Invariants

[Left: the two dimensional stable manifold of the origin in the Lorenz system; Right: two dimensional unstable of an equilibrium point in a four dimensional dynamical system modeling two pendula that are coupled by a torsional spring; from here, and no idea what it means! :-)]

Anyone involved in algorithm design, or related disciplines, will no doubt appreciate the importance of invariants. An invariant is a condition that does not change, or should not, ever change. For example, i should always be smaller than j. Or the distance between two objects should always remain constant.

If you start out, and then decide to mess with your invariants, question them, try to change them, or just ignore them, then all hell breaks loose.

But sometimes you just have to...