[Tainnor]

> 2. Personally, though, I find the topic of numerical stability to be a little bit depressing, since it focuses on all the ways computers don't work!

Maybe a way to more positively reformulate this would be: There is no a priori reason to assume that floating point numbers are well behaved. The fact that we were able to come up with a structure so that it approximates real numbers adequately, that arithmetic operations on it are fast (which they aren't for infinite precision) and that, if we design the algorithms correctly, errors are well-behaved, is an astonishing feat of engineering.

[kevin_thibedeau]

Computers work perfectly fine. Engineering was done for a long time with slide rules to avoid the tedium of looking up values in a book and grinding out results by hand or adding machine. Using them correctly requires knowing their limitations just as knowing the limitations of a computer is important. They aren't magic oracles that always give correct answers.