Emergent Dynamics

We know from the Reverse Law of Large Numbers (RLLN) that as the ratio of sample-size to number-of-options gets smaller, a normally balanced system becomes unbalanced.  This has very interesting implications when applied to a large system of many “adaptive” elements.

Collective Reinforcement

Ultimately all fluid-like systems will, over time, spontaneously move to equilibrium thanks to the Law of Large Numbers (LLN).  If however such a system happened to be populated with adaptive elements, then it is possible that some of these elements could start to copy each other and in so doing initiate ”Positive Feedback” within the system which would effectively weaken the LLN as a result of “Collective Behaviour”.

Positive feedback induces collective behaviour  which consequently acts to reduce the independence of the agents within the systems.  When every element’s choice of state is based, in some part, on what other elements are doing, then the independence of the elements is significantly reduced which weakens the LLN and thereby weakens the gravitational pull of system equilibrium and thereby the system ability to suppress any emergent asymmetry…

Taken to the extreme, positive feedback can cause “Collective Mutual Reinforcement” where every element within the system is effectively acting, more or less, as one.

Asymmetric Lock-in

The fact that everything is correlated to everything else however does not necessarily mean that the system will behave like a single element (which would still be able to choose between all of its available options).

In a highly correlated system, since every element chooses its state based on what everyone else is doing, then no one element will actually change its state by itself, and as a result the whole system can get “locked-in” (as every element is doing what every other element is doing).  Lock-in is basically mutual reinforcement on steroids.   Lock-in can permanently hold a system away from system equilibrium.

Positive feedback, collective mutual reinforcement and lock-in are very real phenomena; which we can see everywhere.  We see it within biology, within ecosystems, in economies, in politics and religions; mutual reinforcement and lock-in not only cause structures to emerge, but to lock themselves in…

Thus positive feedback can cause a normally symmetric system to symmetry break, pulling the system away from a bland and featureless equilibrium to a structured asymmetric order.  In Physics, Economics, Politics, and Religion, this “emergent asymmetry”, this “locked-in behavior”, is often referred to simply as “Order”…