I appreciated this post because I'm more interested in the 
philosophical implications (which I'm hoping to find at the end of Bruno's 
UDA bridge to Valhalla) of these goings-on  ...than in the mathematical 
ones. Best,
                                                                    marty a.

----- Original Message ----- 
From: "David Nyman" <david.ny...@gmail.com>
To: <everything-list@googlegroups.com>
Sent: Thursday, July 16, 2009 8:38 PM
Subject: Dreams and Machines

With Bruno and his mighty handful engaged in the undodgeable (though
constantly dodged) task of working towards an elementary grasp of the
technical underpinnings of COMP, and patently lacking the fortitude of
these valorous Stakhanovites, I have been spending my time lurking,
reading and musing. My philosophical position on possible relations
between computation and mind has long (well before this list) been
that it would indeed require something like Bruno's reversal of the
'normal' relationship between computation and physics, so that mind
could emerge in some at least comprehensible manner; certainly not -
per impossibile - in the ghostly shrouds of the 'deus ex machina' of
'computational materialism'. Consequently, parallel to the strenuous
effort ongoing in the other thread, I have been wrapping my mind more
loosely around 'interpretations of COMP-mechanics' in order to attempt
a better personal grasp of what it might mean as a metaphysics. As
always, I need help, so here goes for starters.

Bruno has sometimes remarked (if I'm not misrepresenting him) that
COMP introduces us to machines and their dreams and I find this
metaphor very cogent and suggestive. Certainly it seems to me that my
present state could coherently be characterised as a peculiarly
consistent dream - one that I nonetheless assume to be correlated
systematically with features of some otherwise unreachable
'elsewhere'. In COMP, the 'mechanism and language of dreams' is
posited to be those elements of the number realm and its operators
that are deemed necessary to instantiate a 'universal TM' (i.e. one
that - assuming CT to be true - is capable of computing any computable
function). Given this point of departure, it follows that machines so
instantiated would be capable of implementing any computable 'dream'
whatsoever - including dreams instantiating yet further levels of
machines and their dreams. With an additional dovetailing assumption,
we find ourselves in a position to construct a sort of hyper-threaded
layer-cake of dreaming where, from any arbitrary level, recursively
nested dreams disappear towards infinity both 'upwards' and

As we 'drill down' into this gateau, we are looking for emergent
patterns of invariance representing the self-referential viewpoints of
layers of 'dreaming machines' - their experience and their 'external
reality'. The lowest level of recursion that any particular system of
dreaming requires for its instantiation is taken to constitute its
'substitution level'. Since which layer of the cake this corresponds
to must be unknowable from the viewpoint of any level we currently
occupy, we ineluctably take a gamble if we say 'yes' to any doctor who
claims to know what he's about. BTW, on this topic, I would refer you
to an interesting analogy that I append as a footnote below.

So, what can we take 'reality' (i.e. real, as you will recall, "in the
sense that I am real") to mean in this schema? We cannot know, but we
do want to say that it corresponds self-referentially - in some sense
- to the number realm, and that the true language of the dreaming
machines therefore corresponds - also in some self-referential sense -
to numbers and their inter-relations. This 'sense of correspondence'
can be defined in two ways: 'truth', which is taken to correspond
self-referentially to the unknowably 'real', and 'provability', which
is taken to correspond to what this reality can consistently claim,
express, or represent to itself.

This is about as far as I've got, and broad as it is, it seems to
point more or less in the direction of a detailed research programme
such as Bruno has outlined. I can see that stipulations on 'reality'
such as universal computability make implicit claims that are
empirically falsifiable in principle, which is most encouraging.
Also, this general approach seems to me to have striking resonances
with metaphysics such as Bohm's notions of implication and
explication, as well as MWI.  Anyway - Bruno, I would be grateful as
ever - when you have a moment - if you would tell me which end of what
wrong stick I've got hold of this time.



One day a group of scientists got together and decided that man had
come a long way and no longer needed God. So they picked one scientist
to go and tell Him that they were done with Him. The scientist walked
up to God and said, "God, we've decided that we no longer need you.
We're to the point that we can clone people and do many miraculous
things, so why don't you just go on and get lost."

God listened very patiently and kindly to the man and after the
scientist was done talking, God said, "Very well, how about this,
let's say we have a man making contest." To which the scientist
replied, "OK, great!" But God added, "Now, we're going to do this just
like I did back in the old days with Adam." The scientist said, "Sure,
no problem" and bent down and grabbed himself a handful of dirt. God
just looked at him and said, "No, no, no. You go get your own dirt!"


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