Book of Numbers

“ For, the several simple modes of numbers being in our minds but so many combinations of units, which have no variety, nor are capable of any other difference but more or less, names or marks for each distinct combination seem more necessary than in any other sort of ideas. For, without such names or marks, we can hardly well make use of numbers in reckoning, especially where the combination is made up of any great multitude of units ”

“ The attentive student will not fail to notice the wide use of numbers throughout, and the effect of addition, subtraction, multiplication, and division, upon the symbolism of the simpler numbers. The author believes that a cautious use can often be made of numbers in the interpretation not only of the Revelation where their use is so manifest, but of many other parts of Scripture, if not too much stress be laid on the symbolic meaning, for the Hebrew mind delighted itself in symbols. ”

“ Again, let none be alarmed at vast numbers and fractions, for in calculation it is as easy to set down or to reflect upon a thou­sand as a unit, or the thousandth part of an integer as an integer itself. ”

“ The seventh, eighth, and ninth books are arithmetical, that is, treat of the properties of numbers. The definitions relating to them occur at the beginning of the seventh book, and some of these show perhaps the tendency of the Greeks, natural enough to a scientific people with a defective numerical notation, to consider quantity from a geometrical point of view. ”

“ Hence (says he, Ennead vi. lib. vi.) number is either the essence or the energy of being, and animal itself, and intellect is number. But, perhaps, we must call being, number united (ἀριθμὸς ηνωμένος) , but beings, number evolved, or unfolded; (ἐξεληλεγμένος ἀριθμὸς) intellect, number moving in itself; (ἀριθμὸς ἐν ἐαυτῶ κινούμενος) [xix] and lastly, animal, number comprehending (ἀριθμὸς περιέχων.“) It was in consequence of this reasoning, that the Pythagoreans called ideas numbers; because the gradual evolution of these from ineffable unity, produced all the beautiful variety of forms. ”

“ But of the arithmetical [2] art, which by composition contains philosophy, number became a first principle, which is an indefinable and incomprehensible (entity) , comprising in itself all the numbers that can go on ad infinitum by aggregation. But the first monad became a principle, according to substance, of the numbers, which (principle) is a male [3] monad, pro-creating paternally all the rest of the numbers. ”

“ But as the Pythagoreans define a point to be unity having position, let us consider what they mean. That numbers, indeed, are more immaterial and more pure than magnitudes, and that the principle of numbers is more simple than the principle of magnitudes, is manifest to every one: but when they say that a [122] point is unity endued with position, they appear to me to evince that unity and number subsist in opinion: I mean monadic number [131] . On which account, every number, as the pentad and the heptad, is one in every soul, and not many; ”

“ In so small a volume, however, it would be folly to attempt so pretentious a task, especially in view of the fact that, for all present purposes, it Is sufficient that we should realize that the Science of Numbers has been known and credited since very early in the world’s history, and that, having been cherished with most tender solicitude through the turmoil and storms of the centuries, it has come to us with the signs of truth and authenticity indelibly fixed by the stamp of years. ”

“ The merit of our actual system of numeration consists in including the expression of all numbers in a single idea, making the value of each figure ten times that to the right, and filling all intervals with zeros. ”

“ The fundamental truths of the science of Number all rest on the evidence of sense; they are proved by showing to our eyes and our fingers that any given number of objects, ten balls for example, may by separation and re-arrangement exhibit to our sense all the different sets of numbers the sum of which is equal to ten. All the improved methods of teaching arithmetic to children proceed on a knowledge of this fact. ”

“ You believe in Number as the foundation on which rests the edifice of what you call the exact sciences. Without number mathematics are impossible. Well, then, what impossible being, to whom life everlasting should be granted, could ever [Pg 99] finish counting—and in what sufficiently concise language could he utter—the numbers contained in the infinite number of which the existence is demonstrated by your reason. Ask the greatest human genius, and suppose him to sit for a thousand years leaning on a table, his head in his hands, what would he answer? ”

“ In the third place, the real desideratum about such a definition as that of number is not that it should represent as nearly as possible the ideas of those who have not gone through the analysis required in order to reach a definition, but that it should give us objects having the requisite properties. Numbers, in fact, must satisfy the formulae of arithmetic ”

“ Thus we speak of counting up to a certain number; and similarly mathematicians speak of high and ascending powers, while engineers speak of high pressure, high speed, high power, &c. This tendency is probably aided by the use of bricks or cubes in elementary number-teaching.
24. Primitive Ideas of Number.—The names of numbers give an idea of the way in which the idea of number has developed. Where civilization is at all advanced, there are usually certain names, the origin of which cannot be traced ”

“ The Science of Numbers teaches that each letter, or number, possesses certain distinct characteristics, and that, in accordance with the manner of the occurance of these forces in the name and birth of the individual, such qualities manifest themselves for good or for evil. ”

“ It is not easy to find a definition for the Science of Numbers that shall be both brief and comprehensive. We may say, however, that it is a method of enumeration by means of which the life of men and things may be fixed and rounded out to a state of approximate completion by being brought into harmony with the laws of Omnipotence. ”

“ Few tests of relative stages of civilisation are more trustworthy than that of the definite conception of high numbers. The prevalence of a decimal system of numerals among widely severed nations, alike in ancient and modern times, has been universally ascribed to the simple process of counting with the aid of the fingers. ”

“ To a great extent proficiency in applying the the principles of the Science of Numbers is a question of practice, for, while the rules are exact, the phenomena of their manifestation varies so materially in each individual case that it would require a volume of huge proportions to describe all the operations of each rule, to say nothing of the many exceptions that affect this play of lights and shadows. ”

“ But the grand agent for transforming experimental into deductive sciences, is the science of number. The properties of numbers, alone among all known phenomena, are, in the most rigorous sense, properties of all things whatever. All things are not coloured, or ponderable, or even extended; but all things are numerable. And if we consider this science in its whole extent, from common arithmetic up to the calculus of variations, the truths already ascertained seem all but infinite, and admit of indefinite extension. ”

“ Number is everything, and is the essence of things, but the triad includes all number, since it contains the beginning, middle, and end. Everything is derived from the primitive one and from the principal number; and since this number in breathing its vital evolution into the void is divided into many units, everything is derived from the multiplicity of these units or numbers. ”

“ In the Science of Numbers, the same rule must be applied; for it is not until a student has attained full comprehension of the introductory laws that govern names and numbers that he can hope to understand the more intricate vibrations that exert their influence upon the course of human events. ”

“ The NAME NUMBER, as will be shown later, exerts a most powerful influence in shaping the life of every individual, but the character of the influence exerted, or the nature of the vibrations, depends largely upon the degree of harmony which may exist between the NAME NUMBER and the BIRTH NUMBER, the latter being the day of the individual’s birth.
To ascertain to what degree these two numbers are harmonious or inharmonious, the nine lines of letters and numbers shown in the First Table have been divided into three distinct classes, designated. for the sake of convenience, the “Triads.” ”

“ 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. ”

“ To detect the relations of Number considered directly as Number, is not easy: and we might 205 contemplate for a long time a Table of recorded Numbers without perceiving the order of their increase and diminution, even if the law were moderately simple; as any one may satisfy himself by looking at a Tide Table. ”

“ Is it a breath emanating from God to organize the material universe where nothing obtains form except by the Divinity which is an effect of Number? The least as well as the greatest of creations are distinguishable from each other by quantities, qualities, dimensions, forces,—all attributes created by Number. The infinitude of Numbers is a fact proved to your soul, but of which no material proof can be given. The mathematician himself tells you that the infinite of numbers exists, but cannot be proved. ”

“ In 1624 appeared in London a curious work on the subject of numbers, bearing the following title: The Secrets of Numbers, according to Theological, Arithmetical, Geometrical, and Harmonical Computation; drawn, for the better part, out of those Ancients, as well as Neoteriques. Pleasing to read, profitable to understand, opening themselves to the capacities of both learned and unlearned; being no other than a key to lead men to any doctrinal knowledge whatsoever. In the ninth chapter the author has given many notable opinions from learned men, to prove the excellency of the number seven. ”

“ Therefore, in future, on this part of the subject I shall cease to talk of any particular units, such as pebbles or acres, and speak of numbers only. A number, considered without intending to allude to any particular things, is called an abstract number: and it then merely signifies repetitions of a unit, or the number of times a unit is repeated. ”

“ Before we proceed to the number ten, or to the new series of numeration which succeeds to it, we should make our pupils perfectly masters of the combinations which we have mentioned, both in the direct order in which they are arranged, and in various modes of succession; by these means, not only the addition, but the subtraction, of numbers as far as nine, will be perfectly familiar to them. ”

“ That the first numbers of a numeral scale are usually derived from other sources, we have some reason to believe; but that all above 2, 3, or at most 4, are almost universally of digital origin we must admit. Exception should properly be made of higher units, say 1000 or anything greater, which could not be expected to conform to any law of derivation governing the first few units of a system. ”

“ When infinite numbers are first introduced to people, they are apt to refuse the name of numbers to them, because their behaviour is so different from that of finite numbers that it seems a wilful misuse of terms to call them numbers at all. In order to meet this feeling, we must now turn to the logical basis of arithmetic, and consider the logical definition of numbers. ”

“ The NAME NUMBER, 3, stands for some universal work, the 3 being one of the Universal numbers. The number 2, on the other hand, holds the strong love of home. The Cornerstone, “A,” would lead one to begin many things, but there are no vibrations in the name that would help such a person to finish them. ”

“ Arithmetic is the prose of Mathematics where everything is stated and nothing left to the imagination, but Algebra is very different. 'Known Numbers are usually represented by the first letters of the alphabet, as a, b, c. Unknown Numbers, or those whose values are to be determined, are usually represented by the last letters of the alphabet, as x, y, z.' The unknown numbers,—the mysterious numbers,—for what is unknown is in a measure mysterious and what is mysterious is romantic or poetic. ”

“ In seeking a definition of number, the first thing to be clear about is what we may call the grammar of our inquiry. Many philosophers, when attempting to define number, are really setting to work to define plurality, which is quite a different thing. Number is what is characteristic of numbers, as man is what is characteristic of men. A plurality is not an instance of number, but of some particular number. A trio of men, for example, is an instance of the number 3, and the number 3 is an instance of number ”

“ Francis Galton, respecting what he designated "visualized numerals," and the association of colors with various numbers. The term "visualized numerals" in its simplest sense means the conception, or mental vision, when any number is spoken or thought of, of that number as it is written, the power to form which may extend in some cases to lines of considerable length. ”