Piece of eight

“ 'Well, I do not mind telling you I have been at work upon this geometry of Four Dimensions for some time. Some of my results are curious. For instance, here is a portrait of a man at eight years old, another at fifteen, another at seventeen, another at twenty-three, and so on. All these are evidently sections, as it were, Three-Dimensional representations of his Four-Dimensioned being, which is a fixed and unalterable thing. ”

“ Visual Repetition: Eight is the highest number that can be held in a rhythmic group, and some subjects can only hold seven. Many more units can be felt in a group, when the size of the including space is taken as the measure and compared; but no more than eight can be felt and recognized as the number of units it is. (There may be exceptions to this rule in either auditory or visual rhythm, but this is the norm in both cases.) ”

“ These new figures (as well as those that follow) are called the daughters or secondaries and are placed beside the primaries, by confrontation with which (i,e, 5 with 1, 6 with 2, 7 with 3 and with 4) four fresh figures are obtained after the same fashion and placed side by side below the first eight. ”

“ But most of the other trisyllabic rising and falling metres, except the Septenary, occur first in English poetry at the end of the eighteenth and during the course of the nineteenth century.
It must also be noted that in many cases, especially in the eight-, four-, and two-foot verses of this kind (i.e. in those metres that are connected with the old four-stressed verse) , the rising and falling rhythms are not strictly separated, but frequently intermingle and even supplement one another. ”

“ Number reveals itself to art by rhythm, which is the beating of the heart of the Infinite. In rhythm, law of order, God is felt. A verse is a gathering like a crowd; its feet take the cadenced step of a legion. Without number, no science; without number, no poetry. The strophe, the epic poem, the drama, the riotous palpitation of man, the bursting forth of love, the irradiation of the imagination, all this cloud with its flashes, the passion,—all is lorded over by the mysterious word number, even as geometry and arithmetic. ”

“ Seven and nine are important numbers in transformation. When seven girls are born of one marriage, one is [Pg 7] thought to turn into a wer-wolf and the seventh child of the seventh child is predestined to the same fate. The spell is said to last nine days. ”

“ Number, too, is part of the supersensuous world that is thoroughly religious. We can see and touch seven apples, but seven itself, that wonderful thing that shifts from object to object, giving it its SEVENness, that living thing, for it begets itself anew in multiplication—surely seven is a fit denizen of the upper-world. ”

“ ONE-EYE, TWO-EYES, AND THREE-EYES There was once a woman who had three daughters, the eldest of whom was called One-Eye, because she had only one eye in the middle of her forehead, and the second, Two-Eyes, because she had two eyes like other folks, and the youngest, Three-Eyes, because she had three eyes; and her third eye was in the centre of her forehead.
Now, as Two-Eyes saw just as other human beings did, her sisters and her mother could not endure her. They said to her, “You, with your two eyes, are no better than common folk. You do not belong to us!” ”

“ It is, however, in the old Romances (where it is common, and from its commonness in which it is better called the "Romance-six") often found in multiples of three other than six; and it is at the batch of three that the title looks—the couplet of eights constituting the body, and the odd six the tail. ”

“ The first eight stanzas of the edition of 1798 are therefore reprinted in this Appendix; and a Table is added, by means of which the various transpositions effected from time to time may be readily ascertained. In the Table 'a' stands for lines 1-4, and 'b' for lines 5-8 of a stanza.
In the sweet shire of Cardigan,
Not far from pleasant Ivor-hall,
An old man dwells, a little man,
I've heard he once was tall. ”

“ Never at any time therefore do they seat together more than nine; and then only when they are very distinguished persons indeed. In like manner they look upon seven as God’s own number; the one that means rest after labour; for, as you will remember, in six days God made Heaven and Earth, and on the seventh day He rested. Furthermore, they know that just as in the Alphabet, A, B and C, contain the lines and curves of all the other letters, so in ordinary numbers, 1, 2 and 3, contain all the lines and curves of all the others. ”

“ The number six, expressed by ‏ו‎, the third letter, which is likewise revered in the Pythagorean school, is formed by the combination of one, two, and three, the symbol of all perfection. Moreover the number six is the symbol of the cube, the bodies (solida) , or the world. Hence it is evident that the world has in it the imprint of divine perfection. ”

“ Perhaps everything in life is symmetry? But no. On the contrary, this is life"—and I drew an oblong figure on the board—"and after life the soul passes to eternity"—here I drew a line from one end of the oblong figure to the edge of the board. ”

“ Then the mother said, ‘Little Three-eyes, do you climb up; you with your three eyes can see round better than Little One-eye.’ So Little One-eye slid down, and Little Three-eyes climbed up; but she was not any more successful; look round as she might, the golden apples bent themselves back. ”

“ Ten, according to some, is a perfect number, not in its composition like six, but because it contains inclosed in itself all the simple numbers and all the properties, as of even and odd, perfect and imperfect, and it is the beginning of all numbers composed of tens, and also for the foundation of our law. ”

“ He does not tell us which is the true one, and in this he is wise. But if he is to have more than one, why limit the number to three? Our Heavenly Father has given His sons more than three rings, and they are not able to discern which is the original, the true ring. ”

“ Man recognises in himself Five Senses, Touch, Taste, Sight, Hearing, Smell—but as a matter of fact he has Seven, for he should include Intuition and Instinct, which are more important than all the others as the means of communicating with his surroundings. Now ‘the culmination of the Eighth’ is neither Five nor Seven nor Twelve,—it is the close or rebound of the Octave—the end of the leading Seven—the point where a fresh Seven begins. ”

“ The theory so long held of three primary and four secondary colors is purely exoteric, for since the earliest periods it has been known that there are seven, and not three, primary colors, the human eye being capable of estimating only three of them. ”

“ We shall then obtain the exact size of the figure at that height, which will make it look the same size as the lower one, N. The same rule applies to the picture K, when it is of large proportions. As an example in painting, take Michelangelo’s large altar-piece in the Sistine Chapel, ‘The Last Judgement’; here the figures forming the upper group, with our Lord in judgement surrounded by saints, are about four times the size, that is, about twice the height, of those at the lower part of the fresco. ”

“ The small Five ― and the small Six ― with a piece of white sugar ― and a parcel of beans ― the small Five likes to go high up ― and he climbs up to the tip of the branch of the willow tree ― the tip of the willow branch is weak ― and the small Five tumbles down and hurts himself so that he shows the white of his eyes. ”

“ 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 mention is made of the twenty seventh day of the month; as we have already seen the significance of the square in the beams. Here especially it is significant; for as twenty-seven is the cube of three, there is a trinity in the means by which we are, as it were, squared, or fitted for every good work. ”

“ Four, representing the square, is in the highest degree perfect; and Ten, as it contains the sum of the four prime numbers, comprehends all musical and arithmetical proportions, and denotes the system of the world. ”

“ Here are the count’s notes; they are most of them incomprehensible, owing to the abbreviations he used: probably he thought he would have future opportunities of examining the hieroglyphics, but the most important is clear enough, it runs thus: ‘Let the serpent be thy guide on thy right hand.’ This the count told me referred to the direction to be followed: that is to say, in going and returning through the labyrinth of apartments we must follow the direction in which the figure of the serpent appeared to be travelling. The rest of the notes you can look over at your leisure, if you like. ”

“ And the intellectual gods produce all things hebdomically; for they evolve the intelligible, and at the same time intellectual triads, into intellectual hebdomads, and expand their contracted powers into intellectual variety.” Seven is what is called by arithmeticians a prime number, that is, it cannot be produced by the multiplication of other numbers. In the language of the New Platonists, the number seven is said to be a virgin, and without a mother, and it is therefore sacred to Minerva. The number six is a perfect number, and is consecrated to Venus. ”

“ Father—“You are very backward in your arithmetic. When I was your age I was doing cube roots.”
Boy—“What’s them?”
Father—“What! You don’t know what they are? My! my! that’s terrible! There, give me your pencil. Now, we take, say, 28764289, and find the cube root. First, you divide—no, you point off—no—let me see?—um—yes—no—don’t stand there grinning like a Cheshire cat; go upstairs and stay in your bedroom for an hour.” ”

“ THE PARTS.—If we inquire into the means employed, in the larger Part-forms, to effect the division of the whole into its broader Parts, we find that the prime factors, here again, are Cadence and Melody. The strongest sign of the consummation of a Part is a decisive perfect cadence, resting, as usual, upon the tonic harmony of the chosen key; a cadence sufficiently emphatic to interrupt the closer cohesion of the phrases which, precede, and bring them, as completed Part, to a conclusion. ”

“ The important point for the student of poetry to grasp is that this divergence of opinion turns upon the question of relative emphasis. Even pure form, or "a-priori form" as it has sometimes been called,—such as a rectangle, a square, a cube,—carries a certain element of association which gives it a degree of significance. There is no absolutely bare or blank pattern. "Four-square" means something to the mind, because it is intimately connected with our experience. [Footnote: See Bosanquet, Three Lectures on Aesthetic, pp. 19, 29, 39, and Santayana, The Sense of Beauty, p. 83.] ”

“ On the divergence of the basis itself and the confusion caused—for it is five, or it is six, or ten or twelve, or sixty or a hundred, or three hundred and sixty or the double hundred, the thousand. The reason, not clearly understood by the people, is that Six and the Dozen are first, and Sixty is a compromise in condescending to the people. ”

“ The conjunctions and minglings of p. 11. which make for the birth of increase and complete naturally the fruitful number. For when the square is multiplied [40] by itself, it becomes a square squared; when into the cube, the square cubed; when the cube is multiplied by the cube, it becomes a cube cubed. So that all the numbers from which comes the birth of things which are, are seven; to wit: number, monad, square, cube, square of square, cube of square and cube of cube.
He declared also that the soul is immortal and that there is a change from one body to another. ”

“ For a thousand is the cube of ten. For ten times ten makes a hundred, that is, the square on a plane superficies. But to give this superficies height, and make it a cube, the hundred is again multiplied by ten, which gives a thousand. ”

“ 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. ”

“ Touching to be thirty; more touching to be forty; tragic to be fifty and heartbreaking to be sixty. As to seventy, as to eighty, one would feel as one did during the last dance of a ball, tired but fey in the paling dawn, desperately making the most of each bar of music before one went home to bed. ”

“ I have made, however, a three-quarter length, thus giving the head larger than it would have been had I done the whole figure, as well as showing the composition of the principal motive. Much of the expression of a face is necessarily lost in engraving it on a small scale on wood. ”

“ Nevertheless we should like to learn the scientific explanation why seven should ever form itself as a preeminent number—six concentric circles around a seventh, and seven rings within one another round a central point, etc.—in this illusion, produced by a swaying saucer, or any other vessel. We give the solution refused by Science in the Section which follows. ”

“ He that thinks on a cube of an inch diameter, has a clear and positive idea of it in his mind, and so can frame one of 1/2, 1/4, 1/8, and so on, till he has the idea in his thoughts of something very little ”