Dreams and Machines

[david.nyman]

With Bruno and his mighty handful engaged in the undodgeable (though
constantly dodged) task of working towards an elementary grasp of the
technical underpinnings of COMP, and patently lacking the fortitude of
these valorous Stakhanovites, I have been spending my time lurking,
reading and musing. My philosophical position on possible relations
between computation and mind has long (well before this list) been
that it would indeed require something like Bruno's reversal of the
'normal' relationship between computation and physics, so that mind
could emerge in some at least comprehensible manner; certainly not -
per impossibile - in the ghostly shrouds of the 'deus ex machina' of
'computational materialism'.  Consequently, parallel to the strenuous
effort ongoing in the other thread, I have been wrapping my mind more
loosely around 'interpretations of COMP-mechanics' in order to attempt
a better personal grasp of what it might mean as a metaphysics.  As
always, I need help, so here goes for starters.

Bruno has sometimes remarked (if I'm not misrepresenting him) that
COMP introduces us to machines and their dreams and I find this
metaphor very cogent and suggestive.  Certainly it seems to me that my
present state could coherently be characterised as a peculiarly
consistent dream - one that I nonetheless assume to be correlated
systematically with features of some otherwise unreachable
'elsewhere'.  In COMP, the 'mechanism and language of dreams' is
posited to be those elements of the number realm and its operators
that are deemed necessary to instantiate a 'universal TM' (i.e. one
that - assuming CT to be true - is capable of computing any computable
function).  Given this point of departure, it follows that machines so
instantiated would be capable of implementing any computable 'dream'
whatsoever - including dreams instantiating yet further levels of
machines and their dreams.  With an additional dovetailing assumption,
we find ourselves in a position to construct a sort of hyper-threaded
layer-cake of dreaming where, from any arbitrary level, recursively
nested dreams disappear towards infinity both 'upwards' and
'downwards'.

As we 'drill down' into this gateau, we are looking for emergent
patterns of invariance representing the self-referential viewpoints of
layers of 'dreaming machines' - their experience and their 'external
reality'.  The lowest level of recursion that any particular system of
dreaming requires for its instantiation is taken to constitute its
'substitution level'.  Since which layer of the cake this corresponds
to must be unknowable from the viewpoint of any level we currently
occupy, we ineluctably take a gamble if we say 'yes' to any doctor who
claims to know what he's about.  BTW, on this topic, I would refer you
to an interesting analogy that I append as a footnote below.

So, what can we take 'reality' (i.e. real, as you will recall, "in the
sense that I am real") to mean in this schema?  We cannot know, but we
do want to say that it corresponds self-referentially - in some sense
- to the number realm, and that the true language of the dreaming
machines therefore corresponds - also in some self-referential sense -
to numbers and their inter-relations.  This 'sense of correspondence'
can be defined in two ways: 'truth', which is taken to correspond
self-referentially to the unknowably 'real', and 'provability', which
is taken to correspond to what this reality can consistently claim,
express, or represent to itself.

This is about as far as I've got, and broad as it is, it seems to
point more or less in the direction of a detailed research programme
such as Bruno has outlined.  I can see that stipulations on 'reality'
such as universal computability make implicit claims that are
empirically falsifiable in principle, which is most encouraging.
Also, this general approach seems to me to have striking resonances
with metaphysics such as Bohm's notions of implication and
explication, as well as MWI.  Anyway - Bruno, I would be grateful as
ever - when you have a moment - if you would tell me which end of what
wrong stick I've got hold of this time.

Footnote:

http://www.getyourowndirt.com/

One day a group of scientists got together and decided that man had
come a long way and no longer needed God. So they picked one scientist
to go and tell Him that they were done with Him. The scientist walked
up to God and said, "God, we've decided that we no longer need you.
We're to the point that we can clone people and do many miraculous
things, so why don't you just go on and get lost."

God listened very patiently and kindly to the man and after the
scientist was done talking, God said, "Very well, how about this,
let's say we have a man making contest." To which the scientist
replied, "OK, great!" But God added, "Now, we're going to do this just
like I did back in the old days with Adam." The scientist said, "Sure,
no problem" and bent down and grabbed himself a handful of dirt. God
just looked at him and said, "No, no, no. You go get your own dirt!"

David

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[m.a.-2]

David,
            I appreciated this post because I'm more interested in the
philosophical implications (which I'm hoping to find at the end of Bruno's
UDA bridge to Valhalla) of these goings-on  ...than in the mathematical
ones. Best,
                                                                             
                                                                             
                                                                             
                                                                    marty a.



----- Original Message -----
From: "David Nyman" <david.nyman@...>
To: <everything-list@...>
Sent: Thursday, July 16, 2009 8:38 PM
Subject: Dreams and Machines



With Bruno and his mighty handful engaged in the undodgeable (though
constantly dodged) task of working towards an elementary grasp of the
technical underpinnings of COMP, and patently lacking the fortitude of
these valorous Stakhanovites, I have been spending my time lurking,
reading and musing. My philosophical position on possible relations
between computation and mind has long (well before this list) been
that it would indeed require something like Bruno's reversal of the
'normal' relationship between computation and physics, so that mind
could emerge in some at least comprehensible manner; certainly not -
per impossibile - in the ghostly shrouds of the 'deus ex machina' of
'computational materialism'. Consequently, parallel to the strenuous
effort ongoing in the other thread, I have been wrapping my mind more
loosely around 'interpretations of COMP-mechanics' in order to attempt
a better personal grasp of what it might mean as a metaphysics. As
always, I need help, so here goes for starters.

Bruno has sometimes remarked (if I'm not misrepresenting him) that
COMP introduces us to machines and their dreams and I find this
metaphor very cogent and suggestive. Certainly it seems to me that my
present state could coherently be characterised as a peculiarly
consistent dream - one that I nonetheless assume to be correlated
systematically with features of some otherwise unreachable
'elsewhere'. In COMP, the 'mechanism and language of dreams' is
posited to be those elements of the number realm and its operators
that are deemed necessary to instantiate a 'universal TM' (i.e. one
that - assuming CT to be true - is capable of computing any computable
function). Given this point of departure, it follows that machines so
instantiated would be capable of implementing any computable 'dream'
whatsoever - including dreams instantiating yet further levels of
machines and their dreams. With an additional dovetailing assumption,
we find ourselves in a position to construct a sort of hyper-threaded
layer-cake of dreaming where, from any arbitrary level, recursively
nested dreams disappear towards infinity both 'upwards' and
'downwards'.

As we 'drill down' into this gateau, we are looking for emergent
patterns of invariance representing the self-referential viewpoints of
layers of 'dreaming machines' - their experience and their 'external
reality'. The lowest level of recursion that any particular system of
dreaming requires for its instantiation is taken to constitute its
'substitution level'. Since which layer of the cake this corresponds
to must be unknowable from the viewpoint of any level we currently
occupy, we ineluctably take a gamble if we say 'yes' to any doctor who
claims to know what he's about. BTW, on this topic, I would refer you
to an interesting analogy that I append as a footnote below.

So, what can we take 'reality' (i.e. real, as you will recall, "in the
sense that I am real") to mean in this schema? We cannot know, but we
do want to say that it corresponds self-referentially - in some sense
- to the number realm, and that the true language of the dreaming
machines therefore corresponds - also in some self-referential sense -
to numbers and their inter-relations. This 'sense of correspondence'
can be defined in two ways: 'truth', which is taken to correspond
self-referentially to the unknowably 'real', and 'provability', which
is taken to correspond to what this reality can consistently claim,
express, or represent to itself.

This is about as far as I've got, and broad as it is, it seems to
point more or less in the direction of a detailed research programme
such as Bruno has outlined. I can see that stipulations on 'reality'
such as universal computability make implicit claims that are
empirically falsifiable in principle, which is most encouraging.
Also, this general approach seems to me to have striking resonances
with metaphysics such as Bohm's notions of implication and
explication, as well as MWI.  Anyway - Bruno, I would be grateful as
ever - when you have a moment - if you would tell me which end of what
wrong stick I've got hold of this time.

Footnote:

http://www.getyourowndirt.com/

One day a group of scientists got together and decided that man had
come a long way and no longer needed God. So they picked one scientist
to go and tell Him that they were done with Him. The scientist walked
up to God and said, "God, we've decided that we no longer need you.
We're to the point that we can clone people and do many miraculous
things, so why don't you just go on and get lost."

God listened very patiently and kindly to the man and after the
scientist was done talking, God said, "Very well, how about this,
let's say we have a man making contest." To which the scientist
replied, "OK, great!" But God added, "Now, we're going to do this just
like I did back in the old days with Adam." The scientist said, "Sure,
no problem" and bent down and grabbed himself a handful of dirt. God
just looked at him and said, "No, no, no. You go get your own dirt!"

David



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[Rex Allen]

On Thu, Jul 16, 2009 at 8:38 PM, David Nyman<david.nyman@...> wrote:
> In COMP, the 'mechanism and language of dreams' is
> posited to be those elements of the number realm and its operators
> that are deemed necessary to instantiate a 'universal TM' (i.e. one
> that - assuming CT to be true - is capable of computing any computable
> function).

So it occurs to me to ask:  do abstract concepts other than numbers
also exist in a platonic sense?

What about "red", for example?  Does the concept of red exist in a way
that is similar to the concept of "3"?

So if I write a computer program that deals with colors, red might be
represented by the hex number 0xff000000.  The hex number itself is
represented in memory by a sequence of 32 bits.  Each bit is
physically represented by some electrons and atoms in a microchip
being in some specific state.

But ultimately what is being represented is the idea of "red".  So in
this particular example, does this not make "red" a more fundamental
concept than the number that is used to represent it in the computer
program?  Is not "red" the MOST fundamental concept in this scenario?

So the typical materialist view is that we are in some way made from
atoms, though they don't usually go so far as to say that we ARE those
atoms.  Rather we are the information that is stored by virtue of the
atoms being in a particular configuration.  The "actually existing"
atoms of our body form a vessel for our information, and thus for our
consciousness.  But in their view, we exist only because the atoms
exist.  When the vessel is destroyed, so are we.  The atoms are
fundamental, our consciousness is derivative.

But taking a more platonic view, abstract concepts also exist.  And if
this is so, could we not just as well say that our conscious
subjective experience is formed from particular configurations of
these platonically existing abstract concepts?

In this view, these abstract concepts stand in specific relations to
one another, like symbols on a map, representing the layout (the
landscape) of a particular moment of consciousness.

And such subjective conscious experiences would include (but are not
limited to) those that lead us to mistakenly infer the actual
existence of an external world whose fundamental constituents are
electrons and atoms and photons and all the rest.

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[david.nyman]

On 17 July, 08:08, Rex Allen <rexallen...@...> wrote:

> But taking a more platonic view, abstract concepts also exist.  And if
> this is so, could we not just as well say that our conscious
> subjective experience is formed from particular configurations of
> these platonically existing abstract concepts?
>
> In this view, these abstract concepts stand in specific relations to
> one another, like symbols on a map, representing the layout (the
> landscape) of a particular moment of consciousness.
>
> And such subjective conscious experiences would include (but are not
> limited to) those that lead us to mistakenly infer the actual
> existence of an external world whose fundamental constituents are
> electrons and atoms and photons and all the rest.

Yes, just so. This is more or less what I was trying to convey in my
sally on 'what is real? (in the sense that I am real)'.  Finally - 'in
some sense' - we needs must ground any such discourse about the number
realm in 'my-existence-in-the-world': i.e. no longer 'abstracted', but
centred on the self.  Consequently any attempt at a non-dual account
must be reflexive or self-referential - i.e. "I am the singular
mysterious qualitative referent of this abstracted set of entities and
their relations".  I suppose this 'embedded' account - the unknowable
ground of our being - could be thought of, if only poetically, as the
true, ontic, or implicit 'language of the dreaming machines', towards
which any explicit version can gesture only partially and
indicatively.

David

> On Thu, Jul 16, 2009 at 8:38 PM, David Nyman<david.ny...@...> wrote:
> > In COMP, the 'mechanism and language of dreams' is
> > posited to be those elements of the number realm and its operators
> > that are deemed necessary to instantiate a 'universal TM' (i.e. one
> > that - assuming CT to be true - is capable of computing any computable
> > function).
>
> So it occurs to me to ask:  do abstract concepts other than numbers
> also exist in a platonic sense?
>
> What about "red", for example?  Does the concept of red exist in a way
> that is similar to the concept of "3"?
>
> So if I write a computer program that deals with colors, red might be
> represented by the hex number 0xff000000.  The hex number itself is
> represented in memory by a sequence of 32 bits.  Each bit is
> physically represented by some electrons and atoms in a microchip
> being in some specific state.
>
> But ultimately what is being represented is the idea of "red".  So in
> this particular example, does this not make "red" a more fundamental
> concept than the number that is used to represent it in the computer
> program?  Is not "red" the MOST fundamental concept in this scenario?
>
> So the typical materialist view is that we are in some way made from
> atoms, though they don't usually go so far as to say that we ARE those
> atoms.  Rather we are the information that is stored by virtue of the
> atoms being in a particular configuration.  The "actually existing"
> atoms of our body form a vessel for our information, and thus for our
> consciousness.  But in their view, we exist only because the atoms
> exist.  When the vessel is destroyed, so are we.  The atoms are
> fundamental, our consciousness is derivative.
>
> But taking a more platonic view, abstract concepts also exist.  And if
> this is so, could we not just as well say that our conscious
> subjective experience is formed from particular configurations of
> these platonically existing abstract concepts?
>
> In this view, these abstract concepts stand in specific relations to
> one another, like symbols on a map, representing the layout (the
> landscape) of a particular moment of consciousness.
>
> And such subjective conscious experiences would include (but are not
> limited to) those that lead us to mistakenly infer the actual
> existence of an external world whose fundamental constituents are
> electrons and atoms and photons and all the rest.

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[Bruno Marchal]

Hi David,

I comment your post with an apology to Kim and Marty, then I make a comment to Marty, and then I comment your (very nice) post.

Kim, Marty, I apologize for my bad sense of humor. Rereading some post, I realize some nuance in the tone does not go through mailings. Please indulge professional deformation of an old math teacher ...

On 17 Jul 2009, at 03:12, m.a. wrote:

David,
           I appreciated this post because I'm more interested in the
philosophical implications (which I'm hoping to find at the end of Bruno's
UDA bridge to Valhalla) of these goings-on  ...than in the mathematical
ones. Best,

Marty, I can understand you. At the same time, many discussion have been more philosophical, and the problem here, is that without some amount of math, and of computer science, things will look like a crackpot-like thing. It is almost in the nature of the subject. Big statements needs big arguments, and at least enough precise pointers toward the real thing.

You can have a still more passive understanding of the UDA, if you understand the first sixth steps. Then for the seventh, it is enough to believe in the existence of universal dovetailer (itself a quasi direct consequence of the existence of a universal machine). 

Then the 8th step alone can help you to have an idea why the Universal dovetailer is immaterial, so that physics has to be reduced to math and "machine psuchology/theology".

But then, I will not been able to answer some remark which have been done by Stathis, Russell, Brent and some others, and which are relalted to the difference between a computation (be it mathematical or physical)  and a description of a computation (be it mathematical or physical), and this is the key for understanding that when we assume brain are digitalizable, eventually we have to abandon the idea that consciousness supervene on physical computations, and to accept that it supervenes on mathematical computations.

You know, the discovery of the universal machine is the real (creative) bomb here. I could say that "nature" has never stopped to invent it and reinvent it, like with the apparition of brain, of life and the possible other many big bangs.

Then, it is hard to explain, without learning a bit on numbers, functions, sets and mathematical structures, that arithmetic, simple elementary arithmetic, already describes that universal thing which can't help itself to reinvent hitself again and again and again, and this in an atemporal, aspatial frames.

Sri Aurobindo made once a nice summary:

What, you ask, was the beginning of it all?

And it is this ...

Existence that multiplied itself

For sheer delight of being

And plunged into numberless trillions of forms

So that it might

Find 

Itself

Innumerably

----- Original Message -----
From: "David Nyman" <david.nyman@...>
To: <everything-list@...>
Sent: Thursday, July 16, 2009 8:38 PM
Subject: Dreams and Machines



With Bruno and his mighty handful engaged in the undodgeable (though
constantly dodged) task

Well said!

of working towards an elementary grasp of the
technical underpinnings of COMP, and patently lacking the fortitude of
these valorous Stakhanovites, I have been spending my time lurking,
reading and musing. My philosophical position on possible relations
between computation and mind has long (well before this list) been
that it would indeed require something like Bruno's reversal of the
'normal' relationship between computation and physics, so that mind
could emerge in some at least comprehensible manner; certainly not -
per impossibile - in the ghostly shrouds of the 'deus ex machina' of
'computational materialism'. Consequently, parallel to the strenuous
effort ongoing in the other thread, I have been wrapping my mind more
loosely around 'interpretations of COMP-mechanics' in order to attempt
a better personal grasp of what it might mean as a metaphysics. As
always, I need help, so here goes for starters.

This points to another problem I have. The UDA, and probably even more the AUDA, has deeply changed my "philosophy", up to a point where I think that philosophy and metaphysics can be handled with the doubting attitude of the (ideal) scientist, and that this attitude is a vaccine against the most inhuman aspect of "human science". But then I have reason to suggest that everything becomes far more clearer if we drop the expression "fundamental science", philosophy", "metaphysics" (unless we use them in their original greek senses) and come back to the expression "theology". If you want, assuming comp, metaphysics becomes a theology, with its communicable and non communicable parts. Assuming comp we can already listen to the course on machine theology provided by the machines.

But then I know that I look over-provocative. 

At the same time, I feel that this is important, because, I don't see how we could ever win the war against authoritative arguments and fundamentalism of all kinds without bringing back modesty (that is science) in that field.

When you grasp comp, you can understand that those scientist who pretend not doing theology are those who take Aristotle theology for granted. (Actually even a simplification of Aristotle. Aristotle was more Platonist than we usually imagine).

Bruno has sometimes remarked (if I'm not misrepresenting him) that
COMP introduces us to machines and their dreams and I find this
metaphor very cogent and suggestive.

You don't misrepresent me ... too much. Just that dreams is no more really use as a metaphor, but as a literal thing. It is a point of using digital mechanism, and assuming it clearly, and not just a vague mechanist intuition, which is already at play in all rationalist approach to inquiry.

If someone accept an artificial heart, he/she does not got a metaphor in his/her thorax. It is the same for an artificial brain, and eventually for a purely arithmetical one.

Certainly it seems to me that my
present state could coherently be characterised as a peculiarly
consistent dream - one that I nonetheless assume to be correlated
systematically with features of some otherwise unreachable
'elsewhere'.

So you are a critical realist. A "believer" in the large open minded sense. Nice.

The key lesson of UDA here is that, although you are right to bet that your present state belongs to a consistent dream, the 'truth' (a theorem in comp) is that there is an infinity of consistent dreams matching your observations, and there is a sense in which you (first person you) actually belong to an infinity of them. It is the many dreams aspect of the comp theory, partially confirmed by the quantum empirical MW observations.

In COMP, the 'mechanism and language of dreams' is
posited to be those elements of the number realm and its operators
that are deemed necessary to instantiate a 'universal TM' (i.e. one
that - assuming CT to be true - is capable of computing any computable
function). Given this point of departure,

Well the point of departure is really that I can survive with an artificial "physical" brain. And the result is that "physical" can no more be a primitive notion, and that the physical appearance has to be explained from the numbers, and indeed from their relative self-reference modalities. This leads to the arithmetical 'hypostases'.

it follows that machines so
instantiated would be capable of implementing any computable 'dream'
whatsoever - including dreams instantiating yet further levels of
machines and their dreams. With an additional dovetailing assumption,
we find ourselves in a position to construct a sort of hyper-threaded
layer-cake of dreaming where, from any arbitrary level, recursively
nested dreams disappear towards infinity both 'upwards' and
'downwards'.

All right. Except that the dovetailing is not an additional assumption. The dovetailing is already there, like the primes numbers are already there, once you posit the sixth first axioms of (Robinson) arithmetic. Sorry for being technical.

As we 'drill down' into this gateau, we are looking for emergent
patterns of invariance representing the self-referential viewpoints of
layers of 'dreaming machines' - their experience and their 'external
reality'.

It is good idea to put 'external reality' in quote. It is a very ambiguous notion. It can be the simple pure third person provable relations among the numbers, like it can be the first person plural emerging appearance of multiverse(s).

And it can be something in between, all that can depend, or not, of our substitution level, and of the meaning "we" can give to words "we", "our", ...

Obviously we do share a long and rich history.

The lowest level of recursion that any particular system of
dreaming requires for its instantiation is taken to constitute its
'substitution level'.

I guess that I agree with what you want to mean, but I would have said "the highest level" level required, in the sense that there is no lowest level. In case of doubt, the doctor can always bet on a lowest level of comp, just to diminish the probability that his patient become a zombie. Of course in practice this will cost more money.

Since which layer of the cake this corresponds
to must be unknowable from the viewpoint of any level we currently
occupy, we ineluctably take a gamble if we say 'yes' to any doctor who
claims to know what he's about. BTW, on this topic, I would refer you
to an interesting analogy that I append as a footnote below.

So, what can we take 'reality' (i.e. real, as you will recall, "in the
sense that I am real") to mean in this schema? We cannot know, but we
do want to say that it corresponds self-referentially - in some sense
- to the number realm, and that the true language of the dreaming
machines therefore corresponds - also in some self-referential sense -
to numbers and their inter-relations. This 'sense of correspondence'
can be defined in two ways: 'truth', which is taken to correspond
self-referentially to the unknowably 'real', and 'provability', which
is taken to correspond to what this reality can consistently claim,
express, or represent to itself.

Good summary!

This is about as far as I've got, and broad as it is, it seems to
point more or less in the direction of a detailed research programme
such as Bruno has outlined.

Well, here I disagree in the probably looking immodest claim of mine that the research has already be done up to the sad point that now, only math and physics remains. My initial goal, unless mistakes (fatal or not) has been attained: now we know that the "comp theology" is science, in the Popper sense that the "comp theology" has been shown refutable.

What would be nice is that the Z1* logics leads to new quantum tautologies so that the digital quantum nature can be tested against the quantum empirical one.

I can see that stipulations on 'reality'
such as universal computability make implicit claims that are
empirically falsifiable in principle, which is most encouraging.

This is CT, and you are correct, that part of comp is also refutable. But this we already have good reason to believe that nature will not, and cannot really refute it, unless quantum mechanics is wrong in the large proportion.

Actually, I believe that Church thesis can be proved in higher order logic, but this is a point I prefer to range out of the topic, because it is not essential, and it can lead to confusions (and it needs even bigger familiarity with mathematical computer science).

The yes doctor is highly more doubtable, and the main goal consisted in showing that it leads to a refutable 'theology'. Indeed, like in Plotinus, both the sharable and non sharable part of physics is completely determined by that "theology".

Also, this general approach seems to me to have striking resonances
with metaphysics such as Bohm's notions of implication and
explication, as well as MWI.  

You may develop. I like very much Bohm, because he is an honest inquirer. I appreciate him as a respectable adversary. 

To keep his materialist philosophy he honestly posit a non-comp assumption, and he is not attracted at all by the MWI. But many of its intuition fit nicely with the comp hyp, as we can see by taking computer science seriously. Bohm, like many, has still a "pre-Godelian" conception of comp, so to speak. Well I should perhaps reread him because I don't remember how far he is a (weak) materialist.

Anyway - Bruno, I would be grateful as
ever - when you have a moment - if you would tell me which end of what
wrong stick I've got hold of this time.

Very nice post, David. The only general but key point where I would like to add precision, if not insistence, is that "metaphor" thing. Einstein would not have been glad if people told him that energy is a good metaphor for matter, when all his work consists in a coherent theory (= clear refutable assumption) where the relations between matter and energy are described by testable/refutable facts. The whole point of saying yes to the doctor, qua computatio, is for helping the understanding that the comp assumption is not metaphorical and that it leads to a theory which implies the reversal that you are most correctly intuiting. 

You are correct about truth and provability. You may have insisted a bit more on the first person/third person important , and still unsolved, to be sure, relationship, and the first person indeterminacy which follows. You certainly motivate me to explain better AUDA and its relation with UDA. 

I am glad that Marty enjoy your post. At the same time, the point of my work did consist in making this utterly clear (if not shocking for those Aristotelian fundamentalist). Clarity in an hot field has to be technical or it looks too much provocative.

Thanks for this very clear post. You have a good intuition of the ultimate consequences of the comp hyp, I think.

Footnote:

http://www.getyourowndirt.com/

One day a group of scientists got together and decided that man had
come a long way and no longer needed God. So they picked one scientist
to go and tell Him that they were done with Him. The scientist walked
up to God and said, "God, we've decided that we no longer need you.
We're to the point that we can clone people and do many miraculous
things, so why don't you just go on and get lost."

God listened very patiently and kindly to the man and after the
scientist was done talking, God said, "Very well, how about this,
let's say we have a man making contest." To which the scientist
replied, "OK, great!" But God added, "Now, we're going to do this just
like I did back in the old days with Adam." The scientist said, "Sure,
no problem" and bent down and grabbed himself a handful of dirt. God
just looked at him and said, "No, no, no. You go get your own dirt!"

Cute simple story illustrating a key point that most forget. 

Bruno

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

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[m.a.-2]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Bruno,

           Be assured that I still fully intend to follow the logic of UDA as far as I can. And I'm grateful for your frequent efforts to suggest its meaning in words and to explain why words alone are inadequate. I wonder if you could clarify your use of the term "supervene" in the context below and elsewhere. How can consciousness supervene on the mathematical computations that produce that consciousness? Is this the ultimate in self-referential authoring? Best wishes,  

                                                                                                                                                                                                                                                                                                                                    marty a.

 

 

 

 

 

 

----- Original Message -----

From: marchal@...

To: everything-list@...

Sent: Friday, July 17, 2009 8:00 AM

Subject: Re: Dreams and Machines

Hi David,

I comment your post with an apology to Kim and Marty, then I make a comment to Marty, and then I comment your (very nice) post.

Kim, Marty, I apologize for my bad sense of humor. Rereading some post, I realize some nuance in the tone does not go through mailings. Please indulge professional deformation of an old math teacher ...

On 17 Jul 2009, at 03:12, m.a. wrote:

David,
           I appreciated this post because I'm more interested in the
philosophical implications (which I'm hoping to find at the end of Bruno's
UDA bridge to Valhalla) of these goings-on  ...than in the mathematical
ones. Best,

Marty, I can understand you. At the same time, many discussion have been more philosophical, and the problem here, is that without some amount of math, and of computer science, things will look like a crackpot-like thing. It is almost in the nature of the subject. Big statements needs big arguments, and at least enough precise pointers toward the real thing.

You can have a still more passive understanding of the UDA, if you understand the first sixth steps. Then for the seventh, it is enough to believe in the existence of universal dovetailer (itself a quasi direct consequence of the existence of a universal machine). 

Then the 8th step alone can help you to have an idea why the Universal dovetailer is immaterial, so that physics has to be reduced to math and "machine psuchology/theology".

But then, I will not been able to answer some remark which have been done by Stathis, Russell, Brent and some others, and which are relalted to the difference between a computation (be it mathematical or physical)  and a description of a computation (be it mathematical or physical), and this is the key for understanding that when we assume brain are digitalizable, eventually we have to abandon the idea that consciousness supervene on physical computations, and to accept that it supervenes on mathematical computations.

You know, the discovery of the universal machine is the real (creative) bomb here. I could say that "nature" has never stopped to invent it and reinvent it, like with the apparition of brain, of life and the possible other many big bangs.

Then, it is hard to explain, without learning a bit on numbers, functions, sets and mathematical structures, that arithmetic, simple elementary arithmetic, already describes that universal thing which can't help itself to reinvent hitself again and again and again, and this in an atemporal, aspatial frames.

Sri Aurobindo made once a nice summary:

What, you ask, was the beginning of it all?

And it is this ...

Existence that multiplied itself

For sheer delight of being

And plunged into numberless trillions of forms

So that it might

Find 

Itself

Innumerably

----- Original Message -----
From: "David Nyman" <david.nyman@...>
To: <everything-list@...>
Sent: Thursday, July 16, 2009 8:38 PM
Subject: Dreams and Machines



With Bruno and his mighty handful engaged in the undodgeable (though
constantly dodged) task

Well said!

of working towards an elementary grasp of the
technical underpinnings of COMP, and patently lacking the fortitude of
these valorous Stakhanovites, I have been spending my time lurking,
reading and musing. My philosophical position on possible relations
between computation and mind has long (well before this list) been
that it would indeed require something like Bruno's reversal of the
'normal' relationship between computation and physics, so that mind
could emerge in some at least comprehensible manner; certainly not -
per impossibile - in the ghostly shrouds of the 'deus ex machina' of
'computational materialism'. Consequently, parallel to the strenuous
effort ongoing in the other thread, I have been wrapping my mind more
loosely around 'interpretations of COMP-mechanics' in order to attempt
a better personal grasp of what it might mean as a metaphysics. As
always, I need help, so here goes for starters.

This points to another problem I have. The UDA, and probably even more the AUDA, has deeply changed my "philosophy", up to a point where I think that philosophy and metaphysics can be handled with the doubting attitude of the (ideal) scientist, and that this attitude is a vaccine against the most inhuman aspect of "human science". But then I have reason to suggest that everything becomes far more clearer if we drop the expression "fundamental science", philosophy", "metaphysics" (unless we use them in their original greek senses) and come back to the expression "theology". If you want, assuming comp, metaphysics becomes a theology, with its communicable and non communicable parts. Assuming comp we can already listen to the course on machine theology provided by the machines.

But then I know that I look over-provocative. 

At the same time, I feel that this is important, because, I don't see how we could ever win the war against authoritative arguments and fundamentalism of all kinds without bringing back modesty (that is science) in that field.

When you grasp comp, you can understand that those scientist who pretend not doing theology are those who take Aristotle theology for granted. (Actually even a simplification of Aristotle. Aristotle was more Platonist than we usually imagine).

Bruno has sometimes remarked (if I'm not misrepresenting him) that
COMP introduces us to machines and their dreams and I find this
metaphor very cogent and suggestive.

You don't misrepresent me ... too much. Just that dreams is no more really use as a metaphor, but as a literal thing. It is a point of using digital mechanism, and assuming it clearly, and not just a vague mechanist intuition, which is already at play in all rationalist approach to inquiry.

If someone accept an artificial heart, he/she does not got a metaphor in his/her thorax. It is the same for an artificial brain, and eventually for a purely arithmetical one.

Certainly it seems to me that my
present state could coherently be characterised as a peculiarly
consistent dream - one that I nonetheless assume to be correlated
systematically with features of some otherwise unreachable
'elsewhere'.

So you are a critical realist. A "believer" in the large open minded sense. Nice.

The key lesson of UDA here is that, although you are right to bet that your present state belongs to a consistent dream, the 'truth' (a theorem in comp) is that there is an infinity of consistent dreams matching your observations, and there is a sense in which you (first person you) actually belong to an infinity of them. It is the many dreams aspect of the comp theory, partially confirmed by the quantum empirical MW observations.

In COMP, the 'mechanism and language of dreams' is
posited to be those elements of the number realm and its operators
that are deemed necessary to instantiate a 'universal TM' (i.e. one
that - assuming CT to be true - is capable of computing any computable
function). Given this point of departure,

Well the point of departure is really that I can survive with an artificial "physical" brain. And the result is that "physical" can no more be a primitive notion, and that the physical appearance has to be explained from the numbers, and indeed from their relative self-reference modalities. This leads to the arithmetical 'hypostases'.

it follows that machines so
instantiated would be capable of implementing any computable 'dream'
whatsoever - including dreams instantiating yet further levels of
machines and their dreams. With an additional dovetailing assumption,
we find ourselves in a position to construct a sort of hyper-threaded
layer-cake of dreaming where, from any arbitrary level, recursively
nested dreams disappear towards infinity both 'upwards' and
'downwards'.

All right. Except that the dovetailing is not an additional assumption. The dovetailing is already there, like the primes numbers are already there, once you posit the sixth first axioms of (Robinson) arithmetic. Sorry for being technical.

As we 'drill down' into this gateau, we are looking for emergent
patterns of invariance representing the self-referential viewpoints of
layers of 'dreaming machines' - their experience and their 'external
reality'.

It is good idea to put 'external reality' in quote. It is a very ambiguous notion. It can be the simple pure third person provable relations among the numbers, like it can be the first person plural emerging appearance of multiverse(s).

And it can be something in between, all that can depend, or not, of our substitution level, and of the meaning "we" can give to words "we", "our", ...

Obviously we do share a long and rich history.

The lowest level of recursion that any particular system of
dreaming requires for its instantiation is taken to constitute its
'substitution level'.

I guess that I agree with what you want to mean, but I would have said "the highest level" level required, in the sense that there is no lowest level. In case of doubt, the doctor can always bet on a lowest level of comp, just to diminish the probability that his patient become a zombie. Of course in practice this will cost more money.

Since which layer of the cake this corresponds
to must be unknowable from the viewpoint of any level we currently
occupy, we ineluctably take a gamble if we say 'yes' to any doctor who
claims to know what he's about. BTW, on this topic, I would refer you
to an interesting analogy that I append as a footnote below.

So, what can we take 'reality' (i.e. real, as you will recall, "in the
sense that I am real") to mean in this schema? We cannot know, but we
do want to say that it corresponds self-referentially - in some sense
- to the number realm, and that the true language of the dreaming
machines therefore corresponds - also in some self-referential sense -
to numbers and their inter-relations. This 'sense of correspondence'
can be defined in two ways: 'truth', which is taken to correspond
self-referentially to the unknowably 'real', and 'provability', which
is taken to correspond to what this reality can consistently claim,
express, or represent to itself.

Good summary!

This is about as far as I've got, and broad as it is, it seems to
point more or less in the direction of a detailed research programme
such as Bruno has outlined.

Well, here I disagree in the probably looking immodest claim of mine that the research has already be done up to the sad point that now, only math and physics remains. My initial goal, unless mistakes (fatal or not) has been attained: now we know that the "comp theology" is science, in the Popper sense that the "comp theology" has been shown refutable.

What would be nice is that the Z1* logics leads to new quantum tautologies so that the digital quantum nature can be tested against the quantum empirical one.

I can see that stipulations on 'reality'
such as universal computability make implicit claims that are
empirically falsifiable in principle, which is most encouraging.

This is CT, and you are correct, that part of comp is also refutable. But this we already have good reason to believe that nature will not, and cannot really refute it, unless quantum mechanics is wrong in the large proportion.

Actually, I believe that Church thesis can be proved in higher order logic, but this is a point I prefer to range out of the topic, because it is not essential, and it can lead to confusions (and it needs even bigger familiarity with mathematical computer science).

The yes doctor is highly more doubtable, and the main goal consisted in showing that it leads to a refutable 'theology'. Indeed, like in Plotinus, both the sharable and non sharable part of physics is completely determined by that "theology".

Also, this general approach seems to me to have striking resonances
with metaphysics such as Bohm's notions of implication and
explication, as well as MWI.  

You may develop. I like very much Bohm, because he is an honest inquirer. I appreciate him as a respectable adversary. 

To keep his materialist philosophy he honestly posit a non-comp assumption, and he is not attracted at all by the MWI. But many of its intuition fit nicely with the comp hyp, as we can see by taking computer science seriously. Bohm, like many, has still a "pre-Godelian" conception of comp, so to speak. Well I should perhaps reread him because I don't remember how far he is a (weak) materialist.

Anyway - Bruno, I would be grateful as
ever - when you have a moment - if you would tell me which end of what
wrong stick I've got hold of this time.

Very nice post, David. The only general but key point where I would like to add precision, if not insistence, is that "metaphor" thing. Einstein would not have been glad if people told him that energy is a good metaphor for matter, when all his work consists in a coherent theory (= clear refutable assumption) where the relations between matter and energy are described by testable/refutable facts. The whole point of saying yes to the doctor, qua computatio, is for helping the understanding that the comp assumption is not metaphorical and that it leads to a theory which implies the reversal that you are most correctly intuiting. 

You are correct about truth and provability. You may have insisted a bit more on the first person/third person important , and still unsolved, to be sure, relationship, and the first person indeterminacy which follows. You certainly motivate me to explain better AUDA and its relation with UDA. 

I am glad that Marty enjoy your post. At the same time, the point of my work did consist in making this utterly clear (if not shocking for those Aristotelian fundamentalist). Clarity in an hot field has to be technical or it looks too much provocative.

Thanks for this very clear post. You have a good intuition of the ultimate consequences of the comp hyp, I think.

Footnote:

http://www.getyourowndirt.com/

One day a group of scientists got together and decided that man had
come a long way and no longer needed God. So they picked one scientist
to go and tell Him that they were done with Him. The scientist walked
up to God and said, "God, we've decided that we no longer need you.
We're to the point that we can clone people and do many miraculous
things, so why don't you just go on and get lost."

God listened very patiently and kindly to the man and after the
scientist was done talking, God said, "Very well, how about this,
let's say we have a man making contest." To which the scientist
replied, "OK, great!" But God added, "Now, we're going to do this just
like I did back in the old days with Adam." The scientist said, "Sure,
no problem" and bent down and grabbed himself a handful of dirt. God
just looked at him and said, "No, no, no. You go get your own dirt!"

Cute simple story illustrating a key point that most forget. 

Bruno

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

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[david.nyman]

2009/7/17 Bruno Marchal <marchal@...>:

> You are correct about truth and provability. You may have insisted a bit
> more on the first person/third person important , and still unsolved, to be
> sure, relationship, and the first person indeterminacy which follows. You
> certainly motivate me to explain better AUDA and its relation with UDA.
> I am glad that Marty enjoy your post. At the same time, the point of my work
> did consist in making this utterly clear (if not shocking for those
> Aristotelian fundamentalist). Clarity in an hot field has to be technical or
> it looks too much provocative.
> Thanks for this very clear post. You have a good intuition of the ultimate
> consequences of the comp hyp, I think.

Bruno, many thanks for your helpful commentary on my post - many of
your points are well taken and will help me amplify and clarify my
views.  I'm just off for a long weekend in Oxford, but I'll muse
further and try to respond on some of your points on my return
mid-week.

David

> Hi David,
> I comment your post with an apology to Kim and Marty, then I make a comment
> to Marty, and then I comment your (very nice) post.
>
> Kim, Marty, I apologize for my bad sense of humor. Rereading some post, I
> realize some nuance in the tone does not go through mailings. Please indulge
> professional deformation of an old math teacher ...
> On 17 Jul 2009, at 03:12, m.a. wrote:
>
> David,
>            I appreciated this post because I'm more interested in the
> philosophical implications (which I'm hoping to find at the end of Bruno's
> UDA bridge to Valhalla) of these goings-on  ...than in the mathematical
> ones. Best,
>
>
> Marty, I can understand you. At the same time, many discussion have been
> more philosophical, and the problem here, is that without some amount of
> math, and of computer science, things will look like a crackpot-like thing.
> It is almost in the nature of the subject. Big statements needs big
> arguments, and at least enough precise pointers toward the real thing.
> You can have a still more passive understanding of the UDA, if you
> understand the first sixth steps. Then for the seventh, it is enough to
> believe in the existence of universal dovetailer (itself a quasi direct
> consequence of the existence of a universal machine).
> Then the 8th step alone can help you to have an idea why the Universal
> dovetailer is immaterial, so that physics has to be reduced to math and
> "machine psuchology/theology".
> But then, I will not been able to answer some remark which have been done by
> Stathis, Russell, Brent and some others, and which are relalted to the
> difference between a computation (be it mathematical or physical)  and a
> description of a computation (be it mathematical or physical), and this is
> the key for understanding that when we assume brain are digitalizable,
> eventually we have to abandon the idea that consciousness supervene on
> physical computations, and to accept that it supervenes on mathematical
> computations.
> You know, the discovery of the universal machine is the real (creative) bomb
> here. I could say that "nature" has never stopped to invent it and reinvent
> it, like with the apparition of brain, of life and the possible other many
> big bangs.
> Then, it is hard to explain, without learning a bit on numbers, functions,
> sets and mathematical structures, that arithmetic, simple elementary
> arithmetic, already describes that universal thing which can't help itself
> to reinvent hitself again and again and again, and this in an atemporal,
> aspatial frames.
> Sri Aurobindo made once a nice summary:
> What, you ask, was the beginning of it all?
> And it is this ...
> Existence that multiplied itself
> For sheer delight of being
> And plunged into numberless trillions of forms
> So that it might
> Find
> Itself
> Innumerably
>
>
>
>
> ----- Original Message -----
> From: "David Nyman" <david.nyman@...>
> To: <everything-list@...>
> Sent: Thursday, July 16, 2009 8:38 PM
> Subject: Dreams and Machines
>
>
>
> With Bruno and his mighty handful engaged in the undodgeable (though
> constantly dodged) task
>
> Well said!
>
>
> of working towards an elementary grasp of the
> technical underpinnings of COMP, and patently lacking the fortitude of
> these valorous Stakhanovites, I have been spending my time lurking,
> reading and musing. My philosophical position on possible relations
> between computation and mind has long (well before this list) been
> that it would indeed require something like Bruno's reversal of the
> 'normal' relationship between computation and physics, so that mind
> could emerge in some at least comprehensible manner; certainly not -
> per impossibile - in the ghostly shrouds of the 'deus ex machina' of
> 'computational materialism'. Consequently, parallel to the strenuous
> effort ongoing in the other thread, I have been wrapping my mind more
> loosely around 'interpretations of COMP-mechanics' in order to attempt
> a better personal grasp of what it might mean as a metaphysics. As
> always, I need help, so here goes for starters.
>
> This points to another problem I have. The UDA, and probably even more the
> AUDA, has deeply changed my "philosophy", up to a point where I think that
> philosophy and metaphysics can be handled with the doubting attitude of the
> (ideal) scientist, and that this attitude is a vaccine against the most
> inhuman aspect of "human science". But then I have reason to suggest that
> everything becomes far more clearer if we drop the expression "fundamental
> science", philosophy", "metaphysics" (unless we use them in their original
> greek senses) and come back to the expression "theology". If you want,
> assuming comp, metaphysics becomes a theology, with its communicable and non
> communicable parts. Assuming comp we can already listen to the course on
> machine theology provided by the machines.
> But then I know that I look over-provocative.
> At the same time, I feel that this is important, because, I don't see how we
> could ever win the war against authoritative arguments and fundamentalism of
> all kinds without bringing back modesty (that is science) in that field.
> When you grasp comp, you can understand that those scientist who pretend not
> doing theology are those who take Aristotle theology for granted. (Actually
> even a simplification of Aristotle. Aristotle was more Platonist than we
> usually imagine).
>
>
>
>
>
> Bruno has sometimes remarked (if I'm not misrepresenting him) that
> COMP introduces us to machines and their dreams and I find this
> metaphor very cogent and suggestive.
>
> You don't misrepresent me ... too much. Just that dreams is no more really
> use as a metaphor, but as a literal thing. It is a point of using digital
> mechanism, and assuming it clearly, and not just a vague mechanist
> intuition, which is already at play in all rationalist approach to inquiry.
> If someone accept an artificial heart, he/she does not got a metaphor in
> his/her thorax. It is the same for an artificial brain, and eventually for a
> purely arithmetical one.
>
>
> Certainly it seems to me that my
> present state could coherently be characterised as a peculiarly
> consistent dream - one that I nonetheless assume to be correlated
> systematically with features of some otherwise unreachable
> 'elsewhere'.
>
> So you are a critical realist. A "believer" in the large open minded sense.
> Nice.
> The key lesson of UDA here is that, although you are right to bet that your
> present state belongs to a consistent dream, the 'truth' (a theorem in comp)
> is that there is an infinity of consistent dreams matching your
> observations, and there is a sense in which you (first person you) actually
> belong to an infinity of them. It is the many dreams aspect of the comp
> theory, partially confirmed by the quantum empirical MW observations.
>
>
>
>
> In COMP, the 'mechanism and language of dreams' is
> posited to be those elements of the number realm and its operators
> that are deemed necessary to instantiate a 'universal TM' (i.e. one
> that - assuming CT to be true - is capable of computing any computable
> function). Given this point of departure,
>
> Well the point of departure is really that I can survive with an artificial
> "physical" brain. And the result is that "physical" can no more be a
> primitive notion, and that the physical appearance has to be explained from
> the numbers, and indeed from their relative self-reference modalities. This
> leads to the arithmetical 'hypostases'.
>
>
> it follows that machines so
> instantiated would be capable of implementing any computable 'dream'
> whatsoever - including dreams instantiating yet further levels of
> machines and their dreams. With an additional dovetailing assumption,
> we find ourselves in a position to construct a sort of hyper-threaded
> layer-cake of dreaming where, from any arbitrary level, recursively
> nested dreams disappear towards infinity both 'upwards' and
> 'downwards'.
>
> All right. Except that the dovetailing is not an additional assumption. The
> dovetailing is already there, like the primes numbers are already there,
> once you posit the sixth first axioms of (Robinson) arithmetic. Sorry for
> being technical.
>
>
>
> As we 'drill down' into this gateau, we are looking for emergent
> patterns of invariance representing the self-referential viewpoints of
> layers of 'dreaming machines' - their experience and their 'external
> reality'.
>
> It is good idea to put 'external reality' in quote. It is a very ambiguous
> notion. It can be the simple pure third person provable relations among the
> numbers, like it can be the first person plural emerging appearance of
> multiverse(s).
> And it can be something in between, all that can depend, or not, of our
> substitution level, and of the meaning "we" can give to words "we", "our",
> ...
> Obviously we do share a long and rich history.
>
> The lowest level of recursion that any particular system of
> dreaming requires for its instantiation is taken to constitute its
> 'substitution level'.
>
> I guess that I agree with what you want to mean, but I would have said "the
> highest level" level required, in the sense that there is no lowest level.
> In case of doubt, the doctor can always bet on a lowest level of comp, just
> to diminish the probability that his patient become a zombie. Of course in
> practice this will cost more money.
>
>
>
> Since which layer of the cake this corresponds
> to must be unknowable from the viewpoint of any level we currently
> occupy, we ineluctably take a gamble if we say 'yes' to any doctor who
> claims to know what he's about. BTW, on this topic, I would refer you
> to an interesting analogy that I append as a footnote below.
>
> So, what can we take 'reality' (i.e. real, as you will recall, "in the
> sense that I am real") to mean in this schema? We cannot know, but we
> do want to say that it corresponds self-referentially - in some sense
> - to the number realm, and that the true language of the dreaming
> machines therefore corresponds - also in some self-referential sense -
> to numbers and their inter-relations. This 'sense of correspondence'
> can be defined in two ways: 'truth', which is taken to correspond
> self-referentially to the unknowably 'real', and 'provability', which
> is taken to correspond to what this reality can consistently claim,
> express, or represent to itself.
>
> Good summary!
>
>
> This is about as far as I've got, and broad as it is, it seems to
> point more or less in the direction of a detailed research programme
> such as Bruno has outlined.
>
> Well, here I disagree in the probably looking immodest claim of mine that
> the research has already be done up to the sad point that now, only math and
> physics remains. My initial goal, unless mistakes (fatal or not) has been
> attained: now we know that the "comp theology" is science, in the Popper
> sense that the "comp theology" has been shown refutable.
> What would be nice is that the Z1* logics leads to new quantum tautologies
> so that the digital quantum nature can be tested against the quantum
> empirical one.
>
>
> I can see that stipulations on 'reality'
> such as universal computability make implicit claims that are
> empirically falsifiable in principle, which is most encouraging.
>
> This is CT, and you are correct, that part of comp is also refutable. But
> this we already have good reason to believe that nature will not, and cannot
> really refute it, unless quantum mechanics is wrong in the large proportion.
> Actually, I believe that Church thesis can be proved in higher order logic,
> but this is a point I prefer to range out of the topic, because it is not
> essential, and it can lead to confusions (and it needs even bigger
> familiarity with mathematical computer science).
> The yes doctor is highly more doubtable, and the main goal consisted in
> showing that it leads to a refutable 'theology'. Indeed, like in Plotinus,
> both the sharable and non sharable part of physics is completely determined
> by that "theology".
>
>
>
> Also, this general approach seems to me to have striking resonances
> with metaphysics such as Bohm's notions of implication and
> explication, as well as MWI.
>
> You may develop. I like very much Bohm, because he is an honest inquirer. I
> appreciate him as a respectable adversary.
> To keep his materialist philosophy he honestly posit a non-comp assumption,
> and he is not attracted at all by the MWI. But many of its intuition fit
> nicely with the comp hyp, as we can see by taking computer science
> seriously. Bohm, like many, has still a "pre-Godelian" conception of comp,
> so to speak. Well I should perhaps reread him because I don't remember how
> far he is a (weak) materialist.
>
>
> Anyway - Bruno, I would be grateful as
> ever - when you have a moment - if you would tell me which end of what
> wrong stick I've got hold of this time.
>
> Very nice post, David. The only general but key point where I would like to
> add precision, if not insistence, is that "metaphor" thing. Einstein would
> not have been glad if people told him that energy is a good metaphor for
> matter, when all his work consists in a coherent theory (= clear refutable
> assumption) where the relations between matter and energy are described by
> testable/refutable facts. The whole point of saying yes to the doctor, qua
> computatio, is for helping the understanding that the comp assumption is not
> metaphorical and that it leads to a theory which implies the reversal that
> you are most correctly intuiting.
> You are correct about truth and provability. You may have insisted a bit
> more on the first person/third person important , and still unsolved, to be
> sure, relationship, and the first person indeterminacy which follows. You
> certainly motivate me to explain better AUDA and its relation with UDA.
> I am glad that Marty enjoy your post. At the same time, the point of my work
> did consist in making this utterly clear (if not shocking for those
> Aristotelian fundamentalist). Clarity in an hot field has to be technical or
> it looks too much provocative.
> Thanks for this very clear post. You have a good intuition of the ultimate
> consequences of the comp hyp, I think.
>
>
> Footnote:
>
> http://www.getyourowndirt.com/
>
> One day a group of scientists got together and decided that man had
> come a long way and no longer needed God. So they picked one scientist
> to go and tell Him that they were done with Him. The scientist walked
> up to God and said, "God, we've decided that we no longer need you.
> We're to the point that we can clone people and do many miraculous
> things, so why don't you just go on and get lost."
>
> God listened very patiently and kindly to the man and after the
> scientist was done talking, God said, "Very well, how about this,
> let's say we have a man making contest." To which the scientist
> replied, "OK, great!" But God added, "Now, we're going to do this just
> like I did back in the old days with Adam." The scientist said, "Sure,
> no problem" and bent down and grabbed himself a handful of dirt. God
> just looked at him and said, "No, no, no. You go get your own dirt!"
>
> Cute simple story illustrating a key point that most forget.
> Bruno
> http://iridia.ulb.ac.be/~marchal/
>
>
>
> >
>

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[Bruno Marchal]

Marty,

           Be assured that I still fully intend to follow the logic of UDA as far as I can. And I'm grateful for your frequent efforts to suggest its meaning in words and to explain why words alone are inadequate. I wonder if you could clarify your use of the term "supervene" in the context below and elsewhere.

The term comes from philosophy of mind. It designates usually the idea that consciousness is related to the physical activity of a brain. Consciousness is not necessarily seen as being produced than as being concomitant, so that supervenience can be used in both dualist and monist philosophies. 

But such supervenience needs weak materialism, i.e. the assumption that there is a physical activity, on which consciousness could supervene on. In french I used to say "vehiculated by" instead of "supervene on".

Note also that the supervenience thesis is not obvious to picture in some many worlds theories. Is it one consciousness----one brain, one consciousness---an infinity of brains, or what ? tricky question.

 I call this notion of supervenience the physical supervenience, to distinguish it from what I call the computational supervenience. 

With the computational supervenience, consciousness is associated with all the computations going through a computational state. Those computational states, and the pieces of computations going through them are well defined mathematical objects, even arithmetical objects. So computational supervenience is mathematicalist, even arithmeticalist.

You can see the UD Argument has an argument showing that comp, which in appearance needs weak materialism,  implies the computational supervenience.

How can consciousness supervene on the mathematical computations that produce that consciousness? Is this the ultimate in self-referential authoring? 

How can consciousness supervene on the physical computations that produce that consciousness? 

The difficulty is the same, except that consciousness is typically not "material", and seems to be more "informational", if not "psychological", or even "spiritual".

An entity is conscious when it believes in a reality. Then there is a ladder of higher consciousness and knowledge states, but their self-referential logics converge quickly. A theory as simple as Peano arithmetic, is already as introspective as any possible machine can be, and already very wise: she stays mute on the question "do you believe in a reality?", but Peano Arithmetic can already explain why it has to be so, if we provide the information that "she" is Peano Arithmetic (Peano's arithmetic version of the "yes doctor").

Peano Arithmetic is already a Löbian machine. Universal machine which believes in any Peano-like induction principle can "know", in a technical, but very weak sense, that they are universal, and when they know that they are Löbian.

Peano induction is the principle that IF you have an infinity of dominoes ranged in a infinite row, then if the first fall, then all dominoes will fall. (or if you prefer: each domino will fall, soon or later).

P(0) and  for all n (P(n) -> P(n+1))   implies that for all n we have P(n). 

I stop because I get technical and we are in AUDA here ... we will come back on this.

Hope this help, but ask any precision, or summary, of what has been said, or of what will be said.

Best,

Bruno

 

----- Original Message -----

From: marchal@...

To: everything-list@...

Sent: Friday, July 17, 2009 8:00 AM

Subject: Re: Dreams and Machines

Hi David,

I comment your post with an apology to Kim and Marty, then I make a comment to Marty, and then I comment your (very nice) post.

Kim, Marty, I apologize for my bad sense of humor. Rereading some post, I realize some nuance in the tone does not go through mailings. Please indulge professional deformation of an old math teacher ...

On 17 Jul 2009, at 03:12, m.a. wrote:

David,
           I appreciated this post because I'm more interested in the 
philosophical implications (which I'm hoping to find at the end of Bruno's 
UDA bridge to Valhalla) of these goings-on  ...than in the mathematical 
ones. Best,

Marty, I can understand you. At the same time, many discussion have been more philosophical, and the problem here, is that without some amount of math, and of computer science, things will look like a crackpot-like thing. It is almost in the nature of the subject. Big statements needs big arguments, and at least enough precise pointers toward the real thing.

You can have a still more passive understanding of the UDA, if you understand the first sixth steps. Then for the seventh, it is enough to believe in the existence of universal dovetailer (itself a quasi direct consequence of the existence of a universal machine). 

Then the 8th step alone can help you to have an idea why the Universal dovetailer is immaterial, so that physics has to be reduced to math and "machine psuchology/theology".

But then, I will not been able to answer some remark which have been done by Stathis, Russell, Brent and some others, and which are relalted to the difference between a computation (be it mathematical or physical)  and a description of a computation (be it mathematical or physical), and this is the key for understanding that when we assume brain are digitalizable, eventually we have to abandon the idea that consciousness supervene on physical computations, and to accept that it supervenes on mathematical computations.

You know, the discovery of the universal machine is the real (creative) bomb here. I could say that "nature" has never stopped to invent it and reinvent it, like with the apparition of brain, of life and the possible other many big bangs.

Then, it is hard to explain, without learning a bit on numbers, functions, sets and mathematical structures, that arithmetic, simple elementary arithmetic, already describes that universal thing which can't help itself to reinvent hitself again and again and again, and this in an atemporal, aspatial frames.

Sri Aurobindo made once a nice summary:

What, you ask, was the beginning of it all?

And it is this ...

Existence that multiplied itself

For sheer delight of being

And plunged into numberless trillions of forms

So that it might

Find 

Itself

Innumerably

----- Original Message ----- 
From: "David Nyman" <david.nyman@...>
To: <everything-list@...>
Sent: Thursday, July 16, 2009 8:38 PM
Subject: Dreams and Machines



With Bruno and his mighty handful engaged in the undodgeable (though
constantly dodged) task

Well said!

of working towards an elementary grasp of the
technical underpinnings of COMP, and patently lacking the fortitude of
these valorous Stakhanovites, I have been spending my time lurking,
reading and musing. My philosophical position on possible relations
between computation and mind has long (well before this list) been
that it would indeed require something like Bruno's reversal of the
'normal' relationship between computation and physics, so that mind
could emerge in some at least comprehensible manner; certainly not -
per impossibile - in the ghostly shrouds of the 'deus ex machina' of
'computational materialism'. Consequently, parallel to the strenuous
effort ongoing in the other thread, I have been wrapping my mind more
loosely around 'interpretations of COMP-mechanics' in order to attempt
a better personal grasp of what it might mean as a metaphysics. As
always, I need help, so here goes for starters.

This points to another problem I have. The UDA, and probably even more the AUDA, has deeply changed my "philosophy", up to a point where I think that philosophy and metaphysics can be handled with the doubting attitude of the (ideal) scientist, and that this attitude is a vaccine against the most inhuman aspect of "human science". But then I have reason to suggest that everything becomes far more clearer if we drop the expression "fundamental science", philosophy", "metaphysics" (unless we use them in their original greek senses) and come back to the expression "theology". If you want, assuming comp, metaphysics becomes a theology, with its communicable and non communicable parts. Assuming comp we can already listen to the course on machine theology provided by the machines.

But then I know that I look over-provocative. 

At the same time, I feel that this is important, because, I don't see how we could ever win the war against authoritative arguments and fundamentalism of all kinds without bringing back modesty (that is science) in that field.

When you grasp comp, you can understand that those scientist who pretend not doing theology are those who take Aristotle theology for granted. (Actually even a simplification of Aristotle. Aristotle was more Platonist than we usually imagine).

Bruno has sometimes remarked (if I'm not misrepresenting him) that
COMP introduces us to machines and their dreams and I find this
metaphor very cogent and suggestive.

You don't misrepresent me ... too much. Just that dreams is no more really use as a metaphor, but as a literal thing. It is a point of using digital mechanism, and assuming it clearly, and not just a vague mechanist intuition, which is already at play in all rationalist approach to inquiry.

If someone accept an artificial heart, he/she does not got a metaphor in his/her thorax. It is the same for an artificial brain, and eventually for a purely arithmetical one.

Certainly it seems to me that my
present state could coherently be characterised as a peculiarly
consistent dream - one that I nonetheless assume to be correlated
systematically with features of some otherwise unreachable
'elsewhere'.

So you are a critical realist. A "believer" in the large open minded sense. Nice.

The key lesson of UDA here is that, although you are right to bet that your present state belongs to a consistent dream, the 'truth' (a theorem in comp) is that there is an infinity of consistent dreams matching your observations, and there is a sense in which you (first person you) actually belong to an infinity of them. It is the many dreams aspect of the comp theory, partially confirmed by the quantum empirical MW observations.

In COMP, the 'mechanism and language of dreams' is
posited to be those elements of the number realm and its operators
that are deemed necessary to instantiate a 'universal TM' (i.e. one
that - assuming CT to be true - is capable of computing any computable
function). Given this point of departure,

Well the point of departure is really that I can survive with an artificial "physical" brain. And the result is that "physical" can no more be a primitive notion, and that the physical appearance has to be explained from the numbers, and indeed from their relative self-reference modalities. This leads to the arithmetical 'hypostases'.

it follows that machines so
instantiated would be capable of implementing any computable 'dream'
whatsoever - including dreams instantiating yet further levels of
machines and their dreams. With an additional dovetailing assumption,
we find ourselves in a position to construct a sort of hyper-threaded
layer-cake of dreaming where, from any arbitrary level, recursively
nested dreams disappear towards infinity both 'upwards' and
'downwards'.

All right. Except that the dovetailing is not an additional assumption. The dovetailing is already there, like the primes numbers are already there, once you posit the sixth first axioms of (Robinson) arithmetic. Sorry for being technical.

As we 'drill down' into this gateau, we are looking for emergent
patterns of invariance representing the self-referential viewpoints of
layers of 'dreaming machines' - their experience and their 'external
reality'.

It is good idea to put 'external reality' in quote. It is a very ambiguous notion. It can be the simple pure third person provable relations among the numbers, like it can be the first person plural emerging appearance of multiverse(s).

And it can be something in between, all that can depend, or not, of our substitution level, and of the meaning "we" can give to words "we", "our", ...

Obviously we do share a long and rich history.

The lowest level of recursion that any particular system of
dreaming requires for its instantiation is taken to constitute its
'substitution level'.

I guess that I agree with what you want to mean, but I would have said "the highest level" level required, in the sense that there is no lowest level. In case of doubt, the doctor can always bet on a lowest level of comp, just to diminish the probability that his patient become a zombie. Of course in practice this will cost more money.

Since which layer of the cake this corresponds
to must be unknowable from the viewpoint of any level we currently
occupy, we ineluctably take a gamble if we say 'yes' to any doctor who
claims to know what he's about. BTW, on this topic, I would refer you
to an interesting analogy that I append as a footnote below.

So, what can we take 'reality' (i.e. real, as you will recall, "in the
sense that I am real") to mean in this schema? We cannot know, but we
do want to say that it corresponds self-referentially - in some sense
- to the number realm, and that the true language of the dreaming
machines therefore corresponds - also in some self-referential sense -
to numbers and their inter-relations. This 'sense of correspondence'
can be defined in two ways: 'truth', which is taken to correspond
self-referentially to the unknowably 'real', and 'provability', which
is taken to correspond to what this reality can consistently claim,
express, or represent to itself.

Good summary!

This is about as far as I've got, and broad as it is, it seems to
point more or less in the direction of a detailed research programme
such as Bruno has outlined.

Well, here I disagree in the probably looking immodest claim of mine that the research has already be done up to the sad point that now, only math and physics remains. My initial goal, unless mistakes (fatal or not) has been attained: now we know that the "comp theology" is science, in the Popper sense that the "comp theology" has been shown refutable.

What would be nice is that the Z1* logics leads to new quantum tautologies so that the digital quantum nature can be tested against the quantum empirical one.

I can see that stipulations on 'reality'
such as universal computability make implicit claims that are
empirically falsifiable in principle, which is most encouraging.

This is CT, and you are correct, that part of comp is also refutable. But this we already have good reason to believe that nature will not, and cannot really refute it, unless quantum mechanics is wrong in the large proportion.

Actually, I believe that Church thesis can be proved in higher order logic, but this is a point I prefer to range out of the topic, because it is not essential, and it can lead to confusions (and it needs even bigger familiarity with mathematical computer science).

The yes doctor is highly more doubtable, and the main goal consisted in showing that it leads to a refutable 'theology'. Indeed, like in Plotinus, both the sharable and non sharable part of physics is completely determined by that "theology".

Also, this general approach seems to me to have striking resonances
with metaphysics such as Bohm's notions of implication and
explication, as well as MWI.  

You may develop. I like very much Bohm, because he is an honest inquirer. I appreciate him as a respectable adversary. 

To keep his materialist philosophy he honestly posit a non-comp assumption, and he is not attracted at all by the MWI. But many of its intuition fit nicely with the comp hyp, as we can see by taking computer science seriously. Bohm, like many, has still a "pre-Godelian" conception of comp, so to speak. Well I should perhaps reread him because I don't remember how far he is a (weak) materialist.

Anyway - Bruno, I would be grateful as
ever - when you have a moment - if you would tell me which end of what
wrong stick I've got hold of this time.

Very nice post, David. The only general but key point where I would like to add precision, if not insistence, is that "metaphor" thing. Einstein would not have been glad if people told him that energy is a good metaphor for matter, when all his work consists in a coherent theory (= clear refutable assumption) where the relations between matter and energy are described by testable/refutable facts. The whole point of saying yes to the doctor, qua computatio, is for helping the understanding that the comp assumption is not metaphorical and that it leads to a theory which implies the reversal that you are most correctly intuiting. 

You are correct about truth and provability. You may have insisted a bit more on the first person/third person important , and still unsolved, to be sure, relationship, and the first person indeterminacy which    follows. You certainly motivate me to explain better AUDA and its relation with UDA. 

I am glad that Marty enjoy your post. At the same time, the point of my work did consist in making this utterly clear (if not shocking for those Aristotelian fundamentalist). Clarity in an hot field has to be technical or it looks too much provocative.

Thanks for this very clear post. You have a good intuition of the ultimate consequences of the comp hyp, I think.

Footnote:

http://www.getyourowndirt.com/

One day a group of scientists got together and decided that man had
come a long way and no longer needed God. So they picked one scientist
to go and tell Him that they were done with Him. The scientist walked
up to God and said, "God, we've decided that we no longer need you.
We're to the point that we can clone people and do many miraculous
things, so why don't you just go on and get lost."

God listened very patiently and kindly to the man and after the
scientist was done talking, God said, "Very well, how about this,
let's say we have a man making contest." To which the scientist
replied, "OK, great!" But God added, "Now, we're going to do this just
like I did back in the old days with Adam." The scientist said, "Sure,
no problem" and bent down and grabbed himself a handful of dirt. God
just looked at him and said, "No, no, no. You go get your own dirt!"

Cute simple story illustrating a key point that most forget. 

Bruno

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

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

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[Bruno Marchal]

On 17 Jul 2009, at 09:08, Rex Allen wrote:

>
> On Thu, Jul 16, 2009 at 8:38 PM, David Nyman<david.nyman@...>  
> wrote:
>> In COMP, the 'mechanism and language of dreams' is
>> posited to be those elements of the number realm and its operators
>> that are deemed necessary to instantiate a 'universal TM' (i.e. one
>> that - assuming CT to be true - is capable of computing any  
>> computable
>> function).
>
> So it occurs to me to ask:  do abstract concepts other than numbers
> also exist in a platonic sense?
>
> What about "red", for example?  Does the concept of red exist in a way
> that is similar to the concept of "3"?
>
> So if I write a computer program that deals with colors, red might be
> represented by the hex number 0xff000000.  The hex number itself is
> represented in memory by a sequence of 32 bits.  Each bit is
> physically represented by some electrons and atoms in a microchip
> being in some specific state.
>
> But ultimately what is being represented is the idea of "red".  So in
> this particular example, does this not make "red" a more fundamental
> concept than the number that is used to represent it in the computer
> program?  Is not "red" the MOST fundamental concept in this scenario?
>
> So the typical materialist view is that we are in some way made from
> atoms, though they don't usually go so far as to say that we ARE those
> atoms.  Rather we are the information that is stored by virtue of the
> atoms being in a particular configuration.  The "actually existing"
> atoms of our body form a vessel for our information, and thus for our
> consciousness.  But in their view, we exist only because the atoms
> exist.  When the vessel is destroyed, so are we.  The atoms are
> fundamental, our consciousness is derivative.
>
> But taking a more platonic view, abstract concepts also exist.  And if
> this is so, could we not just as well say that our conscious
> subjective experience is formed from particular configurations of
> these platonically existing abstract concepts?
>
> In this view, these abstract concepts stand in specific relations to
> one another, like symbols on a map, representing the layout (the
> landscape) of a particular moment of consciousness.
>
> And such subjective conscious experiences would include (but are not
> limited to) those that lead us to mistakenly infer the actual
> existence of an external world whose fundamental constituents are
> electrons and atoms and photons and all the rest.

I am OK with all this. It has to be like this if we take the comp hyp  
(this is not trivial).
It remains to explain the relative stability of that illusion. How and  
why some dreams glue, in a way sufficiently precise for making  
predictions about them. Computer science provides hints.

Bruno


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




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[Rex Allen]

On Sat, Jul 18, 2009 at 11:55 AM, Bruno Marchal<marchal@...> wrote:
>
> I am OK with all this. It has to be like this if we take the comp hyp

So what are your thoughts on my question as to whether abstract
concepts other than numbers also exist in a platonic sense?  For
example, the idea of "red"?

So obviously we can cast everything as numbers and say, "In this
program, 0xff000000 represents red".  But RED is what we're really
talking about here, and 0xff000000 is just a place holder...a symbol
for what actually exists.

In your view, Bruno (or David, or anyone else who has an opinion),
what kinds of things actually "exist"?  What does it mean to say that
something "exists"?

It seems to me that maybe consciousness is actually very simple.  It
is just a group of platonic ideals, like red, that are related to each
other by a point of view:  "I like red", or "I see a red sphere."

Maybe what is complicated is constructing or identifying a causal
structure (e.g., a machine, a brain, a program, etc) whose evolving
state can be interpreted as representing a series of "connected" or
"related" instances of consciousness.  But the machine (physical or
otherwise) is NOT that consciousness, the machine just represents that
consciousness.

In this view, consciousness itself consists directly of the abstract
platonic ideals that form the contents of a given moment of
consciousness.


> It remains to explain the relative stability of that illusion. How and
> why some dreams glue, in a way sufficiently precise for making
> predictions about them.

Maybe unstable illusions exist, but, being unstable, don't ponder such
questions?

Obviously we have such conscious beings here in this world, with
schizophrenics and the like.

So your questions about "why are my perceptions so orderly", would NOT
be universally valid questions, because there are conscious entities
whose perceptions are NOT orderly.

And I would say that even my perceptions are not consistently orderly,
as when I dream I often experience strange scenarios.

To say that dreaming and hallucinating are special cases I think is to
make an unfounded assumption.  It would seem to me that orderly
perceptions are the special case, and dream-logic realities would be
the norm.

If consciousness is in some way a result of computation, then a
program that generates all possible mind-simulations will surely
result in the vast majority of resulting minds experiencing
dream-logic realities, not "law-and-order" realities like ours.

I think Sean Carroll (who I'm reasonably sure would disagree with
everything I've proposed above, but still) had a pretty good point on
such "counter-intuitive" predictions:

"The same logic applies, for example, to the highly contentious case
of the multiverse. The multiverse isn’t, by itself, a theory; it’s a
prediction of a certain class of theories. If the idea were simply
“Hey, we don’t know what happens outside our observable universe, so
maybe all sorts of crazy things happen,” it would be laughably
uninteresting. By scientific standards, it would fall woefully short.
But the point is that various theoretical attempts to explain
phenomena that we directly observe right in front of us — like
gravity, and quantum field theory — lead us to predict that our
universe should be one of many, and subsequently suggest that we take
that situation seriously when we talk about the “naturalness” of
various features of our local environment. The point, at the moment,
is not whether there really is or is not a multiverse; it’s that the
way we think about it and reach conclusions about its plausibility is
through exactly the same kind of scientific reasoning we’ve been using
for a long time now. Science doesn’t pass judgment on phenomena; it
passes judgment on theories."

So, I could continue further and go into a lengthy defense of why I
think this supports what I'm saying, BUT maybe you'll come to the same
conclusion I have and I can save myself a lot of typing!  So, I'll
just try that approach first.

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[Bruno Marchal]

On 19 Jul 2009, at 04:43, Rex Allen wrote:

>
> On Sat, Jul 18, 2009 at 11:55 AM, Bruno Marchal<marchal@...>  
> wrote:
>>
>> I am OK with all this. It has to be like this if we take the comp hyp
>
> So what are your thoughts on my question as to whether abstract
> concepts other than numbers also exist in a platonic sense?  For
> example, the idea of "red"?



Numbers are not enough. Even assuming first order logic.

Then assuming "we" are digitalizable machine, this can be proved:

Numbers are not enough.
Numbers together with addition and multiplication are enough, and it  
is "absolutely" undecidable (for us, and us = any universal machine/
number) if there is any richer ontology.

Numbers and addition + multiplication is a structure already "Turing  
universal". With addition and multiplication (and logic) you can  
already define the computational states and the pieces of histories  
going through them.

You can understand that if you assume comp, all the computations going  
through the state of self-introspecting agent  imagining "red" already  
exists as much as numbers. All the proposition of the shape "the  
machine i goes through states S" are, when true, elementary theorem of  
arithmetic, and they are accompagnying by "dense sets of proofs or  
relative realisations").

In the arithmetical Platonia, you already have all universal machines,  
and all their computations, which makes already place for big amount  
of "abstract concept" existing "platonically" (= like the numbers).

And then you can define the modalities or point of view of those  
machines, by realizing that they will be aware (they have access too)  
the gap between platonist truth and what they can prove, and ...

You may read the paper on Plotinus here, i.e. click on "pdf" on the  
right of "A purely arithmetical, yet empirically falsifiable,  
intepretation of Plotinus" on my url

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

You can see, well, not my thought on the subject, but the thought of  
the universal platonist machine. A machine is platonist when she  
believes, proves, asserts, the instanciations of the principle of  
excluded middle principle.




>
>
> So obviously we can cast everything as numbers and say, "In this
> program, 0xff000000 represents red".  But RED is what we're really
> talking about here, and 0xff000000 is just a place holder...a symbol
> for what actually exists.

Probably so.


>
>
> In your view, Bruno (or David, or anyone else who has an opinion),
> what kinds of things actually "exist"?  What does it mean to say that
> something "exists"?

Assuming comp, something S exists ontologically when you can prove  
that S exists in Robinson Arithmetic (a very weak, yet universal,  
theory),

And something S exists epistemologically when, let us say, you can  
prove in Robinson Arithmetic that there is a universal machine  
mentioning S.

Technically it is far more elegant and sophisticate. See the eight  
hypostases (points of view) in the plotinus paper (or look for  
Plotinus or hypostases in the archive of the list).

Instead of Robinson Arithmetic, you can take any first order  
specification of any universal system, machine or lnaguage (be it  
Conway's Game of Life, FORTRAN, LISP, prolog, Basic, c++,  ... up to  
modular functor from quantum topology or knot theory, or number theory  
itself.

>
>
> It seems to me that maybe consciousness is actually very simple.  It
> is just a group of platonic ideals, like red, that are related to each
> other by a point of view:  "I like red", or "I see a red sphere."

Yes.


>
>
> Maybe what is complicated is constructing or identifying a causal
> structure (e.g., a machine, a brain, a program, etc) whose evolving
> state can be interpreted as representing a series of "connected" or
> "related" instances of consciousness.

Yes. The difficulty is that consciousness, from its internal view, can  
only be related to an infinity of states belonging to high infinities  
of infinite computations. Third person consciousness, like the  
consciousness of my friend, is locally attachable (by guess) to a  
brain. "My consciousness" is not "attachable to a brain, only to an  
enumerable infinity of brains/machines/numbers weighted by non  
enumerable infinite histories.



> But the machine (physical or
> otherwise) is NOT that consciousness, the machine just represents that
> consciousness.

Indeed.
The machine can represent 3-consciousness, like my identity cart can  
represent myself.
1-consciousness is related to a continuum of machines. This follows  
form the UDA.
1-consciousness is ignorant which "places" it occupies among continuum  
of histories.

>
>
> In this view, consciousness itself consists directly of the abstract
> platonic ideals that form the contents of a given moment of
> consciousness.

Not directly. It needs a self-reference, that is no more than two  
diagonalisations. Computer science suggests, and arguably forces  
entities to relate to themselves relatively to most probable local  
universal history. This needs already virtual substitutions. Purely  
arithmetical one do the job very well.

>
>
>
>> It remains to explain the relative stability of that illusion. How  
>> and
>> why some dreams glue, in a way sufficiently precise for making
>> predictions about them.
>
> Maybe unstable illusions exist, but, being unstable, don't ponder such
> questions?
>
> Obviously we have such conscious beings here in this world, with
> schizophrenics and the like.
>
> So your questions about "why are my perceptions so orderly", would NOT
> be universally valid questions, because there are conscious entities
> whose perceptions are NOT orderly.

Nice try!
See UDA for making this precise in term of relative probabilities. And  
we have to recover the "observable probabilities".
We can come back on this, but I cannot explain all this is any shorter  
way than what is in the papers.
(Your intuition is correct, and I am perhaps playing with the  
flexibility of "NOT orderly".

>
>
> And I would say that even my perceptions are not consistently orderly,
> as when I dream I often experience strange scenarios.
>
> To say that dreaming and hallucinating are special cases I think is to
> make an unfounded assumption.  It would seem to me that orderly
> perceptions are the special case, and dream-logic realities would be
> the norm.

At first sight! This is akin to the white rabbit problem.  So we have  
to justify the "norm" from the structure of Platonia.



>
>
> If consciousness is in some way a result of computation, then a
> program that generates all possible mind-simulations will surely
> result in the vast majority of resulting minds experiencing
> dream-logic realities, not "law-and-order" realities like ours.


You are close to the UDA, which we discuss since years here ...
All the problem is there.
But once you look closely, you can see the beginning of the reason why  
"law-and-order" realities win against "dream-logic" realities. This is  
eventually coming from the fact that numbers TOGETHER with addition  
and multiplication give already a very rich, complex (even non  
axiomatizable) reality, with a strong tendency to repeat itself in an  
universal dovetailing way. Look at the youtube videos on the  
Mandelbrot set (M) to see a "platonic simple sequence of arithmetical  
objects illustrating a similar (perhaps equivalent) multiplication of  
itself and variants. It is a simple object because the definition of M  
is not much longer than the definition of the circle. The sequences  
are simple too, because their are just successive enlargements (zooms)  
in different places)

Examples:
http://www.youtube.com/watch?v=eCUFiFuUj00&feature=channel_page
http://www.youtube.com/watch?v=BUhFLpC2EfU
http://www.youtube.com/watch?v=YSQCpBN8QuA&feature=channel_page

>
>
> I think Sean Carroll (who I'm reasonably sure would disagree with
> everything I've proposed above, but still) had a pretty good point on
> such "counter-intuitive" predictions:
>
> "The same logic applies, for example, to the highly contentious case
> of the multiverse. The multiverse isn’t, by itself, a theory; it’s a
> prediction of a certain class of theories. If the idea were simply
> “Hey, we don’t know what happens outside our observable universe, so
> maybe all sorts of crazy things happen,” it would be laughably
> uninteresting. By scientific standards, it would fall woefully short.
> But the point is that various theoretical attempts to explain
> phenomena that we directly observe right in front of us — like
> gravity, and quantum field theory — lead us to predict that our
> universe should be one of many, and subsequently suggest that we take
> that situation seriously when we talk about the “naturalness” of
> various features of our local environment. The point, at the moment,
> is not whether there really is or is not a multiverse; it’s that the
> way we think about it and reach conclusions about its plausibility is
> through exactly the same kind of scientific reasoning we’ve been using
> for a long time now. Science doesn’t pass judgment on phenomena; it
> passes judgment on theories."

Well, yeah, OK.
It is already true for the theory saying: there is 0 physical  
universes, 1, 2, ..., infinity, bigger infinities ... of physical  
universes.
Comp seems to go in the direction 0 physical universes, 1 local  
(apparent) multiverses. It is too early to really say.
Scientist don't commit themselves ontologically, and many theories  
does the same, yet most assume numbers, or any universal frame.

>
>
> So, I could continue further and go into a lengthy defense of why I
> think this supports what I'm saying, BUT maybe you'll come to the same
> conclusion I have and I can save myself a lot of typing!  So, I'll
> just try that approach first.

I basically agree with all what you say, and I hope you will take as  
good news that the classical (platonist) universal machine agrees too,  
and even can justify all this, and makes those things sufficiently  
precise so that we can test it.
And retrospectively, the quantum facts, as understood by Everett  &  
Al. in Physics, saves the Classical Machine discourses from a too easy  
refutation (given that comp predicts huge self-multiplication  
indirectly observable when we look at ourself below our common  
substitution level).

I will be a bit slowed down this week, due to work, but I intend to be  
able to explain what is a universal function, what are universal  
numbers, and what are computations, and how they exist in the tiniest  
part of math where actually classical (platonist) mathematicans and  
intuitionist (non classical) mathematicians understand themselves very  
well.

I did not comment your other post because I rarely comment post where  
I tend to agree completely.

Bruno




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




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[Brent Meeker-2]

Rex Allen wrote:

> On Sat, Jul 18, 2009 at 11:55 AM, Bruno Marchal<marchal@...> wrote:
>  
>> I am OK with all this. It has to be like this if we take the comp hyp
>>    
>
> So what are your thoughts on my question as to whether abstract
> concepts other than numbers also exist in a platonic sense?  For
> example, the idea of "red"?
>
> So obviously we can cast everything as numbers and say, "In this
> program, 0xff000000 represents red".  But RED is what we're really
> talking about here, and 0xff000000 is just a place holder...a symbol
> for what actually exists.
>
> In your view, Bruno (or David, or anyone else who has an opinion),
> what kinds of things actually "exist"?  What does it mean to say that
> something "exists"?
>  

Well, since you asked, I think "exist" is always relative to some
domain; so we should use "exist" in different senses.  First of all I
think epistemology precedes ontology.  We first get knowledge of some
facts and then we create an ontology as part of a theory to explain
these facts.  Facts are obtained in different ways.  Chairs and tables
and people exist at the most basic level of epistemology, i.e. we
directly perceive them.  Sometimes it is argued that we don't really see
tables and chairs, we see 2-D patches of color and infer tables and
chairs.  This is the error of the misplaced concrete.  Perhaps as
infants we saw patches of color, but as adults our brain processes
information differently and we directly perceive 3D objects.  That we
have theories of vision that tells us we're "really" experience certain
excitations of the visual cortex or that tables and chairs are "really"
quarks and electrons with lots of empty space are beside the point.  
Those are ontologies built on other theories that were inferred from
perception of macroscopic 3D objects.

Something similar happens with mathematical objects.  We learn language
intuitively and built into language are certain logical and mathematical
structures so that we come to perceive conjunction and disjunction and
the natural numbers and some other concepts directly.  Do these
mathematical objects "really" exist?  I'd say they have
logico-mathematical existence, not the same existence as tables and
chairs, or quarks and electrons.  Similarly we may, in another domain,
say that Sherlock Holmes violin exists but Sherlock Holmes tuba does
not, based on the reading of Conan Doyle.

Brent Meeker

> It seems to me that maybe consciousness is actually very simple.  It
> is just a group of platonic ideals, like red, that are related to each
> other by a point of view:  "I like red", or "I see a red sphere."
>
> Maybe what is complicated is constructing or identifying a causal
> structure (e.g., a machine, a brain, a program, etc) whose evolving
> state can be interpreted as representing a series of "connected" or
> "related" instances of consciousness.  But the machine (physical or
> otherwise) is NOT that consciousness, the machine just represents that
> consciousness.
>
> In this view, consciousness itself consists directly of the abstract
> platonic ideals that form the contents of a given moment of
> consciousness.
>
>
>  
>> It remains to explain the relative stability of that illusion. How and
>> why some dreams glue, in a way sufficiently precise for making
>> predictions about them.
>>    
>
> Maybe unstable illusions exist, but, being unstable, don't ponder such
> questions?
>
> Obviously we have such conscious beings here in this world, with
> schizophrenics and the like.
>
> So your questions about "why are my perceptions so orderly", would NOT
> be universally valid questions, because there are conscious entities
> whose perceptions are NOT orderly.
>
> And I would say that even my perceptions are not consistently orderly,
> as when I dream I often experience strange scenarios.
>
> To say that dreaming and hallucinating are special cases I think is to
> make an unfounded assumption.  It would seem to me that orderly
> perceptions are the special case, and dream-logic realities would be
> the norm.
>
> If consciousness is in some way a result of computation, then a
> program that generates all possible mind-simulations will surely
> result in the vast majority of resulting minds experiencing
> dream-logic realities, not "law-and-order" realities like ours.
>
> I think Sean Carroll (who I'm reasonably sure would disagree with
> everything I've proposed above, but still) had a pretty good point on
> such "counter-intuitive" predictions:
>
> "The same logic applies, for example, to the highly contentious case
> of the multiverse. The multiverse isn’t, by itself, a theory; it’s a
> prediction of a certain class of theories. If the idea were simply
> “Hey, we don’t know what happens outside our observable universe, so
> maybe all sorts of crazy things happen,” it would be laughably
> uninteresting. By scientific standards, it would fall woefully short.
> But the point is that various theoretical attempts to explain
> phenomena that we directly observe right in front of us — like
> gravity, and quantum field theory — lead us to predict that our
> universe should be one of many, and subsequently suggest that we take
> that situation seriously when we talk about the “naturalness” of
> various features of our local environment. The point, at the moment,
> is not whether there really is or is not a multiverse; it’s that the
> way we think about it and reach conclusions about its plausibility is
> through exactly the same kind of scientific reasoning we’ve been using
> for a long time now. Science doesn’t pass judgment on phenomena; it
> passes judgment on theories."
>
> So, I could continue further and go into a lengthy defense of why I
> think this supports what I'm saying, BUT maybe you'll come to the same
> conclusion I have and I can save myself a lot of typing!  So, I'll
> just try that approach first.
>
> >
>
>  

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[Rex Allen]

Brent, I intend to reply more directly to your post soon, as I think
there's a lot to be said in response.

But in the meantime:

So I just finished reading David Deutsch's "The Fabric of Reality",
and I'm curious what you (Brent, Bruno, and anyone else) make of the
following passage at the end of chapter 10, The Nature of Mathematics.
 The first paragraph is at least partly applicable to Brent's recent
post, and the second seems relevant to Bruno's last response.  It
makes one wonder what other darkly esoteric abstractions may stalk the
abyssal depths of Platonia???

The passage:

"Mathematical entities are part of the fabric of reality because they
are complex and autonomous.  The sort of reality they form is in some
ways like the realm of abstractions envisaged by Plato or Penrose:
although they are by definition intangible, they exist objectively and
have properties that are independent of the laws of physics.  However,
it is physics that allows us to gain knowledge of this realm.  And it
imposes stringent constraints.  Whereas everything in the physical
reality is comprehensible, the comprehensible mathematical truths are
precisely the infinitesimal minority which happen to correspond
exactly to some physical truth - like the fact that if certain symbols
made of ink on paper are manipulated in certain ways, certain other
symbols appear.  That is, they are the truths that can be rendered in
virtual reality.  We have no choice but to assume that the
incomprehensible mathematical entities are real too, because they
appear inextricably in our explanations of the comprehensible ones.

There are physical objects - such as fingers, computers and brains -
whose behaviour can model that of certain abstract objects.  In this
way the fabric of physical reality provides us with a window on the
world of abstractions.  It is a very narrow window and gives us only a
limited range of perspectives.  Some of the structures that we see out
there, such as the natural numbers or the rules of inference of
classical logic, seem to be important or 'fundamental' to the abstract
world, in the same way as deep laws of nature are fundamental to the
physical world.  But that could be a misleading appearance.  For what
we are really seeing is only that some abstract structures are
fundamental to our understanding of abstractions.  We have no reason
to suppose that those structures are objectively significant in the
abstract world.  It is merely that some abstract entities are nearer
and more easily visible from our window than others."

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[Brent Meeker-2]

Rex Allen wrote:

> Brent, I intend to reply more directly to your post soon, as I think
> there's a lot to be said in response.
>
> But in the meantime:
>
> So I just finished reading David Deutsch's "The Fabric of Reality",
> and I'm curious what you (Brent, Bruno, and anyone else) make of the
> following passage at the end of chapter 10, The Nature of Mathematics.
>  The first paragraph is at least partly applicable to Brent's recent
> post, and the second seems relevant to Bruno's last response.  It
> makes one wonder what other darkly esoteric abstractions may stalk the
> abyssal depths of Platonia???
>
> The passage:
>
> "Mathematical entities are part of the fabric of reality because they
> are complex and autonomous.  The sort of reality they form is in some
> ways like the realm of abstractions envisaged by Plato or Penrose:
> although they are by definition intangible, they exist objectively and
> have properties that are independent of the laws of physics.  However,
> it is physics that allows us to gain knowledge of this realm.  And it
> imposes stringent constraints.  Whereas everything in the physical
> reality is comprehensible,

I find that dubious.  Even if it were true, I don't think we could ever
*know* it was true.

> the comprehensible mathematical truths are
> precisely the infinitesimal minority which happen to correspond
> exactly to some physical truth
There seem to be many mathematical truths that do not correspond to
physical facts.  In any case the correspondence is what needs explanation.

> - like the fact that if certain symbols
> made of ink on paper are manipulated in certain ways, certain other
> symbols appear.  That is, they are the truths that can be rendered in
> virtual reality.  We have no choice but to assume that the
> incomprehensible mathematical entities are real too, because they
> appear inextricably in our explanations of the comprehensible ones.
>  

I don't think Godel sentences "appear intextricably in our explanations
(proofs?) of other theorems."  They are entailed by the same axioms and
rules of inference, but that seems different to me.  They come from
infinites, which I regard as convenient approximations of "very big".

> There are physical objects - such as fingers, computers and brains -
> whose behaviour can model that of certain abstract objects.  
A very Platonic way of putting it.

> In this
> way the fabric of physical reality provides us with a window on the
> world of abstractions.  It is a very narrow window and gives us only a
> limited range of perspectives.  Some of the structures that we see out
> there, such as the natural numbers or the rules of inference of
> classical logic, seem to be important or 'fundamental' to the abstract
> world, in the same way as deep laws of nature are fundamental to the
> physical world.  But that could be a misleading appearance.  For what
> we are really seeing is only that some abstract structures are
> fundamental to our understanding of abstractions.  

What??

> We have no reason
> to suppose that those structures are objectively significant in the
> abstract world.  It is merely that some abstract entities are nearer
> and more easily visible from our window than others."
What would it mean for a structure in the abstract world (of
mathematics?) to be insignificant?

Brent

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[Bruno Marchal]

On 21 Jul 2009, at 07:22, Rex Allen wrote:

>
> Brent, I intend to reply more directly to your post soon, as I think
> there's a lot to be said in response.

I agree! I let you comment first.

>
>
> But in the meantime:
>
> So I just finished reading David Deutsch's "The Fabric of Reality",
> and I'm curious what you (Brent, Bruno, and anyone else) make of the
> following passage at the end of chapter 10, The Nature of Mathematics.
> The first paragraph is at least partly applicable to Brent's recent
> post, and the second seems relevant to Bruno's last response.  It
> makes one wonder what other darkly esoteric abstractions may stalk the
> abyssal depths of Platonia???
>
> The passage:
>
> "Mathematical entities are part of the fabric of reality because they
> are complex and autonomous.  The sort of reality they form is in some
> ways like the realm of abstractions envisaged by Plato or Penrose:
> although they are by definition intangible, they exist objectively and
> have properties that are independent of the laws of physics.

OK. Note that assuming comp, the laws of physics are dependent of the  
math.




> However,
> it is physics that allows us to gain knowledge of this realm.

This is a physicalist assumption.




> And it
> imposes stringent constraints.

Assuming comp, those constraints are themselves a mathematical origin.




> Whereas everything in the physical
> reality is comprehensible,

Everything? This is an assumption (and is probably wrong in the comp  
frame).



> the comprehensible mathematical truths are
> precisely the infinitesimal minority which happen to correspond
> exactly to some physical truth - like the fact that if certain symbols
> made of ink on paper are manipulated in certain ways, certain other
> symbols appear.  That is, they are the truths that can be rendered in
> virtual reality.

This follows from comp.



> We have no choice but to assume that the
> incomprehensible mathematical entities are real too, because they
> appear inextricably in our explanations of the comprehensible ones.

They appear in the mind or dreams of the universal machine. Here the  
comp hyp. makes possible to distinguish ontological mathematics (no  
need to take more than a tiny part of arithmetic), and the  
epistemological mathematics, which has no mathematically definable  
bound.



>
>
> There are physical objects - such as fingers, computers and brains -
> whose behaviour can model that of certain abstract objects.  In this
> way the fabric of physical reality provides us with a window on the
> world of abstractions.

Physicalist assumption. With comp the physical world emerges itself  
from a statistical sum on infinitely many computations.



> It is a very narrow window and gives us only a
> limited range of perspectives.  Some of the structures that we see out
> there, such as the natural numbers or the rules of inference of
> classical logic, seem to be important or 'fundamental' to the abstract
> world, in the same way as deep laws of nature are fundamental to the
> physical world.

Yes. Comp explains this, and exploits this.



> But that could be a misleading appearance.  For what
> we are really seeing is only that some abstract structures are
> fundamental to our understanding of abstractions.  We have no reason
> to suppose that those structures are objectively significant in the
> abstract world.

Comp does make them significant.


>  It is merely that some abstract entities are nearer
> and more easily visible from our window than others."

Comp explains this.

I appreciate very much the FOR book, but Deutsch does not take into  
account the fact that if we are digitalizable machines, our  
predictions have to rely eventually on the infinitely many relations  
between numbers. From the first person point of view, those relations  
rely themselves on many infinities which goes beyond elementary  
arithmetic.

With the comp assumption, we have a simple theory of everything:  
elementary arithmetic (without the induction axioms). In that theory  
we can prove the existence of universal machine, and their (finite)  
pieces of dreams, and why those machines will, from their own point of  
view infer the "induction axioms" and glue their dreams in projecting  
physical universe. Comp makes a tiny part of arithmetic a virtual  
"matrix" or "video game", which viewed from inside, will seem as a  
locally concrete reality. Problem: there could be too much "white  
rabbits", and other non computable manifestations predictable in our  
neighborhood. It could be no more than the 'quantum indeterminacy',  
but this remain to be completely proved (a part of this has been  
verified though).

Note that the epistemology is far richer than the ontology. The 'first  
person plenitude' (cf George Levy) is MUCH bigger than the minimal  
third person reality we need to explain the origin of the appearances.

Bruno

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




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[Rex Allen]

Brent,

So my first draft addressed many of the points you made, but it that
email got too big and sprawling I thought.

So I've focused on what seems to me like the key passage from your
post.  If you think there was some other point that I should have
addressed, let me know.

So, key passage:

> Do these mathematical objects "really" exist?  I'd say they have
> logico-mathematical existence, not the same existence as tables and
> chairs, or quarks and electrons.

So which kind of existence do you believe is more fundamental?  Which
is primary?  Logico-mathematical existence, or quark existence?  Or
are they separate but equal kinds of existence?

In what way, exactly, does logico-mathematical existence differ from
quark existence?  Is logico-mathematical existence a lesser kind of
existence?  Is logico-mathematical existence derivative of and
dependant on quark existence?

Further, do tables and chairs even have the same kind of existence as
quarks and electrons?  A table is something that we perceive visually,
but we intellectually take "tables" to be ultimately and fully
reducible to "quarks and electrons".   So chairs and quarks certainly
exist at different levels.  Quarks would seem to be more fundamental
than chairs.  But obviously we don't actually perceive quarks or
electrons...instead we infer their existence from our actual
perceptions of various types of experimental equipment and from there
associate them back with tables.

As for our experience of logico-mathematical objects, we certainly can
translate them into more "chair-like" perceptions by visualization via
computer programs, right?  This would put them very much on similar
footing with our experience of quarks and electrons at least, which we
also only visualize via computer reconstructions.

And, presumably it is possible for a human with exceptional
visualization abilities to experience logico mathematical objects in a
way that is even more "chair-like" than that.  For instance, there are
people with Synesthesia (http://en.wikipedia.org/wiki/Synesthesia),
for whom some letters or numbers are perceived as inherently colored,
or for whom numbers, months of the year, and/or days of the week
elicit precise locations in space (for example, 1980 may be "farther
away" than 1990).

But what if this type of synesthesia had some use that strongly aided
in human survival and reproduction?  Then (speaking in materialist
terms) as we evolved synesthesia would have become a standard feature
for humans and would now be considered just part of our normal sensory
apparatus.  We would be able to "sense" numbers in a way similar to
how we sense chairs.  In this case we would almost certainly consider
numbers to be unquestionably objectively real and existing.  Though
maybe we would ponder their peculiar qualities, in the same way we now
puzzle over the strangeness of quantum mechanics.

A further example:

"Autistic savant Daniel Tammet shot to fame when he set a European
record for the number of digits of pi he recited from memory (22,514).
 For afters, he learned Icelandic in a week. But unlike many savants,
he's able to tell us how he does it.

Q.  But how do you visualise a number? In the same way that I
visualise a giraffe?

A.  Every number has a texture. If it is a "lumpy" number, then
immediately my mind will relate it to other numbers which are lumpy -
the lumpiness will tell me there is a relationship, there is a common
divisor, or a pattern between the digits.

Q. Can you give an example of a "lumpy" number?

A.  For me, the ideal lumpy number is 37. It's like porridge. So 111,
a very pretty number, which is 3 times 37, is lumpy but it is also
round. It takes on the properties of both 37 and 3, which is round.
It's an intuitive and visual way of doing maths and thinking about
numbers.  For me, the ideal lumpy number is 37. It's like porridge."

I think we can say (again, speaking in materialist/physicalist terms)
that it's purely an accident of evolution that numbers don't seem as
intuitively real to us as chairs, or colors, or love, or free will
(ha!).

Speaking in platonist terms, it's an accident of our particular
mental/symbolic structure that numbers don't seem as intuitively real
to us as chairs, or colors, or love, or free will (ha!).

Speaking in computationalist terms, it's an accident of our
causal/representational/algorithmic structure that numbers don't seem
as intuitively real to us as chairs, or colors, or love, or free will
(ha!).

But, no matter what terms you use, it's conceivable, and we have
significant evidence that points to the possibility, that our
conscious perceptions could be modified in a way such that numbers and
other abstractions would seem much more substantial and real than they
do currently, even as substantial and real as chairs and tables.  And
this wouldn't require any change in what actually exists or "how"
these things exists (logico-mathematical or otherwise).

So based on all of the above, returning to your original statement:

"I'd say they have logico-mathematical existence, not the same
existence as tables and chairs, or quarks and electrons."

I would say that most people PERCEIVE logico-mathematical objects
differently than they perceive tables and chairs, or quarks and
electrons.  But this doesn't tell us anything about whether these
things really have different kinds of existence.  That we perceive
them differently is just an accident of fate.

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[Brent Meeker-2]

Rex Allen wrote:

> Brent,
>
> So my first draft addressed many of the points you made, but it that
> email got too big and sprawling I thought.
>
> So I've focused on what seems to me like the key passage from your
> post.  If you think there was some other point that I should have
> addressed, let me know.
>
> So, key passage:
>
>> Do these mathematical objects "really" exist?  I'd say they have
>> logico-mathematical existence, not the same existence as tables and
>> chairs, or quarks and electrons.
>
> So which kind of existence do you believe is more fundamental?  Which
> is primary?  Logico-mathematical existence, or quark existence?  Or
> are they separate but equal kinds of existence?

The way I look at it there is knowledge we gain from perception, including the
inner perception of logical and mathematical facts.  We make up theories that
unify and explain these perceptions and which extend beyond what we perceive.
These theories have ontologies: things they assume to exist - within the domain
of the theory.  There's no way to say that one is more fundamental than the
other so long as they are in separate theories.  Only if they are subsumed
within one theory can there be some sense in which one is more fundamental than
the other.  I don't think we have such a theory yet.  And note that even if we
have theory including both mathematical and physical objects in its ontology it
may turn out that either one can be used to explain the other; so it's not
necessarily the case that one is more fundmental.

>
> In what way, exactly, does logico-mathematical existence differ from
> quark existence?  

You can kick quarks and they kick back.

>Is logico-mathematical existence a lesser kind of
> existence?  Is logico-mathematical existence derivative of and
> dependant on quark existence?

See above.


>
> Further, do tables and chairs even have the same kind of existence as
> quarks and electrons?  

Although the explanation of the macroscopic world from the quantum world is not
worked out it is generally supposed that tables and chairs will eventually be
explained in terms of quarks and electrons.  The interesting thing is that from
the standpoint of epistemology, the tables and chairs are more fundamental,
while the theory makes the quarks and electrons more fundamental to the
ontology.  So there are different senses of "fundamental" too.

>A table is something that we perceive visually,
> but we intellectually take "tables" to be ultimately and fully
> reducible to "quarks and electrons".   So chairs and quarks certainly
> exist at different levels.  Quarks would seem to be more fundamental
> than chairs.  But obviously we don't actually perceive quarks or
> electrons...instead we infer their existence from our actual
> perceptions of various types of experimental equipment and from there
> associate them back with tables.
>
> As for our experience of logico-mathematical objects, we certainly can
> translate them into more "chair-like" perceptions by visualization via
> computer programs, right?  

I'm doubtful of that.  Certainly many mathematical objects can be illustrated
because they were invented to describe something we could perceive - like
spheres or symmetries.  But I don't see how you would visualize Shannon
information or strings in ten dimensional space.

>This would put them very much on similar
> footing with our experience of quarks and electrons at least, which we
> also only visualize via computer reconstructions.

But there's more than visualization.  We can also manipulate and use quarks and
electrons, i.e. we can make them kick each other and us.

>
> And, presumably it is possible for a human with exceptional
> visualization abilities to experience logico mathematical objects in a
> way that is even more "chair-like" than that.  For instance, there are
> people with Synesthesia (http://en.wikipedia.org/wiki/Synesthesia),
> for whom some letters or numbers are perceived as inherently colored,
> or for whom numbers, months of the year, and/or days of the week
> elicit precise locations in space (for example, 1980 may be "farther
> away" than 1990).

I don't think that's good example. Synesthesia comes from cross coupling in the
brain of concepts that are usually separate.  I synesthesia were like perception
then all synesthesists would see the same numbers as having the same color, etc.
  The main thing that causes us to attribute a form of existence to mathematical
objects is that everyone who understands them agrees on their properties.

>
> But what if this type of synesthesia had some use that strongly aided
> in human survival and reproduction?  Then (speaking in materialist
> terms) as we evolved synesthesia would have become a standard feature
> for humans and would now be considered just part of our normal sensory
> apparatus.  We would be able to "sense" numbers in a way similar to
> how we sense chairs.  In this case we would almost certainly consider
> numbers to be unquestionably objectively real and existing.  Though
> maybe we would ponder their peculiar qualities, in the same way we now
> puzzle over the strangeness of quantum mechanics.
>
> A further example:
>
> "Autistic savant Daniel Tammet shot to fame when he set a European
> record for the number of digits of pi he recited from memory (22,514).
>  For afters, he learned Icelandic in a week. But unlike many savants,
> he's able to tell us how he does it.
>
> Q.  But how do you visualise a number? In the same way that I
> visualise a giraffe?
>
> A.  Every number has a texture. If it is a "lumpy" number, then
> immediately my mind will relate it to other numbers which are lumpy -
> the lumpiness will tell me there is a relationship, there is a common
> divisor, or a pattern between the digits.
>
> Q. Can you give an example of a "lumpy" number?
>
> A.  For me, the ideal lumpy number is 37. It's like porridge. So 111,
> a very pretty number, which is 3 times 37, is lumpy but it is also
> round. It takes on the properties of both 37 and 3, which is round.
> It's an intuitive and visual way of doing maths and thinking about
> numbers.  For me, the ideal lumpy number is 37. It's like porridge."
>
> I think we can say (again, speaking in materialist/physicalist terms)
> that it's purely an accident of evolution that numbers don't seem as
> intuitively real to us as chairs, or colors, or love, or free will
> (ha!).
>
> Speaking in platonist terms, it's an accident of our particular
> mental/symbolic structure that numbers don't seem as intuitively real
> to us as chairs, or colors, or love, or free will (ha!).
>
> Speaking in computationalist terms, it's an accident of our
> causal/representational/algorithmic structure that numbers don't seem
> as intuitively real to us as chairs, or colors, or love, or free will
> (ha!).

But numbers don't cause anything and they are not caused by other things.  So
it's not an accident.

>
> But, no matter what terms you use, it's conceivable, and we have
> significant evidence that points to the possibility, that our
> conscious perceptions could be modified in a way such that numbers and
> other abstractions would seem much more substantial and real than they
> do currently, even as substantial and real as chairs and tables.  And
> this wouldn't require any change in what actually exists or "how"
> these things exists (logico-mathematical or otherwise).
>
> So based on all of the above, returning to your original statement:
>
> "I'd say they have logico-mathematical existence, not the same
> existence as tables and chairs, or quarks and electrons."
>
> I would say that most people PERCEIVE logico-mathematical objects
> differently than they perceive tables and chairs, or quarks and
> electrons.  But this doesn't tell us anything about whether these
> things really have different kinds of existence.  That we perceive
> them differently is just an accident of fate.

It is more than just perceiving them differently.  For example mathematical
objects are not located in space or time.  They exist timelessly and in no
particular place.

Brent

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[Torgny Tholerus]

Rex Allen skrev:

> Brent,
>
> So my first draft addressed many of the points you made, but it that
> email got too big and sprawling I thought.
>
> So I've focused on what seems to me like the key passage from your
> post.  If you think there was some other point that I should have
> addressed, let me know.
>
> So, key passage:
>
>  
>> Do these mathematical objects "really" exist?  I'd say they have
>> logico-mathematical existence, not the same existence as tables and
>> chairs, or quarks and electrons.
>>    
>
> So which kind of existence do you believe is more fundamental?  Which
> is primary?  Logico-mathematical existence, or quark existence?  Or
> are they separate but equal kinds of existence?
>
>  

The most general form of existence is: All mathematical possible
universes exist.  Our universe is one of those mathematical possible
existing universes.

The inside of a specific universe constitutes an other form of
existence.  In a specific universe there are objects inside that
universe.  In the Game of Life universe, you have the Glider object, the
Glider gun object, the Exploder object, the Tumbler object, etc.  In a
specific instance of the GoL-universe, there exist some objects and some
objects does not exist there.

In our own universe, there exist tables and chairs and quarks and
electrons.  This is the specific form of existence.  But the
mathematical objects does not exist in our universe, in this form of
existence.  You can not find the "17" object anywhere inside our universe.

Then we have the general form of existence saying that our universe
exists because it is a mathematical possibility.

--
Torgny Tholerus

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[Bruno Marchal]

Hi,

Ma connection at home is no functioning. So I am temporarily
disconnected. I hope I will be able to solve that problem. I am sending
here some little comments from my office.

I include some more material for Kim and Marty, and others, just to
think about, in case I remain disconnected for some time. Sorry.

Bruno

Le 22-juil.-09, à 10:27, Torgny Tholerus a écrit :

>
> Rex Allen skrev:
>> Brent,
>>
>> So my first draft addressed many of the points you made, but it that
>> email got too big and sprawling I thought.
>>
>> So I've focused on what seems to me like the key passage from your
>> post.  If you think there was some other point that I should have
>> addressed, let me know.
>>
>> So, key passage:
>>
>>
>>> Do these mathematical objects "really" exist?  I'd say they have
>>> logico-mathematical existence, not the same existence as tables and
>>> chairs, or quarks and electrons.
>>>
>>
>> So which kind of existence do you believe is more fundamental?  Which
>> is primary?  Logico-mathematical existence, or quark existence?  Or
>> are they separate but equal kinds of existence?
>>
>>
>
> The most general form of existence is: All mathematical possible
> universes exist.  Our universe is one of those mathematical possible
> existing universes.

This is non sense. Proof: see UDA. Or interrupt me when you have an
objection in the current explanation. I have explained this many times,
but the notion of universe or mathematical universe just makes no
sense. The notion of "our universe" is too far ambiguous for just
making even non sense.

I could say the same to Brent. First I don't think it makes sense to
say that epistemology comes before ontology, given that the ontology,
by definition, in concerned with what we agree exist independently of
the observer/knower ... Then what you say contradict the results in the
computationalist theory, where the appearances of universe emerges from
the collection of all computations

BTW, thanks to Brent for helping Marty.

Rex, when you say:

> I would say that most people PERCEIVE logico-mathematical objects
> differently than they perceive tables and chairs, or quarks and
> electrons.  But this doesn't tell us anything about whether these
> things really have different kinds of existence.  That we perceive
> them differently is just an accident of fate.

We perceive them differently because "observation" is a different
modality of self-reference than "proving". It has nothing to do with
accident or fate. The comp physics is defined by what is invariant,
from the "observation" point of view of universal machine. Later this
will shown to be given by the 3th, 4th, and 5th hypostases.

==== math lesson ==== (2 posts):

Hi,

I wrote:
<<
The cardinal of { } = 0. All singletons have cardinal one. All pairs,
or doubletons, have cardinal two.  

Problem 1 has been solved. They have the same cardinal, or if you
prefer, they have the same number of elements. The set of all subsets
of a set with n elements has the same number of elements than the set
of all strings of length n.

Let us write  B_n for the sets of binary strings of length n. So,

B_0 = { }
B_1 = {0, 1}
B_2 = {00, 01, 10, 11}
B_3 = {000, 010, 100, 110, 001, 011, 101, 111}

We have seen, without counting, that the cardinal of the powerset of a
set with cardinal n is the same as the cardinal of B_n.
 >>


And now the killing question by the sadistic math teacher:

What is the cardinal, that is, the number of element, of B_0, that is
the set of strings of length 0.

The student: let see, you wrote above B_0 = { },, and you were kind
enough to recall that the cardinal of { } is zero (of course, there is
zero element in the empty set). So the cardinal of B_0 is zero. 'zero"
said the student.

'zero' indeed, said the teacher, but it is your note. You are wrong.

B_0 is not empty! It *looks* empty, but beware the appearance, it looks
empty because it contains the empty string, which, if you remember some
preceding post is invisible (even under the microscope, telescope,
radioscope, ..).

A solution could have been to notate the empty string by a symbol like
"_", and write all sequences "0111000100" starting from "_":
 _0111000100, with rules __ = _, etc. Then B_0 = { _ },  B_1 = {_0,
_1}, etc. But this is too much notation.


And now the time has come for contrition when the teacher feels guilty!

Ah...,  I should have written directly something like

B_0 = { _  }, with _ representing the empty sequence.
B_1 = {0, 1}
B_2 = {00, 01, 10, 11}
B_3 = {000, 010, 100, 110, 001, 011, 101, 111}

OK?

Remember we have seen that the cardinal of the powerset of a set with n
elements is equal to the cardinal of B_n, is equal to 2^n.

The cardinal of B_0 has to be equal to to 2^0, which is equal to one.
Why?

if a is a number, usually, a^n is the result of effectuating (a times a
times a time a ... times a), with n occurences of a. For example: 2^3 =
2x2x2 = 8.

so a^n times a^m is equal to a^(n+m)

This extends to the rational by defining a^(-n) by 1/a^n. In that case
a^(m-n) = a^m/a^n. In particular a^m/a^m = 1 (x/x = 1 always), and
a^m/a^m = a^(m-m) = a^0. So a^0 = 1. So in particular 2^0 = 1.

But we will see soon a deeper reason to be encouraged to guess that a^0
= 1, but for this we need to define the product and the exponentiation
of sets. if A is a set, and B is a set: the exponential B^A is a very
important object, it is where the functions live. 

Take it easy, and ask. Verify the statements a^n/a^m = a^(n-m), with n
= 3 and m = 5. What is a*a*a/a*a*a*a*a  "/" = division, and * = times).

Bruno
 


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

-----------------

Hi,

I am thinking aloud, for the sequel. 


There will be a need for a geometrical and number theoretical interlude.

Do you know what is a periodic decimal?

Do you know that a is periodic decimal if and only if it exists n and
m, integers,  such that a = n/m. And that for all n m, n/m is a
periodic decimal?

Could you find n and m, such that
12.95213213213213213213213213213213213213 ... (= 12.95 213 213 ...)

Solution:

Let k be a name for 12.95213213213213213213213213213213213213213 ... 

Let us multiply k by 100 000.

100 000k = 1295213.213213213213213213213213213213213213 ...  = 1295213
+ 0.213213213 ...

Let us multiply k by 100

100k = 1295.213213213213... = 1295 + 0.213213213213213..


We have 100000k - 100k  = 1295213 + 0.213213213... - 1295
- 0.213213213... = 1295213 - 1295 = 1293918

So 99900k = 1293918

Dividing by 99900 the two sides of the egality we get:

k = 1293918/99900

We have n and m such that k = n/m = 12.95213213213213213...
n = 1293918, and m = 99900.

This should convince you that all periodic decimal are fractions.

Exercice: find two numbers n and m such that n/m =
31,2454545454545454545... = 31, 2 45 45 45 45 ...


Convince yourself that for all n and m, n/m gives always a periodic
decimal.(hint: when n is divided by m, m bounds the number of possible
remainders).

And now geometry (without picture, do them).

Do you know that the length of the circle divided by its diameter is
PI? (PI = 3.141592...)
Do you know that the length of the square divided by its diagonal is
the square root of 2? (sqrt(2)= 1,414213562...)
   - can you show this?
   - can you show this without Pythagorus theorem?  (like in Plato!)

Do you know if it exists n and m such that n/m = the square root of 2  
 (relation with incommensurability)
Do you know if the Diophantine equation  x^2 = 2y^2 has a solution?

No. 
I think I will prove this someday, if only to have an example of
simple, yet non trivial, proof.

This entails that the sqaure root of 2 cannot be equal to any fraction
n/m.
And it means the square root of 2 is a non periodic decimal.  (its
decimal will provide a good example of a non trivial computable
function).

Bruno

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

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[david.nyman]

2009/7/22 Bruno Marchal <marchal@...>:

> Ma connection at home is no functioning.

As a linguistic aside, Bruno has cleverly expressed the above
statement in perfect Glaswegian (i.e. the spoken tongue of Glasgow,
Scotland - my home town). Other well-known examples are: "Is'arra
marra on yer barra Clarra?" (Is that large vegetable on your barrow a
marrow, Clara?); and "Gie's'a sook on yer soor ploom" (Let me taste
the "sour plum" (a globular sweet-sour confection) that you are
presently sucking).

Perhaps he intends to continue further in this vein?

David ;-)

> Hi,
>
> Ma connection at home is no functioning. So I am temporarily
> disconnected. I hope I will be able to solve that problem. I am sending
> here some little comments from my office.
>
> I include some more material for Kim and Marty, and others, just to
> think about, in case I remain disconnected for some time. Sorry.
>
> Bruno
>
> Le 22-juil.-09, à 10:27, Torgny Tholerus a écrit :
>
>>
>> Rex Allen skrev:
>>> Brent,
>>>
>>> So my first draft addressed many of the points you made, but it that
>>> email got too big and sprawling I thought.
>>>
>>> So I've focused on what seems to me like the key passage from your
>>> post.  If you think there was some other point that I should have
>>> addressed, let me know.
>>>
>>> So, key passage:
>>>
>>>
>>>> Do these mathematical objects "really" exist?  I'd say they have
>>>> logico-mathematical existence, not the same existence as tables and
>>>> chairs, or quarks and electrons.
>>>>
>>>
>>> So which kind of existence do you believe is more fundamental?  Which
>>> is primary?  Logico-mathematical existence, or quark existence?  Or
>>> are they separate but equal kinds of existence?
>>>
>>>
>>
>> The most general form of existence is: All mathematical possible
>> universes exist.  Our universe is one of those mathematical possible
>> existing universes.
>
> This is non sense. Proof: see UDA. Or interrupt me when you have an
> objection in the current explanation. I have explained this many times,
> but the notion of universe or mathematical universe just makes no
> sense. The notion of "our universe" is too far ambiguous for just
> making even non sense.
>
> I could say the same to Brent. First I don't think it makes sense to
> say that epistemology comes before ontology, given that the ontology,
> by definition, in concerned with what we agree exist independently of
> the observer/knower ... Then what you say contradict the results in the
> computationalist theory, where the appearances of universe emerges from
> the collection of all computations
>
> BTW, thanks to Brent for helping Marty.
>
> Rex, when you say:
>
>> I would say that most people PERCEIVE logico-mathematical objects
>> differently than they perceive tables and chairs, or quarks and
>> electrons.  But this doesn't tell us anything about whether these
>> things really have different kinds of existence.  That we perceive
>> them differently is just an accident of fate.
>
> We perceive them differently because "observation" is a different
> modality of self-reference than "proving". It has nothing to do with
> accident or fate. The comp physics is defined by what is invariant,
> from the "observation" point of view of universal machine. Later this
> will shown to be given by the 3th, 4th, and 5th hypostases.
>
> ==== math lesson ==== (2 posts):
>
> Hi,
>
> I wrote:
> <<
> The cardinal of { } = 0. All singletons have cardinal one. All pairs,
> or doubletons, have cardinal two.
>
> Problem 1 has been solved. They have the same cardinal, or if you
> prefer, they have the same number of elements. The set of all subsets
> of a set with n elements has the same number of elements than the set
> of all strings of length n.
>
> Let us write  B_n for the sets of binary strings of length n. So,
>
> B_0 = { }
> B_1 = {0, 1}
> B_2 = {00, 01, 10, 11}
> B_3 = {000, 010, 100, 110, 001, 011, 101, 111}
>
> We have seen, without counting, that the cardinal of the powerset of a
> set with cardinal n is the same as the cardinal of B_n.
>  >>
>
>
> And now the killing question by the sadistic math teacher:
>
> What is the cardinal, that is, the number of element, of B_0, that is
> the set of strings of length 0.
>
> The student: let see, you wrote above B_0 = { },, and you were kind
> enough to recall that the cardinal of { } is zero (of course, there is
> zero element in the empty set). So the cardinal of B_0 is zero. 'zero"
> said the student.
>
> 'zero' indeed, said the teacher, but it is your note. You are wrong.
>
> B_0 is not empty! It *looks* empty, but beware the appearance, it looks
> empty because it contains the empty string, which, if you remember some
> preceding post is invisible (even under the microscope, telescope,
> radioscope, ..).
>
> A solution could have been to notate the empty string by a symbol like
> "_", and write all sequences "0111000100" starting from "_":
>  _0111000100, with rules __ = _, etc. Then B_0 = { _ },  B_1 = {_0,
> _1}, etc. But this is too much notation.
>
>
> And now the time has come for contrition when the teacher feels guilty!
>
> Ah...,  I should have written directly something like
>
> B_0 = { _  }, with _ representing the empty sequence.
> B_1 = {0, 1}
> B_2 = {00, 01, 10, 11}
> B_3 = {000, 010, 100, 110, 001, 011, 101, 111}
>
> OK?
>
> Remember we have seen that the cardinal of the powerset of a set with n
> elements is equal to the cardinal of B_n, is equal to 2^n.
>
> The cardinal of B_0 has to be equal to to 2^0, which is equal to one.
> Why?
>
> if a is a number, usually, a^n is the result of effectuating (a times a
> times a time a ... times a), with n occurences of a. For example: 2^3 =
> 2x2x2 = 8.
>
> so a^n times a^m is equal to a^(n+m)
>
> This extends to the rational by defining a^(-n) by 1/a^n. In that case
> a^(m-n) = a^m/a^n. In particular a^m/a^m = 1 (x/x = 1 always), and
> a^m/a^m = a^(m-m) = a^0. So a^0 = 1. So in particular 2^0 = 1.
>
> But we will see soon a deeper reason to be encouraged to guess that a^0
> = 1, but for this we need to define the product and the exponentiation
> of sets. if A is a set, and B is a set: the exponential B^A is a very
> important object, it is where the functions live.
>
> Take it easy, and ask. Verify the statements a^n/a^m = a^(n-m), with n
> = 3 and m = 5. What is a*a*a/a*a*a*a*a  "/" = division, and * = times).
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
> -----------------
>
> Hi,
>
> I am thinking aloud, for the sequel.
>
>
> There will be a need for a geometrical and number theoretical interlude.
>
> Do you know what is a periodic decimal?
>
> Do you know that a is periodic decimal if and only if it exists n and
> m, integers,  such that a = n/m. And that for all n m, n/m is a
> periodic decimal?
>
> Could you find n and m, such that
> 12.95213213213213213213213213213213213213 ... (= 12.95 213 213 ...)
>
> Solution:
>
> Let k be a name for 12.95213213213213213213213213213213213213213 ...
>
> Let us multiply k by 100 000.
>
> 100 000k = 1295213.213213213213213213213213213213213213 ...  = 1295213
> + 0.213213213 ...
>
> Let us multiply k by 100
>
> 100k = 1295.213213213213... = 1295 + 0.213213213213213..
>
>
> We have 100000k - 100k  = 1295213 + 0.213213213... - 1295
> - 0.213213213... = 1295213 - 1295 = 1293918
>
> So 99900k = 1293918
>
> Dividing by 99900 the two sides of the egality we get:
>
> k = 1293918/99900
>
> We have n and m such that k = n/m = 12.95213213213213213...
> n = 1293918, and m = 99900.
>
> This should convince you that all periodic decimal are fractions.
>
> Exercice: find two numbers n and m such that n/m =
> 31,2454545454545454545... = 31, 2 45 45 45 45 ...
>
>
> Convince yourself that for all n and m, n/m gives always a periodic
> decimal.(hint: when n is divided by m, m bounds the number of possible
> remainders).
>
> And now geometry (without picture, do them).
>
> Do you know that the length of the circle divided by its diameter is
> PI? (PI = 3.141592...)
> Do you know that the length of the square divided by its diagonal is
> the square root of 2? (sqrt(2)= 1,414213562...)
>    - can you show this?
>    - can you show this without Pythagorus theorem?  (like in Plato!)
>
> Do you know if it exists n and m such that n/m = the square root of 2
>  (relation with incommensurability)
> Do you know if the Diophantine equation  x^2 = 2y^2 has a solution?
>
> No.
> I think I will prove this someday, if only to have an example of
> simple, yet non trivial, proof.
>
> This entails that the sqaure root of 2 cannot be equal to any fraction
> n/m.
> And it means the square root of 2 is a non periodic decimal.  (its
> decimal will provide a good example of a non trivial computable
> function).
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
> >
>

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