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1 " However, questions arise. Are there people who aren't naive realists, or special situations in which naive realism disappears? My theory—the self-model theory of subjectivity—predicts that as soon as a conscious representation becomes opaque (that is, as soon as we experience it as a representation), we lose naive realism. Consciousness without naive realism does exist. This happens whenever, with the help of other, second-order representations, we become aware of the construction process—of all the ambiguities and dynamical stages preceding the stable state that emerges at the end. When the window is dirty or cracked, we immediately realize that conscious perception is only an interface, and we become aware of the medium itself. We doubt that our sensory organs are working properly. We doubt the existence of whatever it is we are seeing or feeling, and we realize that the medium itself is fallible. In short, if the book in your hands lost its transparency, you would experience it as a state of your mind rather than as an element of the outside world. You would immediately doubt its independent existence. It would be more like a book-thought than a book-perception. Precisely this happens in various situations—for example, In visual hallucinations during which the patient is aware of hallucinating, or in ordinary optical illusions when we suddenly become aware that we are not in immediate contact with reality. Normally, such experiences make us think something is wrong with our eyes. If you could consciously experience earlier processing stages of the representation of the book In your hands, the image would probably become unstable and ambiguous; it would start to breathe and move slightly. Its surface would become iridescent, shining in different colors at the same time. Immediately you would ask yourself whether this could be a dream, whether there was something wrong with your eyes, whether someone had mixed a potent hallucinogen into your drink. A segment of the wall of the Ego Tunnel would have lost its transparency, and the self-constructed nature of the overall flow of experience would dawn on you. In a nonconceptual and entirely nontheoretical way, you would suddenly gain a deeper understanding of the fact that this world, at this very moment, only appears to you. "
2 " the pattern appears so ethereally, that it is hard to remember that the shape is an attractor. It is not just any trajectory of a dynamical system. It is the trajectory toward which all other trajectories converge. "
― James Gleick , Chaos: Making a New Science
3 " There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula. "
― George Boole
4 " If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos. "