[mjevans]

Mathematicians vs Computer / Systems Engineers. The machine only has so much space, so it's best to imagine every value also has a corresponding error range attached and that managing the growth of that error range so that it remains under the target value is key.

[taneq]

And that operations combine those error bars in unintuitive (until you develop that intuition… but then does that still count as intuition?) ways.

[phire]

IMO, the way the error bars combine is very intuitive. You are really just rounding to 6 or 12 sig-figs after every operation.

People just seem to get really hung up on the point that error bars exist in the first place, and combine.

I suspect it has a lot to do with the way that rounding is taught in school. It's absolutely hammered into use that you should never round until the very end, otherwise you lose precision.