Add discussion of many-stage RK methods to JOSS paper.

As suggested in #56.

paper.md

@@ -60,7 +60,29 @@ development of optimized methods for specific applications.  Different
 accuracy, stability, performance, and other properties may be relevant or
 essential depending on the nature of the equations to be solved.
 
-`RK-Opt` provides code that can enforce desired properties and/or objective
+An s-stage Runge-Kutta method has roughly s^2 coefficients (roughly s^2/2 for
+explicit methods), which can be chosen so as to provide high accuracy,
+stability, or other properties. Historically, most interest in Runge-Kutta
+methods has focused on methods using the minimum number of stages for a given
+order of accuracy. However, in the past few decades there has been increasing
+recognition that using extra stages can be worthwhile in order to improve other
+method properties. Some areas where this is particularly useful are in the
+enhancement of linear and nonlinear stability properties, the reduction of
+storage requirements, and the design of embedded pairs. Methods with dozens or
+even hundreds of stages are not unheard of.
+
+At the same time, most existing Runge-Kutta methods have been designed by hand,
+by researchers laboriously solving the order conditions. When using extra
+stages, the number of available parameters makes the selection of a
+near-optimal choice by hand impossible, and one resorts to computational
+optimization. This leads to a different paradigm of numerical method design, in
+which we use sophisticated numerical (optimization) algorithms to design
+sophisticated numerical (integration) algorithms. It can be expected that this
+trend will accelerate in the future, and perhaps one day simple
+manually-constructed algorithms will be the exception.
+
+RK-Opt contains a set of tools for designing Runge-Kutta methods in this paradigm.
+It provides code that can enforce desired properties and/or objective
 functions.  The constraints and objective are then used within an optimization
 framework, to determine coefficients of methods that best achieve the desired
 goal.  Thus, `RK-Opt` is a sort of meta-software, consisting of algorithms whose