Inspirational quotes with gradient.
Anarchy and Liberty are synonymous. Anything less is merely gradient levels of slavery.
Trust has no gradient.
Darwin singled out the eye as posing a particularly challenging problem: 'To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest degree.' Creationists gleefully quote this sentence again and again. Needless to say, they never quote what follows. Darwin's fulsomely free confession turned out to be a rhetorical device. He was drawing his opponents towards him so that his punch, when it came, struck the harder. The punch, of course, was Darwin's effortless explanation of exactly how the eye evolved by gradual degrees. Darwin may not have used the phrase 'irreducible complexity', or 'the smooth gradient up Mount Improbable', but he clearly understood the principle of both. 'What is the use of half an eye?' and 'What is the use of half a wing?' are both instances of the argument from 'irreducible complexity'. A functioning unit is said to be irreducibly complex if the removal of one of its parts causes the whole to cease functioning. This has been assumed to be self-evident for both eyes and wings. But as soon as we give these assumptions a moment's thought, we immediately see the fallacy. A cataract patient with the lens of her eye surgically removed can't see clear images without glasses, but can see enough not to bump into a tree or fall over a cliff. Half a wing is indeed not as good as a whole wing, but it is certainly better than no wing at all. Half a wing could save your life by easing your fall from a tree of a certain height. And 51 per cent of a wing could save you if you fall from a slightly taller tree. Whatever fraction of a wing you have, there is a fall from which it will save your life where a slightly smaller winglet would not. The thought experiment of trees of different height, from which one might fall, is just one way to see, in theory, that there must be a smooth gradient of advantage all the way from 1 per cent of a wing to 100 per cent. The forests are replete with gliding or parachuting animals illustrating, in practice, every step of the way up that particular slope of Mount Improbable. By analogy with the trees of different height, it is easy to imagine situations in which half an eye would save the life of an animal where 49 per cent of an eye would not. Smooth gradients are provided by variations in lighting conditions, variations in the distance at which you catch sight of your prey—or your predators. And, as with wings and flight surfaces, plausible intermediates are not only easy to imagine: they are abundant all around the animal kingdom. A flatworm has an eye that, by any sensible measure, is less than half a human eye. Nautilus (and perhaps its extinct ammonite cousins who dominated Paleozoic and Mesozoic seas) has an eye that is intermediate in quality between flatworm and human. Unlike the flatworm eye, which can detect light and shade but see no image, the Nautilus 'pinhole camera' eye makes a real image; but it is a blurred and dim image compared to ours. It would be spurious precision to put numbers on the improvement, but nobody could sanely deny that these invertebrate eyes, and many others, are all better than no eye at all, and all lie on a continuous and shallow slope up Mount Improbable, with our eyes near a peak—not the highest peak but a high one.
...the whole configuration of human development needs to be reconceptualized. A lifetime ought not to be thought of in linear manner, an ascending upward gradient, or a kind of bell-shaped curve in which persons develop from one stage of helplessness as an infant through a lifetime to a final stage of helplessness in old age... In...God resides the ultimate coherence from whom each passion for understanding, each new insight, new stage, new vision of the universe, derives its ultimate intelligibility and toward which all such phenomena point.
(Q: From an outsider’s perspective, what you call “chaos magick” has a lot of rules, discipline, and order involved, and doesn’t seem very chaotic at all. What would you say to such a person?)A: I differentiate sternly between Chaos and Entropy. Only highly ordered and structured systems can display complex creative and unpredictable behaviour, and then only if they have the capacity to act with a degree of freedom and randomness. Systems which lack structure and organisation usually fail to produce anything much, they just tend to drift down the entropy gradient. This applies both to people and to organisations.
Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..."Klapaucius thought, and thought some more. Finally he nodded and said:"Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit.""Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming:Come, let us hasten to a higher plane,Where dyads tread the fairy fields of Venn,Their indices bedecked from one to n,Commingled in an endless Markov chain!Come, every frustum longs to be a cone,And every vector dreams of matrices.Hark to the gentle gradient of the breeze:It whispers of a more ergodic zone.In Reimann, Hilbert or in Banach spaceLet superscripts and subscripts go their ways.Our asymptotes no longer out of phase,We shall encounter, counting, face to face.I'll grant thee random access to my heart,Thou'lt tell me all the constants of thy love;And so we two shall all love's lemmas prove,And in bound partition never part.For what did Cauchy know, or Christoffel,Or Fourier, or any Boole or Euler,Wielding their compasses, their pens and rulers,Of thy supernal sinusoidal spell?Cancel me not--for what then shall remain?Abscissas, some mantissas, modules, modes,A root or two, a torus and a node:The inverse of my verse, a null domain.Ellipse of bliss, converge, O lips divine!The product of our scalars is defined!Cyberiad draws nigh, and the skew mindCuts capers like a happy haversine.I see the eigenvalue in thine eye,I hear the tender tensor in thy sigh.Bernoulli would have been content to die,Had he but known such a^2 cos 2 phi!
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