> What if the knowledge behind that device hadn't been lost and we were 1k years further along into our understanding of mathematics and computing?
I believe that knowledge is overrated on the long run. It is methods for knowledge creation what really matters. And incentives to apply the best known methods.
Had you read Bret Devereaux talking on an absence of Roman Industrial Revolution?[1] No practical steam engine before it's time has come. Knowledge is created when it is needed. I believe the same stands for computing. It must be some new demand for calculation that created computing. Probably the development of economics.
[1] https://acoup.blog/2022/08/26/collections-why-no-roman-indus...