Pattern Quotes (26 quotes)
A mathematician … has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.
Fractals are patterns which occur on many levels. This concept can be applied to any musical parameter. I make melodic fractals, where the pitches of a theme I dream up are used to determine a melodic shape on several levels, in space and time. I make rhythmic fractals, where a set of durations associated with a motive get stretched and compressed and maybe layered on top of each other. I make loudness fractals, where the characteristic loudness of a sound, its envelope shape, is found on several time scales. I even make fractals with the form of a piece, its instrumentation, density, range, and so on. Here I’ve separated the parameters of music, but in a real piece, all of these things are combined, so you might call it a fractal of fractals.
I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid—a term used in this work to denote all of standard geometry—Nature exhibits not simply a higher degree but an altogether different level of complexity … The existence of these patterns challenges us to study these forms that Euclid leaves aside as being “formless,” to investigate the morphology of the “amorphous.”
I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
I maintain that the human mystery is incredibly demeaned by scientific reductionism, with its claim in promissory materialism to account eventually for all of the spiritual world in terms of patterns of neuronal activity. This belief must be classed as a superstition. ... We have to recognize that we are spiritual beings with souls existing in a spiritual world as well as material beings with bodies and brains existing in a material world.
If we lived on a planet where nothing ever changed, there would be little to do. There would be nothing to figure out. There would be no impetus for science. And if we lived in an unpredictable world, where things changed in random or very complex ways, we would not be able to figure things out. But we live in an in-between universe, where things change, but according to patterns, rules, or as we call them, laws of nature. If I throw a stick up in the air, it always falls down. If the sun sets in the west, it always rises again the next morning in the east. And so it becomes possible to figure things out. We can do science, and with it we can improve our lives.
In the preface to his great History of Europe, H. A. L. Fisher wrote: “Men wiser than and more learned than I have discerned in history a plot, a rhythm, a predetermined pattern. These harmonies are concealed from me. I can see only one emergency following upon another as wave follows upon wave …” It seems to me that the same is true of the much older [geological stratigraphical] history of Europe.
Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.
Such propositions are therefore called Eternal Truths, not because they are Eternal Truths, not because they are External Propositions actually formed, and antecedent to the Understanding, that at any time makes them; nor because they are imprinted on the Mind from any patterns, that are any where out of the mind, and existed before: But because, being once made, about abstract Ideas, so as to be true, they will, whenever they can be supposed to be made again at any time, past or to come, by a Mind having those Ideas, always actually be true. For names being supposed to stand perpetually for the same ideas, and the same ideas having immutably the same habitudes one to another, Propositions concerning any abstract Ideas that are once true, must needs be eternal Verities.
The Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.
[Describing Charles Babbage's machine.]
[Describing Charles Babbage's machine.]
The brain is waking and with it the mind is returning. It is as if the Milky Way entered upon some cosmic dance. Swiftly the head-mass becomes an enchanted loom where millions of flashing shuttles weave a dissolving pattern, always a meaningful pattern though never an abiding one.
The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.
The invention of IQ did a great disservice to creativity in education. ... Individuality, personality, originality, are too precious to be meddled with by amateur psychiatrists whose patterns for a “wholesome personality” are inevitably their own.
The lives of scientists, considered as Lives, almost always make dull reading. For one thing, the careers of the famous and the merely ordinary fall into much the same pattern, give or take an honorary degree or two, or (in European countries) an honorific order. It could be hardly otherwise. Academics can only seldom lead lives that are spacious or exciting in a worldly sense. They need laboratories or libraries and the company of other academics. Their work is in no way made deeper or more cogent by privation, distress or worldly buffetings. Their private lives may be unhappy, strangely mixed up or comic, but not in ways that tell us anything special about the nature or direction of their work. Academics lie outside the devastation area of the literary convention according to which the lives of artists and men of letters are intrinsically interesting, a source of cultural insight in themselves. If a scientist were to cut his ear off, no one would take it as evidence of a heightened sensibility; if a historian were to fail (as Ruskin did) to consummate his marriage, we should not suppose that our understanding of historical scholarship had somehow been enriched.
The mathematician's patterns … must be beautiful … Beauty is the first test; there is no permanent place in the world for ugly mathematics.
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way.
The psychiatric interviewer is supposed to be doing three things: considering what the patient could mean by what he says; considering how he himself can best phrase what he wishes to communicate to the patient; and, at the same time, observing the general pattern of the events being communicated. In addition to that, to make notes which will be of more than evocative value, or come anywhere near being a verbatim record of what is said, in my opinion is beyond the capacity of most human beings.
The reactions follow a pattern, which is valid for the blood of all humans... Basically, in fact, there are four different types of human blood, the so-called blood groups. The number of the groups follows from the fact that the erythrocytes evidently contain substances (iso-agglutinogens) with two different structures, of which both may be absent, or one or both present, in the erythrocytes of a person. This alone would still not explain the reactions; the active substances of the sera, the iso-agglutinins, must also be present in a specific distribution. This is actually the case, since every serum contains those agglutinins which react with the agglutinogens not present in the cells—a remarkable phenomenon, the cause of which is not yet known for certain.
The theory here developed is that mega-evolution normally occurs among small populations that become preadaptive and evolve continuously (without saltation, but at exceptionally rapid rates) to radically different ecological positions. The typical pattern involved is probably this: A large population is fragmented into numerous small isolated lines of descent. Within these, inadaptive differentiation and random fixation of mutations occur. Among many such inadaptive lines one or a few are preadaptive, i.e., some of their characters tend to fit them for available ecological stations quite different from those occupied by their immediate ancestors. Such groups are subjected to strong selection pressure and evolve rapidly in the further direction of adaptation to the new status. The very few lines that successfully achieve this perfected adaptation then become abundant and expand widely, at the same time becoming differentiated and specialized on lower levels within the broad new ecological zone.
Today's water institutions—the policies and laws, government agencies and planning and engineering practices that shape patterns of water use—are steeped in a supply-side management philosophy no longer appropriate to solving today's water problems.
We do not know of any enzymes or other chemical defined organic substances having specifically acting auto-catalytic properties such as to enable them to construct replicas of themselves. Neither was there a general principle known that would result in pattern-copying; if there were, the basis of life would be easier to come by. Moreover, there was no evidence to show that the enzymes were not products of hereditary determiners or genes, rather than these genes themselves, and they might even be products removed by several or many steps from the genes, just as many other known substances in the cell must be. However, the determiners or genes themselves must conduct, or at least guide, their own replication, so as to lead to the formation of genes just like themselves, in such wise that even their own mutations become .incorporated in the replicas. And this would probably take place by some kind of copying of pattern similar to that postulated by Troland for the enzymes, but requiring some distinctive chemical structure to make it possible. By virtue of this ability of theirs to replicate, these genes–or, if you prefer, genetic material–contained in the nuclear chromosomes and in whatever other portion of the cell manifests this property, such as the chloroplastids of plants, must form the basis of all the complexities of living matter that have arisen subsequent to their own appearance on the scene, in the whole course of biological evolution. That is, this genetic material must underlie all evolution based on mutation and selective multiplication.
What can be more curious than that the hand of a man, formed for grasping, that of a mole for digging, the leg of the horse, the paddle of the porpoise, and the wing of the bat, should all be constructed on the same pattern?
When carbon (C), Oxygen (o) and hydrogen (H) atoms bond in a certain way to form sugar, the resulting compound has a sweet taste. The sweetness resides neither in the C, nor in the O, nor in the H; it resides in the pattern that emerges from their interaction. It is an emergent property. Moreover, strictly speaking, is not a property of the chemical bonds. It is a sensory experience that arises when the sugar molecules interact with the chemistry of our taste buds, which in turns causes a set of neurons to fire in a certain way. The experience of sweetness emerges from that neural activity.
[The] complex pattern of the misallocation of credit for scientific work must quite evidently be described as “the Matthew effect,” for, as will be remembered, the Gospel According to St. Matthew puts it this way: For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath. Put in less stately language, the Matthew effect consists of the accruing of greater increments of recognition for particular scientific contributions to scientists of considerable repute and the withholding of such recognition from scientists who have not yet made their mark.
… on these expanded membranes [butterfly wings] Nature writes, as on a tablet, the story of the modifications of species, so truly do all changes of the organisation register themselves thereon. Moreover, the same colour-patterns of the wings generally show, with great regularity, the degrees of blood-relationship of the species. As the laws of nature must be the same for all beings, the conclusions furnished by this group of insects must be applicable to the whole world.
“Archaeology is made up entirely of anomalies,” said Terrence, “rearranged to make them fit in a fluky pattern. There'd be no system to it otherwise.”