The way I like to explain it, which is how I have seen it explained several times, is that all AI can be reduced to search/optimization. ML is just applying the search over the function that will search for the final answer over a dataset (either generated on the fly or prepared beforehand). For neural networks the hypothesis space (all the solutions you are searching through to find the best ones) is the weights for the neural network, and your search strategy/optimization is (usually) backpropagation. If you translate the weights to something traversable by other algorithms they could do just "fine" (assuming infinite time and space) in it's place. It really opens the mind up for experimentation on every bit of the process. The book that really hammered it in for me was Intelligence Emerging by Keith Downing, short, great book on bio-inspired AI.