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Our civil rights have no dependence on our religious opinions any more than our opinions in physics or geometry...
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science
geometry
opinions
physics
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Thomas Jefferson |
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You don't see something until you have the right metaphor to let you perceive it
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geometry
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James Gleick |
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A circle has no end.
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geometry
riddles
paradox
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Isaac Asimov |
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dbaedf5
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Of all the possible pathways of disorder, nature favors just a few.
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geometry
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James Gleick |
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0d223ec
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Billions of years ago there were just blobs of protoplasm; now billions of years later here we are. So information has been created and stored in our structure. In the development of one person's mind from childhood, information is clearly not just accumulated but also generated--created from connections that were not there before
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geometry
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James Gleick |
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35ade38
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"The little Hexagon meditated on this a while and then said to me; "But you have been teaching me to raise numbers to the third power: I suppose three-to-the-third must mean something in Geometry; what does it mean?" "Nothing at all," replied I, "not at least in Geometry; for Geometry has only Two Dimensions." And then I began to shew the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by three; and how a Line of three inches, moving parallel to itself through a length of three inches, makes a Square of three inches every way, which may be represented by three-to-the-second. xxx Upon this, my Grandson, again returning to his former suggestion, took me up rather suddenly and exclaimed, "Well, then, if a Point by moving three inches, makes a Line of three inches represented by three; and if a straight Line of three inches, moving parallel to itself, makes a Square of three inches every way, represented by three-to-the-second; it must be that a Square of three inches every way, moving somehow parallel to itself (but I don't see how) must make Something else (but I don't see what) of three inches every way--and this must be represented by three-to-the-third." "Go to bed," said I, a little ruffled by this interruption: "if you would talk less nonsense, you would remember more sense."
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dimensions
squared
geometry
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Edwin A. Abbott |
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57eb267
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the brain does not own any direct copies of stuff in the world. There is no library of forms and ideas against which to compare the images of perception. Information is stored in a plastic way, allowing fantastic juxtapositions and leaps of imagination. Some chaos exists out there, and the brain seems to have more flexibility than classical physics in finding the order in it.
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geometry
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James Gleick |
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38a32aa
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Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world.
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geometry
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James Gleick |
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0f49cea
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it struck me as an operational way to define free will, in a way that allowed you to reconcile free will with determinism. The system is deterministic, but you can't say what it's going to do next.
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geometry
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James Gleick |
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9ffb63e
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IN THE MIND'S EYE, a fractal is a way of seeing infinity.
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geometry
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James Gleick |
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b4c28c0
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The fractal structure nature has devised works so efficiently that, in most tissue, no cell is ever more than three or four cells away from a blood vessel. Yet the vessels and blood take up little space, no more than about five percent of the body.
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geometry
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James Gleick |
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ebf3e96
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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.
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geometry
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James Gleick |
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4202913
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The only things that can ever be universal, in a sense, are scaling things.
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geometry
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James Gleick |
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141a371
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The early sense of self-similarity as an organizing principle came from the limitations on the human experience of scale.
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geometry
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James Gleick |
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4510fe6
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One simple but powerful consequence of the fractal geometry of surfaces is that surfaces in contact do not touch everywhere. The bumpiness at all scales prevents that. Even in rock under enormous pressure, at some sufficiently small scale it becomes clear that gaps remain, allowing fluid to flow.
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geometry
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James Gleick |