How would communities develop? It looks like fractals development on an ongoing basis.
Keith says in his post:
In the explainer, Michael quotes Benoit Mandelbrot “Bottomless wonders spring from simple rules which are repeated without end“. It seems to me that open education has this potential. Like fractals I do think open courses are scalable.
Is openness spreading like fractals?
I am re-posting part of them here:
Let me put all these into a social context.
(a) Social interaction
When a person A interacts with a person B, within a social media (e.g. a blog, Twitter, Facebook, or Quora), which is denoted by c, then the emergent learning (or knowledge) that may result from such interaction is
z = z*2 + c
The development of this fractal into different fractal patterns would depend on (a) the z (ideas, information, knowledge) themselves
(b) the boundary conditions (and the ecology)
(c) how the interaction occurs
This concept could be applied to the interaction in case of communication between two persons, or interaction between an actor (a person) with a non human actor (could be an animal, a machine, a media, an artifact) or a network.
The product of such interaction would be emergent and its development is also based on the initial boundary condition.
So, the synergy emerging out of an interaction of actors (in networks) is greater than the sum of its parts mainly because z*2 +c = (a+bi)(a+bi) +c= a*2 + 2abi – b*2 +c is normally greater than a*2. and so “network” collaboration or cooperation would likely generate more ideas than those coming from individuals.
However, using the above formula, there may also be noises involved in the interaction, which may be denoted by c being a negative value. So if the noise – c value is big enough, then the resultant value of z*2 +c could be less than z*2 meaning that there could be a loss of synergy. This also explains why conflicts (which may be denoted by c) could often hinder or even lessen the resultant synergy out of the interaction. This explains why some ideas are amplified, resonated, and other ideas being dampened.
Further explanation about how these ideas are resonated, developed are explained here.
The above could also be used to explain the formation, development of networks, Networks, ecology under Connectivism, and that of Actor Network Theory and Community of Practice, all based on the Fractals.
Openness could be an important feature of network formation and development, and as illustrated above, would be exhibited like fractals, when examined under a community framework.
Openness in education is still at an early stage of fractal formation, as exemplified in the cMOOCs and xMOOCs, though it is still limited due to various constraints. Openness is the catalyst that would foster fractal multiplication – in ideas, pedagogy, community and ideology.