Lev,
Right on. This very same insight, that points lack the degrees of freedom to participate in an evolving system, led me to conclude that the algebraically closed C* provides the means for non-ordered dimensionless points of definite values to self-organize, allowing time dependence.
So I truly grok what you mean when you say that information string geometry is richer -- the transformation of random fields into ordered structures and novel forms reminds one of Darwinian random mutation and natural selection.
In my NECSI ICCS 2006 paper ("Self organization in real and complex analysis") I put it this way:
"2.0 The Geometry of Counting
2.1 Let us introduce some interrelated tools that differentiate our continuous experience of time, from the discrete metric that imposes a moment of time onto our experience:
2.2 Suppose time is an independent physical quantity, a 0-dimensional point on a random self-avoiding walk in n dimensions. The singularity imposes the limit. (Therefore, just as in discrete counting we say that the set is not empty, we say that the point is not dimensionless. An important distinction, since a series of zero-dimensional points is not self-limiting.) Suppose the point is self-similarly extended on a 1-dimensional metric whose (arbitrarily chosen) endpoints define relative positions of the evolving point and its
complex conjugate on the complex (Riemann) sphere.
2.3 The Euler equation, e^ipi = - 1, therefore describes the least path such a point travels in the complex plane, as the Euler Identity: e^ipi 1 = 0 . (The unit radius is therefore self similar to a point; we will explain, in 5.11, this fact of analysis.)"
The "indpendent physical quantity" that we call time, then, has to be identical to quantum information bits creating structures from unstructured relations.
Tom
