Exactly. I consider it much like "types" in programming languages: middling to weak "formal verification". In the case of most calculations I've ever carried out substantially 'by hand' in physics / chemistry / etc., it still made / makes a substantial difference in error rate.
Without propagating dimensions, my error rate can be a real issue. I wouldn't trust the final number on a full, say, roughly "letter-sized" (US 'wonderland' system) page. By propagating, I might trust the result 75 or 80% of the time...
(I do rather doubt I could have been an even average NASA "computer" given the opportunity to do a great deal more of these kinds of calculations than I have had to... my mind is much better at generating random numbers and nonsense than doing anything 'mechanical'. AFAIK, NASA had no call for such skills in the "age of human computers".) :)
Without propagating dimensions, my error rate can be a real issue. I wouldn't trust the final number on a full, say, roughly "letter-sized" (US 'wonderland' system) page. By propagating, I might trust the result 75 or 80% of the time...
(I do rather doubt I could have been an even average NASA "computer" given the opportunity to do a great deal more of these kinds of calculations than I have had to... my mind is much better at generating random numbers and nonsense than doing anything 'mechanical'. AFAIK, NASA had no call for such skills in the "age of human computers".) :)