Or more simply, we can observe that a program that prints out all possible books in order, is much simpler than a program that prints out only Romeo and Juliet. To put it another way, Borge's "Library of Babel" containing every possible book has far lower algorithmic complexity than an Earth library containing only some books.
Is true. As far as I can tell, the above statement requires some of the following to be true:
The set of all possible books is something more like the set of all possible strings above a certain length (that the content of those strings be coherent, and constitute legitimate books is not required).
The shortest program encoding Romeo and Juliet in our reference UTM does so by explicitly locating it within the set of all possible books.
I see no reason to assume that 2 is true, and I feel that if 1 is assumed, then it should be stated as such or it would be misleading.
It is not clear to me that:
Is true. As far as I can tell, the above statement requires some of the following to be true:
I see no reason to assume that 2 is true, and I feel that if 1 is assumed, then it should be stated as such or it would be misleading.