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" Our knowledge springs from two fundamental sources of our mind; the first is to receive representations (receptivity of impressions), the second is the faculty of knowing an object through these representations (spontaneity of concepts). Through the first an object is *given* to us, through the second the object is *thought* in relation to that representation (which is a mere determination of the mind). Intuition and concepts constitute, therefore, the elements of all our knowledge, so that neither concepts without an intuition in some way corresponding to them, nor intuition without concepts can yield knowledge. Both are either pure or empirical. They are empirical when they contain sensation (sensation presupposes the actual presence of the object). They are *pure* when no sensation is mixed in with the representation. Sensation may be called the matter of sensible knowledge. Pure intuition, therefore, contains only the form under which something is intuited, and the pure concepts contains only the form of thinking an object in general. Pure intuitions and pure concepts alone are possible *a priori*, empirical intuitions and empirical concepts only *a posteriori*. We call *sensibility* the *receptivity* of our mind to receive representations insofar as it is in some wise affected, while the *understanding*, on the other hand, is our faculty of producing representations by ourselves, or the *spontaneity* of knowledge. We are so constituted that our intuition can never be other than *sensible*; that is, it contains only the mode in which we are affected by objects. The faculty, on the contrary, which enables us to *think* the object of sensible intuition is the *understanding*. Neither of these properties is to be preferred to the other. Without sensibility no object would be given to us, without understanding no object would be thought. Thoughts without content are empty, intuitions without concepts are blind. It is, therefore, just as necessary to make our concepts sensible (i.e., to add the object to them in intuition) as to make our intuitions understandable (i.e., to bring them under concepts). These two faculties or capacities cannot exchange their functions. The understanding cannot intuit anything, the senses cannot think anything. Only from their union can knowledge arise. But this is no reason for confounding their respective contributions; rather, it gives us a strong reason for carefully separating and distinguishing the one from the other. We therefore distinguish the science of the rules of sensibility in general, i.e., aesthetic, from the science of the rules of the understanding in general, i.e., logic." ―Transcendental Doctrine of Elements. Transcendental Logic: The Idea of a Transcendental Logic "
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" Neel cuts in: " Where'd you grow up?" " Palo Alto," she says. From there to Stanford to Google: for a girl obsessed with the outer limits of human potential, Kat has stayed pretty close to home. Neel nods knowingly. " The suburban mind cannot comprehend the emergent complexity of a New York sidewalk." " I don't know about that," Kat says, narrowing her eyes. " I'm pretty good with complexity." " See, I know what you're thinking," Neel says, shaking his head." You're thinking it's just an agent-based simulation, and everybody out here follows a pretty simple set of rules" -- Kat is nodding--" and if you can figure out those rules, you can model it. You can simulate the street, then the neighborhood, then the whole city. Right?" " Exactly. I mean, sure, I don't know what the rules are yet, but I could experiment and figure them out, and then it would be trivial--" " Wrong," Neel says, honking like a game-show buzzer. " You can't do it. Even if you know the rules-- and by the way, there are no rules--but even if there were, you can't model it. You know why?" My best friend and my girlfriend are sparring over simulations. I can only sit back and listen. Kat frowns. " Why?" " You don't have enough memory." " Oh, come on--" " Nope. You could never hold it all in memory. No computer's big enough. Not even your what's-it-called--" " The Big Box." " That's the one. It's not big enough. This box--" Neel stretches out his hands, encompasses the sidewalk, the park, the streets beyond--" is bigger." The snaking crowd surges forward. "
