Re: UDA query
We're not circling around it. Bruno asserts it. But then we need to
explain the things that were formerly explained by physical existence -
e.g. intersubjective agreement about a physical world, the dependence
of thought on brains, etc.
Brent
Stephen Paul King wrote:
Hi Folks,
I would like to append a question that we all seem to circle around: Why
do we even need to have a physical existance at all? Why isn't Platonic
existence sufficient?
Onward!
Stephen
- Original Message -
From: "Nick Prince"
To: "Everything List"
Sent: Sunday, January 03, 2010 4:30 PM
Subject: Re: UDA query
Stathis wrote
Yes, but a critic could still say that no conscious observer could be
conjured up by a computation unless the computation is physically
implemented. At least at first glance that seems to be the case: the
brain is required for consciousness, since if the brain is destroyed
consciousness is destroyed. And if the mind is generated by a computer
program, it would be normal to think that if the computer is
destroyed, so is the mind, although the program in Platonia remains
unaffected even if the entire universe blows up. These are the common
sense objections. So the question is, is physical implementation
necessary for consciousness, and what does it actually mean to
physically implement a program?
>From what I surmised and what Bruno wrote earlier in the discussion, I
thought that consciousness might supervene over all computations that
were essentially equivalent (whatever that might mean— i.e. some sort
of equivalence class?). Anyway, this would imply that if the brain
was destroyed, then consciousness would simply be continued on by the
rest of the (competing) and remaining equivalent computations.
These would presumably be consistent extensions of the consciousness
in other worlds (MW interpretation) or in a platonic UD.
SP
(and of course, this hardware may itself be part
of the virtual world generated in Platonia).
I thought that this would be a consequence of comp since the
probability of consciousness staying in any “concrete” universe would
seem to be essentially zero. see below from earlier in the discussion:
NP> In other words every observer
moment of his life (not just the one just before being blown up - but
any of them) could just as easily be followed by a suitable one in
the virtual UD rather than one in the initial run of the universe.
BM
Absolutely. Would a real *singular* concrete material universe exist,
the probability to stay in that universe is zero.
Brent
>I think you give an excellent explication of the problem, Stathis.
However, one thing about it that still worries me is the role of time.
You >say the mapping need not be consistent even moment to moment, and
yet the mapping is a timeless Platonic object. To be a timeless
object the the moments need some timeless representation. In Bruno's
theory time arises from the computational sequence. But in the
mapping, time is just a relation of similarity (closest continuation)
of states. So three states which when ordered by closest continuation
are XYZ may have been computed in the order XZY. So I find myself
seeing the hardwareless computer as a reductio against
consciousness=computation thesis and support for Peter's view that ur-
stuff and contingency are fundamental.
The time bit confuses me too but if the UD is recursive (as I thought
it would have to be) and a successor function was implicit in the
algorithm then the timeless algorithm would give a perception of time
to the internal observers that Stathis spoke of earlier generated by
the computation.
However I am still not convinced about this myself and get this
feeling that there is a dynamic element missing from the static or
timeless representations which I am assuming to be existent in the
platonic realm
Nick
On Jan 3, 6:57 pm, Brent Meeker wrote:
Stathis Papaioannou wrote:2010/1/4 Nick Prince:Thank
you Stathis This has helped move me on a bit. The hardwareless computer
has been giving me some real problems. Let me replay my understanding of
what you said back just to check it is on the right lines. As a possible
example of one of these lurking computations we could consider the one
which begins with no-thing and think of the null set as made of it phi
={ } and then associating it with the number 0. Then imagine the set {
phi} associating it with 1, then { phi,{phi }} associating this with 2,
then { phi, { phi} , { ,{phi }} }, associating it with 3 etc. Hence we get
an infinite sequence of abstract (platonic) entities which can conjure up
(compute) the natural numbers and the implied successor function simply
from the abstract (platonic) notion of a set and an association rule (also
a platonic relation). More and more structure can be built up until - as
you sa
Re: UDA query
Hi Folks,
I would like to append a question that we all seem to circle around: Why
do we even need to have a physical existance at all? Why isn't Platonic
existence sufficient?
Onward!
Stephen
- Original Message -
From: "Nick Prince"
To: "Everything List"
Sent: Sunday, January 03, 2010 4:30 PM
Subject: Re: UDA query
Stathis wrote
>Yes, but a critic could still say that no conscious observer could be
>conjured up by a computation unless the computation is physically
>implemented. At least at first glance that seems to be the case: the
>brain is required for consciousness, since if the brain is destroyed
>consciousness is destroyed. And if the mind is generated by a computer
>program, it would be normal to think that if the computer is
>destroyed, so is the mind, although the program in Platonia remains
>unaffected even if the entire universe blows up. These are the common
>sense objections. So the question is, is physical implementation
>necessary for consciousness, and what does it actually mean to
>physically implement a program?
>From what I surmised and what Bruno wrote earlier in the discussion, I
thought that consciousness might supervene over all computations that
were essentially equivalent (whatever that might mean— i.e. some sort
of equivalence class?). Anyway, this would imply that if the brain
was destroyed, then consciousness would simply be continued on by the
rest of the (competing) and remaining equivalent computations.
These would presumably be consistent extensions of the consciousness
in other worlds (MW interpretation) or in a platonic UD.
SP
>(and of course, this hardware may itself be part
>of the virtual world generated in Platonia).
I thought that this would be a consequence of comp since the
probability of consciousness staying in any “concrete” universe would
seem to be essentially zero. see below from earlier in the discussion:
NP> In other words every observer
> moment of his life (not just the one just before being blown up - but
> any of them) could just as easily be followed by a suitable one in
> the virtual UD rather than one in the initial run of the universe.
BM
>Absolutely. Would a real *singular* concrete material universe exist,
>the probability to stay in that universe is zero.
Brent
>I think you give an excellent explication of the problem, Stathis.
However, one thing about it that still worries me is the role of time.
You >say the mapping need not be consistent even moment to moment, and
yet the mapping is a timeless Platonic object. To be a timeless
>object the the moments need some timeless representation. In Bruno's
theory time arises from the computational sequence. But in the
>mapping, time is just a relation of similarity (closest continuation)
of states. So three states which when ordered by closest continuation
>are XYZ may have been computed in the order XZY. So I find myself
seeing the hardwareless computer as a reductio against
>consciousness=computation thesis and support for Peter's view that ur-
stuff and contingency are fundamental.
The time bit confuses me too but if the UD is recursive (as I thought
it would have to be) and a successor function was implicit in the
algorithm then the timeless algorithm would give a perception of time
to the internal observers that Stathis spoke of earlier generated by
the computation.
However I am still not convinced about this myself and get this
feeling that there is a dynamic element missing from the static or
timeless representations which I am assuming to be existent in the
platonic realm
Nick
On Jan 3, 6:57 pm, Brent Meeker wrote:
> Stathis Papaioannou wrote:2010/1/4 Nick Prince:Thank
> you Stathis This has helped move me on a bit. The hardwareless computer
> has been giving me some real problems. Let me replay my understanding of
> what you said back just to check it is on the right lines. As a possible
> example of one of these lurking computations we could consider the one
> which begins with no-thing and think of the null set as made of it phi
> ={ } and then associating it with the number 0. Then imagine the set {
> phi} associating it with 1, then { phi,{phi }} associating this with 2,
> then { phi, { phi} , { ,{phi }} }, associating it with 3 etc. Hence we get
> an infinite sequence of abstract (platonic) entities which can conjure up
> (compute) the natural numbers and the implied successor function simply
> from the abstract (platonic) notion of a set and an association rule (also
> a platonic relation). More and more structure can be built up until - as
> you say - the entire structure of the computation contained in the mapping
> can be envisioned. Now although no external observers might be able to
> access these computations, the computations might just create conscious
> observers bootstrapped into existence by the special class of computations
> which these (internal) observers (if they believed in comp) would
> naturally consider as non tr
Re: UDA query
Stathis wrote
>Yes, but a critic could still say that no conscious observer could be
>conjured up by a computation unless the computation is physically
>implemented. At least at first glance that seems to be the case: the
>brain is required for consciousness, since if the brain is destroyed
>consciousness is destroyed. And if the mind is generated by a computer
>program, it would be normal to think that if the computer is
>destroyed, so is the mind, although the program in Platonia remains
>unaffected even if the entire universe blows up. These are the common
>sense objections. So the question is, is physical implementation
>necessary for consciousness, and what does it actually mean to
>physically implement a program?
>From what I surmised and what Bruno wrote earlier in the discussion, I
thought that consciousness might supervene over all computations that
were essentially equivalent (whatever that might mean— i.e. some sort
of equivalence class?). Anyway, this would imply that if the brain
was destroyed, then consciousness would simply be continued on by the
rest of the (competing) and remaining equivalent computations.
These would presumably be consistent extensions of the consciousness
in other worlds (MW interpretation) or in a platonic UD.
SP
>(and of course, this hardware may itself be part
>of the virtual world generated in Platonia).
I thought that this would be a consequence of comp since the
probability of consciousness staying in any “concrete” universe would
seem to be essentially zero. see below from earlier in the discussion:
NP> In other words every observer
> moment of his life (not just the one just before being blown up - but
> any of them) could just as easily be followed by a suitable one in
> the virtual UD rather than one in the initial run of the universe.
BM
>Absolutely. Would a real *singular* concrete material universe exist,
>the probability to stay in that universe is zero.
Brent
>I think you give an excellent explication of the problem, Stathis.
However, one thing about it that still worries me is the role of time.
You >say the mapping need not be consistent even moment to moment, and
yet the mapping is a timeless Platonic object. To be a timeless
>object the the moments need some timeless representation. In Bruno's
theory time arises from the computational sequence. But in the
>mapping, time is just a relation of similarity (closest continuation)
of states. So three states which when ordered by closest continuation
>are XYZ may have been computed in the order XZY. So I find myself
seeing the hardwareless computer as a reductio against
>consciousness=computation thesis and support for Peter's view that ur-
stuff and contingency are fundamental.
The time bit confuses me too but if the UD is recursive (as I thought
it would have to be) and a successor function was implicit in the
algorithm then the timeless algorithm would give a perception of time
to the internal observers that Stathis spoke of earlier generated by
the computation.
However I am still not convinced about this myself and get this
feeling that there is a dynamic element missing from the static or
timeless representations which I am assuming to be existent in the
platonic realm
Nick
On Jan 3, 6:57 pm, Brent Meeker wrote:
> Stathis Papaioannou wrote:2010/1/4 Nick Prince:Thank
> you Stathis This has helped move me on a bit. The hardwareless computer has
> been giving me some real problems. Let me replay my understanding of what you
> said back just to check it is on the right lines. As a possible example of
> one of these lurking computations we could consider the one which begins with
> no-thing and think of the null set as made of it phi ={ } and then
> associating it with the number 0. Then imagine the set { phi} associating it
> with 1, then { phi,{phi }} associating this with 2, then { phi, { phi} , {
> ,{phi }} }, associating it with 3 etc. Hence we get an infinite sequence of
> abstract (platonic) entities which can conjure up (compute) the natural
> numbers and the implied successor function simply from the abstract
> (platonic) notion of a set and an association rule (also a platonic
> relation). More and more structure can be built up until - as you say - the
> entire structure of the computation contained in the mapping can be
> envisioned. Now although no external observers might be able to access these
> computations, the computations might just create conscious observers
> bootstrapped into existence by the special class of computations which these
> (internal) observers (if they believed in comp) would naturally consider as
> non trivial. As you say the entire structure of the mapping which describes
> the computation is a platonic object too hence the world comes from nothing
> and computation. Have I got this roughly right? I would be grateful for any
> critical comments from you, Bruno (or anyone).Yes, but a critic could still
> say that no conscious observer c
Re: UDA query
Stathis Papaioannou wrote:
2010/1/4 Nick Prince :
Thank you Stathis
This has helped move me on a bit. “The hardwareless computer” has been
giving me some real problems. Let me replay my understanding of what
you said back just to check it is on the right lines.
As a possible example of one of these “lurking computations” we could
consider the one which begins with no-thing and think of the null set
as made of it phi ={ } and then associating it with the number 0. Then
imagine the set { phi} associating it with 1, then { phi,{phi }}
associating this with 2, then { phi, { phi} , { ,{phi }} },
associating it with 3 etc. Hence we get an infinite sequence of
abstract (platonic) entities which can conjure up (compute) the
natural numbers and the implied successor function simply from the
abstract (platonic) notion of a set and an association rule (also a
platonic relation). More and more structure can be built up until - as
you say - the entire structure of the computation contained in the
mapping can be envisioned. Now although no external observers might be
able to access these computations, the computations might just create
conscious observers – bootstrapped into existence by the special class
of computations which these (internal) observers (if they believed in
comp) would naturally consider as non trivial. As you say the entire
structure of the mapping which describes the computation is a platonic
object too – hence the world comes from nothing and computation.
Have I got this roughly right? I would be grateful for any critical
comments from you, Bruno (or anyone).
Yes, but a critic could still say that no conscious observer could be
conjured up by a computation unless the computation is physically
implemented. At least at first glance that seems to be the case: the
brain is required for consciousness, since if the brain is destroyed
consciousness is destroyed. And if the mind is generated by a computer
program, it would be normal to think that if the computer is
destroyed, so is the mind, although the program in Platonia remains
unaffected even if the entire universe blows up. These are the common
sense objections. So the question is, is physical implementation
necessary for consciousness, and what does it actually mean to
physically implement a program?
Suppose we agree that it is necessary to physically implement a
program in order to get the consciousness. Physical implementation
then involves, essentially, causing a machine to go through a sequence
of causally connected configurations such that the configurations and
the state transition rules match up with the abstract program. There
is a mapping from the abstract program to the machine so that the
engineer, programmer and end user know what's going on. But "write 1
and then move the head to the left" could be represented in an
infinite number of ways. If a man walks down the street chewing gum,
that could represent "write 1 then move the head to the left", while
if he stood still humming "Jingle Bells" that would have represented
"write 0 then move the head to the right". Moreover the mapping does
not have to be consistent from moment to moment: chewing gum could
mean "0" on Fridays and "1" on other days. There is no reason why a
computer could not be designed to function in such an inconsistent
way, other than the practical necessity of keeping track of what's
going on, which is necessary if the computer is to be of any use to
anyone. But if we don't care about its usefulness to an outside
observer we could say that any abstract computation maps to any
physical process: a random physical process, a repetitive physical
process, or a single physical state. The man walking down the street
chewing gum over the course of a second could be seen as representing
the one thousand steps of a Turing machine adding two numbers
together, although of course it wouldn't be of any use to anyone
interested in the result of the calculation. You can see no doubt that
if you accept the argument so far the physical process is irrelevant,
and all of the computation, such as it is, consists in the abstract
machine and the mapping, which are timeless platonic objects. Arguable
the mapping is also irrelevant, since there are an infinite number of
possible mappings for an infinite number of possible physical
processes. The only thing that seems to make a difference is the
abstract machine or program itself. The program "runs" necessarily,
even in the absence of a physical universe, and it only need run on
physical hardware in order to interact with the environment at the
level of the hardware (and of course, this hardware may itself be part
of the virtual world generated in Platonia).
I think you give an excellent explication of the problem, Stathis.
However, one thing about it that still worries me is the role of time.
You say the mapping need not be consistent even moment to moment, and
yet the mapping is a timeless Platonic object
Re: UDA query
2010/1/4 Nick Prince :
> Thank you Stathis
> This has helped move me on a bit. “The hardwareless computer” has been
> giving me some real problems. Let me replay my understanding of what
> you said back just to check it is on the right lines.
> As a possible example of one of these “lurking computations” we could
> consider the one which begins with no-thing and think of the null set
> as made of it phi ={ } and then associating it with the number 0. Then
> imagine the set { phi} associating it with 1, then { phi,{phi }}
> associating this with 2, then { phi, { phi} , { ,{phi }} },
> associating it with 3 etc. Hence we get an infinite sequence of
> abstract (platonic) entities which can conjure up (compute) the
> natural numbers and the implied successor function simply from the
> abstract (platonic) notion of a set and an association rule (also a
> platonic relation). More and more structure can be built up until - as
> you say - the entire structure of the computation contained in the
> mapping can be envisioned. Now although no external observers might be
> able to access these computations, the computations might just create
> conscious observers – bootstrapped into existence by the special class
> of computations which these (internal) observers (if they believed in
> comp) would naturally consider as non trivial. As you say the entire
> structure of the mapping which describes the computation is a platonic
> object too – hence the world comes from nothing and computation.
> Have I got this roughly right? I would be grateful for any critical
> comments from you, Bruno (or anyone).
Yes, but a critic could still say that no conscious observer could be
conjured up by a computation unless the computation is physically
implemented. At least at first glance that seems to be the case: the
brain is required for consciousness, since if the brain is destroyed
consciousness is destroyed. And if the mind is generated by a computer
program, it would be normal to think that if the computer is
destroyed, so is the mind, although the program in Platonia remains
unaffected even if the entire universe blows up. These are the common
sense objections. So the question is, is physical implementation
necessary for consciousness, and what does it actually mean to
physically implement a program?
Suppose we agree that it is necessary to physically implement a
program in order to get the consciousness. Physical implementation
then involves, essentially, causing a machine to go through a sequence
of causally connected configurations such that the configurations and
the state transition rules match up with the abstract program. There
is a mapping from the abstract program to the machine so that the
engineer, programmer and end user know what's going on. But "write 1
and then move the head to the left" could be represented in an
infinite number of ways. If a man walks down the street chewing gum,
that could represent "write 1 then move the head to the left", while
if he stood still humming "Jingle Bells" that would have represented
"write 0 then move the head to the right". Moreover the mapping does
not have to be consistent from moment to moment: chewing gum could
mean "0" on Fridays and "1" on other days. There is no reason why a
computer could not be designed to function in such an inconsistent
way, other than the practical necessity of keeping track of what's
going on, which is necessary if the computer is to be of any use to
anyone. But if we don't care about its usefulness to an outside
observer we could say that any abstract computation maps to any
physical process: a random physical process, a repetitive physical
process, or a single physical state. The man walking down the street
chewing gum over the course of a second could be seen as representing
the one thousand steps of a Turing machine adding two numbers
together, although of course it wouldn't be of any use to anyone
interested in the result of the calculation. You can see no doubt that
if you accept the argument so far the physical process is irrelevant,
and all of the computation, such as it is, consists in the abstract
machine and the mapping, which are timeless platonic objects. Arguable
the mapping is also irrelevant, since there are an infinite number of
possible mappings for an infinite number of possible physical
processes. The only thing that seems to make a difference is the
abstract machine or program itself. The program "runs" necessarily,
even in the absence of a physical universe, and it only need run on
physical hardware in order to interact with the environment at the
level of the hardware (and of course, this hardware may itself be part
of the virtual world generated in Platonia).
--
Stathis Papaioannou
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Re: UDA query
Thank you Stathis
This has helped move me on a bit. “The hardwareless computer” has been
giving me some real problems. Let me replay my understanding of what
you said back just to check it is on the right lines.
As a possible example of one of these “lurking computations” we could
consider the one which begins with no-thing and think of the null set
as made of it phi ={ } and then associating it with the number 0. Then
imagine the set { phi} associating it with 1, then{ phi,{phi }}
associating this with 2, then { phi, { phi} , { ,{phi }} },
associating it with 3 etc. Hence we get an infinite sequence of
abstract (platonic) entities which can conjure up (compute) the
natural numbers and the implied successor function simply from the
abstract (platonic) notion of a set and an association rule (also a
platonic relation). More and more structure can be built up until - as
you say - the entire structure of the computation contained in the
mapping can be envisioned. Now although no external observers might be
able to access these computations, the computations might just create
conscious observers – bootstrapped into existence by the special class
of computations which these (internal) observers (if they believed in
comp) would naturally consider as non trivial. As you say the entire
structure of the mapping which describes the computation is a platonic
object too – hence the world comes from nothing and computation.
Have I got this roughly right? I would be grateful for any critical
comments from you, Bruno (or anyone).
Many thanks
Nick
On Jan 3, 11:05 am, Stathis Papaioannou wrote:
> 2010/1/3 Nick Prince :
>
>
>
>
>
> > HI Bruno
> > Thank you so much for your answers to my queries so far. I really
> > need to do some more thinking about all that you have said so far and
> > to understand why I am having difficulty replacing a real physical
> > universal machine existing in the future (like Tipler suggests) or a
> > great programmer existing now (like schmidhuber suggests) with your
> > arithmetical realism. I also need to search some previous posts to
> > make use of past discussion topics that are relevant. Perhaps my
> > background makes me a physicalist who can currently accept a milder
> > form of comp. However, I want to explore your position because I
> > think it makes sense in so far as I think it is less vulnerable to the
> > threat of infinite regressions like in Schmidhuber’s great programmer
> > (or even the greater programmer that programmed him). Your version of
> > computationalism would still be valid if either or both of the two
> > options above were true. Herein lies its appeal to me (both
> > fundamental and universal).
> > I would like to read up on logic and computation as you suggest. I
> > have read about all the books you recommend . However, can you suggest
> > topic areas within these texts which I can focus on to help me get up
> > to speed with the problems I have regarding arithmetical realism with
> > the UDA? There is much that could perhaps be left out on a first
> > reading and to my untrained eyes, it’s difficult to know what to omit
> > (for example what would godels arithmetisation technique come under?
> > (Googling it brings not much up). Sorry but I haven’t ordered any
> > books yet so I can’t look into them.
> > Is there an English translation of your Ph.D. thesis yet? Sorry but I
> > can’t do French. My thanks and best wishes.
>
> My justification for the hardwareless computer is the fact that any
> computation can be mapped onto any physical process, in the same way
> that any English sentence can be mapped onto any string of symbols.
> Such a post hoc mapping would be useless to an observer trying to
> extract meaning from the symbols or the result of a calculation from
> the computer, since he would have to figure out the mapping himself
> and he would have to know the answer he wants before doing this. With
> the right key Bruno's PhD thesis contains an account of next week's
> news, but so what? If you look at it the right way the dust swept up
> by a storm is implementing a Turing machine calculating the digits of
> pi, but what good does that do anyone? The claim that codes and
> computations lurk hidden all around us could be taken as true but
> trivial, or perhaps defined away as untrue on account of its
> triviality. However, there is a special class of computations to
> consider: computations that give rise to conscious observers in
> virtual universes that do not interact with the environment at the
> level of the substrate of implementation. If such computations are
> possible (i.e. if comp is true) then it doesn't matter that no
> external observers have access to the mapping that would allow them to
> recognise them, for these computations create their own observers,
> bootstrapping themselves into non-triviality. The physical process
> "sustaining" the computation need not even be as complex in structure
> as the computation: the compu
Re: UDA query
2010/1/3 Nick Prince : > HI Bruno > Thank you so much for your answers to my queries so far. I really > need to do some more thinking about all that you have said so far and > to understand why I am having difficulty replacing a real physical > universal machine existing in the future (like Tipler suggests) or a > great programmer existing now (like schmidhuber suggests) with your > arithmetical realism. I also need to search some previous posts to > make use of past discussion topics that are relevant. Perhaps my > background makes me a physicalist who can currently accept a milder > form of comp. However, I want to explore your position because I > think it makes sense in so far as I think it is less vulnerable to the > threat of infinite regressions like in Schmidhuber’s great programmer > (or even the greater programmer that programmed him). Your version of > computationalism would still be valid if either or both of the two > options above were true. Herein lies its appeal to me (both > fundamental and universal). > I would like to read up on logic and computation as you suggest. I > have read about all the books you recommend . However, can you suggest > topic areas within these texts which I can focus on to help me get up > to speed with the problems I have regarding arithmetical realism with > the UDA? There is much that could perhaps be left out on a first > reading and to my untrained eyes, it’s difficult to know what to omit > (for example what would godels arithmetisation technique come under? > (Googling it brings not much up). Sorry but I haven’t ordered any > books yet so I can’t look into them. > Is there an English translation of your Ph.D. thesis yet? Sorry but I > can’t do French. My thanks and best wishes. My justification for the hardwareless computer is the fact that any computation can be mapped onto any physical process, in the same way that any English sentence can be mapped onto any string of symbols. Such a post hoc mapping would be useless to an observer trying to extract meaning from the symbols or the result of a calculation from the computer, since he would have to figure out the mapping himself and he would have to know the answer he wants before doing this. With the right key Bruno's PhD thesis contains an account of next week's news, but so what? If you look at it the right way the dust swept up by a storm is implementing a Turing machine calculating the digits of pi, but what good does that do anyone? The claim that codes and computations lurk hidden all around us could be taken as true but trivial, or perhaps defined away as untrue on account of its triviality. However, there is a special class of computations to consider: computations that give rise to conscious observers in virtual universes that do not interact with the environment at the level of the substrate of implementation. If such computations are possible (i.e. if comp is true) then it doesn't matter that no external observers have access to the mapping that would allow them to recognise them, for these computations create their own observers, bootstrapping themselves into non-triviality. The physical process "sustaining" the computation need not even be as complex in structure as the computation: the computation could be mapped for example onto a repetitive process, the idle passage of time, even a single instant of time implementing the parts of the computation in parallel. And if we get that far, it's obvious that the physical process does nothing, and we may as well map the computation onto the null set. It is obvious that the entire structure of the computation is contained in the mapping, and the mapping is a platonic object, not dependent on being written down or even understood in the mind of an external observer. -- Stathis Papaioannou -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
