@chris-2 Harshman

Funny you mention "I'd be more likely to miss one or make a mistake" because this too is a sign of laziness (and I am very afflicted with it myself.) In the wikipedia entry for Babbage, there is this quote from a book on his works: http://en.wikipedia.org/wiki/Charles_Babbage

In 1812 he was sitting in his rooms in the Analytical Society looking at a table of logarithms, which he knew to be full of mistakes, when the idea occurred to him of computing all tabular functions by machinery...

—B. V. Bowden, Faster than thought, Pitman

If his mind had gone to the idea of just fixing the tables, that problem could have been solved, but instead of that laborious task, he went off on a tangent to find a better way that didn't involve a slide rule and meticulous work. Of course, computers aren't perfect (and less so when humans write the programs) but for all practical purposes, they can do 99.99999% of calculations (perhaps even more) well enough that it is definitely better than spending the time otherwise.