Calculator Accuracy & Usefulness

[Claudio L.]

(05-24-2015 09:28 AM)Tugdual Wrote:  We don't need very deep accuracy simply because the measurement systems already include this concept in the real life. You don't measure bacteria sizes in km and/or the distance in between galaxies in mm.

Reading this thread it gives the impression that in engineering there's no need for precision. Far from reality!
Engineers don't only use "measured" quantities. We also use complex algorithms with thousands of computations.
Just try an ODE (Runge-Kutta anyone?), do a shootout at various precisions and see where it takes you when you are thousands of tiny steps away from the boundary condition.
We can take the final result and only use a few digits, and we can round the input to a few digits, but all intermediate calculations NEED some precision or it'll be a disaster. Changing the third digit on the boundary condition might get you off only by 5% or so, but after a thousand steps, you'll be an order of magnitude off if you only use 3 digits at every step.

Surveyors are a good example: they use exclusively measured quantities, yet they were historically desperate to get more precision: multiple measurements with the tape, compensating for the temperature of the tape, compensating for the sag, compensating for the stretching of the tape due to axial stress, etc. are just examples of how much they needed that precision in the past. Today, they use GPS to get an accuracy within 1 cm anywhere on earth. Satellites are orbiting 20200 km above earth, and within 1 cm you need to operate with numbers of the order of 2 020 000 000 cm, that's 10 digits bare minimum right there.

In electronics, engineers need to count 'ticks' of clocks that are gigahertz in frequency. Lots of digits there. Transmission of signals needs accurate clocking (GPS receivers are again a good example).

Old engineers with slide rules didn't have to deal with this, or simply couldn't even if they wanted to. These examples are a consequence of the gradual increase in precision over the years, of which early calculators were a very important part.

Some areas of engineering need more precision than others, but for sure calculators with more precision (and later computers) enabled a LOT of progress.