“Whew, this might be getting a bit confusing. I hope you are following me so far. This is the point in every Theory of Computation course at which students either throw up their hands and say "I can't get my mind around this stuff!" or clap their hands and say "I love this stuff!"
Needless to say, I was the second kind of student, even though I shared the confusion of the first.”
― quote from Complexity: A Guided Tour
“This statement is not provable.” Think about it for a minute. It’s a strange statement, since it talks about itself—in fact, it asserts that it is not provable. Let’s call this statement “Statement A.” Now, suppose Statement A could indeed be proved. But then it would be false (since it states that it cannot be proved). That would mean a false statement could be proved—arithmetic would be inconsistent. Okay, let’s assume the opposite, that Statement A cannot be proved. That would mean that Statement A is true (because it asserts that it cannot be proved), but then there is a true statement that cannot be proved—arithmetic would be incomplete. Ergo, arithmetic is either inconsistent or incomplete.”
― quote from Complexity: A Guided Tour
“complex system: a system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution.”
― quote from Complexity: A Guided Tour
“Linearity is a reductionist’s dream, and nonlinearity can sometimes be a reductionist’s nightmare. Understanding the distinction between linearity and nonlinearity is very important and worthwhile. To”
― quote from Complexity: A Guided Tour
“As the nineteenth-century philosopher Henry David Thoreau put it, “All perception of truth is the detection of an analogy.”
― quote from Complexity: A Guided Tour
“In short, what Brown, Enquist, and West are saying is that evolution structured our circulatory systems as fractal networks to approximate a “fourth dimension” so as to make our metabolisms more efficient. As West, Brown, and Enquist put it, “Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional … Fractal geometry has literally given life an added dimension.”
― quote from Complexity: A Guided Tour
“Turing’s first goal was to make very concrete this notion of definite procedure. The idea is that, given a particular problem to solve, you can construct a definite procedure for solving it by designing a Turing machine that solves it. Turing machines were put forth as the definition of “definite procedure,” hitherto a vague and ill-defined notion.”
― quote from Complexity: A Guided Tour
“idea models—models that are simple enough to study via mathematics or computers but that nonetheless capture fundamental properties of natural complex systems.”
― quote from Complexity: A Guided Tour
“Tony Rothman points out, “Why the second law should distinguish between past and future while all the other laws of nature do not is perhaps the greatest mystery in physics.”
― quote from Complexity: A Guided Tour
“Information, as narrowly defined by Shannon, concerns the predictability of a message source. In the real world, however, information is something that is analyzed for meaning, that is remembered and combined with other information, and that produces results or actions. In short, information is processed via computation.”
― quote from Complexity: A Guided Tour
“reached. In dynamical systems theory, each of these abrupt period doublings is called a bifurcation. This succession of bifurcations culminating in chaos has been called the “period doubling route”
― quote from Complexity: A Guided Tour
“Her cheek against the moss, the young princess she had been - Aelin Galathynius - reached a hand for her. 'Get up', she said softly.”
― Sarah J. Maas, quote from Heir of Fire
“Your face is my heart Sassenach, and the love of you is my soul”
― Diana Gabaldon, quote from Drums of Autumn
“You saw my leg?"
"How can a man help what he sees?" he said. "And, if I could add, you possess a very fine leg.”
― Shannon Hale, quote from The Goose Girl
“After a great blow, or crisis, after the first shock and then after the nerves have stopped screaming and twitching, you settle down to the new condition of things and feel that all possibility of change has been used up. You adjust yourself, and are sure that the new equilibrium is for eternity. . . But if anything is certain it is that no story is ever over, for the story which we think is over is only a chapter in a story which will not be over, and it isn't the game that is over, it is just an inning, and that game has a lot more than nine innings. When the game stops it will be called on account of darkness. But it is a long day.”
― Robert Penn Warren, quote from All the King's Men
“Then he [The Star Child] waited, marshaling his thoughts and brooding over his still untested powers. For though he was master of the world, he was not quite sure what to do next. But he would think of something.”
― Arthur C. Clarke, quote from 2001: A Space Odyssey
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