On Aug 23, 1:13 pm, John Larkin
highNOTlandTHIStechnologyPART.com> wrote:

The way you describe the problem made me think of "counter-intuitive
network logic" but the feedback stuff has probably more to do with
Sensitive Dependence on Initial Conditions...

Sensitive Dependence on Initial Conditions
http://www.schuelers.com/ChaosPsyche/part_1_14.htm
http://en.wikipedia.org/wiki/Butterfly_effect
http://everything2.com/index.pl?node_id=861246
http://www.perkel.com/nerd/butterflyeffect.htm

Network logic is counterintuitive. Say you need to lay a telephone
cable that will connect a bunch of cities; let's make that three for
illustration: Kansas City, San Diego, and Seattle. The total length of
the lines connecting those three cities is 3,000 miles. Common sense
says that if you add a fourth city to your telephone network, the
total length of your cable will have to increase. But that's not how
network logic works. By adding a fourth city as a hub (let's make that
Salt Lake City) and running the lines from each of the three cities
through Salt Lake City, we can decrease the total mileage of cable to
2,850 or 5 percent less than the original 3,000 miles. Therefore the
total unraveled length of a network can be shortened by adding nodes
to it! Yet there is a limit to this effect. Frank Hwang and Ding Zhu
Du, working at Bell Laboratories in 1990, proved that the best savings
a system might enjoy from introducing new points into a network would
peak at about 13 percent. More is different.

On the other hand, in 1968 Dietrich Braess, a German operations
researcher, discovered that adding routes to an already congested
network will only slow it down. Now called Braess's Paradox,
scientists have found many examples of how adding capacity to a
crowded network reduces its overall production. In the late 1960s the
city planners of Stuttgart tried to ease downtown traffic by adding a
street. When they did, traffic got worse; then they blocked it off and
traffic improved. In 1992, New York City closed congested 42nd Street
on Earth Day, fearing the worst, but traffic actually improved that
day.

Then again, in 1990, three scientists working on networks of brain
neurons reported that increasing the gain-the responsivity-of
individual neurons did not increase their individual signal detection
performance, but it did increase the performance of the whole network
to detect signals.

http://www.kk.org/outofcontrol/ch2-g.html

The prime variable Kauffman played with was the connectivity of the
network. In a sparsely connected network, each node would on average
only connect to one other node, or less. In a richly connected
network, each node would link to ten or a hundred or a thousand or a
million other nodes. In theory the limit to the number of connections
per node is simply the total number of nodes, minus one. A million-
headed network could have a million-minus-one connections at each
node; every node is connected to every other node. To continue our
rough analogy, every employee of GM could be directly linked to all
749,999 other employees of GM.

As Kauffman varied this connectivity parameter in his generic
networks, he discovered something that would not surprise the CEO of
GM. A system where few agents influenced other agents was not very
adaptable. The soup of connections was too thin to transmit an
innovation. The system would fail to evolve. As Kauffman increased the
average number of links between nodes, the system became more
resilient, "bouncing back" when perturbed. The system could maintain
stability while the environment changed. It would evolve. The
completely unexpected finding was that beyond a certain level of
linking density, continued connectivity would only decrease the
adaptability of the system as a whole.

Kauffman graphed this effect as a hill. The top of the hill was
optimal flexibility to change. One low side of the hill was a sparsely
connected system: flat-footed and stagnant. The other low side was an
overly connected system: a frozen grid-lock of a thousand mutual
pulls. So many conflicting influences came to bear on one node that
whole sections of the system sank into rigid paralysis. Kauffman
called this second extreme a "complexity catastrophe." Much to
everyone's surprise, you could have too much connectivity. In the long
run, an overly linked system was as debilitating as a mob of
uncoordinated loners.

Somewhere in the middle was a peak of just-right connectivity that
gave the network its maximal nimbleness. Kauffman found this
measurable "Goldilocks'" point in his model networks. His colleagues
had trouble believing his maximal value at first because it seemed
counterintuitive at the time. The optimal connectivity for the
distilled systems Kauffman studied was very low, "somewhere in the
single digits." Large networks with thousands of members adapted best
with less than ten connections per member. Some nets peaked at less
than two connections on average per node! A massively parallel system
did not need to be heavily connected in order to adapt. Minimal
average connection, done widely, was enough.

Kauffman's second unexpected finding was that this low optimal value
didn't seem to fluctuate much, no matter how many members comprised a
specific network. In other words, as more members were added to the
network, it didn't pay (in terms of systemwide adaptability) to
increase the number of links to each node. To evolve most rapidly, add
members but don't increase average link rates. This result confirmed
what Craig Reynolds had found in his synthetic flocks: you could load
a flock up with more and more members without having to reconfigure
its structure.

Kauffman found that at the low end, with less than two connections per
agent or organism, the whole system wasn't nimble enough to keep up
with change. If the community of agents lacked sufficient internal
communication, it could not solve a problem as a group. More exactly,
they fell into isolated patches of cooperative feedback but didn't
interact with each other.

At the ideal number of connections, the ideal amount of information
flowed between agents, and the system as a whole found the optimal
solutions consistently. If their environment was changing rapidly,
this meant that the network remained stable-persisting as a whole over
time.

Kauffman's Law states that above a certain point, increasing the
richness of connections between agents freezes adaptation. Nothing
gets done because too many actions hinge on too many other
contradictory actions. In the landscape metaphor, ultra-connectance
produces ultra-ruggedness, making any move a likely fall off a peak of
adaptation into a valley of nonadaptation. Another way of putting it,
too many agents have a say in each other's work, and bureaucratic
rigor mortis sets in. Adaptability conks out into grid-lock. For a
contemporary culture primed to the virtues of connecting up, this low
ceiling of connectivity comes as unexpected news.

We postmodern communication addicts might want to pay attention to
this. In our networked society we are pumping up both the total number
of people connected (in 1993, the global network of networks was
expanding at the rate of 15 percent additional users per month!), and
the number of people and places to whom each member is connected.
Faxes, phones, direct junk mail, and large cross-referenced data bases
in business and government in effect increase the number of links
between each person. Neither expansion particularly increases the
adaptability of our system (society) as a whole.

http://www.kk.org/outofcontrol/ch20-d.html