On 3/1/2012 19:06, meekerdb wrote:
On 3/1/2012 10:39 AM, acw wrote:
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.

Hmmm. I thought the idea of the UD was to abstract computation away from
any particular machine, so that states (or consciousness or the world)
were identified with states of finitely many (but arbitrarily
increasing) threads of computation.

The UD has to be implemented somehow (for example in arithmetic or a physical machine, or in some other Turing Universal machine). The UD is a concrete program that can run on a TM or in any other language (as long as the language allows for universal computation). The mind's body is represented by an equivalency class of machines, which we cannot know exactly which one it happens to be, but if the doctor guessed correctly, we can know at least one, and many other ones equivalent to it, just not all. As for the computations implemented by the UD - given some upper bound, there are always a finite amount of them, but given that the UD is non-halting, the UD* trace contains infinitely many programs (as many as the natural numbers). The UD* does implement all possible bodies and 'physical' continuations for a particular mind, but we cannot know what our next 1p continuation will be or even *when* or at what state it will be (unless we limit ourselves and only look at some particular computation, but we cannot really do that by the UDA, although I suppose we can always construct a local physical model that lets us make quicker predictions which have sometimes a chance of being wrong, but are mostly right for most probable/numerous continuations).

This seems like a highly non-trivial problem to me.

An understatement. :-)



Brent

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
"ourselves"?)

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).

I have some difficulty with this infinity though. If you think of a
dovetailer it is never executing infinitely many programs; it is just
always executing *more* programs. It is only when you make the leap to
Platonia that there are infinitely many computations which go through a
given state infinitely many times (hence producing an uncountable number
of threads). So it all depends on Platonia existing, as Peter Jones
points out.

Let's say we pick an UD and run k future states (which would also exist as number relations, when considering the Platonia view). We could make many predictions about those existing in such a limited UD, but then the question is, why would only k states exist? Why not k+1? It seems to me that the ultrafinitist view is harder to stomach, it adds extra complexity. For each finite state machine that we can conceive, we can conceive of a slightly bigger machine (by induction). If arithmetic turns out to be inconsistent, such a finite view of reality could make sense, but it's immensely harder for me to stomach. The 'everything' view that each possible machine exists is simpler by Occam than the one where only a finite number of machines exist. Using Platonia does simplify a few things, especially the identification of the mind - without it you have the problems described in the MGA (and some other thought experiments) and it also makes the identification of some class of mind (1p view of computation) harder.
Brent




Brent








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