Floating point numbers are not continuous.

Yeah, that is important to recognize, but floating point numbers could obviously sample continuous measurements with less loss than integers.

Only if the measurements span several orders of magnitude and you want to keep the relative error low. Otherwise you'd be better off with fixed-point numbers, which are spread out more evenly (about half of the IEEE floats are less than 1 in magnitude).

And if you don't limit yourself to linear mappings, you can probably do even better with a non-uniform integer encoding.

Only on the human-readable level, which, when your brain is as big as mine is, doesn’t even like matter.

0 or 1 for discrete values when it comes to pattern recognition in vector similarity comparisons. Ask the guys that developed AutoClass at JPL to identify clusters of stars.

Continuous, but if digital systems are limited by bit count precision, analog systems are limited by SNR, distortions and "inertia".

How the brain deals with it is the interesting part (hence why our "adversarial examples" are different from Artificial Neural Network ones)