Number

“ 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. ”

“ 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? ”

“ This distinction, the distinction by which number is assigned to reason and not to sense, is, I think, an important aid towards understanding the Pythagorean philosophy.
9. Number is a necessary form of thought under which we place or subsume whatever is presented to the mind. Hence form, which is another name for number, and not matter, is the essence of all things, at least of all intelligible things. It is the truth and substance of the universe—its truth and substance, not only in so far as it exists for us, but in so far as it exists for intelligence generally. ”

“ But when the number drawn is a multiple of the one they play, it is a sympathetic number, and is next door to winning; and if the number come reversed,—as if, having played 12, it come out 21,—he laughs with delight. "Eh, don't you see, you stupid fellow," said the speziale of a village one day to a dunce of a contadino, of whose infallible terno not a single number had been drawn,—"Don't you see, in substance all your three numbers have been drawn? and it's shameful in you to be discontented. ”

“ 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. ”

“ And, my dear Pastor, believers will tell you that God is Number endowed with motion, to be felt but not proved. He, like the unit, is the origin of number though having nothing in common with numbers. The existence of Number depends on that of the unit, which is not a number, but the parent of them all. And God, dear Pastor Becker, is a stupendous Unit, having nothing in common with His creations, but their Parent nevertheless. ”

“ Is it a breath of God sent forth to organize the material universe, wherein nothing takes shape but as a result of divisibility which is an effect of number? The most minute as well as the most immense objects in creation are distinguished from each other by quantity, quality, dimension, and force,—are not these all conditions of number? That number is infinite is a fact proved to your intellect, but of which no material proof is obtainable. A mathematician will tell you that infinity of number is certain, but cannot be demonstrated. ”

“ We experienced some little trouble in mastering the French numerals, until I tried a new scheme, and called out, "From the right, number, in French!" Then my merry convalescents began shouting gleefully, "Oon," "Doo," "Troy," "Catta," "Sink," etc.; but the French numerals stuck in their heads. Never did any one, I imagine, have such a set of jolly, cheery boys in blue as pupils, and the strong remnant of the child left in many of them made them the more attractive. ”

“ Or if an observer were stationed at a certain point, and 10,000 persons were to pass him in single file without his counting them as they passed, what sort of an estimate would he make of their number? The truth seems to be that our mental conception of number is much more limited than is commonly thought, and that we unconsciously adopt some new unit as a standard of comparison when we wish to render intelligible to our minds any number of considerable magnitude. ”

“ A most inviting field for research is, however, furnished by the primitive methods of counting and of giving visible expression to the idea of number. Our starting-point must, of course, be the sign language, which always precedes intelligible speech; and which is so convenient and so expressive a method of communication that the human family, even in its most highly developed branches, never wholly lays it aside. It may, indeed, be stated as a universal law, that some practical method of numeration has, in the childhood of every nation or tribe, preceded the formation of numeral words. ”

“ Sometimes a number above ten, but not over twenty, is indicated with the hands only by counting up to ten in the ordinary way, and then opening all the fingers and counting again, until they reach the requisite amount in excess of ten. ”

“ If there are two numbers, they are neither of them properly described in this definition, or in any of the preceding ones. There is a gross misconception, in taking each or either of them to be an alternate representation of two incompatible ideas. And this sort of error is far from being confined to the present subject; it runs through a vast number of the various definitions contained in our grammars. (18.) "Number is the inflection of a noun, to indicate one object or more than one. Or, Number is the expression of unity or of more than unity."--Hiley's Gram., p. ”

“ 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. ”

“ Among the speculative questions which arise in connection with the study of arithmetic from a historical standpoint, the origin of number is one that has provoked much lively discussion, and has led to a great amount of learned research among the primitive and savage languages of the human race. ”

“ Number is more an object of reason, and less an object of sense, than either water or air; and therefore we say that, while the position of the Ionic school is more that of sense than that of reason, the position of the Pythagorean school is more that of reason than that of sense.
6. Number is a truer universal than either water or air, or any other sensible thing. It is possible that the conception of number may not be an adequate conception of the universal in all things ”

“ Thus number in the abstract is the number of times that the act of counting is performed in any particular case. This, however, is a description, not a definition, and we still want a definition for “number” in the phrase “number of times.”
10. Definition of “Number.”—Suppose we fix on a certain sequence of names “one,” “two,” “three,” ..., or symbols such as 1, 2, 3, ...; this sequence being always the same. If we take a set of concrete objects, and name them in succession “one,” “two,” “three,” ..., naming each once and once only, we shall not get beyond a certain name, e.g. “six.” ”

“ 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. ”

“ The clearness and distinctness of each mode of number from all others, even those that approach nearest, makes me apt to think that demonstrations in numbers, if they are not more evident and exact than in extension, yet they are more general in their use, and more determinate in their application. ”

“ Words now have an added significance; for this purpose they have become and from this time they will be NUMBERS, as well as WORDS.
Always keep in mind that SOUND determines the number value of the word regardless of how it is spelled.
Forming Larger Number Words
In order to form words for larger numbers first become familiar with the figure value of the one hundred code words. These will often combine to form the larger number pictures. For example:
A combination picture of Nero and Papa would represent 2499. ”

“ 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. ”

“ 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 ”

“ So the Eskimo and the South American Indian are, after all, not so very far behind the “elderly person” of Carnarvon, in the distinct perception of a number which familiarity renders to us absurdly small.
Chapter III. The Origin of Number Words.
In the comparison of languages and the search for primitive root forms, no class of expressions has been subjected to closer scrutiny than the little cluster of words, found in each language, which constitutes a part of the daily vocabulary of almost every human being—the words with which we begin our counting. ”

“ THE ART OF COUNTING. Ideas of Number derived from experience—State of Arithmetic among uncivilized races—Small extent of Numeral-words among low tribes—Counting by fingers and toes—Hand-numerals show derivation of Verbal reckoning from Gesture-counting—Etymology of Numerals—Quinary, Decimal, and Vigesimal notations of the world derived from counting on fingers and toes—Adoption of foreign Numeral-words—Evidence of development of Arithmetic from a low original level of Culture. ”

“ OBS. 18.—Since nouns and adjectives are different parts of speech, the suggestion, that, "Numeral adjectives are also names, or nouns," is, upon the very face of it, a flat absurdity; and the notion that "the name of a number" above unity, conveys only and always the idea of unity, like an ordinary "singular noun," is an other. A number in arithmetic is most commonly an adjective in grammar; and it is always, in form, an expression that tells how many, or—"denotes how many things are spoken of."—Chase, p. 11. But the name of a number is also a number, whenever it is not made plural in form. ”

“ 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. ”

“ It is quite true that the fundamental truths of the science of number all rest on the evidence of sense but, having used eyes and fingers upon ten balls or twenty balls, upon ten nuts, or leaves, or sheep, or what not, the child has formed the association of a given number with objects, and is able to conceive of the association of various other numbers with objects. ”

“ Number may be expressed either by a particular word, expressing number in general, such as the words many, more, &c., or by some variation upon the words which express the things numbered. It is this last expedient which mankind would probably have recourse to, in the infancy of language. Number, considered in general, without relation to any particular set of objects numbered, is one of the most abstract and metaphysical ideas, which the mind of man is capable of forming ”

“ As a Number Primer it teaches in a very simple, logical way, the first steps in number. It is easy, and appeals to the natural interest of the child in counting, besides being adapted to his various capacities. ”

“ But races as fond of metaphor and of linguistic embellishment as are those of the East, or as are our American Indians even, might readily resort to some other source than that furnished by the members of the human body, when in want of a term with which to describe the 5, 10, or any other number of the numeral scale they were unconsciously forming. ”

“ A fresh mental effort is required of the ignorant child of nature; and the result is “all the fingers and one more,” “both hands and one more,” “one on another count,” or some equivalent circumlocution. If he has an independent word for 10, the result will be simply ten-one. When this step has been taken, the base is established. The savage has, with entire unconsciousness, made all his subsequent progress dependent on the number 10, or, in other words, he has established 10 as the base of his number system. ”