Standard solution

“ The solution is definitive, in the sense that it entirely satisfies and convinces all who study it carefully. For over two thousand years the human intellect was baffled by the problem; its many failures and its ultimate success make this problem peculiarly apt for the illustration of method. ”

“ If the problem be solved at all—and I firmly believe it will, though nowhere else has it been—it will be solved by the people most deeply bound in interest, most deeply pledged in honor to its solution. ”

“ With a clear perception of the problem to be solved, a man of science must either think out the particular conjunction of conditions occurring in Nature, which, if found to occur, would give an unequivocal solution, or he must devise such an artificial conjunction of conditions as may lead to the same result. ”

“ When men, whose education has given them the habit of generalizing and everywhere looking for laws, find themselves confronted with a multitude of problems, such as exist in every trade and which have a general similarity one to another, it is inevitable that they should try to gather these problems into certain logical groups, and then search for some general laws or rules to guide them in their solution. ”

“ Not only did organic lengths furnish those approximate measures which satisfied men's needs in ruder ages, but they furnished also the standard measures required in later times. One instance occurs in our own history. ”

“ I am absolutely convinced that, if employed with due method, determinedly, and scientifically, in accordance with a special technique, these resources, after a comparatively simple preparation,—much less in any event than those which have been made in other enterprises,—would lead to very important results which would contribute materially to the final decision. ”

“ To this standard we must conform till the law is changed, and till some other commodity is discovered, by the use of which we shall obtain a more perfect standard, than that which we have established. ”

“ To make it such is in every respect the reverse of scientific. The work immediately in hand, therefore, is to devise such changes in the fundamental law as will tend most effectually to bring about the solution of issues as they may arise, by the most expert, observant and reliable. ”

“ A quick solution was, however, so much of a necessity in our every-day work of running machine-shops, that in spite of the small encouragement received from the mathematicians, we continued at irregular periods, through a term of fifteen years, to give a large amount of time searching for a simple solution. ”

“ A standard remains fixed only until a more perfect standard displaces it. The data from which the standard was derived may be reviewed because of some error, because a further subdivision of the elements studied may prove possible, or because improvements in some factor of the work, i.e., the worker, material, tools, equipment, etc., may make a new standard desirable. ”

“ And where a solution appears possible, the new logic provides a method which enables us to obtain results that do not merely embody personal idiosyncrasies, but must command the assent of all who are competent to form an opinion. ”

“ All, then, are agreed on the pressing nature of this problem, all are bent on its solution, and though it would doubtless be quite Utopian to expect a similar agreement as to the value of any remedy that may be proposed, it is at least of immense importance that, on a subject thus universally regarded as of supreme importance, we have such a consensus of opinion at the outset. This will be the more remarkable and the more hopeful sign when it is shown, as I believe will be conclusively shown in this work, that the answer to this, one of the most pressing questions of the day, makes of comparatively easy solution many other problems which have hitherto taxed the ingenuity of the greatest thinkers and reformers of our time. ”

“ There are others, however, as to which, even if a final solution is not possible at present, yet much can be done to show the direction in which a solution is to be sought, and the kind of solution that may in time prove possible. ”

“ And whenever a workman proposes an improvement, it should be the policy of the management to make a careful analysis of the new method, and if necessary conduct a series of experiments to determine accurately the relative merit of the new suggestion and of the old standard. And whenever the new method is found to be markedly superior to the old, it should be adopted as the standard for the whole establishment. The workman should be given the full credit for the improvement, and should be paid a cash premium as a reward for his ingenuity. ”

“ This is a vast problem, in the solution of which the whole world is vitally interested, and one which, sooner or later, must be solved. If its solution were possible now, coming generations would look back and bless us for the solving. ”

“ With a formally correct method results may be obtained which are meaningless and unimportant, or mere mental tricks may be performed. To set up an arbitrary standard of comparison, to compare, and deduce, and to end by establishing a series of divergencies from this standard ”

“ And hence it is that the Method of Agreement, though applicable in principle to either case, is more emphatically the method of investigation on those subjects where artificial experimentation is impossible; because on those it is, generally, our only resource of a directly inductive nature; while, in the phenomena which we can produce at pleasure, the Method of Difference generally affords a more efficacious process, which will ascertain causes as well as mere laws. ”

“ No one undertaking the study of this problem is likely to underrate the difficulty of the task. To find a solution is obviously a matter of great importance; but it is also a matter in which small success may reasonably be expected. ”

“ The philosophy of the management of initiative and incentive makes it necessary for each workman to bear almost the entire responsibility for the general plan as well as for each detail of his work, and in many cases for his implements as well. In addition to this he must do all of the actual physical labor. The development of a science, on the other hand, involves the establishment of many rules, laws, and formulae which replace the judgment of the individual workman and which can be effectively used only after having been systematically recorded, indexed, etc. ”

“ It thus appears by the combined evidence of the Method of Agreement, the Method of Concomitant Variations, and the most rigorous form of the Method of Difference, that neither of the two kinds of electricity can be excited without an equal excitement of the other and opposite kind: that both are effects of the same cause; that the possibility of the one is a condition of the possibility of the other, and the quantity of the one an impassable limit to the quantity of the other. ”

“ It is 150 very desirable that, if possible, some permanent standard, founded in nature, should be adopted; for the conventional measures are lost in the course of ages; and thus, dimensions expressed by means of them become unintelligible. ”

“ My solution must be simply accepted as affording a guidance by which different people may, along more 39 or less converging lines, approach their particular objectives. For the problem presents itself under ever-changing forms, and demands a continuous development, and almost a progressive interpretation of the concept which I am going to offer as an aid to its solution. ”

“ But to the yoke of necessity every one willingly bows the head. Still, wherever an actually complicated aspect of things presents itself, it is more difficult to discover exactly what is necessary; but by the very acknowledgment of the principle, the problem invariably becomes simpler and the solution easier. ”

“ And yet laws of this kind, which apply to a large majority of men, unquestionably exist, and when clearly defined are of great value as a guide in dealing with men. In developing these laws, accurate, carefully planned and executed experiments, extending through a term of years, have been made, similar in a general way to the experiments upon various other elements which have been referred to in this paper. Perhaps the most important law belonging to this class, in its relation to scientific management, is the effect which the task idea has upon the efficiency of the workman. ”

“ A scheme that distributes marks on anything but a rational and intelligent system; a scheme that excludes the Natural History Sciences, mineralogy and Geology, as well as Psychology and Moral Philosophy from its scope altogether; a scheme that prescribes only Elements and Outlines of such important subjects as Natural Science (Chemistry, Electricity and Magnetism, &c.) and Political Economy—stands self-condemned. ”

“ Considering this remissness in the operator, and shoeing too short at the heels, to constitute the prevalent and principal errors requiring rectification, it is anxiously to be hoped, that those whose minds are open to conviction, will contribute their assistance to inculcate the necessity of adopting one invariable standard as a leading step to general reformation. ”

“ since, looking at the matter more closely, we will always find that the problem itself arises only when the material conditions necessary for its solution already exist or are at least in the process of formation. ”

“ In induction the problem is concerned with a general. In some situation a concept, law, or principle has proven inadequate as a response. The question is then raised as to what is wrong with it and the inductive process is instigated. The problem is solved when the principle or concept is perfected or enlarged--in other words, is made adequate. In deduction the problem is concerned with the individual situation. Some problem is raised by a particular fact or experience and is answered when it is placed under the law or concept to which it belongs. ”

“ All methods should, therefore, as far as possible, be made up of standard elements under standard conditions, with standard devices and appliances, and they should be standardized from the standpoint of all of our senses as to color, shape, size, weight, location, position and surface texture, that the worker may grasp at a single thought by means of each or all his senses, that no special muscles or other fatiguing processes need be operated to achieve the standard result desired. ”

“ Any plan of world reform which leaves out the Human Equation is equivalent to an engineering plan which leaves out of consideration details like the Law of the Dead Centre or the Law of Expansion and contraction of metals. ”

“ The fixing of standards of life and health is just as easy as the fixing of valuations for rates of the price of gas or any other utility, and it is much better for the manufacturer and the public at large that there be some scientific or expert service in the standardization. ”

“ It is unpractical, and it goes against human nature. This is why it is worth carrying out, and that is why one proposes it. For what is a practical scheme? A practical scheme is either a scheme that is already in existence, or a scheme that could be carried out under existing conditions. ”

“ That the solution, if it could be supplied, would involve anything arbitrary, miraculous, or at variance with the observed order of things, need not be assumed; but it might open a new view of the universe, and dissipate for ever the merely mechanical accounts of it. In the meantime we may fairly enter a caveat against the tacit insinuation of an unproved solution. Science can apparently give no reason for assuming that the first cause, and that which gives the law to development, is a blind force rather than an archetypal idea. ”

“ But it certainly does not seem to be a measure insuperably difficult, to preserve whatever is really good in the present system, and even to remedy some of its defects, without departing from the path of experience, and resorting to improvements of theory and experiment. ”

“ It remains to discuss briefly what general requirements may be justly laid down for the solution of a mathematical problem. I should [Pg 5] say first of all, this: that it shall be possible to establish the correctness of the solution by means of a finite number of steps based upon a finite number of hypotheses which are implied in the statement of the problem and which must always be exactly formulated. This requirement of logical deduction by means of a finite number of processes is simply the requirement of rigor in reasoning. ”

“ We have a given problem to solve. If we undertake the solution,{9} there is, of course, always danger that we may not solve it aright; but to refuse to undertake the solution simply renders it certain that we can not possibly solve it aright. ”

“ It must be recognized that the principle of diminishing utility applies to each method of distribution as it does to the productive processes. Each may be best under certain conditions and circumstances, but, extended in application, each reveals its weaknesses. In any productive process the best method depends upon the proper proportion and combination of elements. Progress toward the best possible distribution is to be sought in the wise adjustment of the various methods to human nature and to human needs. ”

“ As nothing can exist if it do not combine all the conditions which render its existence possible, the different parts of each being must be co-ordinated in such a manner as to render the total being possible, not only in itself, but in its relations to those which surround it; and the analysis of these conditions often leads to general laws, as clearly demonstrated as those which result from calculation or from experience. ”