If we do this systematically, we can obtain one of the first serious tests for the scale blindness hypothesis. In the following analysis, I apply an important principle: The failure of a theory alone is not proof of scale blindness. But when a theory collapses, if the cause of the collapse is the incorrect identification of different scales, this supports the hypothesis.
I think this is a very important topic. Like velocity and momentum, for example. In this study, let’s classify all the physics terms used according to their scales. The main reason for many conceptual confusions in the history of physics is the interpretation of parameters belonging to different scales on the same plane. In my opinion, physical quantities should be classified not only as “scalar-vector” or “fundamental-derived,” but also in terms of their scale level.
I believe this application can be very powerful. Because one of the biggest problems in probability theory is this: 𝑃(𝐴) appears as a single number, but in reality, the outcomes depend on the scale of observation. In the language of scale physics, probability now becomes: 𝑃 = 𝑃(𝑥, 𝑡, 𝜆) Meaning, the probability of an event is not constant; it depends on the scale.
If we apply this approach to physics, not the laws of physics themselves, but the way they are interpreted changes. Classical physics says: 𝐹 = 𝑚𝑎 This is a law of motion. In the scale physics interpretation, however: 𝐹 = 𝑚𝑎 also represents a relationship between different scales. So the question is no longer: “How does the object move?” but rather, “At what scale does this motion emerge?”
Let us now proceed by fully accepting the Scale Physics axioms that I have established. Our main assumption will be: 𝑥 = 𝑥(𝑡, 𝜆) and 𝑢 = 𝜕𝑥 / 𝜕𝜆 Furthermore, let us define the scale momentum as: 𝑃𝜆 = −𝑖Σ 𝜕/𝜕𝜆 Here, Σ is the fundamental constant in scale space, analogous to Planck’s constant.
After the introduction, we can establish the outline of “Scale Physics”. This is no longer standard physics, but a new theoretical framework in the direction of Fractal Relativity.
Let’s explain the motifs and scales of velocity, path/position, and time. These four concepts are actually the fundamental components of motion within space-time. From a fractal perspective, they are not independent of each other, but are the faces of the same event appearing at different scales.
Critiquing liberalism from the perspective of fractal mechanics requires questioning its fundamental assumptions through multi-scale and self-similarity principles. Liberalism is an ideology that places the individual at the center and mostly defines freedom as the sphere of individual choices. However, the fractal perspective shows that the individual is not merely a singular point, but part of multi-scale motifs.
Critiquing capitalism from the window of Fractal Mechanics breaks the system’s linear and deterministic assumptions, revealing how it is fundamentally a structure that “repeats itself but produces contradictions at different scales.” Capitalism assumes a straight-line progression as in classical mechanics: capital accumulates, production increases, consumption expands. However, the fractal perspective shows that this process contains scale-independent repeating irregularities.
According to fractal mechanics, chaos and order are not separate from each other; they are self-similar motifs of the same system emerging at different scales. In this approach, chaos is not disorder; it is the complex repetition of order at fractal scales.