Clarifying Nonlinearity
Nonlinearity isn’t just about having too many parameters to predict; it’s fundamentally about how inputs relate to outputs. In linear systems, changes are directly proportional—double the input, double the effect. In nonlinear systems, however, a small change can trigger a disproportionate or entirely unexpected outcome due to interactions like feedback loops and dependent relationships.
For instance, it’s not simply that weather models require countless parameters, but rather that a tiny disturbance can amplify through the system so that traditional, linear predictions become ineffective. Similarly, in ecology or economics, it’s not the number of parameters per se, but the nature of their interactions that leads to unpredictable, dramatic changes from seemingly minor tweaks.
In summary, nonlinearity highlights sensitive dependence and complex interdependencies where cause and effect do not align in a simple, additive way.