I'm not an expert (my only qualification is that I read a part of Babbage's book; others must know a lot more), but see http://tomforsyth1000.github.io/blog.wiki.html#%5B%5BBabbage... and (linked from it) https://www.fourmilab.ch/babbage/cards.html — it looks like he did have a reasonable design of a computer in fact. (Except for the too-many-digits-of-precision thing, that the OP tweet thread is about.) He seems to have well understood how not just arithmetic but a lot more could be done mechanically.