound reasoning respecting true data."

"The first application of this principle [of the division of labor] must have been made in a very early stage of society; for it must soon have been apparent that more comforts and conveniences could be acquired by one man restricting his occupation to the art of making bows, another to that of building houses, a third boats, and so on. This division of labor Into trades was not, however, the result of an opinion that the general riches of the community would be increased by such an arrangement: but it must have arisen from the circumstances, of each individual so employed discovering that he himself could thus make a greater profit of his labour than by pursuing more varied occupations."

"It appears to me, that any explanation of the cheapness of manufactured articles, as consequent upon the division of labour, would be incomplete if the following principle were omitted to be stated."

"We have already mentioned what may, perhaps, appear paradoxical to some of our readers, — that the division of labour can be applied with equal success to mental as to mechanical operations, and that it ensures in both the same economy of time."

"The establishment of "The Times" newspaper is an example, on a large scale, of a manufactory in which the division of labour, both mental and bodily, is admirably illustrated, and in which also the effect of domestic economy is well exemplified. It is scarcely imagined, by the thousands who read that paper in various quarters of the globe, what a scene of organized activity the factory presents during the whole night, or what a quantity of talent and mechanical skill is put in action for their amusement and information."

"ENGLAND has invited the civilized world to meet in its great commercial centre; asking it, in friendly rivalry, to display for the common advantage of all, those objects which each country derives from the gifts of nature, and on which it confers additional utility by processes of industrial art. This invitation, universally accepted, will bring from every quarter a multitude of people greater than has yet assembled in any western city: these welcome visitors will enjoy more time and opportunity for observation than has ever been afforded on any previous occasion. The statesman and the philosopher, the manufacturer and the merchant, and all enlightened observers of human nature, may avail themselves of the opportunity afforded by their visit to this Diorama of the Peaceful Arts, for taking a more correct view of the industry, the science, the institutions, and the government of this country. One object of these pages is, to suggest to such inquirers the agency of those deeper seated and less obvious causes which can be detected only by lengthened observation, and to supply them with a key to explain many of the otherwise incomprehensible characteristics of England."

"The triumph of the industrial arts will advance the cause of civilization more rapidly than its warmest advocates could have hoped, and contribute to the permanent prosperity and strength of the country far more than the most splendid victories of successful war."

"There are in the Exhibition some beautiful examples of such amongst the productions of other countries as well as of our own. They are made by the united labour of many women. The cost of a piece of lace will consist of:"

"In the making both of lace and of statues, the to the artists can only be reduced by producing a larger number of them through more extended education. The expense of the raw material is small in both. The expense of labour in lacemaking is very large, and it is perhaps considerable also in sculpture. The discovery of more convenient localities yielding marble, may make some diminution in its cost; and the improved manufacture of thread may slightly reduce the price of lace. A reduction in the price of labour may to a very moderate extent reduce the cost of the raw material of both. But it is evident that any very great reduction is not to be expected. Let us now contrast this possible reduction with the past history of some industrial art. The plain made at , called patent net, will supply us with a good example. In the year 1813 that lace was sold in the piece at the rate of 218. a-yard. At the present time lace of the same kind, but of a better quality, is sold under the same circumstances at 3d. per yard. Thus, in less than forty years the price of the industrial produce has diminished to one eighty-fourth part of its original price."

"Machinery of a very beautiful kind has been contrived for copying accurately, on a reduced or an enlarged scale, both medals and statues. The itself could not be justly excluded from a purely industrial exhibition, if, placed in the centre of a series diminishing on the one side to a statuette of a foot high, and increasing on the other to a figure double her own height. Such a series, though fairly introduced as an illustration of industrial art, would, indeed, itself be highly interesting to the fine arts, as exhibiting the effect of change of magnitude, when the proportions remain identical."

"The successful construction of all machinery depends on the perfection of the tools employed; and whoever is a master in the arts of tool-making possesses the key to the construction of all machines... The contrivance and construction of tools must therefore ever stand at the head of the ."

"It is not uninteresting to observe in society the opinions of its different classes respecting honours conferred on science. Military and naval men, especially the most eminent, feel that genius is limited by no profession, and themselves sympathizing with it, would gladly hail as brothers in the same distinction, the philosopher and the poet. With lawyers the case is reversed ; genius dwells not in their courts : industry and acuteness, monopolised by one absorbing professional subject, exclude larger views; and ribbons not being amongst the honoraria of their own profession, they reprobate their application to science. To this there are, however, some noble exceptions. Amongst the brightest ornaments, of their own profession, men are to be found of larger experience and more extended views than it often produces, who are themselves qualified to have become discoverers in other sciences. It is much to be regretted when such powers are applied to the mere administration, instead of to the reformation, of the laws of their country."

"It is difficult to pronounce on the opinion of the ministers of our Church as a body: one portion of them, by far the least informed, protests against anything which can advance the honour and the interests of science, because, in their limited and mistaken view, science is adverse to religion. This is not the place to argue that great question. It is sufficient to remark, that the best-informed and most enlightened men of all creeds and pursuits, agree that truth can never damage truth, and that every truth is allied indissolubly by chains more or less circuitous with all other truths; whilst error, at every step we make in its diffusion, becomes not only wider apart and more discordant from all truths, but has also the additional chance of destruction from all rival errors."

"The Church has been reproached with endeavouring to appropriate to itself all those professorships in our Universities which are connected with science: it is however certain that the larger portion of these ill-remunerated offices have been filled by clergymen."

"But a much graver charge attaches itself, if not to our clergy, certainly to those who have the distribution of ecclesiastical patronage. The richest Church in the world maintains that its funds are quite insufficient for the purposes of religion and that our working clergy are ill-paid, and church accommodation insufficient. It calls therefore upon the nation to endow it with larger funds, and yet, while reluctant to sacrifice its own superfluities, it approves of its rich sinecures being given to reward, — not the professional service of its indefatigable parochial clergy, but those of its members who, having devoted the greater part of their time to scientific researches, have political or private interest enough to obtain such advancement. But this mode of rewarding merit is neither creditable to the Church nor advantageous to science. It tempts into the Church talents which some of its distinguished members maintain to be naturally of a disqualifying, if not of an antagonistic nature to the pursuits of religion; whilst, on the other hand, it makes a most unjust and arbitrary distinction amongst men of science themselves. It precludes those who cannot conscientiously subscribe to Articles, at once conflicting and incomprehensible, from the acquisition of that preferment and that position in society, which thus in many cases, must be conferred on less scrupulous, and certainly less distinguished inquirers into the works of nature. As the honorary distinctions of orders of knight hood are not usually bestowed on the clerical profession, its members generally profess to entertain a great contempt for them, and pronounce them unfit for the recognition of scientific merit."

"On two occasions I have been asked, — "Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" In one case a member of the Upper, and in the other a member of the Lower, House put this question. I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."

"The whole of arithmetic now appeared within the grasp of mechanism."

"As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise — by what course of calculation can these results be arrived at by the machine in the shortest time?"

"It is difficult to estimate the misery inflicted upon thousands of persons, and the absolute pecuniary penalty imposed upon multitudes of intellectual workers by the loss of their time, destroyed by organ-grinders and other similar nuisances."

"There remains a third source from which we arrive at the knowledge of the existence of a supreme Creator, namely, from an examination of his works. Unlike transmitted testimony, which is weakened at every stage, this evidence derives confirmation from the progress of the individual as well as from the advancement of the knowledge of the race. Almost all thinking men who have studied the laws which govern the animate and the inanimate world around us, agree that the belief in the existence of one Supreme Creator, possessed of infinite wisdom and power, is open to far less difficulties than the supposition of the absence of any cause, or of the existence of a plurality of causes."

"In the works of the Creator ever open to our examination, we possess a firm basis on which to raise the superstructure of an enlightened creed. The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles. These principles themselves converge, with accelerating force, towards some still more comprehensive law to which all matter seems to be submitted. Simple as that law may possibly be, it must be remembered that it is only one amongst an infinite number of simple laws: that each of these laws has consequences at least as extensive as the existing one, and therefore that the Creator who selected the present law must have foreseen the consequences of all other laws. The works of the Creator, ever present to our senses, give a living and perpetual testimony of his power and goodness far surpassing any evidence transmitted through human testimony. The testimony of man becomes fainter at every stage of transmission, whilst each new inquiry into the works of the Almighty gives to us more exalted views of his wisdom, his goodness, and his power."

"In the course of my inquiries, I met with the work upon the Trinity, by Dr. Samuel Clarke. This I carefully examined, and although very far from being satisfied, I ceased from further inquiry. This change arose probably from my having acquired the much more valuable work of the same author, on the Being and Attributes of God. This I studied, and felt that its doctrine was much more intelligible and satisfactory than that of the former work. I may now state, as the result of a long life spent in studying the works of the Creator, that I am satisfied they afford far more satisfactory and more convincing proofs of the existence of a supreme Being than any evidence transmitted through human testimony can possibly supply."

"The true value of the Christian religion rests, not upon speculative views of the Creator, which must necessarily be different in each individual, according to the extent of the knowledge of the finite being, who employs his own feeble powers in contemplating the infinite : but it rests upon those doctrines of kindness and benevolence which that religion claims and enforces, not merely in favour of man himself but of every creature susceptible of pain or of happiness."

"It has always occurred to my mind that many difficulties touching Miracles might be reconciled, if men would only take the trouble to agree upon the nature of the phenomenon which they call Miracle. That writers do not always mean the same thing when treating of miracles is perfectly clear; because what may appear a miracle to the unlearned is to the better instructed only an effect produced by some unknown law hitherto unobserved. So that the idea of miracle is in some respect dependent upon the opinion of man. Much of this confusion has arisen from the definition of Miracle given in Hume's celebrated Essay, namely, that it is the "violation of a law of nature." Now a miracle is not necessarily a violation of any law of nature, and it involves no physical absurdity. As Brown well observes, "the laws of nature surely are not violated when a new antecedent is followed by a new consequent ; they are violated only when the antecedent, being exactly the same, a different consequent is the result;" so that a miracle has nothing in its nature inconsistent with our belief of the uniformity of nature. All that we see in a miracle is an effect which is new to our observation, and whose cause is concealed. The cause may be beyond the sphere of our observation, and would be thus beyond the familiar sphere of nature; but this does not make the event a violation of any law of nature. The limits of man's observation lie within very narrow boundaries, and it would be arrogance to suppose that the reach of man's power is to form the limits of the natural world. The universe offers daily proof of the existence of power of which we know nothing, but whose mighty agency nevertheless manifestly appears in the most familiar works of creation. And shall we deny the existence of this mighty energy simply because it manifests itself in delegated and feeble subordination to God's omnipotence?"