"[Number theory] produces, without effort, innumerable problems which have a sweet, innocent air about them, tempting flowers; and yet […] number theory swarms with bugs, waiting to bite the tempted flower-lovers who, once bitten, are inspired to excesses of effort!" (Barry Mazur, "Number Theory as Gadfly", The American Mathematical Monthly, Volume 98, 1991)
"A network swarm is all edges and therefore open ended any way you come at it. Indeed, the network is the least structured organization that can be said to have any structure at all. It is capable of infinite rearrangements, and of growing in any direction without altering the basic shape of the thing, which is really no outward shape at all. " (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)
"At the other far extreme, we find many systems ordered as a patchwork of parallel operations, very much as in the neural network of a brain or in a colony of ants. Action in these systems proceeds in a messy cascade of interdependent events. Instead of the discrete ticks of cause and effect that run a clock, a thousand clock springs try to simultaneously run a parallel system. Since there is no chain of command, the particular action of any single spring diffuses into the whole, making it easier for the sum of the whole to overwhelm the parts of the whole. What emerges from the collective is not a series of critical individual actions but a multitude of simultaneous actions whose collective pattern is far more important. This is the swarm model." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)
"Because they are redundant and have no central control, swarm systems are inefficient. Resources are allotted higgledy-piggledy, and duplication of effort is always rampant." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)
"It is the great irony of life that a mindless act repeated in sequence can only lead to greater depths of absurdity, while a mindless act performed in parallel by a swarm of individuals can, under the proper conditions, lead to all that we find interesting." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)
"Light a fire, build up the steam, turn on a switch, and a linear system awakens. It’s ready to serve you. If it stalls, restart it. Simple collective systems can be awakened simply. But complex swarm systems with rich hierarchies take time to boot up. The more complex, the longer it takes to warm up. Each hierarchical layer has to settle down; lateral causes have to slosh around and come to rest; a million autonomous agents have to acquaint themselves. I think this will be the hardest lesson for humans to learn: that organic complexity will entail organic time." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)
"It is, however, fair to say that very few applications of swarm intelligence have been developed. One of the main reasons for this relative lack of success resides in the fact that swarm-intelligent systems are hard to 'program', because the paths to problem solving are not predefined but emergent in these systems and result from interactions among individuals and between individuals and their environment as much as from the behaviors of the individuals themselves. Therefore, using a swarm-intelligent system to solve a problem requires a thorough knowledge not only of what individual behaviors must be implemented but also of what interactions are needed to produce such or such global behavior." (Eric Bonabeau et al, "Swarm Intelligence: From Natural to Artificial Systems", 1999)
"[…] when software systems become so intractable that they can no longer be controlled, swarm intelligence offers an alternative way of designing an ‘intelligent’ systems, in which autonomy, emergence, and distributed functioning replace control, preprogramming, and centralization." (Eric Bonabeau et al, "Swarm Intelligence: From Natural to Artificial Systems", 1999)
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