Equations force a model to be precise, complete, and self-consistent, and they allow its full implications to be worked out. It is not difﬁcult to ﬁnd word models in the conclusions sections of older neuroscience papers that sound reasonable but, when expressed as mathematical models, turn out to be inconsistent and unworkable. Mathematical formulation of a model forces it to be self-consistent and, although self-consistency is not necessarily truth, self-inconsistency is certainly falsehood.1
These reasons are, in my mind, the entirety of the rationale behind mathematical modeling. Those who have read Marvin Minsky’s “Why Programming is a Good Medium for Expressing Poorly Understood and Sloppily-Formulated Ideas” will almost surely appreciate Abbott’s argument.
- L. A. Abbott : Neuron : 60, November 6, 2008 : Theoretical Neuroscience Rising↩