I think I explained it poorly. I used "gradient descent" colloquially there, I just meant following the 'flow' in your vector field like you might in actual gra

I think I explained it poorly. I used "gradient descent" colloquially there, I just meant following the 'flow' in your vector field like you might in actual gradient descent. (Yes in this case it'd be Euler's method, and you can add whatever bells and whistles you would add for GD like to choose step sizes and whatnot.) I'm saying you might still be able to find the zero of your function by doing that. That neither implies that Newton's method would have performed better on your problem (it may perform better, or it may not), nor does it imply that your vector field must have been a gradient of anything. Right? Whereas you're saying "given that you're doing Newton's method, I don't think one problem is easier than the other, right?" as if Newton is somehow guaranteed to give equally good if not better results than e.g. Euler when your vector field isn't a gradient... which I don't believe it is? Certainly there are cases when that happens but it's not implied, right?