Measure

“ The process of measure, instead of being only the wrong infinite of an endless progression, in the shape of an ever-recurrent recoil from quality to quantity, and from quantity to quality, is also the true infinity of coincidence with self in another. In measure, quality and quantity originally confront each other, like some and other. But quality is implicitly quantity, and conversely quantity is implicitly quality. ”

“ Everything is one thing at one time and in some respects, and another at other times and in other respects. We want a new mode of measurement altogether; at present we take what gaps we can find, set up milestones, and declare them irremovable. We want a measure which shall express, or at any rate recognise, the harmonics of resemblance that lurk even in the most absolute differences and vice versa. ”

“ It is said in the Bible that God has ordered all things according to weight, number and measure. Omnia in pondere et numero et mensura disposuit Deus. Weight is equilibrium, number is quantity, measure is proportion—these three, and these are the eternal or divine basis of the science of Nature. Here now is the formula of equilibrium: Harmony results from the analogy of contraries. Number is the scale of analogies, the proportion of which is measure. The entire occult philosophy of the Zohar might be termed the science of equilibrium. ”

“ Size, on the other hand, and its alteration regarded merely as size, is for the qualitative determination, when it is unable to assert itself in terms of measure, an indifferent determination. That is to say, measure is quantity, precisely in so far as it can give to itself an aspect which qualifies it, and thereby a qualitative determination is united to the purely quantitative one. ”

“ For some bodies we count, some we measure, and some we weigh; [8] those which are by nature continuous we apprehend by measure; to those which are divided we apply number (with the exception of those which on account of their fineness are measured) ; while heavy objects are distinguished by the inclination of the balance. ”

“ 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. ”

“ Mathematics contain properly the doctrine of measure; and the object of this science is commonly said to be quantity; therefore quantity ought to be defined, what may be measured. Those who have defined quantity to be whatever is capable of more or less, have given too wide a notion of it, which, I apprehend, has led some persons to apply mathematical reasoning to subjects that do not admit of it. ”

“ Measure is the qualitative quantum, in the first place as immediate,—a quantum, to which a determinate being or a quality is attached.
Measure, where quality and quantity are in one, is thus the completion of Being. Being, as we first apprehend it, is something utterly abstract and characterless: but it is the very essence of Being to characterise itself, and its complete characterisation is reached in Measure. Measure, like the other stages of Being, may serve as a definition of the Absolute: God, it has been said, is the Measure of all things. ”

“ The perception of being and of distinction, that is, of substantive being and of relative not-being, is the perception of number. The science of the relations of every collection, with its measure, which is unity, is the science of numbers. ”

“ In a word, as we understand by the measure of celestial bodies the relation resulting from the comparison of these bodies with each other, so, by the measure of values, we must understand the relation which results from their comparison. ”

“ To measure directly such a portion of the earth as would furnish an element of measure, which might be found again with certainty in all future times, would be too far beyond the competence of our means to be taken into consideration. ”

“ We may now divide this art of measurement into two parts; placing in the one part all the arts which measure the relative size or number of objects, and in the other all those which depend upon a mean or standard. Many accomplished men say that the art of measurement has to do with all things, but these persons, although in this notion of theirs they may very likely be right, are apt to fail in seeing the differences of classes--they jumble together in one the 'more' and the 'too much,' which are very different things. ”

“ In quantity (a translation of the Greek ‘posotes’—‘how-muchness’—and seemingly formed by Aristotle on the analogy of Plato’s ‘poiotēs’, from which we have quality) we can perhaps see the beginning of that interest in the calculable aspect of the objects of the visible world from which the exact sciences have arisen. The human mind had now begun to weigh and measure, to examine and compare; and that weighing and measuring has gone on—with intervals—for twenty-three centuries. ”

“ It is the amount or quantity at which things settle down in equilibrium and produce the quality or characteristic feature of the object. To say that Measure is the supreme category or the truth of being—of that superficial being which merely is—of the mere fact of perception—is to say that the prime or governing feature of reality, its obviously dominant characteristic in this sphere, is a self-imposing harmony and proportion. ”

“ And since we are assured that the all-wise Creator has observed the most exact proportions of number, weight, and measure in the make of all things, the most likely way, therefore, to get any insight into the nature of those parts of the creation which come within our [Pg 30] observation must in all reason be to number, weigh, and measure. ”

“ No! We are mere prosaic mortals: it is beyond us!
In p. 49 I see some strange remarks about ratios. First look at Def. 44. 'When a magnitude is contained an exact number of times in two magnitudes of its kind, it is said to be their common measure.' (The wording is awkward, and suggests the idea of their having only one 'common measure'; but let that pass.) 'The ratio of two magnitudes of the same kind is the number which would express the measure of the first, if the second were taken as unity.'
'The measure of the first'! Do you understand that? ”

“ If all mathematicians had considered this as carefully as Sir Isaac Newton appears to have done, some labour had been saved both to themselves and to their readers. That great man, whose clear and comprehensive understanding appears even in his definitions, having frequent occasion to treat of such improper quantities, never fails to define them, so as to give a measure of them, either in proper quantities, or in such as had a known measure. ”

“ But how are measures of light to give us fractions of a magnitude? How can the vague, qualitative relation, the brighter the light the higher the magnitude, become an exact and quantitative one? The discussion of this question may be of use by showing that, even with matters of so uncertain a nature, science does not proceed by guesswork. It is a general law, that the human senses measure ratios and not differences. ”

“ You see it fails you at the very moment you want it. When we measure our lances against one another, we can express their comparative length by saying that one measures three and the other four spaces,—a space being merely an imaginary measure ”

“ In fact when what you receive is measured out, it’s pressed down so more can be added, spilling out over the top, falling into your lap! For whatever scale you use to measure what you give will be used to measure what you receive. ”

“ As soon as we adventure on the paths of the physicist, we learn to weigh and to measure, to deal with time and space and mass and their related concepts, and to find more and more our knowledge expressed and our needs satisfied through the concept of number, as in the dreams and visions of Plato and Pythagoras; ”

“ Knowledge being scientific, as it can apply number and measure, an attempt is in order to see if a scientific order of values cannot be built "on a number and measure scale of force," ascent in the scale signifying increase of value, descent diminution of value—all other estimations being prejudices, naïvetés, misunderstandings. ”

“ When we consider, further, that value itself is relative, and that two things are necessary to constitute it, independently of the third thing which is to measure it, we may define a Measure of Value to be something, by comparing with which any two other things, we may infer their value in relation to one another. ”

“ It is not easy to say how many kinds of improper quantity may in time be introduced into mathematics, or to what new subjects measures may be applied; but this, I think, we may conclude, that there is no foundation in nature for, nor can any valuable end be served by, applying measure to anything but what has these two properties. ”

“ In this way, we examine them successively, from the first to the last, not by themselves, nor as composed of parts in juxtaposition, but only in their extent; in other words, we consider the magnitudes by themselves, and in an abstract manner, inasmuch as they measure, the greater a greater extent, and the smaller a smaller extent. ”

“ We must also admit, in taking for our guide, the reasoning which discourses to us things which are invisible to the senses, that the most minute magnitudes, those which are not compound magnitudes, and which from the limit of sensible extent, are the first measure of the other magnitudes which are only called greater or less in their relation to the others. ”

“ What is to be the "unit" (i.e. "standard to measure by") in each subject? (2) Are these units to be of equal, or unequal value? The usual "unit" is the knowledge shown by answering the whole paper correctly ”

“ Number supplies the means of measuring other quantities, by the assumption of a unit of measure of the appropriate kind: but where nature supplies the unit, number is applicable directly and immediately. ”

“ That conception implies a general theory that all human things, riches, honour, and power, as well as joy and pain, have their definite measure, the transgression of which brings ruin and destruction. In the world of objects, too, we have measure. We see, in the first place, existences in Nature, of which measure forms the essential structure. ”

“ Direct and inverse ratios have been applied by an ingenious author to measure human affections, and the moral worth of actions. An eminent Mathematician attempted to ascertain by calculation, the ratio in which the evidence of facts must decrease in the course of time, and fixed the period when the evidence of the facts on which Christianity is founded shall become evanescent, and when in consequence no faith shall be found on the earth.—Reid, Thomas. ”

“ General Remarks In the various names of weights and measures there are many general-utility words which offer no difficulty in the sphere of those who use them habitually, yet which are sometimes puzzling to others, while they are interesting to the student of semantics. They form a chapter in the history of weights and measures, itself a volume in the history of the human mind. ”

“ The mention of worshippers proves that the measuring is symbolical. To ‘measure’ is to separate for sacred purposes; what is excluded from the measurement is, accordingly, more or less mingled with evil. ”

“ If we derive units of measurement in spelling, manifestly the attempt would be to measure the changes which have been brought about in any group in terms of units which are comparable. If group one shows ability ten, having advanced during the year from ability seven, it will be considered just as satisfactory as the advance which has been made in group two, which has moved from ability eight to ability eleven. In other words, the purpose of measurement is never to attempt to make all alike. ”

“ You cannot avail yourself of the argument that a foot may measure the variable height of a man, although the variable height of a man cannot truly measure the foot, because you have agreed that under certain circumstances the man's height is not variable, and it is to those circumstances that I always refer. You say of my measure, and say truly, that if all commodities were produced under the same circumstances of time, etc., as itself, it would be a perfect measure, and you say further that it is now a perfect measure for all commodities produced under such circumstances. ”

“ Although measurement is itself a species of classification, it is distinguished by the adoption of a standard unit of comparison, which, being precise and unvarying, enables us to express the comparisons in precise and unvarying symbols. ”

“ What is life but the angle of vision? A man is measured by the angle at which he looks at objects. What is life but what a man is thinking of all day? This is his fate and his employer. Knowing is the measure of the man. By how much we know, so much we are. ”

“ A yard-stick, pocket-rule, tape-measure and any measure or scales convenient.
Use the measures and scales for measuring the height and weight of the different children, and explain to them that if they continue to grow, they will eventually become full grown men and women. So God measures them to-day in moral things, and if they will learn what God requires and be obedient to their parents, they will increase in moral stature as well. ”

“ For one must aim at attaining a certain measure, and yet this measure admits neither weight nor calculation of any kind, by which it may be accurately determined, unless it be the sensation of the body ”

“ A measure, then, is a divisor which leaves no remainder.
92. When one number is a measure of two others, it is called a common measure of the two. Thus, 15 is a common measure of 180 and 75. Two numbers may have several common measures. For example, 360 and 168 have the common measures 2, 3, 4, 6, 24, and several others. Now, this question maybe asked: Of all the common measures of 360 and 168, which is the greatest? The answer to this question is derived from a rule of arithmetic, called the rule for finding the greatest common measure, which we proceed to consider. ”