Hierarchy, Force Monopoly, and Geodesic Societies

[Jim Dixon]

On Sat, 10 Apr 2004, Eugen Leitl wrote:

> > Yes.  I know what a tree is, and I am quite familiar with structure of
> > the Internet.  These very pretty pictures certainly look like the Internet
> > I am familiar with, but don't resemble trees.
>
> There's a continuum between a tree and a high-dimensional grid/mesh/lattice.

A "tree" as the term is used in mathematics and computer science has a
single root.  A continuum has an infinite number of points in it.  A grid
... none of these terms has anything much to do with one another.

> > It isn't a minor point that the Internet is fractal.  This is in fact
> > what is consistent everywhere and has been, to the best of my knowledge,
> > throughout the history of the Internet.  If you go back to your pretty
> > pictures and look, you will see fractal structures.
>
> Dude, hypergrids *are* fractal. Not that it has to do anything with the
> current topology.

I don't know why you introduce hypergrids.  But you might consult a
mathematical dictionary - the term seems irrelevant to the current
discussion.

> > A geodesic is a minimal path in whatever geometry you are talking about.
>
> The geometry on Earth surface is anything but whatever. Way above, with nodes
> in mutual plain view, it's plain old Einstein-Minkowski (basically Euclidian,
> with relativistic corrections).

"The geometry on Earth surface is anything but whatever"?  Sorry,
this makes no sense.  However, a geodesic remains a path of minimal
length in the geometry under consideration.  Or so it was when I last
did some reading in finite dimensional metric spaces.

> I'm claiming peering arrangement evolve to make optimal use of given physical
> cabling. This is quick.

As the term is normally used, "peering" is the settlement-free exchange of
trafic between autonomous systems (ASNs). "Settlement-free" means that no
consideration ($$$) is paid.  This has bugger all to do with cabling.

> On the longer term, physical and virtual (radio, laser) cabling evolves to
> minimize the load on existing links. This is slower, peering arrangements
> change in realtime in comparison, very like Franck-Condon principle.

Peering arrangements generally involve legal departments, and rarely
change once inked.

In the real world, peering policies normally reflect a mixture of common
sense and total misunderstanding of what the Internet is about.  Some
networks just peer with anyone; some have incredibly detailed contracts
and involve months of negotiation.

When senior management is involved, they quite often have a telco
background, and think that peering has something to do with SS7. That is,
they try to insist that the Internet is really just the same as the voice
telephone network, and BGP4 is SS7.  The results are often comic.

> > The end result is that most UK Internet traffic, and a large part of
> > European traffic, passes through what used to be a more or less derelict
> > area of East London, all because of a planning error on the part of some
> > Tokyo-based banks.
>
> A nexus is a classical tree artifact. Once the network progresses along a
> meshed grid hugging Earth surface, we're going to see an increase in
> crosslinks and exchange points, crosslinking the branches.

What do you think "nexus" means??

Conventional definition:
----------------------------------------------------------------------
n. pl. nexus or nexuses

   1. A means of connection; a link or tie: this nexus between New
York's... real-estate investors and its... politicians (Wall Street
Journal).
   2. A connected series or group.
   3. The core or center: The real nexus of the money culture [was] Wall
Street (Bill Barol).
----------------------------------------------------------------------

As Lewis Carroll tried to make clear a long long time ago, it isn't
very useful to conduct arguments by redefining words as you go along.

--
Jim Dixon  jdd at dixons.org   tel +44 117 982 0786  mobile +44 797 373 7881
http://jxcl.sourceforge.net                       Java unit test coverage
http://xlattice.sourceforge.net         p2p communications infrastructure