Sequence And Series Quotes

learn the lessons before they are over. Life is a composition of series and sequence of lessons. Each lesson comes with its own lessons to learn. our failure to learn the lessons of one shall be the reasons to learn another lesson with similar lessons. ~ Ernest Agyemang Yeboah

One needs but to say that, in the case of an unfamiliar sequence of syllables, only about seven can be grasped in one act, but that with frequent repetition and gradually increasing familiarity with the series this capacity of consciousness may be increased. ~ Hermann Ebbinghaus

How obvious, now, was that mathematical ratio of its sides, the quadratic sequence 1:4:9! And how naive to have imagined that the series ended there, in only three dimensions! ~ Arthur C. Clarke

Definitions of number, as given by several later mathematicians, make the limit of an infinite sequence identical with the sequence itself. Under this view, the question as to whether the variable reaches its limit is without logical meaning. Thus the infinite sequence .9, .99, .999,... is the number one, and the question, "Does it ever reach one?" is an attempt to give a metaphysical argument which shall satisfy intuition. ~ Carl B. Boyer

A plot, I used to remind my students, is not merely a sequence of events: "A" followed by "B" followed by "C" followed by "D." Rather, it's a series of events linked by cause and effect: "A" causes "B," which causes "C," and so on. True, a person's (or a fictional character's) destiny may be more than the sum of his choices
fate and luck play a role as well
but only scientists (and not all of them) believe that free will is a sham. People in life
and therefore in fiction
must choose, and their choices must have meaningful consequences. Otherwise, there's no story. ~ Richard Russo

What do people think of when they talk about their lives? Do they really see them as an integral whole, as a chronological sequence of events; as something logical, purposeful, completed? What moments do they remember, and how do they remember them? As words? As a series of images and sounds? My life crumbles into a series of pictures, unconnected scenes which comes to mind only occassionally and at random. But there are key events, the acts of chance or fate, which later enable me to construct a logical whole of my life. One such moment was meeting Jose. The other was my decision to see our love through to the very end. ~ Slavenka Drakulic

I did 'Echo Beach,' a surfing drama that meant I was often topless. Next came 'Demons,' and the opening sequence had me in my boxer shorts; and then there was a scene in 'Trinity' with me walking around in boxer shorts. It was only one scene in each series. ~ Christian Cooke

All revolutionary advances in science may consist less of sudden and dramatic revelations than a series of transformations, of which the revolutionary significance may not be seen (except afterwards, by historians) until the last great step. In many cases the full potentiality and force of a most radical step in such a sequence of transformations may not even be manifest to its author. ~ I. Bernard Cohen

The calamities of tragedy do not simply happen, nor are they sent; they proceed mainly from actions, and those the actions of men.We see a number of human beings placed in certain circumstances; and we see, arising from the co-operation of their characters in these circumstances, certain actions. These actions beget others, and these others beget others again, until this series of inter-connected deeds leads by an apparently inevitable sequence to a catastrophe. ~ A. C. Bradley

At this point, the sequence of my memories is disrupted.

I sank into a chaos of brief, incoherent and bizarre hallucinations, in which the grotesque and the horrible kept close company. Prostrate, as if I were being garrotted by invisible cords, I floundered in anguish and dread, oppressively ridden by the most unbridled nightmares. A whole series of monsters and avatars swarmed in the shadows, coming to life amid draughts of sulphur and phosphorus like an animated fresco painted on the moving wall of sleep.

There followed a turbulent race through space. I soared, grasped by the hair by an invisible hand of will: an icy and powerful hand, in which I felt the hardness of precious stones, and which I sensed to be the hand of Ethal. Dizziness was piled upon dizziness in that flight to the abyss, under skies the colour of camphor and salt, skies whose nocturnal brilliance had a terrible limpidity. I was spun around and around, in bewildering confusion, above deserts and rivers. Great expanses of sand stretched into the distance, mottled here and there by monumental shadows. At times we would pass over cities: sleeping cities with obelisks and cupolas shining milk-white in the moonlight, between metallic palm-trees. In the extreme distance, amid bamboos and flowering mangroves, luminous millennial pagodas descended towards the water on stepped terraces. ~ Jean Lorrain

The conclusion that the Egyptians of the Old Kingdom were acquainted with both the Fibonacci series and the Golden Section, says Stecchini, is so startling in relation to current assumptions about the level of Egyptian mathematics that it could hardly have been accepted on the basis of Herodotus' statement alone, or on the fact that the phi [golden] proportion happens to be incorporated in the Great Pyramid.

But the many measurements made by Professor Jean Philippe Lauer, says Stecchini, definitely prove the occurrence of the Golden Section throughout the architecture of the Old Kingdom.... Schwaller de Lubicz also found graphic evidence that the pharonic Egyptians had worked out a direct relation between pi and phi in that pi = phi^2 x 6/5. ~ Peter Tompkins

What if a demon crept after thee into thy loneliest loneliness some day or night, and said to thee: "This life, as thou livest it at present, and hast lived it, thou must live it once more, and also innumerable times; and there will be nothing new in it, but every pain and every joy and every thought and every sigh, and all the unspeakably small and great in thy life must come to thee again, and all in the same series and sequence - and similarly this spider and this moonlight among the trees, and similarly this moment, and I myself. The eternal sand-glass of existence will ever be turned once more, and thou with it, thou speck of dust!" - Wouldst thou not throw thyself down and gnash thy teeth, and curse the demon that so spake? Or hast thou once experienced a tremendous moment in which thou wouldst answer him: "Thou art a God, and never did I hear anything so divine!" If that thought acquired power over thee as thou art, it would transform thee, and perhaps crush thee; the question with regard to all and everything: "Dost thou want this once more, and also for innumerable times?" would lie as the heaviest burden upon thy activity! Or, how wouldst thou have to become favourably inclined to thyself and to life, so as to long for nothing more ardently than for this last eternal sanctioning and sealing? ~ Friedrich Nietzsche

Prime numbers are divisible only by 1 and by themselves. They hold their place in the infinite series of natural numbers, squashed, like all numbers, between two others, but one step further than the rest. They are suspicious, solitary numbers, which is why Mattia thought they were wonderful. Sometimes he thought that they had ended up in that sequence by mistake, that they'd been trapped, like pearls strung on a necklace. Other times he suspected that they too would have preferred to be like all others, just ordinary numbers, but for some reason they couldn't do it. This second thought struck him mostly at night, in the chaotic interweaving of images that comes before sleep, when the mind is too weak to tell itself lies. ~ Paolo Giordano

Buckminster Fuller explained to me once that because our world is constructed from geometric relations like the Golden Ratio or the Fibonacci Series, by thinking about geometry all the time, you could organize and harmonize your life with the structure of the world. ~ Einar Thorsteinn

Moving lockstep through a series of predictable transitions is no longer a route to personal security. Each man and woman must put together a highly individualized sequence of transitions in and out of school, work, and marriage in order to take advantage of shifting opportunities and respond to unexpected setbacks--a "do-it-yourself biolography. ~ Stephanie Coontz

Studies have shown that the act of looking at something attractive - a person, a product, some honest-to-goodness nature - triggers an involuntary series of synapse firings in the motor cerebellum. As it turns out, this is the exact same neural sequence that causes us to reach out a hand. Beauty, then, literally moves us. We all know this: beauty can easily force a hand. But will we ever shake the pressing delusion, as Tolstoy put it, that beauty is the same as goodness? After all, how often does goodness truly force a hand? more likely it stays it, and even then, barely, and even then, only for a time. ~ Emily Temple

The Engineer smiled (internally, for of course it had no mouth). It was feeling good. It was feeling optimistic. Moving at its current speed, it would arrive back in Ireland in plenty of time to shut everything down before a series of overloads and power loops inevitably led to a sequence of events which would, in turn, eventually lead to the probable destruction of the world. The Engineer wasn't worried.
And then the truck hit it. ~ Derek Landy