Fractal localism, an informational interpretation (some initial ideas).
During a random serendipitous conversation, I realized something I’ve haven’t seen before, that the fractal localism proposal by N.N. Taleb on his “Principia Politica” is not a mere opinion, it is actually the translation of a very deep empirical observation: nature generates scalar compartments.
As I see it, Taleb’s paragraph is a renormalization proposal … suppose that we are able to find the best possible description of a phenomenon. What he proposes in the process of renormalization is that this description changes if we go from one observation scale to another. That is, the information structure necessary to describe a phenomenon on a macroscopic scale is different than the required on a microscopic scale. This is not an opinion, it is an informational reality of the systems and it manifests i.e. in the laws of physics.
Physics tends to generate theoretical or scale domains, the physics that describes phenomena on the atomic nucleus scale, has little or nothing to do with physics on the scale of the atom and in the same way atomic physics does not inform or explain phenomena on the scale of the universe itself. It does not exist a theory of everything, a single set of principles and laws that allow us to calculate properly the physical fields. This theory of everything was the ultimate search for Einstein and many others.
A deeper version of this idea was developed by Okun who took the three fundamental constants of the universe: (1) speed of light in a vacuum; (2) Planck’s constant; and (3) the universal gravitational constant.
The importance of the speed of light in a vacuum (c = 3x108m/s) is not so much that it is the speed of light but that since there really is no true SRI, for the laws of the universe to be the same for all observers, it is necessary that the speed of light in a vacuum be the same for all observers in any SRI and that this be the limit of the speed of transmission of information in the universe. This restriction makes arise a new phenomenology that did not exist in the Newtonian description of the universe where space and time are unified in the space-time on the one hand and on the other hand also the energy, mass and moment are unified.
The Plank constant (h) as in the case of the speed of the light, establishes another limit in the universe, in this case the maximum inference associated to a physical measurement (physical equivalent to the Cramer-Rao inequality in probability, there is no perfect inference) or better known as Heisenberg’s the Uncertainty Principle. This principle states that the level of uncertainty (∆) of a physical measurement of some conjugated variables is always greater than Planck’s constant. For example if we want to measure the position (x) and the linear momentum (p) of a particle, simultaneously, you have an uncertainty relation given by ∆x∆p ≥ h/4π. This means that one can either measure very precisely the position or the moment, but never both simultaneously. In addition, the Planck constant also unifies the energy of a photon with its frequency, E = hf or another way to see it is that it unifies the corpuscular and wave nature of light.
The third universal constant (G) relates Gravity, which may be thought as an entropic force caused by changes in the information associated with the positions of material bodies, through the Holographic principle which states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a light-like boundary like a gravitational horizon. These ideas developed by Verlinde (2011) propose that one can think about this boundary as a storage device for information. Assuming that the holographic principle holds, then G may be interpreted as an upper informational limit for how much information can be stored in the boundary of a space-time volume.With these three universal constants, Okun proposed building a cube in a space of suitable units (with c = h = G = 1), the cube has then three axes, one for each in the range 0–1, where 0 means the effect is not important. In this way, Okun identifies in each vertex scales and theoretical bodies of physics.
Now, why this is so I do not know if it is fully understood, but perhaps it has its origin in that at different scales systems satisfy different symmetries in an informational scheme a la Frieden.
Although there is several critiques I find Frieden’s work useful as a general frame work.
From this perspective; Libertarian, Republican, Democrat, or Socialist might be interpreted as the informational “Laws” of the social phenomena at different scales, depending on the corresponding statement of invariance valid in those scales.
