(1) Yes, the modern ML/AI lot seem to ambiguously use a purely mathematical meaning to "computer" -- which is useless. As useless as any pure mathematics. If we

(1) Yes, the modern ML/AI lot seem to ambiguously use a purely mathematical meaning to "computer" -- which is useless. As useless as any pure mathematics. If we only had this a "computer" would be a theoretical curiosity, like a 200-dim sphere. The real-world computers we care about run algorithms whose semantics is given by the properties of the devices real computers use. This double meaning to "computer" has caused a lot of superstition in the ML/AI space. Real computers are engineering devices which shuffle electrical signals around to useful devices. There is no reason to think that "pure algorithms" have any use at all, as with, eg., a 200-dim sphere. They're only useful if they can be given a semantics which exploits useful properties of devices. (cf. with physics, where a 200-dim sphere could be useful if it models some actual system). (2) This isn't enough. Consider learning the rules of chess; or likewise, the inference rules of mathematics. f(x) = 2x^2, f'(x) = 4x, etc. Search spaces constructed for a grad. desc. search are very infinite; and the solutions we need are infinitely precise. Discrete approaches to search(ing for solutions) are necessary.