The Mathematics of Why Having a Slow, Constipated Poo Feels Like a More Dynamic and Rewarding Experience Than Dealing with the Anglesey County Council's Complaint System

This paper provides a formal mathematical comparison between two nonlinear experiential systems: the Biological Evacuation System (BES), experienced as slow constipation, and the Anglesey Complaint Avoidance System (ACAS), the operational behaviour of Anglesey County Council’s complaint infrastructure. Drawing directly from dynamical systems theory, optimisation analysis, Markov modelling, and entropy measurement, the study demonstrates that BES is a convergent, reward‑bearing process with decreasing resistance and guaranteed termination, whereas ACAS is a divergent bureaucratic attractor characterised by increasing resistance, negative reward gradients, and annihilation of user intent. Extrusion progress is modelled using a sigmoid convergence function: \[x(t) = {L}{1 + e-k(t - t_0)}\] Complaint progress is modelled as a decaying‑hope function with oscillatory bureaucratic noise: \[c(t) = c_0 e-α t + β sin(ω t)\] Resistance curves, satisfaction gradients, and entropy profiles further reinforce the central conclusion: constipation is mathematically, structurally, and experientially superior to the Anglesey County Council complaint system. The document includes full comparative analysis, conceptual diagrams, formal corollaries, and author’s notes. This upload represents a complete, scientific treatment of an intentionally absurd experiential phenomenon. Includes a visualizer that renders the comparative dynamical topology of the paper, mapping the Biological Evacuation System (BES) against the Anglesey County Council Complaint System (ACAS) to prove via optimization theory, Markov modelling, and entropy analysis that a slow, constipated poo is a convergent, rewarding process, whereas the council's complaint infrastructure operates as a non-convergent, maximally hostile bureaucratic attractor. Keywords and Subjects:Constipation dynamics; Biological Evacuation System (BES); Anglesey Complaint Avoidance System (ACAS); optimisation theory; nonlinear experiential systems; sigmoid extrusion model; bureaucratic divergence; resistance curves; reward gradients; satisfaction trajectories; entropy analysis; Markov chain modelling; complaint system failure; experiential convergence vs divergence; negative reward structures; bureaucratic hostility index; anatomical constraints; systemic non‑termination; comparative experiential mathematics; user‑intent annihilation; convergent biological processes; divergent administrative processes; formal corollaries; deadpan scientific humour. Jonathan said, and i quote "Waddahelly" when i showed him this paper i cooked. i think that is a good sign - matt Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com