“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
“Where are we going?”
… “Just this place I know with a waterfall and a cave. It’s part of the estate, so no one uses it.”
“How nice,” I said … “We have a garage at my house. It holds a car and some of my dad’s tools.”
Martin glanced at me, equal parts amused and confused. “Oh?”
“Yes. And a hammock in the back yard.”
“Is that so…”
“Yeah.”
“So no waterfalls?”
“No. But this one time, when it rained a lot, the gutter broke. That was similar to a waterfall.”
― Penny Reid, quote from Attraction
“It is but honest that I should acknowledge at the beginning of my recital that I was born an ordinary Woggle-Bug," began the creature, in a frank and friendly tone.”
― L. Frank Baum, quote from The Complete Oz
“I’m going to remind her why we’re perfect for each other. I’m going to show her that there’s no one else on this earth that can love her like I can.”
― Tara Sivec, quote from Fisher's Light
“When your little girl asks you if she's pretty,
your heart will drop like a wineglass on the hardwood floor.
Part of you will want to say
“Of course you are, don't ever question it,”
and the other part, the part that is clawing at you,
will want to grab her by her shoulders,
look straight into the wells of her eyes
until they echo back to you and say
“You do not have to be if you don't want to. It is not your job.”
Both will feel right.
One will feel better.
She will only understand the first.
When she wants to cut her hair off
or wear her brother's clothes,
you will feel the words in your mouth like marbles.
“You do not have to be pretty if you don't want to.
It is not your job.”
― Caitlyn Siehl, quote from What We Buried
“I remember wanting to laugh, but I held it in. I guess even then I thought laughing at someone's dream was one of the cruelest things one person could do to another.”
― Chris Colfer, quote from Struck by Lightning: The Carson Philips Journal
Castle in the Air
Meant to Be
It Happened One Wedd...
The Unwanted Wife
Storm
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