Complex organisms thwart the simple rectilinear causality paradigm of “necessary and sufficient,” with its experimental strategy of “knock down and overexpress.” This Essay organizes the eccentricities of biology into four categories that call for new mathematical approaches; recaps for the biologist the philosopher's recent refinements to the causation concept and the mathematician's computational tools that handle some but not all of the biological eccentricities; and describes overlooked insights that make causal properties of physical hierarchies such as emergence and downward causation (...) straightforward. Reviewing and extrapolating from similar situations in physics, it is suggested that new mathematical tools for causation analysis incorporating feedback, signal cancellation, nonlinear dependencies, physical hierarchies, and fixed constraints rather than instigative changes will reveal unconventional biological behaviors. These include “eigenisms,” organisms that are limited to quantized states; trajectories that steer a system such as an evolving species toward optimal states; and medical control via distributed “sheets” rather than single control points. (shrink)