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“Dividing one number by another is mere computation ; knowing what to divide by what is mathematics.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Thirty years ago, we used to ask: Can a computer simulate all processes of logic? The answer was yes, but the question was surely wrong. We should have asked: Can logic simulate all sequences of cause and effect? And the answer would have been no.”
― Gregory Bateson, Mind and Nature: A Necessary Unity

“It's always seemed like a big mystery how nature, seemingly so effortlessly, manages to produce so much that seems to us so complex. Well, I think we found its secret. It's just sampling what's out there in the computational universe.”
― Stephen Wolfram

“We're presently in the midst of a third intellectual revolution. The first came with Newton: the planets obey physical laws. The second came with Darwin: biology obeys genetic laws. In today’s third revolution, were coming to realize that even minds and societies emerge from interacting laws that can be regarded as computations. Everything is a computation.”
― Rudy Rucker

“Theory is relevant to you because it shows you a new, simpler, and more elegant side of computers, which we normally consider to be complicated machines. The best computer designs and applications are conceived with elegance in mind. A theoretical course can heighten your aesthetic sense and help you build more beautiful systems.”
― Michael Sipser, Introduction to the Theory of Computation

“The reason [James Clerk] Maxwell's Demon cannot exist is that it does take resources to perform an act of discrimination. We imagine computation is free, but it never is. The very act of choosing which particle is cold or hot itself becomes an energy drain and a source of waste heat. The principle is also known as "no free lunch."
We do our best to implement Maxwell's Demon whenever we manipulate reality with our technologies, but we can never do so perfectly; we certainly can't get ahead of the game, which is known as entropy. All the air conditioners in a city emit heat that makes the city hotter overall. While you can implement what seems to be a Maxwell's Demon if you don't look too far or too closely, in the big picture you always lose more than you gain.
Every bit in a computer is a wannabe Maxwell's Demon, separating the state of "one" from the state of "zero" for a while, at a cost. A computer on a network can also act like a wannabe demon if it tries to sort data from networked people into one or the other side of some imaginary door, while pretending there is no cost or risk involved.”
― Jaron Lanier, Who Owns the Future?

“Often people think of developments in computation as arising when we make our computers more blazingly fast, so they can compute more stuff, bigger data. It's actually just as important to prune away big parts of the data that aren't relevant to the problem at hand! The fastest computation is the one you don't do.”
― Jordan Ellenberg, Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and EverythingElse

“In the future, an executive will be supported by an abundance of computation power and powerful AI.”
― Jorn Lyseggen, Outside Insight: Navigating a World Drowning in External Data

“Computation is not the same as thought and emulation is not the same as imagination.”
― Abhijit Naskar, Mission Reality

“If you understand McCarthy's eval, you understand more than just a stage in the history of languages. These ideas are still the semantic core of Lisp today. So studying McCarthy's original paper shows us, in a sense, what Lisp really is. It's not something that McCarthy designed so much as something he discovered. It's not intrinsically a language for AI or for rapid prototyping, or any other task at that level. It's what you get (or one thing you get) when you try to axiomatize computation.”
― Paul Graham

“It is now plausible at the molecular level to conceive of concerted, non-random changes in the genome guided by cellular computing networks during episodes of evolutionary change. Thus, just as the genome has come to be seen as a highly sophisticated information storage system, its evolution has become a matter of highly sophisticated information processing.”
― Laura F. Landweber, Evolution as Computation