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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 bo
by Fargren 12y ago
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.
- millstone 12y agoNitpick: This is NOT true for only normal sequences. See disjunctive sequences: http://en.wikipedia.org/wiki/Disjunctive_sequence http://en.wikipedia.org/wiki/Disjunctive_sequence . pi may contain all numbers as substrings and yet not be normal.
- brudgers 12y agoExactly. 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.