I'm pretty sure they could learn to write programs. The had algorithms.
We do not have aliens or time travelers to walk us through genomes and fill in the missing pieces of our understanding.
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.
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.
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.
I've thought for many years that there are new intellectual tools waiting to be discovered here that will be as big as arithmetic, calculus, or logic. There was a time when humanity had no idea what mathematics -- the whole field -- was, and today there are probably whole analogues to mathematics waiting to be discovered.
Unfortunately we are still in the phase of trying to attack this problem with old ways of thinking. We probably won't even try until we finally come to terms with the fact that the tools we have at our disposal right now do not work to truly understand the genome. This will take a while as humans become emotionally attached to their tools and cling to them. Try debating a programmer on OSes, languages, or editors to see a simple example. :)
Bonus is that once we understand the genome we'll probably understand a lot of other unknown unknowns we didn't even realize we didn't understand. Maybe this is why physics seems stuck. Maybe the cognitive tools we have right now are simply not up to the task of understanding the whole thing.
Edit:
I actually think Stephen Wolfram's doorstop A New Kind of Science was groping in this direction. The book was problematic because of Wolfram's almost comical narcissism (Wolfram sort of tries to take credit for a lot of things he didn't invent), and the techniques it discusses don't seem to have delivered much fruit in and of themselves. Nevertheless at the "meta" level the notion of trying to invent fundamentally new intellectual tools is absolutely what we should be doing. We will of course fail a lot, but that's what happens when you try to do something new.