Minimum

“ We answer that it is an image in which not one single minimum is in itself reversed, but in which all the minima are transposed merely in relation to one another. The inversion regards merely the relative position of the minima, and not the minima themselves. Thus, the upward part of each minimum in the object must also point upwards in the image on the retina. ”

“ The minimum is, in truth, not a physical but a moral minimum, and as such, is capable of being altered with the changes in the moral character of those whom it affects. In a word, each class has a certain standard of comfort below which it will not consent to live, or at least to multiply,—a standard, however, not fixed, but liable to modification with the changing circumstances of society, and which, in the case of a progressive community, is, in point of fact, constantly rising, as moral and intellectual influences are brought more and more effectually to bear on the masses of the people. ”

“ The Minimum Basis.—Enumerate the entire number of heads of families in the town, village, ward, or neighborhood where you purpose to begin business. Figure out the number of such persons you will require as a minimum basis in order to get on—that is, how many persons or families, spending each on an average a certain amount per day or week at your place of business, you will require in order to make a living. Do not go blindly into your work, trusting to luck. Luck is always on the side of pluck and tact. ”

“ The level of wages depends on a fundamental standard that corresponds to the minimum of resources necessary for a man to live. But this standard is determined, in every era, by opinion. What yesterday was considered to be a sufficient minimum no longer satisfies the requirements of moral conscience today. ”

“ The minimum just mentioned is what the peasant must obtain in exchange for the whole of his surplus produce. But inasmuch as this surplus is not a fixed quantity, but may be either greater or less according to the degree of his industry, a minimum value for the whole of it does not give any minimum value for a definite quantity of the commodity. ”

“ A critical value usually gives a maximum or minimum in the case of a function of one variable, and often in the case of several independent variables, but all maxima and minima, particularly absolutely greatest and least values, are not necessarily critical values. ”

“ In every case we find that the maximum which opens the week is rapidly succeeded by a minimum, which is itself succeeded by a secondary maximum,—usually very secondary, although in 1894 it nearly equals the primary maximum,—followed again by a second minimum—usually nearly identical with the first minimum,—after which there is a rapid rise to the original maximum. ”

“ Give me the statistics of pyrotechnic powder burnt by a people, and I shall tell you the standard measure of their souls and bodies. If the figure be a maximum, then the physical and moral measure will be the minimum, for the ratio is inverse. ”

“ I ask your attention first to a policy that is relevant to many forms of minimum standard, and the beneficial influence of which is open to no dispute. The failure of poor persons to attain the level we deem to be satisfactory in the matter of nourishment, of education and of insurance, is frequently the result, not so much of poverty as of ignorance and mismanagement. ”

“ As a rule it is with our being reduced to a minimum that we live, most of our faculties lie dormant because they can rely upon Habit, which knows what there is to be done and has no need of their services. ”

“ An increase or decrease in nominal wages may mean much or it may mean very little.
The minimum wage level. There is a limit below which real wages cannot fall. This is the point at which the worker can manage to maintain himself and his family. ”

“ It is to the interest of all the rest of us to hold down his powers to an irreducible minimum, and to reduce his compensation to nothing; it is to his interest to augment his powers at all hazards, and to make his compensation all the traffic will bear. ”

“ The maximum limit cannot be fixed, and there is no need of attempting it. But there is great need of knowing and keeping in mind the minimum limit; for in the pressure to hurry forward there is grave danger that even this limit will not be reached. ”

“ As the comparison of numbers with one another, their determination as greater or less, is only possible on the assumption of a unit, a common measure to which each may be referred, so the comparison of bodies with one another, as to quantity and quality alike, demands a corporeal minimum, to which their differences must be reduced. This relation to knowledge carries with it the relativity of the minimum according to the subject-matter with which the knower is for the time being concerned. ”

“ And it is also evident that this minimum of comfort cannot be based on the money a man receives as wages, but on what he needs. What constitutes need is open to argument, but there are certain items of necessity which are beyond dispute. ”

“ Hence we are not surprised that statistics proved the tendency of wages to be toward a minimum under both parties—that is, a sum barely sufficient to provide food, clothing and shelter, and to enable the workman to raise other toilers to take his place when he was no longer able to work. ”

“ Every youth who is physically and mentally sound, and who earns more than a minimum wage, must begin to put by a fixed proportion of that wage as soon as he completes his sixteenth year. His employer is also compelled to contribute the same amount for him. ”

“ A minimum rate is fixed by the condition that they must be at least sufficient to enable a man and his wife to maintain themselves and, in general, bring up a family. The excess above this will depend on the circumstances o\ the country, and the consequent demand for labour—wages being high when national wealth is increasing, low when it is declining. ”

“ Now, the quantities being all positive, the product cannot be increased without limit and must somewhere attain a maximum, and no other form of the product than that in which they are all equal can be the maximum, so that the product is a maximum when they are all equal. Its minimum value is obviously zero. If the restriction that all the quantities shall be positive is removed, the product can be made equal to any quantity, positive or negative. ”

“ For the case of a single variable x, corresponding to a value of x given by the equation du/dx = 0, u is a maximum or minimum as d 2u/dx2 is negative or positive. If d 2u/dx2 vanishes, then there is no maximum or minimum unless d 2u/dx2 vanishes, and there is a maximum or minimum according as d 4u/dx4 is negative or positive. Generally, if the first differential coefficient which does not vanish is even, there is a maximum or minimum according as this is negative or positive. If it is odd, there is no maximum or minimum. ”

“ "A well-used minimum suffices for everything." ”

“ In fact the ratio must be governed by circumstances. It is true, however, that the conditions must be interpreted by a fixed principle in living and not by any mere fashion or prejudice of the moment. ”

“ Who is to be the judge of this sort of necessity? By what measure is the comparative value of lives to be measured? Is it to be strength, or intellect, or what? It is plain that the principle leaves to him who is to profit by it to determine the necessity which will justify him in deliberately taking another's life to save his own. ”

“ You have no standard to estimate by, no measure to make comparisons with. Given a certain small quantity of higher pleasure in collision with a certain large quantity of lower, how can you decide between them? To work the sum you must reduce the data to the same denomination. You must go to quantity or nothing; you decline to go to quantity, and hence you can not get any result. But if you refuse to work the sum, you abandon the greatest amount of pleasure principle. ”

“ Whoever will limit his gaze to a few persons, and try to solve the problems of their lives—planning, for instance, definitely, how he, even with superior advantages of education, self-control, and knowledge, could bring up a given family on given wages, allowing the smallest amount conceivably sufficient for food, rent, clothes, fuel, and the rest—he may find it in most cases a much more difficult thing than he had ever thought, and sometimes may be an impossibility. ”

“ And I for my part cannot but consider the talk of the contemporary sociological school about averages and general laws and predetermined tendencies, with its obligatory undervaluing of the importance of individual differences, as the most pernicious and immoral of fatalisms. Suppose there is a social equilibrium fated to be, whose is it to be,—that of your preference, or mine? There lies the question of questions, and it is one which no study of averages can decide. ”

“ And from hence it may be understood, that the proportions of excess and defect are quantity, being capable of more and less; but the proportion of equality is not quantity, because not capable neither of more, nor of less. ”

“ In a general way and within possibly narrow limits, very different and variable according as the case may be, given the existence in actual society of fortunes and desires of all degrees of importance, one can, in principle, admit that theoretically, the value v of a thing or of a certain quantity of goods, is proportional to the average d of the desire to possess it, which the men demanding it have, either on account of its use, or from any other reason, multiplied by the number h of these men and divided by the number o offered of this thing ”

“ The differing values of men in a social population are determined, as other values are measured, by the working of the law of diminishing returns.
Roughly stated, this law is that successive additions of any valued thing bring ever diminished returns. The first quantity of anything is of infinite value. ”

“ We seek other conditions, by reason we do not understand the use of our own; and go out of ourselves, because we know not how there to reside."
But nevertheless it becomes a necessity for us to understand the wishes of those who demand a change of condition, and it is necessary that they should understand the compensations as well as the limitations of every condition. ”

“ The most significant thing about an estimate is that the estimator is thinking of providing for his group of deficients in a special way. This is the purpose of the estimates. Three important groups of the mentally deficient now demand attention. They are: (1) The group which, for moral and eugenic reasons, society is justified in isolating for life or an indefinite period. (2) The group which needs special simple industrial training in order to get along with social assistance without isolation. ”

“ The standard of living facts and the wage facts are indisputable; low standard conditions are appallingly frequent in some districts. What will the end be?
The members of those families which are forced to live on inefficiency standards are subject to a decrease in (1) physical efficiency, (2) intellectual keenness, (3) disease-resisting power, (4) length of life. No employer who desires to maintain the efficiency of his working force, and what employer does not desire to do so, can afford to tolerate for a moment any one of these four conditions. ”

“ As to equality or any exact proportion, we can only guess at it from a single consideration; except in very short numbers, or very limited portions of extension; which are comprehended in an instant, and where we perceive an impossibility of falling into any considerable error. In all other cases we must settle the proportions with some liberty, or proceed in a more artificial manner. ”

“ By this illustration, then, we obtain a rule to determine what one ought to take from him who has the greater, and what to add to him who has the less. The excess of the mean over the less must be added to the less, and the excess of the greater over the mean be taken from the greater. ”

“ May we, or may we not, without incurring an accusation of injustice to a dependent population, honestly ask ourselves if actual conditions should not sometimes limit or control the application of an abstract principle? ”

“ If we apply this law to society, if we assume the existence of reasonable beings around us, then the demand that all the faculties of the individual should be uniformly cultivated includes also the demand that all reasonable beings should be cultivated uniformly with each other. ”

“ The necessity of such a measure must have been apparent to all, and it had long before engaged their attention in a different form. Men, of their wisdom and forecast, meditating a measure so necessary to their common safety, would not have left it as a mere matter of inference from another measure. ”

“ But other moralists believe that today the amount cannot be fixed mathematically, and that only the general direction can be given that one should be generous according to one’s means, and regulate one’s yearly alms according to the prevalence of poverty.
1254. Is it better to give a little to many, or much to one person in need? (a) If the one person is in great need, and others are only in slight need, it is better to give to the one in great need. ”

“ And if the number of appliers so entitled should be so large as that the sum will not suffice to afford to each as much as might otherwise not be improper, the proportion to each shall be diminished, so as to afford every one some assistance. ”

“ Of natural powers, some are unlimited, others limited in quantity. By an unlimited quantity is of course not meant literally, but practically unlimited: a quantity beyond the use which can in any, or at least in present circumstances, be made of it. ”

“ Whether minima or meer minima may not be compar'd by their sooner or later evanescence, as well as by more or less points, so that one sensible may be greater than another, though it exceeds it not by one point? ”

“ The consequence is, that for all but a few of us the limit of attainment in life in the best case is to live out our term, to pay our debts, to place three or four children in a position to support themselves in a position as good as the father's was, and there to make the account balance. ”