Owen wrote:
> Its all about beyond Metcalf's value of the network being n^2,
> bringing in the power set of subgroups networks can form, thus
> valuing the network as 2^n.
>
For years I have been (falsely) asserting that groups of N have N!
subgroups...
I even started to assert that here but decided to "do the math" and sure
enough
got Reed's Law instead..
I had always imagined that the upper bound of complexity of "small groups"
was even more extreme than it turns out to be. I also attributed this
complexity
a negative effect as much as positive ones... the "tower of babel"
effect of too
many entities (each subgroup having a personality/life of it's own)
unable to
align with any other subgroup. This was naturally a pessimists view.
The only thing I have to contribute (other than an exposure of my own
mistaken
impressions) is that this is an *upper bound* on the "utility". It
seems to me
that the utility function is really a weighted sum of the subgroups.
For example
the trivial N groups of 1 and the 1 group of N might be weighted at 0
as Reed's
Law specifically acknowledges.
I contend that depending on the purpose, the utility of the N groups of
size
N-1 is pretty small for most large values of N. The semantics of these
groups
are essentially "the utility of a group when a single individual is
missing". As
a simple thought experiment... what is the "utility" of FRIAM with any one
of many missing?
Similarly the utility of many pairwise groups is close to zero. While I
might
establish a meaningful conversation with anyone on FRIAM, there are only
perhaps a dozen with whom I do enjoy such conversations... triads are
similarly
scarce... perhaps 3-5 groups of 3 and 2-3 groups of 4 or 5.
My intuition is that Reed's Law is informed by the CogSci 7+-2 number. That
only groups of 9 (or perhaps 7 or even 5) or less should be considered
to have
any significant utility. N choose 9 or 7 or 5 might be the better
estimate of
the utility of a fully networked group (everyone in the same physical space
able to factionate at will, or on an e-mail list, using a wiki, etc.)
N!/(R! * (N-R)!)
For N=100 and R=9 we get numbers like 100!(9! * 91!) or
~100^9/50,000 or about 2,000,000
N=100 and R=5 we get 100^5/125 or about 100,000.
These are much smaller than 2^100 or ~10^30 but still
pretty darn huge numbers. Applying 7+-2 again,
we might imagine that nobody can really participate in
more than this many subgroups effectively... even 5 might
be a bit much. So now, we no longer have N choose 5 or 9,
we have N*5 or N*9. When N=100, we have 500 or 900...
Strogatz, et. al. might have some opinions about these numbers
and in fact would probably bring up the term "power law". If
it weren't already a bit late for me, I might try to wing this one
too. Perhaps there are a few folks (Guerin comes to mind) who
might "know" the entire FRIAM list and thereby enjoy some
measureable utility with the full N-group, or participate in order
N-1 groups of 2. And many (the lurkers) on the list might tend
toward 0 subgroup participation. The rest of us fall somewhere
in between... governed probably by the N*5 rule of thumb.
One other point... Ropella seems to want to dismiss the value of
technologically
mediated social networks completely (merely as a devil's advocate?).
My experience
is that "simple" e-mail is "proof by example" of the utility of
technological mediation.
This comes from several features.
1) Space
I can communicate with people distributed over virtually any
geographic region
without waiting for them to come to the same location as I.
2) Time
I needn't wait for anyone else to be in the mood to talk to me to
talk to them.
I an yack at them at my own convenience and they can read my yack at
theirs
and respond at their own convenience.
3) Persistent record
Most of us have kept our own e-mail archives and certainly lists
like this one
provide an archive of a discussion for later reference.
4) Multiplicity.
It is as easy to write to a dozen or a gross as it is to an
individual. Mail lists
help to organize that multiplicity.
5) Efficient subgrouping
This is the most on-topic. At any time I can send an e-mail to any
chosen
subgroup of FRIAM (up to my knowledge of the full list and my patience
with addressing the To: or CC: line . Spinoff discussions can focus
down
to smaller groups, or perhaps exclude disruptive or otherwise negative
elements.
I don't believe the Utility of FRIAM is order 2^N (Reed's) and I'm not
sure it even
exceeds N^2 (Metcalfe's) but I'm fairly sure it's utility exceeds N ...
and might
approach 5N or something like that.
Hmmm... time for some shut-eye.
> Stephen has the insight that Reed's Law is quite important and
> explains the web 2.0 explosion and a will be a/the major component of
> a web 3.0 future.
>
> Nice to see its now pretty fully on the radar.
>
> -- Owen
>
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
