Actually, I was thinking the same thing, but couldn't express it that well. Thanks, Steve ... I like the connection to the strange attractors. That captures the idea, I think, better than what I was going to attempt. And it's more satisfying than saying, "Well, it doesn't feel like an emergent property." -Ted
On Sun, Jun 7, 2009 at 12:21 PM, Steve Smith <sasm...@swcp.com> wrote: > James Steiner wrote: > >> Its an application of basic geometry. >> >> If the struts of the triangle are made of materials that do not >> stretch, compress, or flex (outside of acceptable parameters for the >> construction in question), then the triangle is *stable*--even if the >> joints are frictionless pivots. This is essentially because the struts >> hold their opposing joints at fixed angles--something no other 2d >> arrangement does. >> >> So, I guess you could say that the stability of a triangle is an >> emergent property of the geometry. >> >> Then again, I"m not a wise man. >> >> >> > James - > Nicely succinct. I sent a much more elaborate version of this to Nick > privately. > But there is a point I want to make publicly: > > Aggregate or Composite properties is not equivalent to Emergence. > > Sadly, defining Emergence (or Complexity or ...) is a bit like defining > Art. > > I have a wonderful collection of "ingenious mechanisms for inventors" from > the Industrial Age > with wonderful collections of levers and wheels and gears and cams and > rivet patterns. Within > those mechanism are hidden a number of triangles and quadrilaterals whose > properties > of rigidity and limited degrees of freedom are exploited to practical ends. > > All of these have wonderful collective properties, but none of which I > would call > "Emergent". > The key (upon reflection) to what I insist on to call something "Emergent" > is > nonlinearity. These rigid-body structures all have linear properties. > If you > draw a phase-space diagram, there will be nothing but a series of > well-defined > lines (or areas) describing the paths of the components through space-time. > > I suspect (but can't muster the intellectual will to prove or even > illustrate it) > that if we add the art and science of tolerances to the discussion, that > some > emergent properties might come in to play. That a well-toleranced > mechanism, > under repeated use, friction, and wear, will settle into an attractor... > that this > is what tolerancing is about. > > I postulate that a mechanism designed without tolerancing is poised on a > ridge between basins of attraction and that such mechanisms "wear out" > by falling off that ridge and undergoing accelerated wear and eventually > catastrophic failure. In a properly toleranced mechanism, we are already, > by design starting out in the middle of a (specifically and well-designed) > basin of attraction and the natural wear of the mechanism will simply cause > it to wander around within that basin. > > Perhaps, in the words of Nick, there are "wise men" here who can speak > to this more eloquently? Does anyone know of such a study on tolerancing > and nonlinear dynamics? > > - Steve > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org >
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
