...who like most of us, agrees with Tim *lots* more often than he likes to admit. :-). Cheers, RAH Who won't wax (too) rhapsodic about how Tim, in his Amazonian example below, described a "geodesic recursive auction" (digital silk road, Hughes "piracy" market, whatever) <ducking>... --- begin forwarded text Date: Tue, 12 Dec 2000 08:02:26 -0700 From: Somebody Subject: Re: Questions of size... To: "R. A. Hettinga" <[EMAIL PROTECTED]> Bob, The distinction between geometry, topology, and, presumably, homology, begs the question. You, following Huber, have used the word geodesic to refer to connections of minimal cost. In the economic manifold (surface) this is presumably the only important metric (local distance function). The analogy is mathematically precise in all respects, and therefore correct. I'd have flogged you into submission long before this if it were not so. Geodesics, or more properly, geodesic paths, are locally defined. There is not necessarily a geodesic between two specific points. In a differentiable manifold with a sufficiently smooth metric, there are geodesic paths in every direction through every point, however. Whether there is one of those paths going to some other given point is a question of connectivity and other topological issues. Two separate spheres are a single differential manifold. No great circle path -- the geodesics of each surface -- connects any point on one sphere with any point of the other. Unfortunately, geodesics may also be the longest paths between two points. Just go the wrong way on the great circle determined by two ends of the Mass Ave bridge. It's a path of stationary length: slight variations in the path make hardly any difference in its length. Unfortunately its length is maximum rather than minimum. By the way, have I mentioned that I HATE it when I agree with Tim? <Somebody's .sig> ------------------------ From: "R. A. Hettinga" <[EMAIL PROTECTED]> Subject: Re: Questions of size... Date: Mon, 11 Dec 2000 19:16:57 -0500 To: Some People, Privately --- begin forwarded text Date: Mon, 11 Dec 2000 15:51:26 -0800 To: [EMAIL PROTECTED] From: Tim May <[EMAIL PROTECTED]> Subject: Re: Questions of size... Sender: [EMAIL PROTECTED] Reply-To: Tim May <[EMAIL PROTECTED]> At 5:56 PM -0500 12/11/00, R. A. Hettinga wrote: >At 9:48 PM +0000 on 12/11/00, Ben Laurie wrote: > > >> Chambers defines geodesic as "the shortest line on a surface between two >> points on it" > >Thank you. It works in all dimensions, and, thus it's topological, right? > Topology is typically not concerned with distance metrics. Doughnuts and coffee cups and all. Geometry is what you're thinking of, presumably. Not as sexy as saying something is "a topologically-invariant geodesic fractally-cleared auction space," but that's what happens when buzzwords are used carelessly. By the way, one topological aspect of a geodesic dome, to go back to that, is that each node is surrounded by some number of neighbors. Applied to a "geodesic economy," this image/metaphor would strongly suggest that economic agents are trading with their neighbors, who then trade with other neighbors, and so on. Tribes deep in the Amazon, who deal only with their neighbors, are then the canonical "geodesic economy." This is precisely the _opposite_ of the mulitiply-connected trading situation which modern systems make possible. So, aside from the cuteness of suggesting a connection with geodesic domes, with buckybits as the currency perhaps?, this all creates confusion rather than clarity. --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.) --- end forwarded text -- ----------------- R. A. Hettinga <mailto: [EMAIL PROTECTED]> The Internet Bearer Underwriting Corporation <http://www.ibuc.com/> 44 Farquhar Street, Boston, MA 02131 USA "... however it may deserve respect for its usefulness and antiquity, [predicting the end of the world] has not been found agreeable to experience." -- Edward Gibbon, 'Decline and Fall of the Roman Empire' ---------------End of Original Message----------------- --- end forwarded text -- ----------------- R. A. Hettinga <mailto: [EMAIL PROTECTED]> The Internet Bearer Underwriting Corporation <http://www.ibuc.com/> 44 Farquhar Street, Boston, MA 02131 USA "... however it may deserve respect for its usefulness and antiquity, [predicting the end of the world] has not been found agreeable to experience." -- Edward Gibbon, 'Decline and Fall of the Roman Empire'
