[iDC] Notworking online collaboration in science and education

[Stephen Downes]

John Hopkins wrote:

> You cannot have a truly distributed creative system without there
> being open channels between (all) nodes. 
I don't think this is true.

Imagine an idealized communications system, where links were created 
directly from person to person. If all channels were open at any given 
time, we would be communicating simultaneously with 6 billion people. We 
do not have the capacity to process this communication, so it has the 
net effect of being nothing but noise and static. Call this the 
congestion problem.

This point was first made to me by Francisco Valera in a talk at the 
University of Alberta Hospital in 1987 or so. He was describing the 
connectivity between elements of the immune system, and showed that most 
effective communication between nodes was obtained at less than maximal 
connection, a mid-way point between zero connectivity and total 
connectivity. Similarly, in human perception, we find that neurons are 
connected, not to every other neuron, but to a subset of neurons.

What this tells me is that what defines a "truly distributed creative 
system" is not the number of open channels (with 'all' being best) but 
rather the structure or configuration of those channels. And in this 
light, I contend that there are two major models to choose from:

- egalitarian configurations - each node has the same number of 
connections to other nodes
- inegalitarian configurations - nodes have unequal numbers of 
connections to other nodes

Now the 'scale free' networks described by Clay Shirky are inegalitarian 
configurations. The evidence of this is the 'power law' diagram that 
graphs the number of connections per member against the number of 
members having this number of connections. Very few members have a high 
number of connections, while very many members have a low number of 
connections - this is the 'long tail' described by Anderson.

The networks are scale free because, theoretically, there is no limit to 
the number of connections a member could have (a status Google appears 
to have achieved on the internet). [*] Other inegalitarian networks have 
practical limits imposed on them. The network of connections between 
airports, for example, is an inegalitarian configuration. Chicago is 
connected to many more places than Moncton. But the laws of physics 
impose a scale on this network. Chicago cannot handle a million times 
more connections than Moncton, because airplanes take up a certain 
amount of space, and no airport could handle a million aircraft. This is 
another example of the congestion problem.

What distinguishes the inegalitarian system from the inegalitarian 
system is its the number of 'hops' through connections required to 
travel from any given one member to another (this can be expressed as an 
average of all possible hops in the network). In a fully inegalitarian 
system, the maximum number of hops is '2' - from one member, who has one 
connection, to the central node, which is connected to every other node, 
to the target node. In a fully egalitarian system, the maximum number of 
hops can be much higher (this, again, is sensitive to configuration).

As the discussion above should have made clear, it should be apparent 
that fully inegalitarian systems suffer as much from congestion as fully 
connected systems, however, this congestion is suffered in only one 
node, the central node. No human, for example, could be the central node 
of communication for 6 billion people. This means that, while the number 
of hops to get from one point to another may be low, the probability of 
the message actually being communicated is also low. In effect, what 
happens is that the inegalitarian system becomes a 'broadcast' system - 
very few messages are actually sent, and they are received by everyone 
in one hop.

In other words - maximal connectivity can result in the *opposite* of a 
truly distributed creative system. It can result in a maximally 
centralized system.

I'm sure there's a reference from critical theory or media theory, but 
what would to me define a truly distributed creative system is 'voice' 
(sometimes called 'reach'). This could be understood in different ways: 
the number of people a person communicates with, the average number of 
people each person communicates with, the minimum number, etc. My own 
approach to 'voice' is to define it in terms of 'capacity'. In short, 
any message by any person /could/ be received by all other people in the 
network. But it is also defined by control. In short, no message by any 
person is /necessarily/ received by all other people in the network.

One way to talk about this is to talk about the entities in the network. 
When you look at Watt and Barabasi, they talk about the probability that 
a message will be forwarded from one node to the next. This, obviously, 
is a property of both the message and the node. Suppose, for example, 
that the message is the ebola virus, and that the node is a human being. 
The virus is very contagious. If contracted to one person, it has a very 
high probability of being passed on to the next. But suppose the person 
is resistant. Then he or she won't contract the virus, and thus, has a 
very low probability of passing it on.

The other way to talk about this is to talk about the structure of the 
network. The probability of the virus being passed on increases with the 
number of connections. This means that in some circumstances - for 
example, a person with many friends - the probability of the virus being 
passed on is virtually certain. So in some network configurations, there 
is no way to stop a virus from sweeping through the membership. These 
networks are, specifically, networks that are highly inegalitarian - 
broadcast networks. Because the virus spreads so rapidly, there is no 
way to limit the spread of the message, either by quarantine (reducing 
the number of connections per carrier) or inoculation (increasing the 
resistance to the message).

In order to create the truly distributed creative system, therefore, you 
need to:

- limit the number of connections for any given node. This limit would 
be based on what might be thought of as the 'receptor capacity' of any 
given node, that is, the maximum number of messages it can receive 
without congestion, which in turn is, the maximum number of messages it 
can receive where each message has a non-zero chance of changing the 
state of the receptor node.

- maximize the number of connections, up to the limit, for any given 
node. This might be thought of as maximizing the voice of individual 
nodes. What this does is to give any message from any given node a good 
start - it has a high probability of propagating at least one step 
beyond its originator. It cannot progress too fast - because of the 
limit to the number of connections - but within that limit, it 
progresses as fast as it can.

- within these constraints, maximize the efficiency of the network - 
that is (assuming no congestion) to minimize the average number of hops 
required for a network to propagate to any other point in the network.

These conditions combine to give a message the best chance possible of 
permeating the entire network, and the network the best chance possible 
of blocking undesirable messages. For any given message, the greatest 
number of people possible are in a position to offer a countervailing 
message, and the network is permeable enough to allow the countervailing 
message the same chance of being propagated.

What sort of network does that look like? I have already argued that it 
is not a broadcast network. Let me take that one step further and argue 
that it is not a 'hub and spokes' network. Such networks are biased 
toward limiting the number of hops - at the expense of voice, and with 
the risk of congestion. That's why, in hub and spoke networks, the 
central networks become 'supernodes', capable of handling many more 
connections than individual nodes. But this increase in capacity comes 
with a trade-off - an increase in congestion. This becomes most evident 
when the supernode attempts to acquire a voice. A centralized node that 
does nothing but reroute messages may handle many messages efficiently, 
but then the same node is used to read those messages and (say) filter 
them for content, congestion quickly occurs, with a dramatic decrease in 
the node's capacity.

Rather, the sort of network that results is what may be called a 
'community of communities' model. Nodes are highly connected in 
clusters. A cluster is defined simply as a set of nodes with multiple 
mutual connections. Nodes also connect - on a less frequent basis - to 
nodes outside the cluster. Indeed (to take this a step further) nodes 
typically belong to multiple clusters. They may be more or less 
connected to some clusters. The propagation of a message is essentially 
the propagation of the message from one community to the next. The 
number of steps is low - but for a message to pass from one step to the 
next, it needs to be 'approved' by a large number of nodes.

When we look at things like Wenger's communities of practice, we see, in 
part, the description of this sort of network. Rather than the 
school-and-teacher model of professional development (which is a hub and 
spokes model) the community of practice maximalizes the voice of each of 
its members. It can be called a cluster around a certain topic or area 
of interest, but the topic or area of interest does not /define/ the 
community, it is rather an empirical description of the community (and 
thus, for example, we see people who came together as a hockey team in 
1980 continue to be drinking buddies in 1990 and go on to form an 
investment club in 2000).

Maximally distributed creativity isn't about opening the channels of 
communication, at least, not directly. It is about each person having 
the potential to be a member of a receptive community, where there is a 
great deal of interactivity among the members of that community, and 
where the community, in turn, is a member of a wider community of 
communities. Each person thus is always heard by some, has the potential 
to be heard by all, and plays a role not only in the creation of new 
ideas, but also, as part of the community, in the evaluation and passing 
on of others' ideas.

==

[*] I just want to amend slightly.

I wrote: "The networks are scale free because, theoretically, there is 
no limit to the number of connections a member could have..."

This should not be confused with the /definition/ of a 'scale free 
network', which is specifically, that "a network that is scale-free will 
have the same properties no matter what the number of its nodes is."

But the relationship between my statement and the more formal definition 
should be clear. If there is a limit to the number of connections 
created by the physical properties of the nodes, then the mathematical 
formula that describes one instance of the network (a small instance) 
cannot be used to describe all instances of the same type of network.



-- Stephen

---
Stephen Downes  ~  Research Officer  ~  National Research Council Canada
http://www.downes.ca  ~  stephen at downes.ca         __\|/__ Free Learning


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