Ümit Arslan

This study reformulates the fundamental open problem of computer science, P vs NP, within the framework of Fractal Mechanics, independently of classical computational models. Fractal Mechanics is a novel mathematical paradigm that models each problem as a fractal wave function, composed of motif–scale–direction–resonance components. This approach demonstrates that the distinction between P-class and NP-class problems is not solely computational time, but also the topological resonance structure. Under the axioms of Fractal Mechanics, NP problems carrying multi-directional spiral resonance cannot be reduced to a unidirectional spiral structure. Therefore, within the FM framework, P ≠ NP is a necessary outcome.

This article examines why the human mind struggles to intuit structures extending across multiple scales, from the microscopic to the macroscopic. This cognitive phenomenon, referred to as “scale blindness,” produces profound effects both in everyday thinking and in scientific practice. The article analyzes the origins of scale blindness across three dimensions: (1) the evolutionary limitations of the human brain, (2) scale-locking within scientific disciplines, and (3) the object-centered ontology of human cognition.

Gravity, in the classical sense, is not the “mutual attraction of masses”; rather, it is the pushing/pulling of matter caused by differences in orientation within the spiral density field of spacetime. So attraction → spiral field gradient.

n fractal mechanics, every structure is defined by: global motif, local variation, direction, resonance (k, q), spiral flow. Religion contains exactly these five components.

From the perspective of fractal mechanics, democracy is: A multi-scale feedback system (individual → neighborhood → city → country → global system), A structure in which each scale generates its own resonance while remaining aligned with higher scales, A mechanism in which motifs (values, demands, orientations) are carried upward in a spiral manner, An order in which energy flow (information, decisions, resources) is distributed downward in a spiral manner

The fundamental assumption of this report is: Spacetime is a fractal fluid. The central spiral nodes of this fluid transform into different physical structures at different scales: at the galactic center → black hole, in a stellar system → stellar magnetic dynamo, in a cell → centrosome. These three structures are scale-transformed versions of the same mathematical motif.

This law appears with the same motif in: physical fields (spin, polarities, flow directions), atomic structure (shells, orbital orientations), planetary systems (stable resonance zones), galactic dynamics (spiral arm directions), information theory (bit strings, number of states), mathematics (number of functions, number of subsets), FM (spiral–fractal energy distribution, minimum-energy directions)

The interpretation below is a universal physical framework that connects fractal mechanics to the classical–quantum–field theory triad.

Fractal geometry abandons the “flat, fixed, scale-independent” structure of classical Euclidean geometry and instead describes a geometry that is: scale-dependent, self-repeating, composed of spiral or multi-layered motifs, preserving the same structure as scale increases. This suggests that the universe is not built from “straight lines and circles,” but from spiral-scaled motifs.

Space-time is a fractal fluid. Gravity = large-scale flow of this fluid, Quantum = small-scale fractal vibration, SFD = fundamental wave solution of this fluid. The theory is built on three pillars: Fractal geometry, Fluid dynamics, Spiral-fractal wave function