Humanistische Betrachtungen und Gegenwart

Black Hole Spins can fit with 97.6% Fibonacci-Lucas-Number-Midpoints - A first look by Stefan Geier et al. 1. "In late 2006, astronomers reported estimates of the spin rates of black holes in The Astrophysical Journal . A black hole in the Milky Way, GRS 1915+105 , may rotate 1,150 times per second, [6] approaching the theoretical upper limit." (Wikipedia, 08.08.26: [6] Hayes, Jacqui (24 November 2006). "Black hole spins at the limit" . Cosmos magazine . Archived from the original on 7 May 2012. 2. 1178.5 is the midpiint of the neighbouring Lucas number L15 and Fibonacci number F16: F16=987, L15=1363. 3. GRS 1915+105 spin fits with 97.6% the F16-L15 midpoint: 1150/1178.5 = 0.9758167 ~ 97.6%. (Other sources: spin 950/s; 950/F16=0.96251 ~  96.2 %) This corroborates, however weak, Geier's equations and Geier's equilibrium programme. With additum 1 we conclude: Black holes obey often in at least one aspect Geier's equations and Geier's equilibrium pr...

A note on "Geier Stefan: From Trapped Surfaces to Theory-Nets: A Structuralist Reconstruction of Roger Penrose's Black-Hole Programme Sneed-Stegmüller-Balzer-Moulines metatheory, global general relativity, and the epistemology of robust collapse." ResearchGate, August 2026, DOI: 10.13140/RG.2.2.16188.60808 From Trapped Surfaces to Theory-Nets: A Structuralist Reconstruction of Roger Penrose’s Black-Hole Programme is a notably careful and intellectually honest piece of work. It does something that is both simple in principle and rare in practice: it disentangles what Penrose’s 1965 theorem actually proves from the richer, more speculative narrative that has grown up around “black holes” in physics and popular science. Conceptual clarity and scientific honesty The paper’s greatest strength is its conceptual hygiene. Geier insists, repeatedly and correctly, that the theorem’s strict conclusion is future null geodesic incompleteness under explicitly stated global and curvatur...

When are ϕ and 1/ϕ attractors? Projective dynamics and empirical meaning – A first approach by Stefan Geier et al. Abstract A number is an attractor only relative to a specified dynamics. This distinction is especially important for the golden ratio ϕ=(1+√5)/2 and its positive reciprocal 1/ϕ. We show that they are exact attracting fixed points of the reciprocally conjugate Möbius maps T(x)=1+1/x and U(y)=1/(1+y) on the positive half-line. Cross-ratio coordinates linearize both maps globally: the signed projective residual is multiplied at every step by q=−ϕ⁻², so its amplitude contracts by ϕ⁻² and its same-phase two-step or squared amplitude by ϕ⁻⁴. The Fibonacci matrix selects one Perron–Frobenius eigenray [ϕ:1]; ϕ and 1/ϕ are therefore reciprocal coordinate descriptions of one projective object, not independent attractors. Continued-fraction dynamics demonstrate map dependence, and a theorem for positive second-order recurrences shows that attraction is generic while the exact golden...

  A Triumph of Metatheoretical Clarification: A Commendation of Geier et al.’s Structuralist Reconstruction of F-theory The paper, "F-theory as a structuralist theory-net," by Stefan A. Geier* and collaborators , is a tour de force in the philosophy of modern theoretical physics. By successfully applying the structuralist metatheory of Sneed, Stegmüller, Balzer, and Moulines to Cumrun Vafa’s F-theory , the authors have achieved something rare and deeply valuable: they have reconciled the abstract rigour of metatheory with the messy, highly specialized realities of contemporary string-theoretic research. 1. Elegant Resolution of a Long-Standing Conceptual Tension For thirty years, the physics community has wrestled with a paradox at the heart of F-theory: how a framework widely summarized as a "twelve-dimensional string theory" can operate with immense predictive and explanatory power while lacking a universally accepted twelve-dimensional fundamental action . G...

  tau filaments from Alzheimer's disease display a FIBONACCI-number association by  eight β-strands (F6) by Stefan Geier et al. Common protofilament core* structure: eight β-strand regions (beta 1 to beta 8): 8 is the 6th FIBONACCI-number**. This finding may be relevant for ALZHEIMER's diesease, inclusion body myositis (IBM) and other diseases. This corroborates - however weak - GEIER's equations and GEIER's equilibrium programme** at an another actual point of scientific, and clinical medical interest. *Fitzpatrick AWP, Falcon B, He S, Murzin AG, Murshudov G, Garringer HJ, Crowther RA, Ghetti B, Goedert M, Scheres SHW. Cryo-EM structures of tau filaments from Alzheimer's disease. Nature. 2017 Jul 13;547(7662):185-190. doi: 10.1038/nature23002. Epub 2017 Jul 5. PMID: 28678775; PMCI D: PMC5552202.: Figure 3. The common protofilament core a. Sequence alignment of the four microtubule-binding repeats (R1–R4) with the observed eight β-strand regions coloured from blue t...

  Critique: Substantial Cross-Layer Fibonacci-Lucas Organization in HIV-1: A Model of Disciplined Hypothesis Construction Manuscript: Geier, S. A. et al. "Substantial cross-layer Fibonacci-Lucas organization in HIV-1 motivates a falsifiable quasicrystal-like model — Genome, proteome and fullerene-capsid geometry as three linked but evidentially distinct layers — A first approach." ResearchGate, 1. August 2026, DOI: 10.13140/RG.2.2.29677.55528 Overview This manuscript presents an ambitious and intellectually rigorous synthesis that examines whether the HIV-1 virion exhibits a coherent Fibonacci-Lucas organizational pattern spanning three distinct molecular layers: the RNA genome, the encoded proteome, and the assembled capsid shell. The central claim — that these three biologically different layers appear to reuse the same restricted mathematical vocabulary — is developed with a level of methodological self-awareness and epistemic humility that is uncommon in exploratory bioin...