R: origin of notion of computable universes

2002-04-15 Thread scerir

Gottfried Wilhelm Leibniz [The Monadology, 64-66] wrote:

But the machines of nature, namely, living bodies, are still machines
in their smallest parts ad infinitum. It is this that constitutes the
difference between nature and art, that is to say, between the divine
art and ours. And the Author of nature has been able to employ this divine
and infinitely wonderful power of art, because each portion of matter is not
only infinitely divisible, as the ancients observed, but is also actually
subdivided without end, each part into further parts, of which each has
some motion of its own; otherwise it would be impossible for each portion
of matter to express the whole universe. Whence it appears that in the
smallest particle of matter there is a world of creatures, living beings,
animals, entelechies, souls. Each portion of matter may be conceived as
like a garden full of plants and like a pond full of fishes. But each
branch of every plant, each member of every animal, each drop of its
liquid parts is also some such garden or pond.
And though the earth and the air which are between the plants of the garden,
or the water which is between the fish of the pond, be neither plant nor
fish; yet they also contain plants and fishes, but mostly so minute as
to be imperceptible to us.

http://testweb.wpunj.edu/cohss/philosophy/COURSES/PHIL312/LEIBNIZ/LEIBNIZ4.H
TM
http://www.wpunj.edu/cohss/philosophy/COURSES/PHIL399/LEIBNIZ.HTM

And Ockam (with Pier Damiani - De Divina Omnipotentia - and
Aristotle) states that not even God, who is in possession of
potentia absoluta - it means: miracles - not just of potentia
ordinata - usual physical laws, could erase the past, or re-write it.
Does it mean that, according to Ockam, simulations are forbidden?
It seems that Ockam (as the Aquinas and also Wyclif) thinks
that God could create the multiverse, or many universes.

Leibniz also wrote: although the whole of this life were
said to be nothing but a dream and the physical world nothing but a
phantasm, I should call this dream or phantasm real enough if, using
reason well, we were never deceived by it..







R: origin of notion of computable universes

2002-04-15 Thread scerir

Karl Svozil, Randomness  Undecidability in
Physics, World Scientific, 1993, [chapters 10.2 - 10.5]
also speaks about the simulaton argument.

It is not unreasonable - he says - to speculate about the 
logico-algebraic  structure of automaton universes (universes 
computer generated). 

If there is a hidden computing entity, and if this computing
entity is universal, there is no reason to exclude the so
called (intrinsic) calculus of propositions.

Physical properties corresponding to _experimental_ propositions
are identified - in the quantum domain - with projection
operators on the Hilbert space. Thus Hilbert lattice corresponds
to a lattice of experimental propositions. Algebraic relations and 
operations between these experimental propositions are called 
calculus of propositions. Hilbert lattice and calculus of propositions 
_should_ be equivalent, even in the quantum domain. (Lattice theory 
is a framework for organizing structures such as experimental 
or logical statements). There is no _recursive_ enumeration 
of the axioms of Hilbert lattices.

It is not unreasonable asking something like: do we live in a 
(quantum) universe created by some universal computation ? 

Thus, to test such speculation, we must look for _phenomena_
which correspond to automaton calculus of propositions _not_ 
contained in a Hilbert lattice (or its subalgebras).