For example, what would be the most efficient binary representation of probabilities values between 0 and 1? In the future, I can imagine hardware + software that is specialized for examples like this.
edit:
Do I really want more resolution between 0.41 and 0.42 than between 0.01 and 0.02?
Some experiments like with liquid crystals early on required purities that what chemical company was it, Merck I think, around the year 1900, complained like they felt insulted. Told the inventor of liquid crystals because it was an absurd amount of purity required to get them actually working. But look at them go! Right in front of your very eyes!
The logistic curve becomes denser close to 0 and 1. Which makes sense: you will want to tell apart 1 defect per million from 0.01 dpm, and 5-sigma process (99.977%) from 6-sigma (99.99966%), much more than tell apart 30% from 30.001%.