But I am not sure the point is clear. There are different levels - and in fact, matrix multiplication is "easy", matrix multiplication
of what (which architecture) is not.
Defining a procedure for arithmetic is easy. Implementing it in silicon is not. To carry on the procedure for the former has low relevance to intelligence. To carry on the job of the latter does have high relevance to intelligence. If the latter is performed by a professional it is intelligence. If it is performed by an algorithm it is artificial intelligence. "Automating finding out good ways to implement ALUs" is AI; the ALUs running are not.
So, studying AI, asking ourselves which new "devices" (abstract sense) we can find so that our algorithms have aspects of cleverness, is productive as it simply and plainly pushes, invests in the production of that class of algorithms.
Surely there is a continuity between "sort" and "genetic alg." - but the direction counts, it is in that direction that we strived to produce them producers.
So, it's very much not about the complexity of the product («sufficiently advanced technology»): it is in the complexity of the intermediate that built the final product, when that intermediate is not human. The pocket calculator is majestic, yes - but there is the strong point: it was human made. That is human intelligence at work. Study how to have it blueprinted by a machine, and if it works properly, you'll attribute a simulation of intelligence to the automated blueprinter - that is artificial intelligence.
> used words that describe what we're actually talking about
Look, people who follow me here know I place radical importance to language and to the awareness of language. It should be one of the aspects I would be most dreaded for.
Surely, most people are unaware of what they say to a large extent.
But in the case of "Artificial Intelligence", it seems you are underplaying the concept of directions - "simple algorithms" vs "advanced algorithms"; "houses" vs "skyscrapers"; "flying machines" vs "air force fighters". There is continuity and yet different position. And intelligence surely can be implemented at different levels.
Another thing (I am strongly selecting what I could reply, and I am forced to be concise). There is also a concept of "unintelligence" - the dire opposite of intelligence is also a thing (if Eliza is ~0, you can go below that). Understanding what intelligence is helps recognize its opposite, which is an experienced pitfall in the area.