Schmidhuber's time

[Nick Prince]

It's not always made clear how many "universes" there are in Everett's approach. According to his biographer, Peter Byrne, Everett thought that there should be an uncountably infinite number of them - this was the only way he could define probabilities appropriately- but as far as I recall, Neil Graham, one of De Witt's graduate students tried to reinterpret Everett's theory using a countably infinite number of worlds. However I think he later abandoned this approach. AFAIK Deutsch (FOR p.279) also thinks uncountably infinite.

A simple experiment tells us that, if space is continuous and described by the real numbers then electrons fired from a source can land anywhere on a screen and so the wave function must have an uncountably infinite number of possible position eigenvalues which implies an uncountably infinite number of worlds.

AFAIK Schmidhuber's scenario has a dovetailer which will produce finite bit strings that describe “worlds”  that  will be only  countably infinite in number.  Note that these bit strings are not supposed to be separate worlds that can be in a superposition – they do not interefere with one another! Rather some of them  will contain computable multiverses themselves that contain universes which will interfere.

 

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

 

[LizR]

Does a dovetailer have to actually run in physical space? The comp version seems to do everything it possibly can without actually doing anything (in a Taoistic sort of way).

[Gary Oberbrunner]

On Sun, Jan 11, 2015 at 6:36 PM, Nick Prince <nickmag...@gmail.com> wrote:

A simple experiment tells us that, if space is continuous and described by the real numbers then electrons fired from a source can land anywhere on a screen and so the wave function must have an uncountably infinite number of possible position eigenvalues which implies an uncountably infinite number of worl

Right, it all comes down to what exactly is quantized.  Space, yes.  Momentum, yes. Gravity? We don't know.  Angle?  Still up in the air I think.

--

Gary

[Gary Oberbrunner]

On Sun, Jan 11, 2015 at 6:36 PM, Nick Prince <nickmag...@gmail.com> wrote:

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It's called a dovetailer because it dovetails the executions -- one step from each one, then on to the next.  So it always makes progress on all the computations -- albeit extremely slowly.  Marchal has a working example in lisp.

--

Gary

[Bruno Marchal]

On 12 Jan 2015, at 00:36, Nick Prince wrote:

It's not always made clear how many "universes" there are in Everett's approach. According to his biographer, Peter Byrne, Everett thought that there should be an uncountably infinite number of them - this was the only way he could define probabilities appropriately- but as far as I recall, Neil Graham, one of De Witt's graduate students tried to reinterpret Everett's theory using a countably infinite number of worlds. However I think he later abandoned this approach. AFAIK Deutsch (FOR p.279) also thinks uncountably infinite.

A simple experiment tells us that, if space is continuous and described by the real numbers then electrons fired from a source can land anywhere on a screen and so the wave function must have an uncountably infinite number of possible position eigenvalues which implies an uncountably infinite number of worlds.

AFAIK Schmidhuber's scenario has a dovetailer which will produce finite bit strings that describe “worlds”  that  will be only  countably infinite in number.  Note that these bit strings are not supposed to be separate worlds that can be in a superposition – they do not interefere with one another! Rather some of them  will contain computable multiverses themselves that contain universes which will interfere.

Schmidhuber, like Tegmark, are not ware of the mind-body problem. They still use an identity thesis which is not compatible with computatiuonalism, which is needed to give some role to a universal dovetailer, which is a program. 

So, the mutltiverse is an emergent structure on all computations. The math does confirms this (and that is a material much older than the work of Schmidhuber and Tegmark, by the way).

 

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse,

There is no multiverse ever generated by a program, because the multiverse is a first person (plural) view bearing on all computations (or on all arithmetical sigma_1 sentences).

then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It take no time at all by the step 2 and 4 of the Universal Dovetailer Argument. There is no time in the universal dovetailing. There is only a number-of-steps, associate to each computations, which are atemporal relation number theoretical relations of a certain type, and the persons emulated in arithmetic cannot be aware of the (gigantic) delays brought by the universal dovetailer.

To conclude: the dreams are uncountably many a priori (but there can be countable quotient by some relation of equivalence). Physical $and* subjective time, and ordering are emerging pattern in the consciousness attached to an infinity (coutable) bodies (relative description of a program with respect to some universal numbers) of the observers.

The difficulty, which is not addressed by Schmidhuber and Tegmark concerns the mind-body relation, which cannot be a one-one relation once we bet on the computationalist hypothesis (eventually this needs the use of the logic of self-reference to make precise). I have explained this in my papers and on the everything list. You can study the Universal Dovetailer Argument, and a sketch on how to make the argument into a purely mathematical problem, in my sane04 paper:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html

Bruno

 

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[Bruno Marchal]

On 12 Jan 2015, at 00:51, LizR wrote:

Does a dovetailer have to actually run in physical space? The comp version seems to do everything it possibly can without actually doing anything (in a Taoistic sort of way).

Yes, but that is not different than in general relativity (or even in Newtonian-Lapacean physics) where time is just a paremeter, and the ultimate stucture is non temporal.

It just happens that once you agree that 2+2=4 is true independently of you, the whole space-time structure, and the discourse in time and place about it are indexicals in the atemporal-aspatial stucture of the arithmetical reality (assumed by all scientists).

The point is that with computationalism, all physical attributes emerge from that internal view of arithmetic, by arithmetically representable creatures. The key is that a computation is a well defined arithmetical notion (pace Landauer and the physicalists who hope to find a physical definition of computation, which can make sense, but not if we assume computationalism).

Bruno

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[LizR]

On 13 January 2015 at 00:24, Bruno Marchal <mar...@ulb.ac.be> wrote:

The key is that a computation is a well defined arithmetical notion (pace Landauer and the physicalists who hope to find a physical definition of computation, which can make sense, but not if we assume computationalism).

And does this mean that computation can "occur" timelessly, in platonia?

(PS Maybe they should look for a computational definition of physical?)

[Nick Prince]

In spite of this dovetailing procedure I don't see how  the dovetailer could complete the steps for this simple experiment  in a finite (Great Programmer's) time.  This is because a countably infinite number of steps * delta t = aleph_0 * delta t = aleph_0  if delta t is the step time and it is constant in duration then it can be put in 1 to 1 correspondence with the naturals N. The infinite number of branches that arise *within* some of the created  programs evolve by the dovetailing procedure causing even further branches etc.

 I do think that well behaved universes will be short (using the universal prior) and earlier in the list rather than later but suppose the program counter was at the 5th program and this was the universe that my experiment was conducted in. Within that 5th program string will be code which accounts for the evolution of the infinite number of worlds that arise from measuring the location of the electron. Each of these infinite worlds also needs incrementing by the program counter by the agreed parallel processing type dovetailing method to evolve. I don't see how it can be completed in Great programmer's time and therefore not in denizen time either. Even great programmer's don't have infinite time - including Bruno!

[Nick Prince]

On Monday, January 12, 2015 at 11:18:02 AM UTC, Bruno Marchal wrote:

On 12 Jan 2015, at 00:36, Nick Prince wrote:

It's not always made clear how many "universes" there are in Everett's approach. According to his biographer, Peter Byrne, Everett thought that there should be an uncountably infinite number of them - this was the only way he could define probabilities appropriately- but as far as I recall, Neil Graham, one of De Witt's graduate students tried to reinterpret Everett's theory using a countably infinite number of worlds. However I think he later abandoned this approach. AFAIK Deutsch (FOR p.279) also thinks uncountably infinite.

A simple experiment tells us that, if space is continuous and described by the real numbers then electrons fired from a source can land anywhere on a screen and so the wave function must have an uncountably infinite number of possible position eigenvalues which implies an uncountably infinite number of worlds.

AFAIK Schmidhuber's scenario has a dovetailer which will produce finite bit strings that describe “worlds”  that  will be only  countably infinite in number.  Note that these bit strings are not supposed to be separate worlds that can be in a superposition – they do not interefere with one another! Rather some of them  will contain computable multiverses themselves that contain universes which will interfere.

Schmidhuber, like Tegmark, are not ware of the mind-body problem. They still use an identity thesis which is not compatible with computatiuonalism, which is needed to give some role to a universal dovetailer, which is a program. 

So, the mutltiverse is an emergent structure on all computations. The math does confirms this (and that is a material much older than the work of Schmidhuber and Tegmark, by the way).

 

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse,

There is no multiverse ever generated by a program, because the multiverse is a first person (plural) view bearing on all computations (or on all arithmetical sigma_1 sentences).

then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It take no time at all by the step 2 and 4 of the Universal Dovetailer Argument. There is no time in the universal dovetailing. There is only a number-of-steps, associate to each computations, which are atemporal relation number theoretical relations of a certain type, and the persons emulated in arithmetic cannot be aware of the (gigantic) delays brought by the universal dovetailer.

To conclude: the dreams are uncountably many a priori (but there can be countable quotient by some relation of equivalence). Physical $and* subjective time, and ordering are emerging pattern in the consciousness attached to an infinity (coutable) bodies (relative description of a program with respect to some universal numbers) of the observers.

The difficulty, which is not addressed by Schmidhuber and Tegmark concerns the mind-body relation, which cannot be a one-one relation once we bet on the computationalist hypothesis (eventually this needs the use of the logic of self-reference to make precise). I have explained this in my papers and on the everything list. You can study the Universal Dovetailer Argument, and a sketch on how to make the argument into a purely mathematical problem, in my sane04 paper:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html

Bruno

Hi Bruno

I can see that if everything is platonic time is not an issue but I have always had problems with the last step of the UDA.

Nick

 

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[LizR]

What this appears to demonstrate is that you need an infinite amount of time to run the UD. I'm wondering if this is an uncountably infinite amount, given all the countable infinities being generated, I feel that there could be some diagonalisation argument that could be invoked here. But hopefully not, because...

If computation can exist within "arithmetical reality" - as defined by Bruno as the integers plus some simple mathemtical operations - then we have at least a countable infinity immediately available. Assuming arithmetical realism, all the operations of the UD are effectively run in parallel. In this view time doesn't exist, it only appears to do so from the "insider's viewpoint".

[LizR]

On 13 January 2015 at 13:29, Nick Prince <nickmag...@gmail.com> wrote:

I can see that if everything is platonic time is not an issue but I have always had problems with the last step of the UDA.

Hi Nick

Yes, me too, assuming the last step is the MGA. Maybe we can thrash it out?

[Nick Prince]

  Hi Liz

Yes I'll try and re read it tomorrow.  ISTM though that if we make the *assumption* that the platonic realm does exist then you can always fall back on it. Like saying ok there is this realm of mathematical forms and since we are made of "stuff" which obeys mathematical rules based on limited arithmetic then we can make the leap and say we essentially exist in platonia as does everything. Indeed we can get rid of the paraphernalia of dovetailers and programs etc.  Why not say it's all just " there" - i.e. I'm in platonia already. This all seems somehow unsatisfying philosophically if we have no good argument for accepting that the platonic realm exists.

Nick

 

[LizR]

This is exactly what comp says. Everything exists timelessly in platonia, including us - and comp does therefore depend on platonia existing!

Arguments in favour of platonia

(a) it's hard to imagine 1+1=2 isn't true universally

(b) if it doesn't exist then we need another ontological foundation for reality, although that's only a "comfort zone" argument.

Arguments against

(a) incredulity

(b) maybe we just made it up somehow. This runs into the "in favour" argument (a) so this is an obvious point of attack.

[Stathis Papaioannou]

The MGA, Tim Maudlin's Olympia thought experiment
(http://www.socphilinfo.org/node/190), and some other arguments such
as Hilary Putnam's (http://consc.net/papers/rock.html) purport to show
that consciousness cannot result from the physical activity involved
in implementing computation. Most who accept these arguments think
that this proves that the computational theory of mind must therefore
be false, since the alternative would be that consciousness is due to
computation but not physical implementation of computation, and that
would be absurd. But Bruno, and others on this list, do *not* think
that alternative would be absurd, accept the computational theory of
mind, and accept that the mere existence of computations as platonic
objects is enough to give rise to mind.

In other words, if you accept that MGA-type arguments are valid, you
have to either drop computationalism or drop the need for a physical
universe to implement the computations.


--
Stathis Papaioannou

[Kim Jones]

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The world is divided into platonists and aristotelians with the majority in the latter thanks to the abrahamic religions all of which have used Aristotle's entirely presumptuous "certainty" about matter as a fast-track conduit for concretizing the much-needed icon of God the religion is advertising. Platonists are still considered a bit gay, it seems. This glorious goal of life: heaven, is thus said to exist as a geographical (ie physically real) place you will (or won't) get to, and is therefore reasonably credible to the average dolt who was educated at Aristotle's knee anyway by his schoolteacher who is a good christian, jew or arab -  no doubt about it. Religion cannot show you heaven, it can merely promise it. But that's good enough to make it worth the wait, particularly if you are wearing a bomb belt.

To this day I would say that this is one of the few cases where you can actually, truthfully say "the world is divided into two types of people" which being said ordinarily makes me want to punch the speaker in the face. I think the only other functional "two types of people" would be "male and female" but I could be wrong about that.

K

Kim Jones B.Mus.GDTL

Email:      kimj...@ozemail.com.au

Web:        http://www.eportfolio.kmjcommp.com

“I’m not saying there aren’t a lot of dangerous people out there. I am saying a lot of them are in government" - Russell Brand

[LizR]

On 13 January 2015 at 18:55, Kim Jones <kmjc...@me.com> wrote:

To this day I would say that this is one of the few cases where you can actually, truthfully say "the world is divided into two types of people" which being said ordinarily makes me want to punch the speaker in the face. I think the only other functional "two types of people" would be "male and female" but I could be wrong about that.

Yes there are occasional hermaphrodites, not to mention people whose chromosomes are neither XX nor XY.

One could find a way to divide people into two groups that would work logically, but would be fairly meaningless (e.g. less than 5 feet tall and more than or equal to 5 feet tall might do it I guess. Or something!)

[Kim Jones]

Yes, but would these really be NECESSARY descriptors of a personality? Napoleon was a puny five footer (like Sarkozy) but his ego (belief in self) apparently a few parsecs taller.

What I am trying to underline is the tribal thing once again. Platonists and Aristotelians (by now we probably need a new name for them) represent fundamental orientations in Homo Sapiens' ability to conceive of reality. These are apparently necessary constraints on behaviour (emanating from our minds) of humans and I observe that Platonists may act differently to Aristotelians, given their entirely different conception of reality, so this is not a trivial observation about human nature by any means.  If you are the kind of person who believes that the world is all there is, you are quite likely to want to claim your chunk of it and even be prepared to shoulder others out of the way in the process. Us gay Platonists are maybe still in the closet because we have difficulty admitting that we don't think the universe is WYSIWYG and therefore not worth investing so much self-belief and rapacious self-inflation. After all, if it is all a hologram of some sort, then we truly "aren't here" so you truly "cannot take it with you to heaven" because it is already there, along with you. So yeah, heaven IS kind of Platonia, or as close to it as the dumb abrahamic religions get to it - complete with the Greek kytthara (guitars) and the togas.

One's predisposition to conceive of this platonic universe as the most likely scenario is a tribal characteristic. You may have had a grandparent who wondered about these things. Just the same, such a tribe as this clearly sits around in caves at night smoking bongs and watching shadows on the wall of the cave, so they didn't really understand how to grab real power in "this world", although Plato definitely went through a fascist phase with his Republic and the "rule of wisdom".

K

[Bruno Marchal]

On 13 Jan 2015, at 00:06, LizR wrote:

On 13 January 2015 at 00:24, Bruno Marchal <mar...@ulb.ac.be> wrote:

The key is that a computation is a well defined arithmetical notion (pace Landauer and the physicalists who hope to find a physical definition of computation, which can make sense, but not if we assume computationalism).

And does this mean that computation can "occur" timelessly, in platonia?

Yes, because "occur", for computation, is defined by some arithmetical relation. The arithmetically reality run all computations (the halting and the non halting one), and "run" is an arithmetical predicate.

(PS Maybe they should look for a computational definition of physical?)

They need a computationalist definition of "physical". Then we can prove that the physical is not computational a priori.

None of the internal views (hypostases), including the physical, can be entirely computational, despite being decidable at the propositional level, there are not decidable (sigma_0) at the first order level.

The quantified version of G is Pi_2 complete (quite non computable).

The quantified version of G* is Pi_1-complete in V (an oracle for the arithmetical truth itself): the "Noùs" is bigger and more complex than ... God.

Bruno

http://iridia.ulb.ac.be/~marchal/

[Bruno Marchal]

On 13 Jan 2015, at 01:29, Nick Prince wrote:

On Monday, January 12, 2015 at 11:18:02 AM UTC, Bruno Marchal wrote:

On 12 Jan 2015, at 00:36, Nick Prince wrote:

It's not always made clear how many "universes" there are in Everett's approach. According to his biographer, Peter Byrne, Everett thought that there should be an uncountably infinite number of them - this was the only way he could define probabilities appropriately- but as far as I recall, Neil Graham, one of De Witt's graduate students tried to reinterpret Everett's theory using a countably infinite number of worlds. However I think he later abandoned this approach. AFAIK Deutsch (FOR p.279) also thinks uncountably infinite.

A simple experiment tells us that, if space is continuous and described by the real numbers then electrons fired from a source can land anywhere on a screen and so the wave function must have an uncountably infinite number of possible position eigenvalues which implies an uncountably infinite number of worlds.

AFAIK Schmidhuber's scenario has a dovetailer which will produce finite bit strings that describe “worlds”  that  will be only  countably infinite in number.  Note that these bit strings are not supposed to be separate worlds that can be in a superposition – they do not interefere with one another! Rather some of them  will contain computable multiverses themselves that contain universes which will interfere.

Schmidhuber, like Tegmark, are not ware of the mind-body problem. They still use an identity thesis which is not compatible with computatiuonalism, which is needed to give some role to a universal dovetailer, which is a program. 

So, the mutltiverse is an emergent structure on all computations. The math does confirms this (and that is a material much older than the work of Schmidhuber and Tegmark, by the way).

 

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse,

There is no multiverse ever generated by a program, because the multiverse is a first person (plural) view bearing on all computations (or on all arithmetical sigma_1 sentences).

then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It take no time at all by the step 2 and 4 of the Universal Dovetailer Argument. There is no time in the universal dovetailing. There is only a number-of-steps, associate to each computations, which are atemporal relation number theoretical relations of a certain type, and the persons emulated in arithmetic cannot be aware of the (gigantic) delays brought by the universal dovetailer.

To conclude: the dreams are uncountably many a priori (but there can be countable quotient by some relation of equivalence). Physical $and* subjective time, and ordering are emerging pattern in the consciousness attached to an infinity (coutable) bodies (relative description of a program with respect to some universal numbers) of the observers.

The difficulty, which is not addressed by Schmidhuber and Tegmark concerns the mind-body relation, which cannot be a one-one relation once we bet on the computationalist hypothesis (eventually this needs the use of the logic of self-reference to make precise). I have explained this in my papers and on the everything list. You can study the Universal Dovetailer Argument, and a sketch on how to make the argument into a purely mathematical problem, in my sane04 paper:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html

Bruno

Hi Bruno

I can see that if everything is platonic time is not an issue but I have always had problems with the last step of the UDA.

The 7 first steps explains the necessity of the reversal, but you can still avoid it by assuming a finite and primitively real physical universe.

The last step is used to show that such an explanation is of the type "God-of-the-gap", and equivalent with using God as a way of not testing a theory. That last step uses some amount of Occam razor, but less than the one needed to stop at step seven. Once we try to talk on reality, science never prove, and we can only evaluate some plausibility of the explanation. 

Bruno

Nick

 

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[Bruno Marchal]

On 13 Jan 2015, at 01:31, LizR wrote:

On 13 January 2015 at 13:22, Nick Prince <nickmag...@gmail.com> wrote:

On Monday, January 12, 2015 at 2:47:14 AM UTC, Gary O wrote:

On Sun, Jan 11, 2015 at 6:36 PM, Nick Prince <nickmag...@gmail.com> wrote:

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It's called a dovetailer because it dovetails the executions -- one step from each one, then on to the next.  So it always makes progress on all the computations -- albeit extremely slowly.  Marchal has a working example in lisp.

--

Gary

In spite of this dovetailing procedure I don't see how  the dovetailer could complete the steps for this simple experiment  in a finite (Great Programmer's) time.  This is because a countably infinite number of steps * delta t = aleph_0 * delta t = aleph_0  if delta t is the step time and it is constant in duration then it can be put in 1 to 1 correspondence with the naturals N. The infinite number of branches that arise *within* some of the created  programs evolve by the dovetailing procedure causing even further branches etc.

 I do think that well behaved universes will be short (using the universal prior) and earlier in the list rather than later but suppose the program counter was at the 5th program and this was the universe that my experiment was conducted in. Within that 5th program string will be code which accounts for the evolution of the infinite number of worlds that arise from measuring the location of the electron. Each of these infinite worlds also needs incrementing by the program counter by the agreed parallel processing type dovetailing method to evolve. I don't see how it can be completed in Great programmer's time and therefore not in denizen time either. Even great programmer's don't have infinite time - including Bruno!

What this appears to demonstrate is that you need an infinite amount of time to run the UD. I'm wondering if this is an uncountably infinite amount, given all the countable infinities being generated, I feel that there could be some diagonalisation argument that could be invoked here. But hopefully not, because...

Indeed, we need only a countable infinities, of the type 0, 1, 2, 3, ...

If computation can exist within "arithmetical reality" - as defined by Bruno as the integers plus some simple mathemtical operations - then we have at least a countable infinity immediately available. Assuming arithmetical realism, all the operations of the UD are effectively run in parallel. In this view time doesn't exist, it only appears to do so from the "insider's viewpoint".

Yes. And the amount of arithmetical realism used is less than the one used by ordinary mathematician, even when they don't do analysis (which asks for much more). Only ultrafinitism assumes less than arithmetical realism.

Bruno

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[Bruno Marchal]

On 13 Jan 2015, at 01:22, Nick Prince wrote:

On Monday, January 12, 2015 at 2:47:14 AM UTC, Gary O wrote:

On Sun, Jan 11, 2015 at 6:36 PM, Nick Prince <nickmag...@gmail.com> wrote:

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It's called a dovetailer because it dovetails the executions -- one step from each one, then on to the next.  So it always makes progress on all the computations -- albeit extremely slowly.  Marchal has a working example in lisp.

--

Gary

In spite of this dovetailing procedure I don't see how  the dovetailer could complete the steps for this simple experiment  in a finite (Great Programmer's) time. 

The "great programmer", which is just elementary arithmetic, has an infinite amount of time, but a countable one.

This is because a countably infinite number of steps * delta t = aleph_0 * delta t = aleph_0  if delta t is the step time

There is no step time, just the ordering of the natural numbers.

and it is constant in duration then it can be put in 1 to 1 correspondence with the naturals N. The infinite number of branches that arise *within* some of the created  programs evolve by the dovetailing procedure causing even further branches etc.

 I do think that well behaved universes will be short (using the universal prior) and earlier in the list rather than later but suppose the program counter was at the 5th program and this was the universe that my experiment was conducted in. Within that 5th program string will be code which accounts for the evolution of the infinite number of worlds that arise from measuring the location of the electron. Each of these infinite worlds also needs incrementing by the program counter by the agreed parallel processing type dovetailing method to evolve. I don't see how it can be completed in Great programmer's time and therefore not in denizen time either. Even great programmer's don't have infinite time - including Bruno!

Why? The UD needs only the reality of 0, s(0), s(s(0)), etc. Your argument would prove that there is a biggest prime number. Keep in mind that in the FPI (First person indeterminacy), no observer is aware of the universal dovetailing time. His soul is distributed on an infinity of computations, even a non countable one (accepting some definitions of infinite computations in arithmetic, this can be debated).

Bruno

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[Bruno Marchal]

On 13 Jan 2015, at 02:15, Nick Prince wrote:

On Tuesday, January 13, 2015 at 12:33:37 AM UTC, Liz R wrote:

On 13 January 2015 at 13:29, Nick Prince <nickmag...@gmail.com> wrote:

I can see that if everything is platonic time is not an issue but I have always had problems with the last step of the UDA.

Hi Nick

Yes, me too, assuming the last step is the MGA. Maybe we can thrash it out?

  Hi Liz

Yes I'll try and re read it tomorrow.  ISTM though that if we make the *assumption* that the platonic realm does exist then you can always fall back on it. Like saying ok there is this realm of mathematical forms and since we are made of "stuff" which obeys mathematical rules based on limited arithmetic then we can make the leap and say we essentially exist in platonia as does everything. Indeed we can get rid of the paraphernalia of dovetailers and programs etc. 

You can, but then things get far more complex. With computationalism, it can be shown that we don't need more than the arithmetical reality, and actually, even a tiny part of it (the Sigma_1 complete part). This part is shared by intuitionist philosophers and classical philosophers alike. Above that part, Platonia is no more really definable in mathematics (so we can't continue to do science, which of course is nice for those who does not want to theorize on the fundamentals).

Why not say it's all just " there" - i.e. I'm in platonia already.

That is what we say at the conclusion. It follows directly from computationalism that "you" are in arithmetic, infinitely distributed in infinitely many computations.

The main point is that this is testable: it predicts that if we look at ourselves beow the substitution level, we must "see" the map of the accessible physical realities, and that is the case thanks to quantum mechanics.  Without quantum mechanics, computationalism would be in trouble.

The other advantage (beyond providing an explanation of where the laws of phsyics come from) is that incompleteness split the math in justifiable (in third person terms) and non justifiable parts, which can explain the qualia-quanta relation, the hard aspect of consciousness, and the theological aspect of reality.

This all seems somehow unsatisfying philosophically if we have no good argument for accepting that the platonic realm exists.

You need only to believe that all natural numbers are prime or not prime, or that for all n phi_n(n) converges or does not converges (that is the nth Turing machine, applied to n, stops or does not stop).

I call that "arithmetical realism", to avoid a confusion with Plato's theology properly understood. Arithmetical realism is part of computationalism, because Church thesis enunciation assumes it. Without arithmetical realism, we can't even define what we mean by machine or mechanical procedure. It is weaker than most common assumption made in analysis or physics. 

Bruno

Nick

 

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[Nick Prince]

  Yes I see what you are saying and something I read on Russells MGA revisited paper has helped but I want to get to the bottom of this one so am going to study the MGA in more detail.
 

[Nick Prince]

On Tuesday, January 13, 2015 at 12:50:20 PM UTC, Bruno Marchal wrote:

On 13 Jan 2015, at 01:29, Nick Prince wrote:

On Monday, January 12, 2015 at 11:18:02 AM UTC, Bruno Marchal wrote:

On 12 Jan 2015, at 00:36, Nick Prince wrote:

It's not always made clear how many "universes" there are in Everett's approach. According to his biographer, Peter Byrne, Everett thought that there should be an uncountably infinite number of them - this was the only way he could define probabilities appropriately- but as far as I recall, Neil Graham, one of De Witt's graduate students tried to reinterpret Everett's theory using a countably infinite number of worlds. However I think he later abandoned this approach. AFAIK Deutsch (FOR p.279) also thinks uncountably infinite.

A simple experiment tells us that, if space is continuous and described by the real numbers then electrons fired from a source can land anywhere on a screen and so the wave function must have an uncountably infinite number of possible position eigenvalues which implies an uncountably infinite number of worlds.

AFAIK Schmidhuber's scenario has a dovetailer which will produce finite bit strings that describe “worlds”  that  will be only  countably infinite in number.  Note that these bit strings are not supposed to be separate worlds that can be in a superposition – they do not interefere with one another! Rather some of them  will contain computable multiverses themselves that contain universes which will interfere.

Schmidhuber, like Tegmark, are not ware of the mind-body problem. They still use an identity thesis which is not compatible with computatiuonalism, which is needed to give some role to a universal dovetailer, which is a program. 

So, the mutltiverse is an emergent structure on all computations. The math does confirms this (and that is a material much older than the work of Schmidhuber and Tegmark, by the way).

 

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse,

There is no multiverse ever generated by a program, because the multiverse is a first person (plural) view bearing on all computations (or on all arithmetical sigma_1 sentences).

then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It take no time at all by the step 2 and 4 of the Universal Dovetailer Argument. There is no time in the universal dovetailing. There is only a number-of-steps, associate to each computations, which are atemporal relation number theoretical relations of a certain type, and the persons emulated in arithmetic cannot be aware of the (gigantic) delays brought by the universal dovetailer.

To conclude: the dreams are uncountably many a priori (but there can be countable quotient by some relation of equivalence). Physical $and* subjective time, and ordering are emerging pattern in the consciousness attached to an infinity (coutable) bodies (relative description of a program with respect to some universal numbers) of the observers.

The difficulty, which is not addressed by Schmidhuber and Tegmark concerns the mind-body relation, which cannot be a one-one relation once we bet on the computationalist hypothesis (eventually this needs the use of the logic of self-reference to make precise). I have explained this in my papers and on the everything list. You can study the Universal Dovetailer Argument, and a sketch on how to make the argument into a purely mathematical problem, in my sane04 paper:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html

Bruno

Hi Bruno

I can see that if everything is platonic time is not an issue but I have always had problems with the last step of the UDA.

The 7 first steps explains the necessity of the reversal, but you can still avoid it by assuming a finite and primitively real physical universe.

The last step is used to show that such an explanation is of the type "God-of-the-gap", and equivalent with using God as a way of not testing a theory. That last step uses some amount of Occam razor, but less than the one needed to stop at step seven. Once we try to talk on reality, science never prove, and we can only evaluate some plausibility of the explanation. 

I am struggling to understand you here but I'm going to get to the bottom of this.
It's good to make contact with you again.

[Nick Prince]

Hi Stathis

Thank you for that. Delivered with your usual incisive clarity. I will look at your references and the MGA now in more detail bearing your comments in mind to help me.

Kind regards
Nick

--
Stathis Papaioannou

[Kim Jones]

I thought it worth cleaning up a few of Bruno's responses in this fascinating thread with Nick. Some sentences now read more easily.

Kim

Nick Prince: It's not always made clear how many "universes" there are in Everett's approach. According to his biographer, Peter Byrne, Everett thought that there should be an uncountably infinite number of them - this was the only way he could define probabilities appropriately- but as far as I recall, Neil Graham, one of De Witt's graduate students tried to reinterpret Everett's theory using a countably infinite number of worlds. However I think he later abandoned this approach. AFAIK Deutsch (FOR p.279) also thinks uncountably infinite.

A simple experiment tells us that, if space is continuous and described by the real numbers then electrons fired from a source can land anywhere on a screen and so the wave function must have an uncountably infinite number of possible position eigenvalues which implies an uncountably infinite number of worlds.

AFAIK Schmidhuber's scenario has a dovetailer which will produce finite bit strings that describe “worlds”  that  will be only  countably infinite in number.  Note that these bit strings are not supposed to be separate worlds that can be in a superposition – they do not interefere with one another! Rather some of them  will contain computable multiverses themselves that contain universes which will interfere. 

Bruno: Schmidhüber, like Tegmark, is not aware of the mind-body problem. Both men still use an identity thesis which is not compatible with computationalism, yet comp is necessary in order to give a role to a universal dovetailer, which is a program. 

So, in this view, the multiverse is an emergent structure arising from all computations. The math does confirm this (and this stuff is much older than the work of Schmidhüber and Tegmark, by the way).

Nick (earlier): The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, 

Bruno: There is no multiverse ever generated by a program, because the multiverse is a first person (plural or public) internal-only view bearing on all computations (or on all arithmetical sigma_1 sentences).

Nick (earlier): then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

Bruno: It takes no time at all via steps 2 and 4 of the Universal Dovetailer Argument. 

There is no time in universal dovetailing. 

There is only a number of steps, associated to each computation. These are atemporal relations or theoretical number relations of a certain type. In addition, persons emulated in arithmetic cannot possibly be aware of the (gigantic) delays brought about by the universal dovetailer.

To conclude: dreams are "uncountably many" a priori (but there can be a countable quotient via some equivalence relation). Physical AND subjective time, and ordering, are emerging patterns in the consciousness attached to a countable infinity of bodies (relative descriptions of a program with respect to some universal numbers) - namely, the observers.

The main difficulty, nowhere addressed by Schmidhüber or Tegmark concerns the mind-body relationship, which cannot be a one-to-one relation once we bet on the computationalist hypothesis (eventually this needs the logic of self-reference to be made precise). I have explained this in my papers and on the Everything list. You can study the Universal Dovetailer Argument, plus a sketch of how to make the argument into a purely mathematical problem, in my sane04 paper:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html

Bruno

Kim Jones B. Mus. GDTL

Email:   kimj...@ozemail.com.au

             kmjc...@icloud.com

Mobile: 0450 963 719

Phone:  02 93894239

Web:     http://www.eportfolio.kmjcommp.com

"I'm not saying there aren't a lot of dangerous people out there. I am saying a lot of them are in government" - Russell Brand

 

--

[Kim Jones]

The world is divided into platonists and aristotelians with the majority in the latter thanks to the abrahamic religions all of which have used Aristotle's entirely presumptuous "certainty" about matter as a fast-track conduit for concretizing the much-needed icon of God the religion is advertising. This glorious goal of life: heaven, is thus said to exist as a geographical (ie physically real) place you will (or won't) get to, and is thus reasonably credible to the average dolt who was educated at Aristotle's knee anyway. Religion cannot show you heaven, it can merely promise it. But that's good enough to make it worth the wait, particularly if you are wearing a bomb belt.

To this day I would say that this is one of the few cases where you can actually, truthfully say "the world is divided into two types of people" which being said ordinarily makes me want to punch the speaker in the face. I think the only other functional "two types of people" would be "male and female" but I could be wrong about that.

Kim

[Nick Prince]

On Tuesday, January 13, 2015 at 12:54:08 PM UTC, Bruno Marchal wrote:

On 13 Jan 2015, at 01:31, LizR wrote:

On 13 January 2015 at 13:22, Nick Prince <nickmag...@gmail.com> wrote:

On Monday, January 12, 2015 at 2:47:14 AM UTC, Gary O wrote:

On Sun, Jan 11, 2015 at 6:36 PM, Nick Prince <nickmag...@gmail.com> wrote:

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It's called a dovetailer because it dovetails the executions -- one step from each one, then on to the next.  So it always makes progress on all the computations -- albeit extremely slowly.  Marchal has a working example in lisp.

--

Gary

In spite of this dovetailing procedure I don't see how  the dovetailer could complete the steps for this simple experiment  in a finite (Great Programmer's) time.  This is because a countably infinite number of steps * delta t = aleph_0 * delta t = aleph_0  if delta t is the step time and it is constant in duration then it can be put in 1 to 1 correspondence with the naturals N. The infinite number of branches that arise *within* some of the created  programs evolve by the dovetailing procedure causing even further branches etc.

 I do think that well behaved universes will be short (using the universal prior) and earlier in the list rather than later but suppose the program counter was at the 5th program and this was the universe that my experiment was conducted in. Within that 5th program string will be code which accounts for the evolution of the infinite number of worlds that arise from measuring the location of the electron. Each of these infinite worlds also needs incrementing by the program counter by the agreed parallel processing type dovetailing method to evolve. I don't see how it can be completed in Great programmer's time and therefore not in denizen time either. Even great programmer's don't have infinite time - including Bruno!

What this appears to demonstrate is that you need an infinite amount of time to run the UD. I'm wondering if this is an uncountably infinite amount, given all the countable infinities being generated, I feel that there could be some diagonalisation argument that could be invoked here. But hopefully not, because...

Indeed, we need only a countable infinities, of the type 0, 1, 2, 3, ...

I've re read this thread a number of times now and still feel uncomfortable about how a dovetailer could compute the worlds in which we make measurements having an infinite number of possible outcomes when only countable infinities are needed. Yes it may be able to complete them all platonically in no time at all (for either infinite or finite steps) but there still must be the possibility that the electron can end up in an infinite number of places. So somehow surely more than the naturals are needed to explain this. Was Gary's comment about quantization appropriate?

 

 

[Nick Prince]

On Tuesday, January 13, 2015 at 12:54:08 PM UTC, Bruno Marchal wrote:

On 13 Jan 2015, at 01:31, LizR wrote:

On 13 January 2015 at 13:22, Nick Prince <nickmag...@gmail.com> wrote:

On Monday, January 12, 2015 at 2:47:14 AM UTC, Gary O wrote:

On Sun, Jan 11, 2015 at 6:36 PM, Nick Prince <nickmag...@gmail.com> wrote:

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It's called a dovetailer because it dovetails the executions -- one step from each one, then on to the next.  So it always makes progress on all the computations -- albeit extremely slowly.  Marchal has a working example in lisp.

--

Gary

In spite of this dovetailing procedure I don't see how  the dovetailer could complete the steps for this simple experiment  in a finite (Great Programmer's) time.  This is because a countably infinite number of steps * delta t = aleph_0 * delta t = aleph_0  if delta t is the step time and it is constant in duration then it can be put in 1 to 1 correspondence with the naturals N. The infinite number of branches that arise *within* some of the created  programs evolve by the dovetailing procedure causing even further branches etc.

 I do think that well behaved universes will be short (using the universal prior) and earlier in the list rather than later but suppose the program counter was at the 5th program and this was the universe that my experiment was conducted in. Within that 5th program string will be code which accounts for the evolution of the infinite number of worlds that arise from measuring the location of the electron. Each of these infinite worlds also needs incrementing by the program counter by the agreed parallel processing type dovetailing method to evolve. I don't see how it can be completed in Great programmer's time and therefore not in denizen time either. Even great programmer's don't have infinite time - including Bruno!

What this appears to demonstrate is that you need an infinite amount of time to run the UD. I'm wondering if this is an uncountably infinite amount, given all the countable infinities being generated, I feel that there could be some diagonalisation argument that could be invoked here. But hopefully not, because...

Indeed, we need only a countable infinities, of the type 0, 1, 2, 3, ...

I've re read this thread a number of times now and still feel uncomfortable about how a dovetailer could compute the worlds in which we make measurements having an infinite number of possible outcomes when only countable infinities are needed. Yes it may be able to complete them all platonically in no time at all (for either infinite or finite steps) but there still must be the possibility that the electron can end up in an infinite number of places. So somehow surely more than the naturals are needed to explain this. Was Gary's comment about quantization appropriate?

 

 

If computation can exist within "arithmetical reality" - as defined by Bruno as the integers plus some simple mathemtical operations - then we have at least a countable infinity immediately available. Assuming arithmetical realism, all the operations of the UD are effectively run in parallel. In this view time doesn't exist, it only appears to do so from the "insider's viewpoint".

Yes. And the amount of arithmetical realism used is less than the one used by ordinary mathematician, even when they don't do analysis (which asks for much more). Only ultrafinitism assumes less than arithmetical realism.

Bruno

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[Nick Prince]

Sorry but I've had reply to bruno from here. I just can't seem to get my answer to his post on Jan 13 about "the naturals 0,1,2,3 being all that is required. Been trying for ages to get the posting to work!!!!!!



 

[Bruno Marchal]

On 18 Jan 2015, at 21:10, Nick Prince wrote:

On Tuesday, January 13, 2015 at 12:54:08 PM UTC, Bruno Marchal wrote:

On 13 Jan 2015, at 01:31, LizR wrote:

On 13 January 2015 at 13:22, Nick Prince <nickmag...@gmail.com> wrote:

On Monday, January 12, 2015 at 2:47:14 AM UTC, Gary O wrote:

On Sun, Jan 11, 2015 at 6:36 PM, Nick Prince <nickmag...@gmail.com> wrote:

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It's called a dovetailer because it dovetails the executions -- one step from each one, then on to the next.  So it always makes progress on all the computations -- albeit extremely slowly.  Marchal has a working example in lisp.

--

Gary

In spite of this dovetailing procedure I don't see how  the dovetailer could complete the steps for this simple experiment  in a finite (Great Programmer's) time.  This is because a countably infinite number of steps * delta t = aleph_0 * delta t = aleph_0  if delta t is the step time and it is constant in duration then it can be put in 1 to 1 correspondence with the naturals N. The infinite number of branches that arise *within* some of the created  programs evolve by the dovetailing procedure causing even further branches etc.

 I do think that well behaved universes will be short (using the universal prior) and earlier in the list rather than later but suppose the program counter was at the 5th program and this was the universe that my experiment was conducted in. Within that 5th program string will be code which accounts for the evolution of the infinite number of worlds that arise from measuring the location of the electron. Each of these infinite worlds also needs incrementing by the program counter by the agreed parallel processing type dovetailing method to evolve. I don't see how it can be completed in Great programmer's time and therefore not in denizen time either. Even great programmer's don't have infinite time - including Bruno!

What this appears to demonstrate is that you need an infinite amount of time to run the UD. I'm wondering if this is an uncountably infinite amount, given all the countable infinities being generated, I feel that there could be some diagonalisation argument that could be invoked here. But hopefully not, because...

Indeed, we need only a countable infinities, of the type 0, 1, 2, 3, ...

I've re read this thread a number of times now and still feel uncomfortable about how a dovetailer could compute the worlds

It does not compute the worlds (unless in some metaphorical or unusual sense). It executes the programs.

It generates all programs, in say LISP, and it executes all programs, in parallel, little, steps by little steps, on all programs works. So it executes them all, including the non-stopping one.

Computationalism assumes that your brain is Turing emulable at some level for you consciousness not experiencing any difference in a substitution done at that level. Then thought experiment explains that you consciousness cannot distinguish a physical computation, from a virtual one, nor from an arithmetical. At least not directly, but eventually we can guess in some way our level of simulation, if we keep comp despite the facts disobey to it.

Take a programming language. Generate all one-input programs P_0, P_1, P_2, ... The universal dovetailer compute all P_i (j) up to k steps, for all i, j, k in N.

in which we make measurements having an infinite number of possible outcomes when only countable infinities are needed. Yes it may be able to complete them all platonically in no time at all (for either infinite or finite steps) but there still must be the possibility that the electron can end up in an infinite number of places. So somehow surely more than the naturals are needed to explain this. Was Gary's comment about quantization appropriate?

I feel sorry because I lost this thread (too much mails). The problem is that your body is distributed in infinitely many histories (all histories or computations are themselves finite or countable, but the set of all histories is a priori not countable, if only because some involve streams, or real numbers. This is just a consequence of the FPI on all computations, that include the machines with oracle (real number).

I hope this help,

Bruno

 

 

If computation can exist within "arithmetical reality" - as defined by Bruno as the integers plus some simple mathemtical operations - then we have at least a countable infinity immediately available. Assuming arithmetical realism, all the operations of the UD are effectively run in parallel. In this view time doesn't exist, it only appears to do so from the "insider's viewpoint".

Yes. And the amount of arithmetical realism used is less than the one used by ordinary mathematician, even when they don't do analysis (which asks for much more). Only ultrafinitism assumes less than arithmetical realism.

Bruno

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[Nick Prince]

On Monday, January 19, 2015 at 6:50:33 PM UTC, Bruno Marchal wrote:

On 18 Jan 2015, at 21:10, Nick Prince wrote:

On Tuesday, January 13, 2015 at 12:54:08 PM UTC, Bruno Marchal wrote:

On 13 Jan 2015, at 01:31, LizR wrote:

On 13 January 2015 at 13:22, Nick Prince <nickmag...@gmail.com> wrote:

On Monday, January 12, 2015 at 2:47:14 AM UTC, Gary O wrote:

On Sun, Jan 11, 2015 at 6:36 PM, Nick Prince <nickmag...@gmail.com> wrote:

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It's called a dovetailer because it dovetails the executions -- one step from each one, then on to the next.  So it always makes progress on all the computations -- albeit extremely slowly.  Marchal has a working example in lisp.

--

Gary

In spite of this dovetailing procedure I don't see how  the dovetailer could complete the steps for this simple experiment  in a finite (Great Programmer's) time.  This is because a countably infinite number of steps * delta t = aleph_0 * delta t = aleph_0  if delta t is the step time and it is constant in duration then it can be put in 1 to 1 correspondence with the naturals N. The infinite number of branches that arise *within* some of the created  programs evolve by the dovetailing procedure causing even further branches etc.

 I do think that well behaved universes will be short (using the universal prior) and earlier in the list rather than later but suppose the program counter was at the 5th program and this was the universe that my experiment was conducted in. Within that 5th program string will be code which accounts for the evolution of the infinite number of worlds that arise from measuring the location of the electron. Each of these infinite worlds also needs incrementing by the program counter by the agreed parallel processing type dovetailing method to evolve. I don't see how it can be completed in Great programmer's time and therefore not in denizen time either. Even great programmer's don't have infinite time - including Bruno!

What this appears to demonstrate is that you need an infinite amount of time to run the UD. I'm wondering if this is an uncountably infinite amount, given all the countable infinities being generated, I feel that there could be some diagonalisation argument that could be invoked here. But hopefully not, because...

Indeed, we need only a countable infinities, of the type 0, 1, 2, 3, ...

I've re read this thread a number of times now and still feel uncomfortable about how a dovetailer could compute the worlds

It does not compute the worlds (unless in some metaphorical or unusual sense). It executes the programs.

It generates all programs, in say LISP, and it executes all programs, in parallel, little, steps by little steps, on all programs works. So it executes them all, including the non-stopping one.

Yes I see that  it executes all programs in dovetailer fashion, but some of these programs will be essentially a "matrix" type version with the detail such that our multiverse is generated including the copies of me typing this now and experiencing what I am now experiencing.  The only difference is that with Schmidhuber's dovetailer the multiverse is generated by a "great programmer" whilst you are thinking that it is a platonic dovetailer which generates our experiences in the programs. Have I understood you correctly?

[Bruno Marchal]

On 23 Jan 2015, at 19:51, Nick Prince wrote:

On Monday, January 19, 2015 at 6:50:33 PM UTC, Bruno Marchal wrote:

On 18 Jan 2015, at 21:10, Nick Prince wrote:

On Tuesday, January 13, 2015 at 12:54:08 PM UTC, Bruno Marchal wrote:

On 13 Jan 2015, at 01:31, LizR wrote:

On 13 January 2015 at 13:22, Nick Prince <nickmag...@gmail.com> wrote:

On Monday, January 12, 2015 at 2:47:14 AM UTC, Gary O wrote:

On Sun, Jan 11, 2015 at 6:36 PM, Nick Prince <nickmag...@gmail.com> wrote:

The dovetailer would have to produce some allowance for the resolution i.e. some limit of accuracy to account for the lack of real numbers, but more importantly, how could such a dovetailer ever compute very much? For instance, say it gets to its nth program which is producing  a multiverse, then although the algorithm for it may be very short,  computing even the countably infinite branches within each output would take a countably infinite number of steps.  Our simple electron firing experiment would take all the time the great programmer has?  

It's called a dovetailer because it dovetails the executions -- one step from each one, then on to the next.  So it always makes progress on all the computations -- albeit extremely slowly.  Marchal has a working example in lisp.

--

Gary

In spite of this dovetailing procedure I don't see how  the dovetailer could complete the steps for this simple experiment  in a finite (Great Programmer's) time.  This is because a countably infinite number of steps * delta t = aleph_0 * delta t = aleph_0  if delta t is the step time and it is constant in duration then it can be put in 1 to 1 correspondence with the naturals N. The infinite number of branches that arise *within* some of the created  programs evolve by the dovetailing procedure causing even further branches etc.

 I do think that well behaved universes will be short (using the universal prior) and earlier in the list rather than later but suppose the program counter was at the 5th program and this was the universe that my experiment was conducted in. Within that 5th program string will be code which accounts for the evolution of the infinite number of worlds that arise from measuring the location of the electron. Each of these infinite worlds also needs incrementing by the program counter by the agreed parallel processing type dovetailing method to evolve. I don't see how it can be completed in Great programmer's time and therefore not in denizen time either. Even great programmer's don't have infinite time - including Bruno!

What this appears to demonstrate is that you need an infinite amount of time to run the UD. I'm wondering if this is an uncountably infinite amount, given all the countable infinities being generated, I feel that there could be some diagonalisation argument that could be invoked here. But hopefully not, because...

Indeed, we need only a countable infinities, of the type 0, 1, 2, 3, ...

I've re read this thread a number of times now and still feel uncomfortable about how a dovetailer could compute the worlds

It does not compute the worlds (unless in some metaphorical or unusual sense). It executes the programs.

It generates all programs, in say LISP, and it executes all programs, in parallel, little, steps by little steps, on all programs works. So it executes them all, including the non-stopping one.

Yes I see that  it executes all programs in dovetailer fashion, but some of these programs will be essentially a "matrix" type version with the detail such that our multiverse is generated including the copies of me typing this now and experiencing what I am now experiencing.  The only difference is that with Schmidhuber's dovetailer the multiverse is generated by a "great programmer" whilst you are thinking that it is a platonic dovetailer which generates our experiences in the programs. Have I understood you correctly?

I assume computationalism, so the execution of some program, by some universal machine (in the sense of Church-Turing), is associated with my consciousness (here-and-now, say). The universal dovetailer is just a universal program.

Now a machine cannot distinguish an execution made by a physical universe (if that exists and means something) from an execution made by anything Turing-Universal, like elementary arithmetic is already. 

I am not sure what you mean by "great programmer". It looks like a metaphor for a universal dovetailer.

Then the interesting problem, is that elementary arithmetic does not only generate the execution of my state (here and now), but it generates it infinitely many times, in different computations. so, by the first person indeterminacy (ignored by Schmidhuber, Tegmark, ... about everyone for some mysterious reason), my "next states", or my "continuations" as expected from my first person point of view, are determined by the statistics on those continuations, as executed by arithmetic (or any universal machine in the mathematical (even arithmetical) sense of the term. So if physics correctly described my continuation (which is needed to associate my consciousness to the program run by my physical brain), then physics must be given by that statistics on the infinitely many executions of programs going through my actual state at and below my substitution level.

From this you can see that a priori, we don't need to assume a physical reality, and actually we cannot assume it and related to my brain, without adding non Turing emulable (and non FPI recoverable) magic in the brain or in the brain-mind relationship.

This predicts that if we look at ourselves, or at our neighborhood, *below* our substitution level, we must see only a map of our possible continuation, and this explains the quantum aspect of the physical reality, as the schoedinger wave describe such a map (an orbital of a electron can be seen as a map where you can find the electron, which is part of the particular computation you can possibly expect).

The constructive theorem is: If computationalism is correct then physics is reduced to statistics on computations (a concept definable in elementary arithmetic). It is constructive in the sense that physics becomes derivable from the logic of self-reference (Gödel, Löb, Solovay) by translating the reasoning just sketched here in the language of any universal machine. It reduces physics (and in fact a whole theology) to elementary number theory (or anything Turing equivalent theory).

Bruno

http://iridia.ulb.ac.be/~marchal/

[Bill Taylor]

On Tuesday, January 13, 2015 at 11:29:47 PM UTC+13, Kim Jones wrote:

 Us gay Platonists are

WE gay Platonists are....

The most remarkable thing about this debate is how believers
in an Abrahamic god allegedly turned out to be WYSIWYG !

My bet is that most previous philosophers would have said
exactly the opposite, claiming it to be almost by definition!

 Plato definitely went through a fascist phase

True dat.    And the Spartans were his S.S.

-- Bill Taylor, your local rep for the Nazi grammar police.

##  Why is it that the "religion of peace" produces
##  more riots and killings than any other?