[bhaak]

> I wonder how sigma notation fits into this. Clearly the notion of expressing arbitrarily repeated operations using a fixed amount of information (which is what a loop is, essentially) was known at least to Euler.

You can even go further back. Algorithms with loops were known already to Babylonian mathematicians. So you don't need to resort to preternatural prescience.

The Z3 was not intended as a general computing device but as a practical help for engineers. Because of that you can't say it was missing something it didn't need to do its job. Whereas when Zuse designed Plankalkül loops and conditional branches where naturally included in the design.