Hierarchy, Force Monopoly, and Geodesic Societies

[Jim Dixon]

On Sun, 11 Apr 2004, Eugen Leitl wrote:

> > A "tree" as the term is used in mathematics and computer science has a
>
> A tree as the term is used in a human language refers to a shape. Ditto

If you want to participate in technical discussions, discipline yourself
to use the relevant language correctly.

The word "tree" is commonly used in this business.  It has a precise
meaning.  It refers to an acyclic graph with a single root.

-------------------------------------------------------------------
"Tree data structure

"From Wikipedia, the free encyclopedia.

"In computer science, a tree is a widely-used computer data structure that
emulates a tree structure with a set of linked nodes. Each node has zero
or more child nodes, which are below it in the tree (in computer science,
unlike in nature, trees grow down, not up). The node of which a node is a
child is called its parent node. A child has at most one parent; a node
without a parent is called the root node (or root). Nodes with no children
are called leaf nodes.

"In graph theory, a tree is a connected acyclic graph. A rooted tree is
such a graph with a vertex singled out as the root. In this case, any two
vertices connected by an edge inherit a parent-child relationship. An
acyclic graph with multiple connected components or a set of rooted trees
is sometimes called a forest."
-------------------------------------------------------------------

The term is used because most or all trees in the region where the English
language originated are shaped just like that: they have a single trunk
which forks into branches which may themselves fork and so on.  These
branches do not connect back to one another.

The Internet doesn't resemble a tree at all.  It is characterized by many
cross-connections, which form cycles.  These are introduced deliberately
by network engineers, because tree-like networks are unreliable.  That is,
when a network engineer sees a tree, his immediate response tends to be to
fix the tree by adding cross-connections.  If you don't have any cross-
connects, then any network failure causes loss of connectivity, a very
Bad Thing.

> > "The geometry on Earth surface is anything but whatever"?  Sorry,
>
> Now you're refusing to parse English, too. I'm not going to diagram it for
> you, look at above cited passage.

I learned how to parse English a long time ago. That is not a sentence in
English.  I have no idea of what you meant to say.

> Look outside the window. Does this look like a finite dimensional metric
> space to you?

Yep.  Most would describe the view as three dimensional.  3 is a finite
number.  Is there a metric?  Certainly.  The one worked out by Descartes
a long time ago will do, the distance between two points in Cartesian
coordinates.

When I did a course in finite dimensional metric spaces, most of the
initial examples were in three dimensional geometries, like what you
see when you look out the window.  After a while we progressed to
things like distortions in space-time AKA gravity.

>          Are you familiar with geodesy? Are you familiar with the term
> geodesic as used by ship captains and pilots? It has nothing whatsoever to do
> with spacetime curvature. You can't travel nor signal through Earth bulk, so
> you have to route your signals around the spherical obstacle. One you're
> sufficiently far removed, it's line of sight in a device cloud (a satellite
> constellation).

I don't believe that I have ever met a ship captain or pilot who knew what
the term "geodesic" meant.  (Mind you, I never asked.) It's a term used in
mathematics and physics.  Given a metric on a space, if the length of a
path between two points is minimal, that path is a geodesic.  In Euclidean
geometry, it's a straight line.  On the surface of a sphere, it's a
segment of a great circle.

> > > 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.
>
> Peered traffic is exchanged over a point. It is frequently called a nexus.

I spent more than seven years running an ISP and in that time set up
over 100 peering relationships.  Throughout that time I never heard anyone
refer to anything as a "nexus".

The term _is_ used by marketing types when they are getting rhapsodic.
And I have heard it used in political discussions.  And in poetry.

On the other hand, peered traffic is often exchanged between networks
(ASNs) at several different points; these might be thousands of miles
apart.  Google on BGP and MED.

> > Peering arrangements generally involve legal departments, and rarely
> > change once inked.
>
> The worse for them. Computers can negotiate, too, and a lot quicker than
> people.

You may not like legal departments, but this is irrelevant to common
practice on the Internet.  Peering agreements are legal documents.
Most companies have them drawn up by lawyers and they are very rarely
changed.  (Exceptions? People in the business might remember Agis and
Exodus.)

Computers are pretty useless in negotiating peering.  It usually
involves friendly chats over the telephone, sometimes a beer down
at the pub.

> I conced you the point that nexus might be not a common term of the trade.
> But it's certainly not my invention, see Google. As such, you could go
> lighter on sarcasm. It can backfire.

Introducing standard term that you insist be misinterpreted according to
your peculiar practice can also waste a great deal of time.  It makes more
sense to use terms in the normal way and spend your time and energy
arguing real issues.

I think that your argument was that telecommunications is moving towards a
future in which traffic will be evenly distributed over the earth's
surface because this is optimal, because a uniform distribution is
dictated by physics.

I think that you are quite wrong in this, but the argument regarding
substance got lost in your insistence that words be used oddly.

--
Jim Dixon  jdd at dixons.org   tel +44 117 982 0786  mobile +44 797 373 7881
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