I'll stipulate your hypothetical, and claim that given a computer, Francis Bacon could have figured out in large part how it works, by suitable empirical tests.
The methods and processes of a hypothetical designer could in the same way be so subtle and advanced as to escape our rational assessments.
This is conjecture. More than that, it may be provably wrong. Mathematics, for example, has explored not just the algebra we use in high-school, but the set of all possible algebras. It has looked at the behaviors on N-dimensional spaces, not just the 3 or 4 dimensional spaces we live in. Moreover, I don't buy the idea that we can't distinguish with a high degree of certainty between a bug and a feature without the source code or a knowledge of the mental processes of the programmer.
Francis Bacon couldn't have done squat. For example, he had no electricity -- not to mention no idea even what electricity is. As such, there's no way he'd have been able to see the computer do much more than sit there. He'd have found himself staring at an odd set of objects, perhaps connected together by the odd flexible doohickeys. He'd have noted that they were covered by strange materials the likes of which he had never seen. He had no way of knowing that pushing the buttons with oddly-placed letters caused things to happen on the softish flat, dark-colored thing, and so on.... He may very well have dismissed it as some sort of odd religious artifact. It would have been highly unlikely indeed that he'd have been able to discern that this hunk of stuff would do math, help him write, and give him light to read by at night.
This is conjecture.
It is. OTOH, we know that it's probably a good conjecture, based on the past history of technology, not to mention the underlying science. I will admit, however, that we're familiar enough with technology now, to perhaps be less surprised by what will be invented in the future.
More than that, it may be provably wrong. Mathematics, for example, has explored not just the algebra we use in high-school, but the set of all possible algebras. It has looked at the behaviors on N-dimensional spaces, not just the 3 or 4 dimensional spaces we live in.
Given that algebraicists are still hard at work, I'd say that there's still plenty of algebra left to be invented. Certainly the depths of algebra have not been fully plumbed, and that is obviously even more true for mathematics in general. I don't see what that has to do with a discussion of evidence for design, however.
Moreover, I don't buy the idea that we can't distinguish with a high degree of certainty between a bug and a feature without the source code or a knowledge of the mental processes of the programmer.
I'm not so confident as you are. I've seen plenty of examples where an apparent "bug" turned out to be a central feature of a software design I did not understand (especially when the documentation is poor, or non-existent). I find that I make the mistake more often as the software I'm looking at becomes more complex. And it's even more difficult to change the software without causing some other, unexpected behavior. Why? Because the subtleties of the design are lost on me.
Francis Bacon couldn't have done squat. For example, he had no electricity - r9etb
I understood you were using a synechoche of "given the use of a computer"
(Why are Biblical Literalists so darn literal?)