and oscillates forever rather than converging and then this is continuous time gradient descent where we have an infinitesimal step size if we use a larger step size then it can actually spiral outward forever so there are actually conditions that you can check to see whether or not simultaneous gradient descent will converge or not and they involve complex eigenvalues of a matrix of second derivatives and I won't go into it because it's not really the kind of thing that makes for a nice talk but the long and short of it is the