“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.”
“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.”
“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.”
“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”
“As the nineteenth-century philosopher Henry David Thoreau put it, “All perception of truth is the detection of an analogy.”
“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.”
“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.”
“idea models—models that are simple enough to study via mathematics or computers but that nonetheless capture fundamental properties of natural complex systems.”
“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.”
“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.”
“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”
“I caught her red-handed with her hands down his pants."
"You did not," Fancy told Madda sternly, with as much dignity as she was able. "It was just one hand.”
“It is the task of the translator to release in his own language that pure language that is under the spell of another, to liberate the language imprisoned in a work in his re-creation of that work.”
“He could not change the man he had been, but these hands would make him the man he could be”
“One of the lessons of history is that the gods can be silent in many languages.”
“You might not think you’re worth fighting for, or breathing for, but let me tell you, sugar – everyone deserves to be fought for, even those who think they aren’t worth it.
Then he lets me go, turns and walks off, leaving me utterly speechless.
Well hell, the biker is deep.
BookQuoters is a community of passionate readers who enjoy sharing the most meaningful, memorable and interesting quotes from great books. As the world communicates more and more via texts, memes and sound bytes, short but profound quotes from books have become more relevant and important. For some of us a quote becomes a mantra, a goal or a philosophy by which we live. For all of us, quotes are a great way to remember a book and to carry with us the author’s best ideas.
We thoughtfully gather quotes from our favorite books, both classic and current, and choose the ones that are most thought-provoking. Each quote represents a book that is interesting, well written and has potential to enhance the reader’s life. We also accept submissions from our visitors and will select the quotes we feel are most appealing to the BookQuoters community.
Founded in 2018, BookQuoters has quickly become a large and vibrant community of people who share an affinity for books. Books are seen by some as a throwback to a previous world; conversely, gleaning the main ideas of a book via a quote or a quick summary is typical of the Information Age but is a habit disdained by some diehard readers. We feel that we have the best of both worlds at BookQuoters; we read books cover-to-cover but offer you some of the highlights. We hope you’ll join us.