On 14 Nov 2014, at 08:46, LizR wrote:
In case anyone isn't acquainte with the library of Babel, it
contains all possible books of a particular length (I think it's
around 400 pages) which use a certain number of characters, say 30.
If we assume there are, say, 2000 characters per page, we get (I
think) 30 to the power of 800,000 books, a large but finite number
of the sort I think Daniel Dennett called "Vast" (meaning
ridiculously larger than any numbers that could be used to count
anything in the observable universe. The LOB would dwarf the
observable universe). It's similar to Russell's TON in that it
contains essentially no information - or certainly no useful
information. As Borges mentioned it contains the accurate catalogue
of the Library (presumably occupying many lightyears of shelves, if
assembled in one place) together with a "Vast" number of innaccurate
catalogues. It also contains every book ever written, including the
one in which the short story in question appears. This is rather
similar to the multiverse, in which every story ever written is
being played out somewhere (in the case of Harry Potter, with the
help of an awful lot of quantum uncertainty happening to come out in
just the right way).
But note that the UD* contains all programs books, but also all
execution of the programs, and all relative state of the "readers" of
all book. Russell does not use computationalism, so he needs some
absolute sampling in his theory. Don't confuse a book, or a
description of a computation (in arithmetic), and an execution of a
computation (in arithmetic). Those are quite different, and that play
some role in the step 8, to graps for example that a movie does not
implement a computation. You really need the truth of some number
relation, which does not exist in the description of computation. It
is a subtle but very important point. In particular, the counting
algorithm 0, 1, 2, 3, ... contains all books, but with addition and
multiplication, you still don't get the UD nor UD* (the execution of
the UD).
To get the UD, and UD*, you cannot start from nothing, you will need
some non-zero information initializing the theory, like the axiom of
arithmetic & logic, of the axioms on combinators and equality. Like
you need the SWE in physics, even if you start from the vacuum. The UD
is a dynamical object (in the math sense, not the physical).
A theory must say what is assumed as initial objects (like the
numbers, the sets, or the particles), and give the basic laws
(addition and multiplication) Then a notion like "nothing" is theory
dependent. The hard part is the choice of the "thing" we need to get
the epistemologies (where physics resides when we assume
computationalism). But then comp shows that physics is theory
independent, so you can assume any theory you want, as long as it is
Turing complete. You should better not take a theory like string or
QM, because it will be confusing when deriving physics from it.
Bruno
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