On 3/1/2012 18:16, meekerdb wrote:
On 3/1/2012 9:57 AM, acw wrote:
On 3/1/2012 16:54, meekerdb wrote:
On 3/1/2012 1:01 AM, Bruno Marchal wrote:

On 29 Feb 2012, at 21:05, meekerdb wrote:

On 2/29/2012 10:59 AM, Bruno Marchal wrote:
Comp says the exact contrary: it makes matter and physical processes
not completely Turing emulable.

But it makes them enough TE so that you can yes to the doctor who
proposes to replace some part of your brain (which is made of matter)
with a Turing emulation of it?

The doctor does not need to emulate the "matter" of my brain. This is
completely not Turing *emulable*. It is only (apparently) Turing
simulable, that is emulable at some digital truncation of my brain.
Indeed matter is what emerges from the 1p indeterminacy on all more
fine grained computations reaching my current states in arithmetic/UD.

OK, but just to clarify: The emergent matter is not emulable because
there are infinitely many computations at the fine grained level
reaching your current state. But it is simulable to an arbitrary degree.

The way I understand it, yes, it should be simulable for certain
bounds, but never globally emulable - this in a twofold way: one in
that the local 3p structure that we infer might contain reals in the
limit (or rationals, computable reals) and another in that we can't
know of all valid 1p continuations some of which could be outside the
local 3p structure we estimated by induction. To elaborate in the
first: consider a mathematical structure which has some symmetries and
can be computed up to some level of detail k, but you can also compute
it to a finer level of detail k+1, and to a finer level 2*k, ... and
so on. Eventually in the limit, you get "reals". We only care that the
abstract structure that we call a mind is implemented in our
bodies/brains which are implemented in some physical or arithmetical
or computational substrate. Such implementations being statistically
common (for example in a quantum dovetailer) make local future
continuations probable. Of course, unusual continuations are possible
and we cannot find them all due to Rice's theorem - we cannot know if
some computation also happens to implement the structure/computations
that represent our mind - we might be able to prove it in some
specific case, but not in all cases.

But I'm still unclear on what constitutes "my current states". Why is
there more than one? Is it a set of states of computations that
constitutes a single state of consciousness?
Even in the trivial case where we're given a particular physics
implementation, we can find another which behaves exactly the same and
still implements the same function (this is trivial because it's
always possible to add useless or equivalent code to a program).
However, for our minds we can allow for a lot more variability - I
conjecture that most quantum randomness is below our substitution
level and it faithfully implements our mind at the higher level
(quasi-classically, at subst. level).

Yes, I think that must be the case simply from considerations of
biological evolution. But that implies that a "state of consciousness"
or a "state of mind" is a computationally fuzzy object.
We cannot know what computation we happen to be and even if we choose a "doctor" that does it correctly, we can find one machine of infinitely many equivalent ones. At the same time, the notion of universal computation is quite fuzzy - we can express it in infinitely many systems, yet even just one interpretation is enough to 'understand' what it is - the consequences of the Church-Turing Thesis.
> It is
constituted by uncountably many threads through each of many (infinitely
many?) states which are not identical but are similar enough to
constitute a "conscious state".
Hmm. There can only be countably (infinitely) many programs or states (enumerable), but there can be uncountably many histories (in the limit, non-enumerable)...

But the 1p view of this is to be
conscious *of something*, which you describe as the "computation seen
from the inside". What is it about these threads through different
states that makes them an equivalence class with respect to the
"computation seen from the inside"?
If they happen to be implementing some particular machine being in some particular state. The problem is that the machine can be self-modifiable (or that the environment can change it), and the machine won't know of this and not always recognize the change. This seems like a highly non-trivial problem to me.


Of course, there are some problems here - there can be continuations
where we will think we are still 'ourselves', but our mind has been
changed by stuff going below the substitution level - in which case,
the notion of observer is too fuzzy and personal (when will we think
we are not "ourselves" anymore? when will others think we are not

A single computation can be implemented by an infinity of other
computations, thus with COMP, an infinity of programs will all have
the same subjective experience (some specific class which implements
the observer).


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