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 isconstituted 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. :-)BrentOf 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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