Unit

“ 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 ”

“ In all scientific calculations there is assumed an unit to start from, though in each branch of science it is a different unit; e.g. in barology, the pound-weight; in harmonics, the quarter-tone; in other branches of science, other units.68 Analytical research teaches us that the corresponding unit in Syllogism is the affirmative or negative proposition which is primary, immediate, indivisible. In Demonstration and Science it is the Noûs or Intellect.69 ”

“ Unit, ū′nit, n. one: a single thing or person: the least whole number: anything taken as one: any known determinate quantity by constant application of which any other quantity is measured.—adj. U′nital.—n. Unitā′rian, one who asserts the unity of the Godhead as opposed to the Trinity, and ascribes divinity to God the Father only.—adj. ”

“ For the unit is the originator of every number, since all multitude is made up by the composition and addition of units; nor is it possible without the unit to conceive the existence of number at all. But the unit itself is independent of multitude, apart from and superior to all number; forming, indeed, and making all, but receiving no increase from any.
13. Kindred to this is the triad; equally indivisible and perfect, the first of those sums which are formed of even and uneven numbers. ”

“ Units, one of which is not the other, constitute multitude or plurality. If unity is the negation of actual division in being, multitude results from a second negation, that, namely, by which the undivided being or unit is marked off or divided from other units.139 We have defined unity by the negation of actual intrinsic dividedness ”

“ As soon as distinct notions have been acquired of the manner in which a collection of ten units becomes a new unit of a higher order, our pupil may be led to observe the utility of this invention by various examples, before he applies it to the rules of arithmetic. ”

“ 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. ”

“ Every unit has a given value.
The value of a unit depends on its attraction; of its character, of its size, of its placement.
A unit near the edge has more attraction than at the center.
Every part of the picture space has some attraction. ”

“ Groups of four dots are grasped as units, familiar words are grasped as units. Notice that these units are our own units, not external units. Physically, a row of six dots is as much a unit as a row of four, but we grasp the four as a unit in a way that we cannot apply to the six. ”

“ An element is a unit, and every empirical unit necessarily conceals in its bosom a plexus of which it is the unification. The very idea of94 unit requires for its complement a manifold of some kind. In hypothetical units, or ideal constructs that have for their purpose to lead to the discovery and arrangement of real phenomena, science abounds. ”

“ You are an integral factor, so to speak, of the social problem, but your value is determined by your relation to other quantifies in the complex system with which you are identified. As a segregated unit, you diminish in value. ”

“ 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. ”

“ Is the unity which is found among sense-beings a quantity? Or is unity a quantity when repeated, while, when considered alone and in itself, it is the principle of quantity, but not a quantity itself? Besides, if unity be the principle of quantity, does it share the nature of quantity, or has it a different nature? Here are a number of points we ought to expound. ”

“ In these and the like, instances it is evident the unit constantly relates to the particular draughts the mind makes of its ideas, to which it affixes names, and wherein it includes more or less as best suits its own ends and purposes. Whatever, therefore, the mind considers as one, that is an unit. Every combination of ideas is considered as one thing by the mind, and in token thereof is marked by one name. ”

“ We compare one discrete quantity with another, or one continual quantity with another, and we thus ascertain many important truths: but we select our unit, or our standard of motion and extension, as we please, or according to convenience, subject only to the necessity of adapting our ulterior calculations consistently to this unit, when once selected. ”

“ The use of a special word to indicate absence of a unit is not hypothesis, but is found in verses in the ancient Indian book on astronomy, the Sourya-Siddhanta, and in numerous other ancient Hindu writings. ”

“ The unity which philosophers rightly feel to be necessary for the assertion of a number is the unity of the general term, and it is the general term which is the proper subject of number. And this applies equally when there is one object or none which falls under the general term. ”

“ Units proper doubtless do not exist apart from the experience of quantity, and I do not mean to say that apart from quantity no distinction is possible, or again that quantity could be developed rationally from anything more simple than itself. And I have emphasized the words ‘as a matter of fact’ in order to leave these questions on one side, since they can be neglected provisionally. Numerical sameness, in the same way, is the persistence of any such bare distinction through diverse contexts, no matter what these contexts are. ”

“ The measure is always homogeneous with the thing measured; the measure of spatial magnitudes is a spatial magnitude, and in particular that of length is a length, that of breadth a breadth, that of articulate sound an articulate sound, that of weight a weight, that of units a unit. (For we must state the matter so, and not say that the measure of numbers is a number; we ought indeed to say this if we were to use the corresponding form of words, but the claim does not really correspond-it is as if one claimed that the measure of units is units and not a unit; number is a plurality of units.) ”

“ It is, indeed, true, that by a modern process of abstraction, we occasionally apply numbers to unequal units, as the furniture at a sale or the various animals on a farm, simply as so many separate entities ”

“ The principal multiplied by its time and divided by the interest, and the quotient being multiplied by the factor less one is the time. The sum of principal and interest divided by unity added to the interest on unity is the principal. ”

“ Such an aggregate it conceives as a new unit, a new number of higher order, and subjecting it to criteria of new and hitherto quite unsuspected kinds such as “potency,” “order,” “equivalence,” “countableness,” and devising laws and operative methods for it in respect of these criteria. Thus is being actualized a last 427extension of the function-theory. ”

“ In every quantity there are the two elements: the 'one,' unity or solidarity, which renders a total number possible, and the 'many' or multiplicity, which gives it real body and character. By this quantitative law, reality must always be both Continuous and Discrete. ”

“ A plurality is therefore a relation of units considered as a sum. Unity is constant only in ultimate particles. Bodies are combined, dissolved again and recombined, making variable units of plurality. ”

“ Now one and eight make nine beyond all possibility of doubt, and the formula—"man's body is a unity—or one"—composed of harmonies of eight, would give the formula nine meaning man's supremacy is expressed in his body. ”

“ The collection of the parts, the parts themselves united. The idea of the parts then enters into the idea of the whole. What is the meaning of greater? One thing is said to be greater than another, when, besides containing an equal quantity, it also contains something else. ”

“ Unity as an absolute has plurality for its relative; extension as an absolute has position for its relative; speed as an absolute has path as its relative; persistence as an absolute has change for its relative, and consciousness as an absolute has choice for its relative. ”

“ Proportion can be considered from our two points of view of unity and variety. In so far as 229the proportions of any picture or object resolve themselves into a simple, easily grasped unity of relationship, a sense of repose and sublimity is produced. In so far as the variety of proportion in the different parts is assertive and prevents the eye grasping the arrangement as a simple whole, a sense of the lively restlessness of life and activity is produced. In other words, as we found in line arrangements, unity makes for sublimity, while variety makes for the expression of life. ”

“ Conformity to rule and symmetry, which are the abstract unity and definition of all that is essentially spatial and its configuration no less than of all which is external under temporal condition, are mainly the co-ordinating principles of quantity and size, as we have already noticed in our consideration of the beauty of Nature. ”

“ All these relations are numerically expressed and are determinations of number, and so in another way are the equal and the like and the same, for all refer to unity. Those things are the same whose substance is one; those are like whose quality is one; those are equal whose quantity is one; and 1 is the beginning and measure of number, so that all these relations imply number, though not in the same way.
(2) The active and the passive imply an active and a passive potency and the actualization of the potencies, e.g. ”

“ The system of derived units which we have been briefly considering, is that which gives the most simple and natural relations between quantitative expressions of different kinds, and therefore conduces to ease of comprehension and saving of laborious calculation. ”

“ The units used for different purposes are entirely distinct [23] from the base of any system, and though always referable to such base, are not practically so referred. It therefore seems useless to burden the people with long scientific names in the ordinary transactions of daily life. ”

“ With its aid objects permit themselves to be described as multiples of one another, and as occupying positions in relation to one another. When all objects are described strictly in terms of one another, they are expressed in terms of arbitrary units, and located in terms of arbitrary spacial or temporal axes of reference. ”

“ for I cannot satisfy myself that, when one is added to one, the one to which the addition is made becomes two, or that the two units added together make two by reason of the addition. I cannot understand how, when separated from the other, each of them was one and not two, and now, when they are brought together, the mere juxtaposition or meeting of them should be the cause of their becoming two: neither can I understand how the division of one is the way to make two; ”

“ The formulae at which we arrive must be such that a person of any nation, by substituting for the different symbols the numerical value of the quantities as measured by his own national units, would arrive at a true result. ”

“ The end and aim of all science is to find the unity, the One out of which the manifold is being manufactured, that One existing as many. ”

“ Only by taking infinitesimally small units for observation (the differential of history, that is, the individual tendencies of men) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history. ”

“ Simplicity of structure means organic unity, whether the organism be simple or complex; and hence in all times the emphasis which critics have laid upon Simplicity, though they have not unfrequently confounded it with narrowness of range. ”

“ ‘The unities, sir,’ he said, ‘are a completeness—a kind of universal dovetailedness with regard to place and time—a sort of a general oneness, if I may be allowed to use so strong an expression. ”

“ Furthermore, quantitative distinctions in the material world, i.e. distinctions of position, shape, and the like, are all of them primarily known to us in universal form, — not as individual but as specific characters of the object that we have before us. Quantity is no more and no less individuated for our reason than is any other object of thought. This place, this shape, this size, and this definite matter, are just as hard to define in an individual way as this angelic nature, or this immaterial soul. ”

“ 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. ”

“ PORTION. Synonyms:
When any whole is divided into parts, any part that is allotted to some person, thing, subject or purpose is called a portion, tho the division may be by no fixed rule or relation; a father may divide his estate by will among his children so as to make their several portions great or small, according to his arbitrary and unreasonable caprice. When we speak of a part as a proportion, we think of the whole as divided according to some rule or scale, so that the different parts bear a contemplated and intended relation or ratio to one another ”

“ Thus, in seeking our definition of number we have arrived so far at the result that numbers are properties of general terms or general descriptions, not of physical things or of mental occurrences.
Instead of speaking of a general term, such as “man,” as the subject of which a number can be asserted, we may, without making any serious change, take the subject as the class or collection of objects—i.e. “mankind” in the above instance—to which the general term in question is applicable. ”