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). 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).


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