Hierarchy, Force Monopoly, and Geodesic Societies

Sun Apr 11 10:59:43 PDT 2004

On Sun, Apr 11, 2004 at 12:29:11AM +0100, Jim Dixon 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
mesh. Have you seen a fisherman's net? Do you think a fisherman or a weaver
uses a mathematical formalism when referring to a specific, familiar shape?
The graph (not a mathematical term, that) I pointed you to did remind you
of...?

http://research.lumeta.com/ches/map/gallery/wired.gif

> single root.  A continuum has an infinite number of points in it.  A grid

Use your imagination. Crosslinking a tree results in a mesh. Are you familiar
with polymer crosslinking? Can you imagine a crosslinked tree, that is
halfway between a tree, and a mesh? I knew you could.

> ... none of these terms has anything much to do with one another.

I'm sorry I'm confusing you with interdisciplinary language. Unfortunately,
I'm not going to lapse into formal definitions of new terms, if these can be
informally explained in downstream text.

> I don't know why you introduce hypergrids.  But you might consult a

You're using "don't know" a lot.

I recognize the symptoms by now. Occasionally, I run into people who're into
heavy formalism & domination. I've almost never been able to communicate
effectively with such people, but I'm going to try anyway.

I use the term hypergrid/hyperlattice/hypermesh as a generic term for higher
dimensional
networks which have a specific connection locality pattern, if mapped to 2d
and 3d
space. Namely, that the connection density decays with distance (in terms of
distance to the current reference node). The higher the dimensionality, the
larger the total number of links. The more random defects (missing edges) in
the
network, the less orthogonal it looks. A hypercube is an instance of a pretty
orthogonal high-dimensional network. Its makeup is fractal, which is visible
in the connectivity matrix. A hypergrid is an orthogonalized hypercube.

You can plot (project) hypercube and hypergrid connectivities on 2d and 3d
arrays of
nodes. If the length of the array edges is a power of 2 you'll get a specific
connectivity distribution pattern, reaching outwards orthogonally in
distances which are doubling in each step.

I generalize this by relaxing the 2^n distance constrant and by allowing
connectivity other than orthogonal, including defectivity. The connection
density still decays exponentially with distance.

Less fuzzy now?

> mathematical dictionary - the term seems irrelevant to the current
> discussion.

Trust me, it's not.

> > > 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,

Now you're refusing to parse English, too. I'm not going to diagram it for
you, look at above cited passage.

> 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.

Look outside the window. Does this look like a finite dimensional metric
space to you? 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'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.
The traffic needs a physical connection to pass through the nexus. Traffic
requires infrastructure, which costs money to buy and to run. Unnecessary
traffic and suboptimal topology incurs unnecessary costs. Current layout is
done by people, and is a political process. Traffic laid out by agorics
within a protocol adjusts in realtime. Because this is not being done now,
this means such protocols will be invented and deployed. They will outcompete
the legacy approach. It doesn't take a genius to make that trivial forecast.

> 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.

> 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.

Immature systems can tolerate inefficiency. Iterated competition results in
progressive loss of leeway. Use of IT in economic areas of human enterprise
is just the beginning of this process.

> 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.

http://computerworld.com.sg/pcwsg.nsf/0/BFED6DE56B76EA4948256CDE00139250?Open
Document

Regional nexus for GPRS
Singapore will be Asia's first neutral Peering Point for GRX (GPRS Roaming
Exchange) providers.

http://www.pch.net/resources/reference/peering/ipv4_with_pch_rs.html

A nexus of fiber, copper, or rights-of-way must exist within or proximal to
the user community, and it must be open and accessible to those companies
which wish to add to or improve upon those facilities.

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.

--
Eugen* Leitl <a href="http://leitl.org">leitl</a>
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