"Homeopathic" dynamical systems

Homeopathy contends that higher dilutions of the active ingredient in a remedy (fewer molecules in each dose) produce stronger medical effects [1]. This idea is inconsistent with observed doseresponse relationships of conventional drugs, where the effects increase with the concentration of the active ingredient in the body [2]. The conventional dose-response relationship has been found in numerous scientific studies on organisms as diverse as nematodes [3], rats [4], and humans [5]. Further it is consistent with the behavior of simple physical and chemical systems, -e.g. the larger the force on a spring, the larger the displacement (Hooke’s law), or the larger the voltage on a resistor, the larger the current (Ohm’s law), and the larger the concentration difference within a solution, the larger the particle flux (Fick’s law), the larger the temperature difference on a solid the larger the heat flow, and so on.