# Gradient descent: Shouldn't step size be proportional to inverse of gradient of residual?

It has been decades since I coded up any type of gradient descent algorithm to drive a function to zero (or to a minimum). I am following this tutorial, which minimizes $$J(\overrightarrow{\theta})$$. It all seems straighforward except for one thing. The step size along any dimension $$i$$ is proportional to the gradient $$\partial J / \partial \theta_i$$.

Doesn't a steeper gradient along dimension $$i$$ mean you should take smaller step sizes because $$J$$ changes rapidly with $$\theta_i$$?