Repeating pattern

“ That every line in a pattern should have its due growth, and be traceable to its beginning, this, which you have doubtless heard before, is undoubtedly essential to the finest pattern work; equally so is it that no stem should be so far from its parent stock as to look weak or wavering. Mutual support and unceasing progress distinguish real and natural order from its mockery, pedantic tyranny.
Every one who has practised the designing of patterns knows the necessity for covering the ground equably and richly. ”

“ It is time we should return to the consideration of abstract forms. Nearest in nature to the example of uniformity in multiplicity, we found those objects, like a reversible pattern, that having some variety of parts invite us to survey them in different orders, and so bring into play in a marked manner the faculty of apperception. ”

“ In the brain are male and female faculties; here is marriage, here is fruit. And there is no limit to this ascending scale, but series on series. Every thing, at the end of one use, is taken up into the next, each series punctually repeating every organ and process of the last. We are adapted to infinity. ”

“ If any one has in his lifetime invented a pattern, he has done something truly remarkable, and as rare as is a really original thought on any subject. Patterns are commonly, like men, the result of many centuries of long descent from ancestors of remote antiquity. ”

“ We have, then, considered variation of units in a repeated series, where they may vary and where they must, and we find the real value of repetition to appear in inverse proportion to the individual significance of the separate units; the more interesting or expressive the unit is in itself with individual significance, the less do we want it repeated ”

“ Emphasis is on the overall effect of pattern, not on its items. The continuous forked-and-angled design, the combinations of hourglass figures, of spaced rhomboids or hexagons, even the simpler fishbone pattern—all have this total-field approach, with relative indifference to figure elements that got squeezed, stretched, or distorted. ”

“ To produce the curved pattern I show you, nothing more is necessary than to bend the tin pattern on a block of the right shape, and we now get a pattern which would puzzle a good many pattern-makers of the old style. ”

“ The results of the different subjects show that the shifting of tendencies occurs as before. (4) As to the way in which regularity functions in the judgment, the notes of one observer are very clear. The blank spaces in the irregular are noticeable, he says, which is not true of the regular, where, on the contrary, one has a feeling of compactness of figure. I am able to confirm this character of the spaces by my experience outside this experiment. A simple pattern is very easily apprehended and irrelevancies of the background dismissed. ”

“ Here it is sufficient to recall4 that the absolutely necessary technique of weaving in all its various forms of interlacing, plaiting, netting, embroidering, etc., implies order, uniformity, and symmetry. The chance introduction of a thread or withe of a different color, brings out at once an ordered pattern in the result; the crowding together or pressing apart of elements, a different alternation of the woof, a change in the order of intersection, all introduce changes by the natural necessities of construction which have the effect of purpose. ”

“ Out of the whole multiplicity of objects of sense, it enables us to single out a small selection, which is an indispensable preliminary to abstraction. For example, attention will enable us to discriminate a coloured pattern which we are seeing, and to separate it from the other things we see and from images and other objects of sense and thoughts which may exist simultaneously. For the sake of simplicity, let us suppose that we discriminate a black and white pattern in the form of a triangle. ”

“ In fact, all these theories are of little use as formulæ of interpretation, for we must study carefully each trait-complex before a conclusion as to its origin can be reached. Their true functions are to define the different ways in which cultural similarities have been observed to come about.
The intensive analytic study of single trait-complexes has developed the pattern theory. [8] The conception is that in certain phases of culture each social unit develops a style, or pattern, for its traits and that borrowed traits will be worked over to make them conform to this pattern. ”

“ This putative pattern R is empirically adequate as a theory of how this sequence of numbers behaves; it fits all the data we have been given. How do we know if this is indeed a genuine pattern, though? Here’s an answer that should occur to us immediately: we can continue to watch how the sequence of numbers behaves, and see if our predictions bear out. If we’ve succeeded in identifying the pattern underlying the generation of these numbers, then we’ll be able to predict what we should see next: we should see a ‘zero’ followed by a 'one,’ and then another ‘zero,’ and so on. ”

“ But when we come to unformulated nature—to the vast world of complex forms, ever changing their aspect, full of life and movement, trees, flowers, woods and waters, birds, beasts, fishes, the human form—the problem how to represent any of these forms, to express and characterize them by means of so abstract a method as line-drawing, seems at first difficult enough. ”

“ We draw with a continuous line, after having looked at, or thought of, our model. How shall we explain such a faculty, except by our habit of discovering at once the organization of the outlines of common objects, that is to say, by a motor tendency to draft their diagram in one continuous line? ”

“ We looked at a few problem cases in pattern identification—including patterns that hold only approximately, and data-sets with partial information loss—and argued that even in cases like that, useful information can be gleaned from a close search for patterns; patterns neither need to be universal nor perfect in order to be informative. We tried to give an intuitive picture of what we might mean when we say that science looks for patterns that can be projected to unobserved cases. ”

“ Variety is one of the great laws of the universe, and alternation is a blending of variety and repetition This will be gathered from a reference to diagram where the braiding alternates, first forming a crow's toe and then a simple eye. It is the succession of two different objects or forms recurring regularly in turn. There can be no alternation without repetition, but there can be repetition without alternation. ”

“ One pattern is an accurate representation of another if every element of the one can be taken as the representative of just one element of the other, and the relations that make the one set into a pattern correspond with relations making the other set into a pattern. In this sense, writing can represent speech with a certain degree of accuracy; to every spoken word a written word corresponds, and to the time-order of the spoken words the space-order of the written words corresponds. ”

“ Any pattern or design which shows prominently any set pattern, or spots which suggest a sum of multiplication, or which, in the half-light of night or early morning, might be likely to fix themselves upon the tired brain, suggesting all kinds of weird forms, are especially to be avoided. The design should be of such a description that, saving as regards colour, it should offer no specially marked pattern. ”

“ Moreover, it was difficult to find a scale of judgment by which to decide whether a series was really alternating or plain repetition. From one point of view, every repetition is alternating, that is, the repeated unit always alternates with an empty space. Although such repetitions bear out the theory still further, and emphasize yet more strongly the invariability of alternates, and the possibility of variations in the principal units, I have used the term in a stricter sense, and only given illustrations of repeated objects, when one unit actually alternated with another definite unit. ”

“ If the conditions are kept as much alike as is possible, is the average number of repetitions, which is necessary for learning similar series to the point of first possible reproduction, a constant mean value in the natural science sense? ”

“ It was in that way that we came to regard repetitions and alternations as illustrations of Harmony rather than of [Pg 59] Rhythm. Rhythm comes into the Harmony of a Repeated Relation when the relation is one which causes the eye to move in one direction rather than another, and when the movement is carried on from repetition to repetition, from measure to measure.
81. The repetition of a motive at equal intervals, when there is no movement in the motive, gives us no feeling of Rhythm.
Fig. 102
In this case, for example, we have a repetition in the line of a certain symmetrical shape. ”

“ We can more or less guess how an occurrence produces a change in the brain, and how its repetition gradually produces something analogous to the channel of a river, along which currents flow more easily than in neighbouring paths. We can perceive that in this way, if we had more knowledge, the tendency to habit through repetition might be replaced by a precise account of the effect of each occurrence in bringing about a modification of the sort from which habit would ultimately result. ”

“ But this general method of comparison is subdivided into three or four sub-methods. Nature has prepared not only one but three or four series, not identical, not mere duplicates of each other, but varied, yet resembling and illustrating each other. ”

“ Classification, logic, and mathematics all result, then, from the mere play of the mind comparing its conceptions, no matter whence the latter may have come. The essential condition for the formation of all these sciences is that we should have grown capable of apprehending series as such, and of distinguishing them as homogeneous or heterogeneous, and as possessing definite directions of what I have called 'increase.' This consciousness of series is a human perfection which has been gradually evolved, and which varies greatly from man to man. ”

“ The persons who have the tendency to build story-type models will be very much disturbed by the repetitions, as the repetition sends them back to the point where the statement appeared for the first time. This will fragment the story- type model. Once fragmented, it cannot be continued and a new story-type model has to be built. ”

“ In the units lies the meaning of the repetition, in the regular alternates the possibility of its expression.
(4) The rhythmic character of repetition is not felt by a certain type of subject, when it goes smoothly. When a variation is made which would destroy any possible rhythm, its lack is felt, and its violation finds expression only in rhythmic terms.
(5) More violation is done to a series to have the size of units varied than the filling. (This corroborates previous experiments.) ”

“ Repetition embodies the principle of uniformity. Now we have found repetition to be a leading characteristic of parallelism; accordingly a close connection may be divined to exist between congruence and parallelism. Furthermore we have just elaborated in outline the principles of normality, pointing out how the property has its origin in the interplay of the relations of extension and cogredience. But—as we know from experience—a leading property of normality is symmetry, namely, symmetry round the normal. ”

“ The definite combination of heterogeneous changes, both simultaneous and successive, is a formula which fails to call up an adequate conception. And it fails from omitting the most distinctive peculiarity—the peculiarity of which we have the most familiar experience, and with which our notion of Life is, more than with any other, associated. ”

“ Because we can often arrange the series of structures in a line extending from the very simple to the more complex, we are apt to become unduly impressed by this fact and conclude that if we found the complete series we should find all the intermediate steps and that they have arisen in the order of their complexity. ”

“ All expert and technical education is built upon the theory that these trunk-lines of habit become more and more sensitive to their accustomed stimuli, and respond more and more readily.
We are apt to overlook the physical basis of habit. Every repetition of an act makes us more likely to perform that act, and discovers in our wonderful mechanism a tendency to perpetual repetition, whose facility increases in exact proportion to the repetition. ”

“ When we do meet with a clear and unmistakable series of such progressive magnitudes or ratios, manifesting themselves in a progressive series of “allied” forms, then we have the phenomenon of “orthogenesis.” ”

“ Just as we tend to assume that all phenomena form one series, so we ascribe to every series one single direction. But this assumption too is baseless. It is natural to set up a point in the future towards which all events run, or from which they arrive, or which may seem to serve in some other way to give direction to the stream. ”

“ It is in the alternate spaces that the feeling of repetition lies. Any material change in them destroys the series, but a slight variation in the lines of decoration, a little rearrangement of the conventional curves in each alternate, gives, even though unattended to, in fact partly because unattended to, a vague feeling of variety, of some superfluous sensation being brought into consciousness, although the regular shape, size, and distance of the objects remains unchanged. ”