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The Turing Principle in a collapsing universe

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  • Charles Goodwin
    In the last chapter of FOR, DD infers - given various assumptions (e.g. that the universe will recollapse) - that intelligence will survive, and knowledge
    Message 1 of 9 , Nov 1, 2004
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      In the last chapter of FOR, DD infers - given various assumptions (e.g. that the universe will recollapse) - that "intelligence will
      survive, and knowledge will continue to be created, until the end of the universe." The amount of knowledge created, and the
      subjective time of survival, would be infinite. This inference appears to be based on the fact that the Turing Principle is our best
      theory of the foundations of computing, and the TP implies that there is no upper bound to the number of computational steps that
      are physically possible. Otherwise, DD argues, we are left with a sort of "approximate Turing Principle" which would be correct,
      given worlds enough and time, but which isn't correct because the universe only allows a very large but finite number of
      computational steps to be performed. For comparison he says that "the theory that the world is *half*-comprehensible explains
      nothing and could not possibly fit in with explanations in other fields unless *they* explained *it*. It simply restates the problem
      and introduces an unexplained constant, one-half. In other words, what justifies assuming that the full Turing Principle holds at
      the end of the universe, is that any other assumption spoils good explanations of what is happening here and now."



      Leaving aside the evidence that the universe may continue to expand forever (which also possibly disallows the full Turing
      Principle, but for other reasons), isn't this a circular argument? The equivalent of the "constant, one-half" in this case would be
      the maximum possible number of steps any possible computer - say, for the sake of argument, one spontaneously assembled from all the
      matter in the universe at the instant of the Big Bang and run at full speed until the Big Crunch - could perform. This constant
      would, however, not be arbitrary, but would emerge from the structure of the universe. The resultant "modified Turing Principle"
      would imply that a computer could only be universal within certain limits in a given universe. Or to put it another way, because
      Turing envisaged an infinite paper tape in order to simplify matters (rather than bothering with practical details), this doesn't
      necessarily imply that, in a collapsing universe, any real computer will *necessarily* run for an infinite amount of (subjective)
      time.



      Or does it?



      (I haven't read the last few pages yet, and it's a few years since I last read FOR, so I don't actually remember where DD is going
      with this...)



      Charles



      [Non-text portions of this message have been removed]
    • Alan Forrester
      ... The Turing Principle states that any finite physical object can be simulated by a universal computer. If only a finite number of computational steps takes
      Message 2 of 9 , Nov 2, 2004
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        --- Charles Goodwin <charles@...> wrote:

        > In the last chapter of FOR, DD infers - given various assumptions (e.g.
        > that the universe will recollapse) - that "intelligence will
        > survive, and knowledge will continue to be created, until the end of the
        > universe." The amount of knowledge created, and the
        > subjective time of survival, would be infinite. This inference appears to
        > be based on the fact that the Turing Principle is our best
        > theory of the foundations of computing, and the TP implies that there is
        > no upper bound to the number of computational steps that
        > are physically possible. Otherwise, DD argues, we are left with a sort of
        > "approximate Turing Principle" which would be correct,
        > given worlds enough and time, but which isn't correct because the
        > universe only allows a very large but finite number of
        > computational steps to be performed. For comparison he says that "the
        > theory that the world is *half*-comprehensible explains
        > nothing and could not possibly fit in with explanations in other fields
        > unless *they* explained *it*. It simply restates the problem
        > and introduces an unexplained constant, one-half. In other words, what
        > justifies assuming that the full Turing Principle holds at
        > the end of the universe, is that any other assumption spoils good
        > explanations of what is happening here and now."
        >
        > Leaving aside the evidence that the universe may continue to expand
        > forever (which also possibly disallows the full Turing
        > Principle, but for other reasons), isn't this a circular argument? The
        > equivalent of the "constant, one-half" in this case would be
        > the maximum possible number of steps any possible computer - say, for the
        > sake of argument, one spontaneously assembled from all the
        > matter in the universe at the instant of the Big Bang and run at full
        > speed until the Big Crunch - could perform. This constant
        > would, however, not be arbitrary, but would emerge from the structure of
        > the universe. The resultant "modified Turing Principle"
        > would imply that a computer could only be universal within certain limits
        > in a given universe. Or to put it another way, because
        > Turing envisaged an infinite paper tape in order to simplify matters
        > (rather than bothering with practical details), this doesn't
        > necessarily imply that, in a collapsing universe, any real computer will
        > *necessarily* run for an infinite amount of (subjective)
        > time.

        The Turing Principle states that any finite physical object can be
        simulated by a universal computer. If only a finite number of computational
        steps takes place or it is only possible to construct a finite number of
        bits then some possible (in the strong sense of actually being realised by the real laws of physics) physical objects will never be simulated.

        One reason for this is that in any physical object that instantiates a computation only a subsystem of that object ever instantiates the computation itself. For example, in an interferometer, the direction in which a photon is
        travelling may be used as a qubit on which a computation will be performed,
        the mirrors and beam splitters are there to ensure that the computation
        works but the single qubit computer never simulates them. Every computer is
        like this and the reason has to do with knowledge. Computations are
        generally knowledge laden physical processes and so they cannot take place
        without a large body of knowledge being created. Most objects don't perform
        Grover's algorithm for instance and the reason is that they would have to
        be specially arranged to do so by a knowledge generating process.

        Now, if it is only possible to perform a finite number N of computational
        steps before the end of the universe certain things will never be simulated
        by any computer. For example, the universe itself at the Nth step will
        never be simulated. Certain problems will never be solved. For example at
        the Nth step, people wll only be able to do error correction to some finite
        accuracy and they will never improve on that. The components out of which
        they build their computer will only have a finite efficiency and this will
        never be improved upon. In other words, error correcting algorithms and
        physical components of computers at the Nth step will never be simulated.

        So why should these particular objects never be simulated? What is it that
        actually separates these and all other possible successors from what went
        before? We can't rule out an explanation that would satisfactorily explain
        sucha breakdown of the Turing Principle. However, would the inhabitants of the finite universe I just described ever understand that explanation? As I have said above, they would never understand the flaws in their current computers and so would never understand why they are doomed. So the idea that universality is restricted implies that we will never have an explanation of the type you envisage - it is an explanation that implies its own unknowability. So the notion that the Turing Principle is false puts a huge dent in the notion of scientific explanation. So we should require a spectacularly good explanation before accepting that it is false and such an explanation does not currently exist.

        Alan
      • Charles Goodwin
        ... Surely the explanation you have already given is just such a spectacularly good explanation - i.e. that the universe is finite in space and time
        Message 3 of 9 , Nov 2, 2004
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          > From: Alan Forrester [mailto:alan_forrester2@...]

          > So why should these particular objects never be simulated? What is it that

          > actually separates these and all other possible successors from what went

          > before? We can't rule out an explanation that would satisfactorily explain

          > sucha breakdown of the Turing Principle. However, would the inhabitants of the finite universe I

          > just described ever understand that explanation? As I have said above, they would never understand

          > the flaws in their current computers and so would never understand why they are doomed. So the idea

          > that universality is restricted implies that we will never have an explanation of the type you

          > envisage - it is an explanation that implies its own unknowability. So the notion that the Turing

          > Principle is false puts a huge dent in the notion of scientific explanation. So we should require a

          > spectacularly good explanation before accepting that it is false and such an explanation does not

          > currently exist.



          Surely the explanation you have already given is just such a "spectacularly good explanation" - i.e. that the universe is finite in
          space and time (assuming it is). It seems no more horrendous to say that the Turing Principle is violated in practice in a given,
          finite universe than to say that that universe doesn't contain an infinite number of atoms (or anything else). My only objection is
          to use the Turing Principle to claim that certain parts of the Omega point theory MUST be realised in a collapsing universe (which
          appears to be what DD is claiming). Suppose that there exists in the multiverse a universe which contains only one atom and which
          only exists for one second before recollapsing. Presumably the Turing Principle would imply that that universe also has to contain a
          complete Omega-point civilisation in its collapse phase, otherwise the Turing Principle doesn't hold (or perhaps doesn't hold in
          that universe). I don't see how you can go from a principle to a definite statement about what mush happen in the future in
          (extremely) unknown conditions. It sounds a bit like Anselm's argument that God must exist.



          I am prepared to be convinced otherwise, but I still don't see the connection. Can you explain how the hypothetical one-atom,
          one-second universe fits in with this argument, or does the Turing Principle rule out the existence of such a universe by fiat? (If
          it does that will make me even more suspicious of it!)



          Charles



          [Non-text portions of this message have been removed]
        • Alan Forrester
          ... The existence of solutions of the equations of motion for finite spacetimes that allow an infinite amount of computation clearly contradict the idea that
          Message 4 of 9 , Nov 2, 2004
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            --- Charles Goodwin <charles@...> wrote:

            > > So why should these particular objects never be simulated? What is it
            > that
            > > actually separates these and all other possible successors from what
            > went
            > > before? We can't rule out an explanation that would satisfactorily
            > explain
            > > sucha breakdown of the Turing Principle. However, would the
            > inhabitants of the finite universe I
            > > just described ever understand that explanation? As I have said above,
            > they would never understand
            > > the flaws in their current computers and so would never understand why
            > they are doomed. So the idea
            > > that universality is restricted implies that we will never have an
            > explanation of the type you
            > > envisage - it is an explanation that implies its own unknowability. So
            > the notion that the Turing
            > > Principle is false puts a huge dent in the notion of scientific
            > explanation. So we should require a
            > > spectacularly good explanation before accepting that it is false and
            > such an explanation does not
            > > currently exist.
            >
            > Surely the explanation you have already given is just such a
            > "spectacularly good explanation" - i.e. that the universe is finite in
            > space and time (assuming it is).

            The existence of solutions of the equations of motion for finite spacetimes
            that allow an infinite amount of computation clearly contradict the idea
            that such a universe is anything like a sufficient condition for the Turing
            Principle to be false.

            > It seems no more horrendous to say that
            > the Turing Principle is violated in practice in a given,
            > finite universe than to say that that universe doesn't contain an
            > infinite number of atoms (or anything else). My only objection is
            > to use the Turing Principle to claim that certain parts of the Omega
            > point theory MUST be realised in a collapsing universe (which
            > appears to be what DD is claiming). Suppose that there exists in the
            > multiverse a universe which contains only one atom and which
            > only exists for one second before recollapsing. Presumably the Turing
            > Principle would imply that that universe also has to contain a
            > complete Omega-point civilisation in its collapse phase, otherwise the
            > Turing Principle doesn't hold (or perhaps doesn't hold in
            > that universe). I don't see how you can go from a principle to a definite
            > statement about what mush happen in the future in
            > (extremely) unknown conditions. It sounds a bit like Anselm's argument
            > that God must exist.

            So in other words we ought not to take seriously the deepest implications
            of our current theories because at some point in the future they might
            break down. Sounds rather inductivist to me.

            > I am prepared to be convinced otherwise, but I still don't see the
            > connection. Can you explain how the hypothetical one-atom,
            > one-second universe fits in with this argument, or does the Turing
            > Principle rule out the existence of such a universe by fiat? (If
            > it does that will make me even more suspicious of it!)

            Well, a one atom universe does not in fact exist. The Turing principle
            wouldn't necessarily rule it out the infinite computation would just have
            to take place 'elsewhere' perhaps in non-baryonic matter or the
            gravitational field.

            Alan





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          • Bill Taylor
            Alan Forrester wrote: - The existence of solutions of the equations of motion for finite spacetimes - that allow an infinite
            Message 5 of 9 , Nov 3, 2004
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              Alan Forrester <alan_forrester2@...> wrote:

              ->The existence of solutions of the equations of motion for finite spacetimes
              ->that allow an infinite amount of computation clearly contradict the idea
              ->that such a universe is anything like a sufficient condition for the Turing
              ->Principle to be false.

              I *DO* wish people would stop calling it the "Turing Principle" !

              It would be far more accurately called the "Matrix Principle".

              It has almost nothing to do with anything Turing wrote about.


              -> So in other words we ought not to take seriously the deepest implications
              -> of our current theories because at some point in the future they might
              -> break down. Sounds rather inductivist to me.

              Sounds like common sense to me! Scientific theories always break down
              somewhere along the line, and the more remote the consequence is,
              the less likely it is to stand the test of time.

              But OC all the not-yet-falsified consequences are *taken* seriously,
              in the sense of working with them to develop their further consequences;
              they're just not taken to be indisputable, (commonly called "believed in"),
              until they have withstood a huge number of failed falsification attempts.

              Is that what's called "inductivism"? Sounds like organised common sense to me.

              ------------------------------------------------------------------------------
              Bill Taylor W.Taylor@...
              ------------------------------------------------------------------------------
              In math we decide on the rules - then try to deduce the consequences.
              In science we observe the consequences, then try to deduce the rules.
              ------------------------------------------------------------------------------
            • Bruno Marchal
              ... I definitely agree. It is very confusing. ... Not sure this will help. I prefer to call it Deutsch s thesis. If only because it is actually a thesis by
              Message 6 of 9 , Nov 4, 2004
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                At 17:45 04/11/04 +1300, Bill Taylor wrote:

                >Alan Forrester <alan_forrester2@...> wrote:
                >
                >->The existence of solutions of the equations of motion for finite spacetimes
                >->that allow an infinite amount of computation clearly contradict the idea
                >->that such a universe is anything like a sufficient condition for the Turing
                >->Principle to be false.
                >
                >I *DO* wish people would stop calling it the "Turing Principle" !


                I definitely agree. It is very confusing.



                >It would be far more accurately called the "Matrix Principle".


                Not sure this will help. I prefer to call it Deutsch's thesis. If only
                because it is actually a thesis by Deutsch.
                The relations between Church's thesis and Deutsch's thesis
                are far from obvious. They are related to many open problems
                both in quantum mechanics and Classical computability theory.


                >It has almost nothing to do with anything Turing wrote about.

                Indeed. And this despite Turing's defense of physicalism
                (according to Emil Post. See Davis 1965).

                Bruno

                http://iridia.ulb.ac.be/~marchal/
              • Charles Goodwin
                ... Maybe a one-atom universe doesn t exist (although surely it s possible, somewhere in the multiverse?) but a universe with a relatively small number of
                Message 7 of 9 , Nov 4, 2004
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                  > From: Alan Forrester [mailto:alan_forrester2@...]
                  > Well, a one atom universe does not in fact exist. The Turing principle
                  > wouldn't necessarily rule it out the infinite computation would just have
                  > to take place 'elsewhere' perhaps in non-baryonic matter or the
                  > gravitational field.

                  Maybe a one-atom universe doesn't exist (although surely it's possible, somewhere in the multiverse?) but a universe with a
                  relatively small number of atoms is created whenever a star collapses to form a black hole, in that the matter becomes cut off from
                  the rest of the universe. (Also, in a universe with a positive cosmological constant, it's quite possible that one-atom universes
                  will come into existence in the far future - although these won't undergo gravitational collapse).

                  In any case, a black hole serves to illustrate the argument. Would you say that (a) the Turing Principle ceases to hold inside a
                  collapsing black hole, or (b) that an Omega-point civilisation necessarily arises in the matter undergoing collapse?

                  Charles
                • Alan Forrester
                  ... There are many options for what could happen inside a black hole, but nobody knows which of them actually happens. One is that the black hole gives rise to
                  Message 8 of 9 , Nov 5, 2004
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                    --- Charles Goodwin <charles@...> wrote:

                    > > Well, a one atom universe does not in fact exist. The Turing principle
                    > > wouldn't necessarily rule it out the infinite computation would just
                    > have
                    > > to take place 'elsewhere' perhaps in non-baryonic matter or the
                    > > gravitational field.
                    >
                    > Maybe a one-atom universe doesn't exist (although surely it's possible,
                    > somewhere in the multiverse?) but a universe with a
                    > relatively small number of atoms is created whenever a star collapses to
                    > form a black hole, in that the matter becomes cut off from
                    > the rest of the universe. (Also, in a universe with a positive
                    > cosmological constant, it's quite possible that one-atom universes
                    > will come into existence in the far future - although these won't undergo
                    > gravitational collapse).
                    >
                    > In any case, a black hole serves to illustrate the argument. Would you
                    > say that (a) the Turing Principle ceases to hold inside a
                    > collapsing black hole, or (b) that an Omega-point civilisation
                    > necessarily arises in the matter undergoing collapse?

                    There are many options for what could happen inside a black hole, but
                    nobody knows which of them actually happens. One is that the black hole
                    gives rise to a daughter universe separated from ours by the event horizon
                    in which the Turing Principle is respected. Another is that the black hole
                    either evaporates or as in the Omega Point and presumably Barrow's
                    alternative a future civilisation gets rid of the event horizon and the
                    informtion inside is let out. Or...?

                    Alan





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                  • charles@halswell.net
                    ... Fair enough. I still wonder whether the Turing Principle is sufficient to cause the existence of a suitable universal computer to come into existence
                    Message 9 of 9 , Nov 5, 2004
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                      > There are many options for what could happen inside a black hole, but
                      > nobody knows which of them actually happens. One is that the black hole
                      > gives rise to a daughter universe separated from ours by the event horizon
                      > in which the Turing Principle is respected. Another is that the black hole
                      > either evaporates or as in the Omega Point and presumably Barrow's
                      > alternative a future civilisation gets rid of the event horizon and the
                      > informtion inside is let out. Or...?

                      Fair enough. I still wonder whether the Turing Principle is sufficient to cause the existence of a suitable universal computer to come into existence *everywhere* in the multiverse, or just *somewhere*. DD was also unsure about this in FOR, although he plumped for everywhere IIRC. I wonder if he's revised that opinion in the intervening 7 years...?

                      Charles
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