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One of my favourite examples of abstraction is the kernel trick. Accessing vectors with restricted interface (inner products, not individual components) enables problem solving in ∞-dimensional vector spaces. Ought to be better known outside the ML worldhttps://en.wikipedia.org/wiki/Kernel_method …
So the “trick” is that what you want to do is map X to an infinite dimensional space Y and compute an inner product there, which is expensive, but instead you have this handy function k that computes the inner product without needing to know the relevant elements of Y?
That's pretty much it. You don't even want Y itself, you just want to be able to "use" it.
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