They could if it were explained to them. I doubt they could figure out a more complex sort of algorithm if they were given the artifact with no explanation. Doubly so if the algorithm involved things like calculus and modern number theory.

We do not have aliens or time travelers to walk us through genomes and fill in the missing pieces of our understanding.

If your are referring to the physical CPU itself, then you are correct as they would lack the technology to even see the circuit paths (much less measure current).

But, if you are suggesting a smart human from 500 B.C. couldn't grasp 'The Art of Programming,' I'd respectfully disagree. Logic and reasoning haven't changed in recorded history. The ancients were no more or less intelligent than the moderns. Whenever I'm tempted to think otherwise, I sit down with my Euclids Elements and see how far into it I can get before I reach the "WTF... How did he figure THAT out!?" An even better cure -- although more recent -- is to see how far you can get through Newton's Principea.

I see your point but I still dont agree.

Everything seems obvious and easy in hindsight because we are viewing it with those intellectual tools deeply embedded into our understanding. They are all over our culture and we pick up bits of them as children through osmosis even before we study them formally.

I think getting an ancient Greek or Roman intellectual to understand a large integer factoring algorithm, a proof of work block chain, or an OS kernel would be pretty painful. It would take a lot of tutoring to first teach a lot of things that were not understood in that time at all.

You can sometimes see this today when you see older people in rapidly developing nations trying to learn advanced concepts. They can do it but it takes a while.

My point is that all this assumes a tutor who knows and can explain. For levels of understanding not yet reached by any human, there is no tutor to teach us how to think about the problem.

Two of your three examples consist of algorithms that take a large number of steps. Without an ability to perform a large number of steps in a short amount of time, there wouldn't be the need to think about such things. That is, your tutoring of the ancient would consist of explaining an algorithm that might take 100,000 calculations. He would grasp it, but shrug and say "so what? It would take years to perform that algorithms. Let me show you a different way that results in a damn good approximation that requires nothing more than a compass, straightedge, stylus and a piece of string."

In short, you are confusing reasoning ability with algorithms designed for a particular form of technology.

Take neural nets. Would someone from the 1970s understand the benefits of a convoluted net vs. a simpler form? Perhaps. But, without the technology to perform millions of training calculations, the lack of comprehension would come from your pupil wondering what the point would be of trying to understand an algorithm that, with his technology, could never be demonstrated, used, or tested.