One of the principal problems of numerical analysis is to determine how accurate the results of certain numerical methods will be. There's a credibility gap: We don't known how much of the computer's answers to believe. Novice computer users solve this problem by implicitly trusting in the computer as an infallible authority; they tend to believe that all digits of a printed answer are significant. Disillusioned computer users have just the opposite approach; they are constantly afraid that their answers are almost meaningless. Many serious mathematicians have attempted to analyze a sequence of floating point operations rigorously, but have found the task so formidable that they have tried to be content with plausibility arguments instead.
Don. Knuth, taocp ii, § 4.2.2.
A bad illustration of interval arithmetic:
Futurama, season 6, episode 6, “Lethal Inspection”.
A knight of Error Analysis in action:
Eastman and Laird's Teenage Mutant Ninja Turtles #4.
Xkcd #2311:
