mathematicians like to skip steps, generalize and the like. 'randomness' for numbers is not really a well defined mathematical property. what i like about the summary is that you can understand the gist of what he is trying to do and why.
> 'randomness' for numbers is not really a well defined mathematical property.
Randomness is a well-defined property. We say that numbers are random, or "normal", if an infinite sequence of their digits forms a uniform distribution. The reason we call them "normal" and not "random" is because they are the norm - almost all real numbers are normal.
If we could read the coordinates of any physical object to infinite precision, we could only influence the higher digits by moving the object very carefully, beyond the digits which we have some influence over, the infinite tail of the real numbers digits must be completely random.
