this post was submitted on 11 Nov 2023
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Technically everything that a computer does can be simulated using any medium, pen and paper for example, or rocks and sand (relevant XKCD).
As for actually creating the parts needed, well a modern computer is just a very advanced Turing Machine which only requires 3 parts to operate: a tape for storing memory, a read/write head for reading/altering the data in memory, and a state transition tape to instruct the head to move left/right on the memory tape.
The memory and state transition tapes themselves can be anything, even a pen or rocks as in the previous examples. The read/write head could be anything as well. In previous iterations of computers we used the state of and turning on and off of vacuum tubes as a read/write head.
So conceptually, any time that humans were intellectually capable of reasoning out the logic. Their computer would just run much slower and be less useful the farther back in time you go.
“Reverse engineering” means tearing a machine down to figure out how it works.
Regardless of how much computation you can do with an abacus or an army of men with flags acting as logic gates, without sufficient microscopy you cannot reverse engineer a microchip.
That’s what this question is getting at: what previous incarnations of civilization would be able to study a computer and figure out what it’s doing?
Well if we're considering alternate histories where a civilization gains access to a working computer then it's basically impossible to tell. It depends on so many variable factors. Whether someone in that time period takes a significant enough interest to even look into it in the first place, whether they're smart enough to solve the question of what it's doing, and even who's hands the computer falls into.
There's a famous example of an ancient Roman trinket that was kept in the collection of a wealthy person. It was a small device that when placed over hot water would spin. We would recognize that device today as a steam turbine and we would know that it has the possibility of sparking the industrial revolution if the right person got a chance to look at it.
So if an ancient civilization got their hands on a modern computer and managed to do anything useful at all with it, it would alter world history in ways that we wouldn't recognize it anymore. Even if they didn't directly reverse engineer the computer but instead gained insight into other technologies like electricity or plastic production, it would alter world history in such a way that the modern computer would almost certainly be produced much earlier than in our own history which kind of nullifies the point of the question.
I'd say before the 19th century, this theoretical computer would be so much slower that even the idea of constructing such a machine wouldn't occur to people, cause there is no problem it would solve and no task it would help with.
It would help with playing solitaire if they didn’t have a deck of cards nearby