[generalizations]

Thanks, I think I understand now. I thought there was a distinction between the mathematical idea of what computation is, and the engineering we've invented to implement that computation, and so I didn't really get the significance/literalness of what you were saying about mechanization.

It does seem weird to me though that we're letting our engineering limitations determine how we think about these things mathematically.

[nl]

It's not as simple as engineering limitations determining how we think.

Turing machines do have mathematical advantages in some areas. See this siblings comment: https://news.ycombinator.com/item?id=28541800