Fractal Time Flow: Empirically Validating a 1/3 Homothetic Ratio – The Cantor-Moirai Hypothesis

We propose the hypothesis, we call it the Cantor-Moirai hypothesis, that time is not a homo- geneous linear continuum but possesses a fractal structure. This structure manifests through the recurrence of intensity cycles in various domains (geophysical, economic, and political) that synchro- nize across major anchor points. Applying a methodology inspired by works on temporal dynamics in complex systems [1], we empirically demonstrate a self-similar system, where each iteration is reduced by a constant factor r, leads – for N=2 copies and a fractal dimension of approximately D ≈ 0.63 – to a ratio of approximately r ≈ 0.33. Thus, a major cycle of duration T subdivides into sub-cycles of duration approximately 0.33T, (0.33)2T, etc. We verify this hypothesis using de- tailed examples and calculations, acknowledging the empirical variability in scaling exponents and homothetic ratios. Furthermore, we present novel empirical evidence for fractal temporal dynamics in Earth systems through Detrended Fluctuation Analysis (DFA) [2] of paleoclimate CO2 records, volcanic eruption time series and, economic and political time series in Europe and the world, reveal- ing statistically significant fractal scaling and persistent long-range correlations, with sigmas ranging around 4 to 10, at synchronized dates, suggesting that fractal time may be an intrinsic feature of complex geophysical and human processes, hinting at a more fundamental and non-linear structure of Time itself, echoing the intertwined threads of time as envisioned by ancient mythologies.