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Arithmetic vs. Reality: The Sawdust Principle
- teddyh 10y agoSomewhat similarly, it annoys me every time someone rounds off decimals in the middle of some calculation. You round at the end, not in the middle, even if the amount rounded off is tinier than a single atom. Edward Norton Lorenz found this out, and called it the “butterfly effect”.
- vanderZwan 10y agoI remember being taught about approximations, rounding and significant numbers near the end of primary school. It was part of explaining why the calculators we used[0] displayed 1/3 as 0.333333 (because they rounded internally, of course). And, we were told, because a lot of calculations with calculators had this rounding error, those last few numbers we saw on the screen would be incorrect, especially if we did repeated multiplications and additions with them. So, our maths book instructed, we had to round down our answers to the same number of digits that we started the calculations with. This, of course, was not at all the right way to explain what significant numbers are, but that's how they were introduced to us. Anyway, I figured that (obviously) rounding after every step would only create a bigger error, so it would be best to only round at the end to get the best approximation. Then my teacher docked points for that. One of many "and I still kinda feel upset at my teacher for that" memories.