| I agree, that's a poor answer by NASA director and chief engineer. Here is a better answer: The precision used for calculations is dependent on the number of "steps" required to get to the final result. Roughly, for N repeated calculations you lose somewhere between sqrt(N) * eps to N * eps of precision (eps=2e-16 for IEEE64). Here are some actual examples: IEEE64 (~16 decimal digits) is OK for interplanetary navigation for few months, where relatively low accuracy is required. With the same precision, you start to lose phase accuracy above 24 hours if you're simulating GPS constellations. You need quad precision or above for simulations > 24 hours. For simulating planet trajectories and solar system stability (Lyapunov time of planets), IEEE64 is good for ~10 mya in the future (Neptune-Pluto Lyapunov time), IEEE128 for ~200-1000mya, above that it is recommended to use 256bit floats and above. This is assuming typically ~1000 steps per simulated orbit. Fun fact: we know from simulations that Pluto trajectory is stable for >10G years, but unpredictable above >10M years because of chaotic (but stable) interaction with Neptune. [1] https://en.wikipedia.org/wiki/Stability_of_the_Solar_System |
Something to add to your list of examples: During the first Gulf war, 28 US soldiers died due to accumulated rounding errors in the Patriot Missile battery computers: https://www.ima.umn.edu/~arnold/disasters/patriot.html
(This was in fact a known issue, and operators had been instructed to reboot the computers every 8 hours. Unfortunately this instruction ignored the fact that, in the field, nobody wanted to be responsible for turning off their defensive systems for a minute.)