kedabra wrote:Sorry its taken me so long to reply. I've re-read the thread and the first 7 steps of your paper.
Please, don't be sorry. It is all normal to take time, and I am happy of your kind interest. The more you are serious about this, the more time you need to get the necessary familiarity with the ideas.
I've tried explaining this to a couple of friends, and not had much luck. I can just about explain the maths but its very hard for me to relate this to consciousness and physics.
OK. I will try to explain.
Correct me if i get this wrong. The Universal Dovetailer sort of makes sense to me - its a kind of mathematical platonia, like a mandelbrot set, that contains all computable functions including those that "crash", and all other universal dovetailers including itself, infinitely many times. It computes all steps on all data entering all programs, in an enumerable way, not necessarily going from step 0 to 1 to 2, but in a pattern tracing through all possible computations, in such a way that that is possible i.e. enumerable.
OK. Actually it is a tiny part of mathematical Platonia, even a very tiny but important part of *arithmetical* platonia. But that is not important now.
Do you know the language instruction "FOR" of some programming language?
You can program the universal dovetailer like this:
FOR I, J, K, non negative integers,
compute phi_I(J)^K (= compute the K first steps of phi_I(J))
Of course "phi_i" has to be generated from a program capable of recognizing the well-formed expressions of some universal programming language. The code above is short and a little bit simplified. The key point is that the UD is given by a (finite) program, and that we might make it run in our physical universe, forever if our universe is robust enough. The necessity of the physical universe is eliminated in the 8th step.
Because it contains all other dovetailers, there will be huge amounts of repetition in this structure, as it traces through infinitely many other kinds of ways of computing the same thing, or nearly the same thing, like the mandelbrot set contains infinite repetition on a theme, except that all themes are contained in the Universal Dovetailer - not just spirals! I would appreciate some clarification on why this repetition occurs, its a bit hazy.
Because for each computable function you have infinities of ways to compute it. You can always add dummy instructions, or even write a code which on some input will compute others functions for a while, then resume the first computations. The UD generates all programs, which means also the very stupid and lengthy circumvolved way to compute functions. This can be proved formally but I think it is intuitively obvious. Also, as you mention, the UD, when run, will generate in particular all UDs. A UD in LISP will run many other UDs in LISP, but it will run also the PROLOG interpretation (in LISP) of the UDs written in prolog, and all this for *all* programming languages (we assume Church thesis).
The important thing is that this does not happen inside some other "real" universe, maths has its own reality, so time doesnt exist, other than as an image in the dovetailer. So there is no sequence in which the computation takes place, its just a structure containing all computable functions on all inputs, that exists outside of time and space in some kind of platonic realm.
OK - I'm not too sure about numbers having their own reality, but why not?
This is really the eighth step. In the seven step we do all the work, before explaining the immaterialist consequence, except that we assume some real universal dovetailing done in our universe. In such universe, the laws of physics have already to be explained by a statistics on *all* computations. This should follow from the seven first steps. I will try to see what you seem missing.
After reading your paper, it seems its very important to understand what you mean by consistent extensions of a 1st person set of beliefs or experience.
I have found it very confusing when you talk about the infinite number of computational histories going through a 1st person.
In your paper, you explain how there is an indeterminacy in the 1st person that doesn't appear from the 3rd person. This seems relevant but I can't grasp why.
What is happening? If i was scanned into the Universal Dovetailer, what would happen to me?
But you *are* scanned into the Universal Dovetailer, in the robust universe where it exists (by definition). Your state, here and now, reading this line, is
some phi_i(j)^k, and the UD generates it, infinitely often, through an infinity of computations going through that (relative) state.
Normally, with the preceding steps, you know that your next state of mind is determined by all the "reconstitutions" of "your phi_i(j)^k states in the universal dovetailing (the running of the UD). The key point is that the indeterminacy does not depend on the delays made by the UD. It might take 1000^1000 steps to get some of those phi_i(j)^k, and it will provably taken more than <any-big-numbers>^<any-big-number> to get other one, but your first person state is unaware of all those delays, by the passage from step 2 to step 4. So, for predicting what you will feel in two seconds from here and now, and being exact, you have to make a statistics on an infinity of computations: all the computations going through your state (they are all done by the UD in the supposedly enough robust universe. So if there is a UD running in our universe, the laws of physics have to be reshaped into a statistics on the UD-computations.
And what does Turing emulable mean?
It mean Turing simulable, but in an exact way. This notion makes sense for the digital processes. If your consciousness can be attributed to the computation done by your brain, then you are Turing emulable. Even if your brain (that is: the portion of physical reality needed for your consciousness to exist) is really the entire galaxy, the UD will generate the relevant state (of the galaxy) if it is Turing emulable. To be sure, we don't know anything not Turing emulale in nature, except for the first indeterminacy, which occurs in self)duplication, and in quantum superposition. But this is well explained by the first person indeterminacy in self-multiplication.
I'm finding it hard to relate the maths/logic (which I am starting to understand) to the physics/psychology...what is the physical world on this view? I keep thinking I understand it, and then it slips away again.
SWIM has the same problem with the salvia experience
The precise link is done when you say "yes" to the doctor who proposed to you an artificial brain. You bet that you will remains conscious, despite a change of a material body. But the duplication illustrates that you have to be uncertain about your possible future, and the UD extends this duplication into a enumerable multiple multiplication. So by betting that your consciousness is invariant for a material change preserving your digital functionality at some level, physics (or anything used to predict your observation) is shown to be derivable from a statistics on the computations. This makes such an hypothesis testable, by comparing this comp-physics with real physics. It predicts that below our substitution level, there are infinitely many computations, and this is what quantum mechanics confirms with the notion of superposition of states (aka parallel universes).
Another question. How is the flow of time computed by the UD?
There are many notion of times related to the Universal dovetailing (that is, the execution of the UD). The most primitive one is the order of the computation of each phi_i(j)^k, for example. now for some i, j and k, this might represent the simulation, at some level (string theory level, for example) of the cluster of galaxies in our neighborhood. This might include a physical times, simply emulated by the UD. The psychological time of all entities is not capture by any of those simulation, but by an average on all computations, by the first person indeterminacy.
It seems like we are only calculating the consistent extensions from all possible inputs, which is only one step (the calculation might have many steps, but the result is just one number, or crash).
The UD never give any results. He does all the computations. Just by theoir cardinality, the one which counts are the infinite one. The idea of doing the computations by each step is to be sure that the UD does never stop generating and executing all computational processes. It emulates all the cellular automata patterns, for which there is no obvious notion of input and output. It is not the result of the computations which counts, but the computations themselves. Just to make it concrete, here is a pdf with a UD implemented in LISP, and some sample of running. But the comment are in French.(pdf of a concrete UD
So how do we go from there, to calculating the next step?
Remember that in a computation, one step of a computation is a little simple, and always stopping elementary procedure, like "erase the memory 45676", or "decode 111010001100001", or copy the content of register 45 into register 23", or "if the content of register 67 is 0 go to next line of the program, else decrement register 98", etc. It always stop, so that the UD can execute and run all programs. The programs i who never stop on some input j will just ... never stop, meaning that the UD will access some phi_i(j)^k for *all* k.
Does the next step already exist in the structure? You just have to put the output as an input.
Given that there are computable composition of programs, and that this gives programs, the UD will indeed run all combination of all programs. And, yes, this exist in the pure arithmetical reality, which has a tiny part already Turing universal. Somewhere in the arithmetical truth Plato smokes some salvia divinorum, no doubt. But not all computations are easily accessible, and the physical laws are what will govern the relative accessibility among computations. first person amnesia will fuse the computations, and nature already fuse some computations (empirically we can guess that by the quantum interferences, and computationalism entails that for what happens below our substitution levels). This is not so easy to prove.
That computation already exists in the UD. Have I answered my own question?
I think you did, or are very close to it.
The UD computes all possible histories as well as instantaneous consistent extensions?
From the third person point of view, of someone looking, from 'outside' at the universal dovetailing, the consistent extension (basically the continuation of computation) are not done instantaneously (at all!). The thrid person observer might wait for 1000^1000^1000^1000 millennia before getting the next step of some programs, but from the first person point of view, by the impoosibility of being aware of the delays, its most probable continuation is given by a measure on all computations instantaneously.
I think you understand well, but that you have perhaps not yet practice enough the slef-multiplication experiences for delineating well the role of the (key) distinction between the first person view, and the (eventually purely statical) entire (infinite) universal dovetailing.
It reminds me of Julian Barbours Platonia. Do you know his work?
I have heard about the time capsules. Did he heard of my work? I dunno. What is similar is what the philosopher call the indexical conception of time. What I show, is that assuming we are digital machine, we get an indexical notion of physicalness, and this in a frame where the indexicality can be handled in arithmetic, making all things precise and making the computationalist hypothesis testable. To be sure I need also the classical theory of knowledge (of Theaetetus) to make the whole thing purely arithmetical.
Another thought - the consistent extensions, the infinity of possible comutations which could be performed on a 1st person - these extensions are not consistent because of any physical laws - you can multiple me by a million or 34, or subtract 5 from all of my atoms, an extension just has to be computable. Are you saying that all these crazy calculations exist, and then physical laws emerge later, because of the way all these extensions interact? If so how do they interact?
They don't interact, but *some* computation emulates all the computable interactions. Empirically we know (by QM) that computations can interact and does interact, but the parallel computations does NOT interact, they only interfere statistically. This is crucial in the working of quantum computer, for example, and easily explained in the comp frame. The precise link between both remains a vast unexplored field (if not still very unknown, if not ignored).
Again, sorry for the delay - I appreciate your patience.
I appreciate yours. Don't worry for the delays, platonists are patient, they can wait for big numbers of millenias
Of course, for helping the others, in this public third person consensual realm, it is nice if you tell us in advance in case you decide to make a tour in some galaxy nearby, and come back in 27 billions of years
Actually, I think that the ball is on my side. I have promised to go through each steps, especially for the benefits of some others, and I will do that soon (I will not take a tour in the galaxy nearby, before!). Thanks for your
patience, kedabra, and for the patience of the edot forum members.