Subject: Re: near/medium future digital media economics
From: Thomas Lord <lord@emf.net>
Date: Wed, 24 May 2006 10:16:57 -0700

I think Ben wins, but not for the reasons he gives.

On the topic of evaluating a network in terms of the value of
personal connections: I could use some math/analysis help.

I notice that all of my phone services (at the moment) charge
two distinct fees: toll charges for connections made and a basic
service fee for membership in the network.  (Things like VOIP
may throw things over towards nothing but the basic service fee
--- see below).

I think the toll fee value of this network clearly grows N log N
*up until* we reach the human capacity limit for connection
after which the toll fee value grows just linearly with N.
(And, in history, aren't we getting at least pretty close to
that point?)  Meanwhile, the cost of toll service falls in
Moore-ish ways thanks to technology improvements.

What about that basic service fee?  Is it Metcalfian?  N log N?
Linear?  What?

It's a little bit hard to tell from prices because the cost of
networks keeps crashing, what with Moore and Moore-like
phenomenon and even lesser-order but significant effects.  I'm
wondering, if we adjust for those technology changes, what the
basic service fee prices look like in history.

I notice that telephony providers keep moving closer and closer
to nothing but the basic service fee ("hello VOIP").  That is
consistent with toll fees (personal connection fees) maxing out
to linear growth in value while marginal cost of prodution is
super-linearly crashing thanks to technology/infrastructure
build-up in a competitive provider environment.

What with competition, and efficient markets, seemingly robust
and universal demand, and yadda yadda, the price of basic
service is going to converge on the marginal cost of production
of a new endpoint.

What we need, therefore, is a robust lower bound on the cost of
a network that connects N users consuming their human-capacity
upper-bound of connectivity.

There's a search problem involved in such a network.  I've
dialed a number -- you find the route to complete my call.  To
be able to solve that search problem in log N, there's a sort
problem involved: N log N.

And, finally, there's a wiring problem involved.  "If we all
went to the same New York deli on the same night and ordered
blintzes, there'd be chaos" [W. Allen] but there are
slashdot-like effects (e.g,. New York phones immediately after
the 9/11 incidents).  I'm a softy on the graph theory to be able
to answer the wiring question off the top of my head but I'll
confidently conjecture N log N.

I think Ben might be right about N log N for phones and the
internet and such -- but I think a better way to see this both a
priori and empirically is to look at the cost of the network and
how it relates to price (all in the context of seemingly maximal
demand -- to the limit of human capacity).

I originally started off arguing that persistence -- an
accumulation of edits -- could make a hypertext-qua-network
Metcalfe-ian.  I have to think about that some more.  Perhaps
it's N log^2 N or some such.  Makes no nevermind to Stephen, of
course.

-t