The debate about "fractal dimensions" and "geodesic networks" and what characterizes them is part of a much larger analysis of systems in general. Minsky once said that most of AI is about people applying their own names to previously studied concepts and phenomena. This applies to _systems_. Agents, actors, self-organizing systems, bionomics, geodesic networks, agoric systems, markets, connectivity, hierarchies (and lack thererof), swarms, multi-agent systems, distributed systems, disintermediation, and economics in general are all part of this Big Picture. Several books have been written about this stuff, including Kevin Kelley's "Out of Control" and the various burblings of Huber, Gilder, the Santa Fe Institute, and so on. (Speaking of the Santa Fe Institute, I could add to the above list various other terms like: computational ecologies, swarms, emergent behavior, artificial life, etc.) In my view, such terms are only shorthand labels meant to trigger associations in the mind of the listener. Thus, when I see Hettinga prattling on about "geodesic fractionally-cleared bearer markets," it just means "oh, the stuff Cypherpunks advocate." That is, free markets, markets free of top-down centralized control. For example, the trade practices of Pacific Islanders, the spice and silk caravans of the Silk Road (ergo "Digital Silk Road," of Tribble, Hardy, and others), the agora of Athens, the bazaars of Baghdad and Damascus (ergo Eric Raymond's "cathedral and the bazaar" metaphor), and on and on. Or physicists could speak of spin glasses. And they could natter on about correlation lengths, long-range order, phase transitions, etc. (People would find it quite confusing if every time I referred to "fractionally-settled spin glasses" as a metaphor for free markets. Thank your lucky stars. Though I do occasionally draw on phase transitions as a metaphor.) Ditto for throwing in junk about "fractals." ("Everything is fractal! Like, wow, like, farm out!") What these _are_ all related to is to systems made up of bits and pieces and interactions which share many similarities. But also some important differences, so care must be taken not to extrapolate from one domain to another. The tendency of the mathematician is to abstract out all of the domain-specific junk and to invent a terminology which isolates only the important features. So instead of talking about students in a classroom passing notes, or talking about positions of atoms in a crystal, we end up with language like: "A ring is defined to be a .... over a set of elements in a subfield...satisfying associativity...but not pairwise-commutable." This cuts out the "intuition" about how students behave, how crystals actually are composed, how hands of poker appear in real life, etc. etc. This abstraction is the beauty of mathematics. Of course, this beauty does not come without a downside. Anyone who has read the hyper-technical, hyper-pure books of "Bourbaki" (an anonymous collection of mostly-French mathematicians who issued a series of math books in the 50s to the 70s), or anyone who picks up nearly any advanced math book, knows that the symbols are mostly meaningless without some intuition or deep immersion in domains using the notation. While not all mathematicians have a _spatial_ imagination, they still "visualize" their domains. Math is a lot more than just formal manipulation of meaningless symbols. Thus it is in our domain, that of "systems made of many parts." Anyway, I have my own views, and calculations, of things like dimensionality and connectivity, and how they are related. And of why many such systems are "self-organizing." (For example, self-interest. Given a set of N farmers and/or fishermen, no one needs to sit down and figure out all of the prices and terms for a market to develop. Self-interest, local actions, are enough for markets to develop, for ecologies of economic actors, for "geodesic networks" (barf) to form. Even for "bearer-instrument settlement" (shells, beads, dollars, cargo). Likewise, there are sociological, economics, and psychological views of these systems. All kinds of views, all kinds of terms, all kinds of similarities. When I was in college, more than 25 years ago, one of my friends was a real fan of Ludwig von Bertanllanfy (sp?) and his "general systems theory." To my friend Alex _everything_ was an example of general systems theory. Everything. Perhaps he moved on later to viewing everything as an example of chaos, or fractals, or bionomics, or geodesic networks. And to others, everything was a branch of ecology (recall that in Heinlein's "Farmer in the Sky," written in the 1950s (!), ecology was the big thing to study. Ditto for "everything is a branch of physics," "everything is a branch of economics," etc. The worm turns. I advise folks not to concentrate on either Gilder's "telecosm" (or whatever) or Hettinga's "fractional geodesic networks" (or whatever) or even my own "crypto anarchy" (or whatever). The interesting stuff is not in the terminology. By the way, the more interesting thing about these systems is NOT that they are locally-connected, nearest neighbor, as a geodesic dome is connected, but that they are _multiply-connected, high-dimensionality_ systems. (Hint: All 270 million Americans live in an N-cube of just 5 units on each side...but with a bunch of dimensions. Geodesics are not the interesting thing. Communication, bandwidth, connectivity, auction systems, etc., are far more important. ) --Tim May -- (This .sig file has not been significantly changed since 1992. As the election debacle unfolds, it is time to prepare a new one. Stay tuned.)