"It has long been appreciated by science that large numbers behave differently than small numbers. Mobs breed a requisite measure of complexity for emergent entities. The total number of possible interactions between two or more members accumulates exponentially as the number of members increases. At a high level of connectivity, and a high number of members, the dynamics of mobs takes hold. " (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)
"Mathematics says the sum value of a network increases as the square of the number of members. In other words, as the number of nodes in a network increases arithmetically, the value of the network increases exponentially. Adding a few more members can dramatically increase the value of the network." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)
"Small changes in the initial conditions in a chaotic system produce dramatically different evolutionary histories. It is because of this sensitivity to initial conditions that chaotic systems are inherently unpredictable. To predict a future state of a system, one has to be able to rely on numerical calculations and initial measurements of the state variables. Yet slight errors in measurement combined with extremely small computational errors (from roundoff or truncation) make prediction impossible from a practical perspective. Moreover, small initial errors in prediction grow exponentially in chaotic systems as the trajectories evolve. Thus, theoretically, prediction may be possible with some chaotic processes if one is interested only in the movement between two relatively close points on a trajectory. When longer time intervals are involved, the situation becomes hopeless." (Courtney Brown, "Chaos and Catastrophe Theories", 1995)
"Swarm systems generate novelty for three reasons: (1) They are 'sensitive to initial conditions' - a scientific shorthand for saying that the size of the effect is not proportional to the size of the cause - so they can make a surprising mountain out of a molehill. (2) They hide countless novel possibilities in the exponential combinations of many interlinked individuals. (3) They don’t reckon individuals, so therefore individual variation and imperfection can be allowed. In swarm systems with heritability, individual variation and imperfection will lead to perpetual novelty, or what we call evolution." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)
"The change from atoms to bits is irrevocable and unstoppable. Why now? Because the change is also exponential - small differences of yesterday can have suddenly shocking consequences tomorrow." (Nicholas Negroponte, "Being Digital", 1995)
"One of the main reasons that large numbers grow so explosively is that multiplication is a powerful engine for growth - even when the only number you happen to be multiplying is insignificantly puny, like the number two." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)
"It is in the nature of exponential growth that events develop extremely slowly for extremely long periods of time, but as one glides through the knee of the curve, events erupt at an increasingly furious pace. And that is what we will experience as we enter the twenty-first century." (Ray Kurzweil, "The Age of Spiritual Machines: When Computers Exceed Human Intelligence", 1999)
"The Law of Accelerating Returns: As order exponentially increases, time exponentially speeds up (that is, the time interval between salient events grows shorter as time passes)." (Ray Kurzweil, "The Age of Spiritual Machines: When Computers Exceed Human Intelligence", 1999)
"The Law of Accelerating Returns applies equally to the evolutionary process of computation, which inherently will grow exponentially and essentially without limit. The two resources it needs - the growing order of the evolving technology itself and the chaos from which an evolutionary process draws its options for further diversity - are unbounded. Ultimately, the innovation needed for further turns of the screw will come from the machines themselves." (Ray Kurzweil, "The Age of Spiritual Machines: When Computers Exceed Human Intelligence", 1999)
No comments:
Post a Comment