• You have to define what you mean by “modern computer.” If we really break things down, an abacus of infinite size would be Turing complete. It would take a really long time to play Doom on it, though. It would also need a person (or people) to operate it. However, the technology to do so would have been available starting around 2500 BCE. It could even be much earlier, if you want to have your time traveller also invent the abacus. If you want something a bit more pragmatic, we can look to Charles Babbage and Ada Lovelace, who are generally credited with creating the world’s first programmable computer with a number of functions still in use today. Babbage was working in the mid-19th century, but given knowledge of his work could probably be reverse engineered back a bit as well. If you want to go in the other direction and make it even weirder and less practical, you can perform computation with a large room filled with people passing slips of paper back and forth after doing a simple logical operation on them.

My point is that there’s the current state of hardware technology, which depends on a whole chain of technological advances, and there’s computation logic, by which we see the “universal” part of the universal Turing machine.

If you’re talking solely about hardware and modern electronics, there’s a whole set of dependencies on industrial engineering and chemistry that goes from gears to vacuum tubes to diodes, which is interesting in its own right. What I guess I’m saying is that the advancements in the theory of computation (elements of theoretical architectures and mathematics) is distinct from the hardware it runs on. If you were to go back and teach the calculus and the theory of computation to Da Vinci, I imagine he’d come up with something clever.