The thing about normality is that if a number is normal, it will contain all books not only for a given encoding of a book, but for any given encoding of any book. That is true only for normal sequences, of which pi is assumed to be an example.
Exactly. So we can choose an encoding that is computationally expensive or one which is cheap. The essence
of mathematical thinking is to use replace complexity with simplicity: a person who insists on calculating the sum of positive integers less than n with n - 1 operations is not to be admired for their mathematical insight [their dogged determination may be another matter].
Some encodings are more useful than others while being equivalent. All encoding requires an arbitrary interpretation. Each is equally valid...finding "books" in Pi is a flight of fantasy.
Comments
The thing about normality is that if a number is normal, it will contain all books not only for a given encoding of a book, but for any given encoding of any book. That is true only for normal sequences, of which pi is assumed to be an example.
Nitpick: This is NOT true for only normal sequences. See disjunctive sequences: http://en.wikipedia.org/wiki/Disjunctive_sequence .
pi may contain all numbers as substrings and yet not be normal.
Exactly. So we can choose an encoding that is computationally expensive or one which is cheap. The essence of mathematical thinking is to use replace complexity with simplicity: a person who insists on calculating the sum of positive integers less than n with n - 1 operations is not to be admired for their mathematical insight [their dogged determination may be another matter].
Some encodings are more useful than others while being equivalent. All encoding requires an arbitrary interpretation. Each is equally valid...finding "books" in Pi is a flight of fantasy.