Consciousness is information?

[m.a.-2]

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Bruno, I feel very much in tune with your definition of science, so I'll trudge along with Kim as far as the UD allows me to follow the reasoning.     m.a.

 

 

 

 

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

From: marchal@...

To: everything-list@...

Sent: Friday, May 29, 2009 6:59 AM

Subject: Re: Consciousness is information?

Hi Marty,

On 29 May 2009, at 02:32, m.a. wrote:

Bruno,

            Thank you for this detailed reply. May I pose one follow-up question? Is the universal dovetailer some sort of God/Machine that is mathematical like the rest of creation but separate from it and of a higher order of purpose?

The universal dovetailer (UD) is a program. A finite piece of code, which, when executed, generates all programs, in all possible programming languages, and which also executes all those programs, by dovetailing on those executions. In that sense the UD is "just" a program among all programs. When it runs (platonistically or not) it generates itself, and executes itself, an infinity of times.

I will explain this in all details to Kim. It is not a trivial subject, and the more you know about the diagonalization technic, the more you are amazed that the UD can exist. But its existence is a consequence of simple axioms defining addition and multiplication of the natural numbers. Its "universal" character is a consequence of Church's thesis, which is needed for accepting the generality of incompleteness and limitation theorems.

If so, is there an explanation for its existence that doesn't exclude a deity?

You can explain the existence of the UD without invoking any deity. But this does not exclude any (non naïve or literal) deity. 

Then, if you are willing to define deities by "non turing emulable" (mathematical) subject or objects, like actual infinities, then, even machines (like us, with comp) cannot NOT invoke deities when trying to learn some truth about just the numbers and the machines. We need even a transfinite ladder of deities to grasp more and more the machine's abilities.

The opposition between science and religion is a red herring. Science is opposed only to authoritative arguments. The confusion comes from the fact that many religions, including some form of atheism, are based on authoritative arguments, apparently as a consequence of their temporal institutionalization. 

But real, ideal perhaps, science leads only to modesty and respect, especially in regard with fundamental question.

Science cannot have definite answers on fundamental questions, it can only enlarge the awe, the astonishment. 

Science cannot kill the mystery, but it can clean it better and better from the superstitions and the fake mysteries, generally brought by the fear sellers and the egocentric manipulators.

If you follow the explanation to Kim, there will be a point where you will understand that science is really what breaks down all possible form of reductive or reductionist explanation. This can explain why the pseudo religious authoritarians are used to fight against science, and against freedom.

Comp superficially looks like a reductionism, but it is the most powerful vaccine against reductionism.

Bruno

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

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[Bruno Marchal]

Marty,

Bruno, I feel very much in tune with your definition of science, so I'll trudge along with Kim as far as the UD allows me to follow the reasoning.     m.a.

You are welcome. 

And why would the UD not allow you to follow the reasoning? All universal number can follow the reasoning, if they want to.

As soon as possible,   ... but I have to think a bit more. I'm afraid I will have to go through a not so short review of elementary math, and I have already written posts for that, but I did not send them, because  I find them too long.  I will probably opt for many, but really short posts in the form of questions/easy exercise. We will see. 

Best,

Bruno

 

 

 

 

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

From: marchal@...

To: everything-list@...

Sent: Friday, May 29, 2009 6:59 AM

Subject: Re: Consciousness is information?

Hi Marty,

On 29 May 2009, at 02:32, m.a. wrote:

Bruno,

            Thank you for this detailed reply. May I pose one follow-up question? Is the universal dovetailer some sort of God/Machine that is mathematical like the rest of creation but separate from it and of a higher order of purpose?

The universal dovetailer (UD) is a program. A finite piece of code, which, when executed, generates all programs, in all possible programming languages, and which also executes all those programs, by dovetailing on those executions. In that sense the UD is "just" a program among all programs. When it runs (platonistically or not) it generates itself, and executes itself, an infinity of times.

I will explain this in all details to Kim. It is not a trivial subject, and the more you know about the diagonalization technic, the more you are amazed that the UD can exist. But its existence is a consequence of simple axioms defining addition and multiplication of the natural numbers. Its "universal" character is a consequence of Church's thesis, which is needed for accepting the generality of incompleteness and limitation theorems.

If so, is there an explanation for its existence that doesn't exclude a deity?

You can explain the existence of the UD without invoking any deity. But this does not exclude any (non naïve or literal) deity. 

Then, if you are willing to define deities by "non turing emulable" (mathematical) subject or objects, like actual infinities, then, even machines (like us, with comp) cannot NOT invoke deities when trying to learn some truth about just the numbers and the machines. We need even a transfinite ladder of deities to grasp more and more the machine's abilities.

The opposition between science and religion is a red herring. Science is opposed only to authoritative arguments. The confusion comes from the fact that many religions, including some form of atheism, are based on authoritative arguments, apparently as a consequence of their temporal institutionalization. 

But real, ideal perhaps, science leads only to modesty and respect, especially in regard with fundamental question.

Science cannot have definite answers on fundamental questions, it can only enlarge the awe, the astonishment. 

Science cannot kill the mystery, but it can clean it better and better from the superstitions and the fake mysteries, generally brought by the fear sellers and the egocentric manipulators.

If you follow the explanation to Kim, there will be a point where you will understand that science is really what breaks down all possible form of reductive or reductionist explanation. This can explain why the pseudo religious authoritarians are used to fight against science, and against freedom.

Comp superficially looks like a reductionism, but it is the most powerful vaccine against reductionism.

Bruno

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

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

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[Bruno Marchal]

On 29 May 2009, at 18:53, Kelly Harmon wrote:

>
> On Thu, May 28, 2009 at 3:49 PM, Bruno Marchal <marchal@...>  
> wrote:
>>
>> What do you thing is the more probable events that you will live  
>> which
>> one is the more probable? What is your most rational choice among
>
> So if nothing is riding on the outcome of my choice, then it seems
> rational to choose the option that will make me right in the most
> futures, which is option 6, white noise.

What a relief ...





> If there's one world for
> each unique pattern of pixels,

It is more or less explicit in the ideal protocol of the experience.



> then most of those worlds will be
> "white noise" worlds, and making the choice that makes me right in the
> most worlds seems as rational as anything else.

Perfect.

>
>
> Though, if there is something significant riding on whether I choose
> correctly or not, then I have to decide what is most important to me:
> minimizing my suffering in the worlds where I'm wrong, or maximizing
> my gains in the worlds where I'm right.
>
> If there isn't significant suffering likely in the losing worlds, then
> I will be much more likely to base my decision on the observed or
> calculated probabilities, as Papineau suggests.

OK. It is not incompatible.


>
>
> BUT, if there is significant suffering likely in the worlds where I
> lose, I might very well focus making a choice that will minimize that
> suffering.  In which case I will generally not base much of my
> decision on the "probabilities", since it is my view that all outcomes
> occur.

?

>
>
> However, going a little further, this assumes that I only make one
> bet.  As I mentioned before, I think that I will make all possible
> bets.

Before the multiplication? I don't see how you could, here and
now, decide to do 2^(16180*10000*60*90*24)  bets.

I am not asking your quantum or comp counterparts. The question is asked
to *the* Kelly to which I send this post.






> So, even if I make the "safe" suffering-minimizing bet in this
> branch, I know that in a closely related branch I will make the risky
> "gain-maximizing" bet and say to hell with the Kellys in the losing
> worlds.

You are hard with yourself, I mean with your selves ...
>
>
> So I know that even if I make the safe bet, there's another Kelly two
> worlds over making the risky bet, which will result in a Kelly
> suffering the consequences of losing over there anyway.  So maybe I'll
> say, "screw it", and make the risky bet myself.


You could as well put your hand in the fire directly.



>
>
> Ultimately, it doesn't matter.  Every Kelly in every situation with
> every history is actualized.  So my subjective feeling that I am
> making choices is irrelevant.  Every choice is going to get made, so
> my "choice" is really just me taking my place in the continuum of
> Kellys.

First, in the multiplication experience, the question of your choice  
is not addressed, nor needed.
The question is really: what will happen to you. You give the right  
answer above.

>
>
>
>> And I am asking you, here and now, what do you expect the most
>> probable experience you will feel tomorrow, when I will do that
>> experiment.
>
> So to speak of expectations is to appeal to my "single world"
> intuitions.  But we know that intuition isn't a reliable guide, since
> there are many aspects of reality that are unintuitive.  So I think
> the fact that I have an intuitive expectation that things will happen
> a certain way, and only that way, is neither here nor there.

We can get counter-intuitive results only by starting with our  
intuition, and we have to succeed in making those basic intuition very  
solid, if we want to be able to make clear the counter-intuitive  
consequences. If not, we can't progress at all, and we lose the  
opportunity to abandon our wrong theories.

Common sense is the ONLY tool to go beyond common sense.

Have you understand UDA1-6?, because I think most get those steps. I  
will soon explain in all details UDA-7, which is not entirely obvious.
If you take your own philosophy seriously, you don't need UDA8. But it  
can be useful to convince others, of the necessity of that  
"philosophy", once we bet on the comp hyp.

Bruno



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




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[Bruno Marchal]

Hi Kim, Hi Marty and others,

So it is perhaps time to do some math. Obviously, once we are open to  
the idea that the fundamental reality could be mathematical, it is  
normal to take some time to do some mathematics. Many people seems  
also to agree here that the computationalist hypothesis could be  
interesting, and this should motivate for some amount of theoretical  
computer science, or recursion theory. This is a branch of mathematics  
which study computability, and mainly uncomputability, as opposed to  
computation theory which study all aspect of computation.

You can easily show that something is computable, by giving an  
explicit procedure to compute it. But to show that something is NOT  
computable, you need a very solid notion of computability. Now,  
computationalism suggest that the interesting and fundamental things,  
like life, consciousness, even matter, "lives" somehow on the border  
of the computable and the non computable, so that it is perhaps time  
to dig a little bit deeper in those direction.

I have already explain this on this list, but never from scratch,  
having in mind those who are, for whatever reason, the mathematical  
basis.

So I guess that many of view will find those preliminaries a bit too  
much simple. yet, by experience, I know that difficulties will appear,  
and it is frequent that I met people with very big baggages in  
mathematics who have some difficulties to understand the final point.  
So I would encourage everyone to be sure everything is clear. For  
those who have already a thorough understanding of UDA1-7, and in  
particular have grasped the difference between a computation and a  
description of a computation, I ask them to just be patient with the  
list. There will be nothing new here, nothing really original, and  
nothing controversial. All what I will explain has been anticipate by  
Emil Post in the 1920, and found or rediscovered by many  
mathematicians independently in USA, and in the ex USSR.

The present post just give a preview, and the beginning . I intent to  
send only short posts, or the shorter as possible. So here is the plan.

1) Set (probably a dozen of posts)
2) Function (I don't know how many posts, could depend on the replies.  
It is the key notion of math)
3) Language, machine and computable function
4) Universal machine, universal language, universal function,  
universal dovetailer, universal number ...

How will I proceed?

By exercise only. I will ask question, and I will wait for either the  
answer. I expect that those "who know" wait for Kim's answer, or for  
answer by those who are not supposed to "know".
  Kim seems to courageously accept the role of the candid, but if  
someone else want to answer it is OK for me.

I will give only VERY SIMPLE exercise. The goal is to be short and  
simple, and as informal as possible. I will explain by examples, and I  
will avoid as much as possible tedious definitions. And when we will  
meet a more difficult question, I will just solve it myself, and even  
explain why it is difficult. So, those preliminaries will not be very  
funny. I will of course adapt myself to the possible replies, and fell  
free to comment or even metacomment.

Obviously this is a not a course in math, but it is an explanation  
from scratch of the seven step of the universal dovetailer argument.  
It is a shortcut, and most probably we will make some digression from  
time to time, but let us try not to digress too much.

Kim, you are OK with this? I have to take into account the problem you  
did have with math, and which makes this lesson a bit challenging for  
me, and I guess for you too.

I begin with the very useful and elementary notion of set, as  
explained in what is called "naive set theory", and which is the base  
of almost all part of math.

============================================= begin  
===============================

1) SET

Informal definition: a set is a collection of object, called elements,  
with the idea that it, the collection or set, can be considered itself  
as an object. It is a many seen as a one, if you want. If the set is  
not to big, we can describe it exhaustively by listing the elements,  
if the set is bigger, we can describe it by some other way. Usually we  
use accolades "{", followed by the elements, separated by commas, and  
then "}", in the exhaustive description of a set.

Example/exercise:

1) The set of odd natural numbers which are little than 10. This is a  
well defined, and not to big set, so we can describe it exhaustively by
{1, 3, 5, 7, 9}. In this case we say that 7 belongs to  {1, 3, 5, 7, 9}.
Exercise 1: does the number 24 belongs to the set {1, 3, 5, 7, 9}?

2) the set of even natural number  which are little than 13. It is {0,  
2, 4, 6, 8, 10, 12}. OK? Some people can have a difficulty which is  
not related to the notion of set, for example they can ask themselves  
if zero (0) is really an even number. We will come back to this.

3) The set of odd natural numbers which are little than 100. This set  
is already too big to describe exhaustively. We will freely describe  
such a set by a quasi exhaustion like {1, 3, 5, 7, 9, 11, ... 95, 97,  
99}.
Exercise 2: does the number 93 belongs to the set of odd natural  
numbers which are little than 100, that is: does 93 belongs to {1, 3,  
5, 7, 9, 11, ... 95, 97, 99}?

4) The set of all natural numbers. This set is hard to define, yet I  
hope you agree we can describe it by the infinite quasi exhaustion by  
{0, 1, 2, 3, ...}.
Exercise 3: does the number 666 belongs to the set of natural numbers,  
that is does 666 belongs to {0, 1, 2, 3, ...}.
Exercice 4: does the real number square-root(2) belongs to {0, 1, 2,  
3, ...}?


5) When a set is too big or cumbersome, mathematician like to give  
them a name. They will usually say: let S be the set {14, 345, 78}.  
Then we can say that 14 belongs to S, for example.
Exercise 5: does 345 belongs to S?

A set is entirely defined by its elements. Put in another way, we will  
say that two sets are equal if they have the same elements.
Exercise 6. Let S be the set {0, 1, 45} and let M be the set described  
by {45, 0, 1}. Is it true or false that S is equal to M?
Exercise 7. Let S be the set {666} and M be the set {6, 6, 6}. Is is  
true or false that S is equal to M?

Seven exercises are enough. Are you ready to answer them. I hope you  
don't find them too much easy, because I intend to proceed in a way  
such that all exercise will be as easy, despite we will climb toward  
very much deeper notion. Feel free to ask question, comments, etc. I  
will try to adapt myself.

Next: we will see some operation on sets (union, intersection), and  
the notion of subset. If all this work, I will build a latex document,  
and make it the standard reference for the seventh step for the non  
mathematician, or for the beginners in mathematics.

Bruno



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




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[Kelly Harmon]

On Sun, May 31, 2009 at 1:46 PM, Bruno Marchal <marchal@...> wrote:
>
>>
>> BUT, if there is significant suffering likely in the worlds where I
>> lose, I might very well focus making a choice that will minimize that
>> suffering.  In which case I will generally not base much of my
>> decision on the "probabilities", since it is my view that all outcomes
>> occur.
>
> ?

For example, if my main concern is to avoid suffering, I might only
make small bets, even in situations with very high odds of success.
In this way I avoid the pain of losing a lot of money in the few
"unlikely" worlds, though at the cost of forfeiting some gains in the
many worlds where the odds come in.

The single-world equivalent is just being very risk averse, I suppose.
 But the motivation is different.  In the single-world view, if I'm
risk averse I just don't want to take the risk of losing a lot of
money, even when given very good odds.  In the many-world view, I know
that a future version of me is going to lose, and I want to minimize
the consequences of that loss even at the expense of limiting the
gains for the winning future-Kellys.

So the idea that I might bet more when given better odds wouldn't hold
in this case because I know that betting more is causing more
suffering for the few but inevitable losing Kellys.

And I can imagine other types of scenarios where I would bet on a
lower probability outcome, if such a bet had less severe consequences
in the case of a loss.

Though the fact that at the time you place your bet, branching may
occur resulting in different bets being placed also has to be
considered.


> First, in the multiplication experience, the question of your choice
> is not addressed, nor needed.
> The question is really: what will happen to you. You give the right
> answer above.
>

You're saying that there are no low probability worlds?  Or only that
they're outnumbered by the high probability worlds?

I guess I'm not clear on what you're getting at with this pixel
thought-experiment.


> Have you understand UDA1-6?, because I think most get those steps. I
> will soon explain in all details UDA-7, which is not entirely obvious.
> If you take your own philosophy seriously, you don't need UDA8. But it
> can be useful to convince others, of the necessity of that
> "philosophy", once we bet on the comp hyp.
>

I think I have a good grasp of 1 through 6.

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[Brian Tenneson]

Thank you for starting this discussion.  I have only joined recently and
have little knowledge of your research.  To see it laid out in the
sequence you describe should make it clear to me what it is all about.

I'm particularly interested in the interaction between consciousness and
computation.  In Max Tegmark's Ensemble TOE paper he alludes to a
self-aware structure.  I take structure to be an object of study in
logic (model theory, in particular) but am not at all sure how
consciousness, which I envision self-awareness to be deeply tied to,
connects to mathematics.  It seems you're going to build up to a
statement such as "consciousness is computable" OR "consciousness is not
computable," or something about consciousness, at least.

In light of that it seems a prudent fundamental step would be to define
what it means for one structure to be aware of another.  This would
apparently be some relation on the aggregate of all structures (which
may be the entire level 4 multiverse in Tegmark's theory).  Perhaps some
basic fundamental step would be to provide some axioms on what this
relation could be but I'm almost convinced this can't be done in a
non-controversial way.

I know I'm putting the cart before the horse here so I don't expect all
to be revealed for some time when it occurs in your exposition.  If
there is some literature by yourself or others on the particular
subjects and issues I mentioned, I'd appreciate links to them.

-Brian

Bruno Marchal wrote:

> Hi Kim, Hi Marty and others,
>
> So it is perhaps time to do some math. Obviously, once we are open to  
> the idea that the fundamental reality could be mathematical, it is  
> normal to take some time to do some mathematics. Many people seems  
> also to agree here that the computationalist hypothesis could be  
> interesting, and this should motivate for some amount of theoretical  
> computer science, or recursion theory. This is a branch of mathematics  
> which study computability, and mainly uncomputability, as opposed to  
> computation theory which study all aspect of computation.
>
> You can easily show that something is computable, by giving an  
> explicit procedure to compute it. But to show that something is NOT  
> computable, you need a very solid notion of computability. Now,  
> computationalism suggest that the interesting and fundamental things,  
> like life, consciousness, even matter, "lives" somehow on the border  
> of the computable and the non computable, so that it is perhaps time  
> to dig a little bit deeper in those direction.
>
> I have already explain this on this list, but never from scratch,  
> having in mind those who are, for whatever reason, the mathematical  
> basis.
>
> So I guess that many of view will find those preliminaries a bit too  
> much simple. yet, by experience, I know that difficulties will appear,  
> and it is frequent that I met people with very big baggages in  
> mathematics who have some difficulties to understand the final point.  
> So I would encourage everyone to be sure everything is clear. For  
> those who have already a thorough understanding of UDA1-7, and in  
> particular have grasped the difference between a computation and a  
> description of a computation, I ask them to just be patient with the  
> list. There will be nothing new here, nothing really original, and  
> nothing controversial. All what I will explain has been anticipate by  
> Emil Post in the 1920, and found or rediscovered by many  
> mathematicians independently in USA, and in the ex USSR.
>
> The present post just give a preview, and the beginning . I intent to  
> send only short posts, or the shorter as possible. So here is the plan.
>
> 1) Set (probably a dozen of posts)
> 2) Function (I don't know how many posts, could depend on the replies.  
> It is the key notion of math)
> 3) Language, machine and computable function
> 4) Universal machine, universal language, universal function,  
> universal dovetailer, universal number ...
>
> How will I proceed?
>
> By exercise only. I will ask question, and I will wait for either the  
> answer. I expect that those "who know" wait for Kim's answer, or for  
> answer by those who are not supposed to "know".
>   Kim seems to courageously accept the role of the candid, but if  
> someone else want to answer it is OK for me.
>
> I will give only VERY SIMPLE exercise. The goal is to be short and  
> simple, and as informal as possible. I will explain by examples, and I  
> will avoid as much as possible tedious definitions. And when we will  
> meet a more difficult question, I will just solve it myself, and even  
> explain why it is difficult. So, those preliminaries will not be very  
> funny. I will of course adapt myself to the possible replies, and fell  
> free to comment or even metacomment.
>
> Obviously this is a not a course in math, but it is an explanation  
> from scratch of the seven step of the universal dovetailer argument.  
> It is a shortcut, and most probably we will make some digression from  
> time to time, but let us try not to digress too much.
>
> Kim, you are OK with this? I have to take into account the problem you  
> did have with math, and which makes this lesson a bit challenging for  
> me, and I guess for you too.
>
> I begin with the very useful and elementary notion of set, as  
> explained in what is called "naive set theory", and which is the base  
> of almost all part of math.
>
> ============================================= begin  
> ===============================
>
> 1) SET
>
> Informal definition: a set is a collection of object, called elements,  
> with the idea that it, the collection or set, can be considered itself  
> as an object. It is a many seen as a one, if you want. If the set is  
> not to big, we can describe it exhaustively by listing the elements,  
> if the set is bigger, we can describe it by some other way. Usually we  
> use accolades "{", followed by the elements, separated by commas, and  
> then "}", in the exhaustive description of a set.
>
> Example/exercise:
>
> 1) The set of odd natural numbers which are little than 10. This is a  
> well defined, and not to big set, so we can describe it exhaustively by
> {1, 3, 5, 7, 9}. In this case we say that 7 belongs to  {1, 3, 5, 7, 9}.
> Exercise 1: does the number 24 belongs to the set {1, 3, 5, 7, 9}?
>
> 2) the set of even natural number  which are little than 13. It is {0,  
> 2, 4, 6, 8, 10, 12}. OK? Some people can have a difficulty which is  
> not related to the notion of set, for example they can ask themselves  
> if zero (0) is really an even number. We will come back to this.
>
> 3) The set of odd natural numbers which are little than 100. This set  
> is already too big to describe exhaustively. We will freely describe  
> such a set by a quasi exhaustion like {1, 3, 5, 7, 9, 11, ... 95, 97,  
> 99}.
> Exercise 2: does the number 93 belongs to the set of odd natural  
> numbers which are little than 100, that is: does 93 belongs to {1, 3,  
> 5, 7, 9, 11, ... 95, 97, 99}?
>
> 4) The set of all natural numbers. This set is hard to define, yet I  
> hope you agree we can describe it by the infinite quasi exhaustion by  
> {0, 1, 2, 3, ...}.
> Exercise 3: does the number 666 belongs to the set of natural numbers,  
> that is does 666 belongs to {0, 1, 2, 3, ...}.
> Exercice 4: does the real number square-root(2) belongs to {0, 1, 2,  
> 3, ...}?
>
>
> 5) When a set is too big or cumbersome, mathematician like to give  
> them a name. They will usually say: let S be the set {14, 345, 78}.  
> Then we can say that 14 belongs to S, for example.
> Exercise 5: does 345 belongs to S?
>
> A set is entirely defined by its elements. Put in another way, we will  
> say that two sets are equal if they have the same elements.
> Exercise 6. Let S be the set {0, 1, 45} and let M be the set described  
> by {45, 0, 1}. Is it true or false that S is equal to M?
> Exercise 7. Let S be the set {666} and M be the set {6, 6, 6}. Is is  
> true or false that S is equal to M?
>
> Seven exercises are enough. Are you ready to answer them. I hope you  
> don't find them too much easy, because I intend to proceed in a way  
> such that all exercise will be as easy, despite we will climb toward  
> very much deeper notion. Feel free to ask question, comments, etc. I  
> will try to adapt myself.
>
> Next: we will see some operation on sets (union, intersection), and  
> the notion of subset. If all this work, I will build a latex document,  
> and make it the standard reference for the seventh step for the non  
> mathematician, or for the beginners in mathematics.
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
> >
>
>  

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[Torgny Tholerus]

Bruno Marchal skrev:
> 4) The set of all natural numbers. This set is hard to define, yet I  
> hope you agree we can describe it by the infinite quasi exhaustion by  
> {0, 1, 2, 3, ...}.
>  

Let N be the biggest number in the set {0, 1, 2, 3, ...}.

Exercise: does the number N+1 belongs to the set of natural numbers,  
that is does N+1 belongs to {0, 1, 2, 3, ...}?

--
Torgny Tholerus

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[Jesse Mazer]

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

> Date: Tue, 2 Jun 2009 19:43:59 +0200
> From: torgny@...
> To: everything-list@...
> Subject: Re: The seven step-Mathematical preliminaries
>
>
> Bruno Marchal skrev:
>> 4) The set of all natural numbers. This set is hard to define, yet I
>> hope you agree we can describe it by the infinite quasi exhaustion by
>> {0, 1, 2, 3, ...}.
>>
>
> Let N be the biggest number in the set {0, 1, 2, 3, ...}.
>
> Exercise: does the number N+1 belongs to the set of natural numbers,
> that is does N+1 belongs to {0, 1, 2, 3, ...}?

Not every well-ordered set has a largest member. Every well-ordered set has a "size" represented by an ordinal (see http://en.wikipedia.org/wiki/Ordinal_number ) and there is a particular type of ordinal called a "limit ordinal" which has no largest member, as discussed in the section of that article at http://en.wikipedia.org/wiki/Ordinal_number#Successor_and_limit_ordinals 

Of course this is just how it works in set theory, I think you have said you are some type of finitist so unlike a set theorist you may not want to "allow" sets with no largest member, but in this case you shouldn't even use notation like {0, 1, 2, 3, ...} that does not specify the largest member. I suppose instead you could write something like {0, 1, 2, 3, ..., N} but in this case you should specify what N is supposed to represent...the largest finite number that any human has conceived of up to the present date? The number of distinct physical entities in the universe (or the observable universe)? For a finitist what defines "largest", and can it change over time?

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[Bruno Marchal]

On 02 Jun 2009, at 18:54, Brian Tenneson wrote:

>
> Thank you for starting this discussion.  I have only joined recently  
> and
> have little knowledge of your research.  To see it laid out in the
> sequence you describe should make it clear to me what it is all about.
>
> I'm particularly interested in the interaction between consciousness  
> and
> computation.  In Max Tegmark's Ensemble TOE paper he alludes to a
> self-aware structure.  I take structure to be an object of study in
> logic (model theory, in particular) but am not at all sure how
> consciousness, which I envision self-awareness to be deeply tied to,
> connects to mathematics.  It seems you're going to build up to a
> statement such as "consciousness is computable" OR "consciousness is  
> not
> computable," or something about consciousness, at least.

In UDA, I avoid the use of consciousness. I just use the hypothesis  
that consciousness, or first person experience remains unchanged for a  
functional substitution made at the correct comp substitution level  
(this is the comp hypothesis).
Then the UD Argument  is supposed to show, that physicalism cannot be  
maintained and that physics is a branch of computer science, or even  
just number theory.
In AUDA, I refine the constructive feature of UDA to begin the  
extraction of physics.
You can read my paper here, and print the UD slides, because I  
currently refer often to the steps of that reasoning:

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

I have written a better one, but I must still put it in my webapge.

It seems to me that Tegmark is a bit fuzzy about the way he attaches  
the first person experience with the "universes"/bodies. Like many  
physicists, he is a bit naive about the mind-body problem. The  
computationalist hypothesis is not a solution per se, just a tool  
making it possible to reformulate the problem. Indeed it forces a  
reduction of the mind-body problem to a highly non trivial body  
problem. It is my whole point.

UDA shows that if I am a machine then the universe, whatever it may  
be, cannot be a machine. An apparent physical universe can, and  
actually must emerge, from inside, but this one too cannot be entirely  
described by a machine.




>
>
> In light of that it seems a prudent fundamental step would be to  
> define
> what it means for one structure to be aware of another.



In AUDA, the arithmetical and more constructive version of UDA,  
consciousness, like truth, will appear to be undefinable, except by  
some fixed point of the doubting procedure. It is then show equivalent  
to an instinctive bet on a reality. It has a relative self-speeding  
role.





> This would
> apparently be some relation on the aggregate of all structures (which
> may be the entire level 4 multiverse in Tegmark's theory).  Perhaps  
> some
> basic fundamental step would be to provide some axioms on what this
> relation could be but I'm almost convinced this can't be done in a
> non-controversial way.


Computationalism is not controversal, nor is my deduction, but few  
people get both the quantum difficulties and the mathematical logic. I  
am more ignored than misunderstood, and then I don't publish so much.  
But I love to explain to people with a genuine interest in those issues.



>
>
> I know I'm putting the cart before the horse here so I don't expect  
> all
> to be revealed for some time when it occurs in your exposition.  If
> there is some literature by yourself or others on the particular
> subjects and issues I mentioned, I'd appreciate links to them.


Almost all my papers dig on that issue. See my url

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

or search in this list for explanations. What is new, and  
counterintuitive is that computationalism entails a reversal between  
physics and machine's biology/psychology/theology .... See my paper on  
Plotinus for a presentation of AUDA in term of Plotinus (neo)platonist  
theology.

We cannot define consciousness (nor the notion of natural numbers),  
but we don't have to define those things to reason about, once we  
agree on some principles (like the "yes doctor" and Church thesis).

Welcome aboard on the train Brian,

Bruno

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[Bruno Marchal]

On 02 Jun 2009, at 19:43, Torgny Tholerus wrote:

>
> Bruno Marchal skrev:
>> 4) The set of all natural numbers. This set is hard to define, yet I
>> hope you agree we can describe it by the infinite quasi exhaustion by
>> {0, 1, 2, 3, ...}.
>>
>
> Let N be the biggest number in the set {0, 1, 2, 3, ...}.
>
> Exercise: does the number N+1 belongs to the set of natural numbers,
> that is does N+1 belongs to {0, 1, 2, 3, ...}?

Yes. N+1 belongs to {0, 1, 2, 3, ...}.
This follows from classical logic and the fact that the proposition "N  
be the biggest number in the set {0, 1, 2, 3, ...}" is always false.  
And false implies all propositions.

But this is a bit advanced matter, Torgny. The math I am explaining to  
Kim and some others are typical classical mathematics.

Bruno



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




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[Bruno Marchal]

Torgny sais he is an ultrafinitist, although in some precedent post, he shows he can be open to usual finitism.

Usual finitism is not in conflict with comp, except that it makes the math more difficult, and the theology a bit too formal for my taste.

But ultrafinitism is incompatible with comp and its classical Church thesis. For an ultrafinitist everything is computable, and by some miracle even the basic program "10 GOTO 10" does stop.

I know only two ultrafinitists on this planet. Torgny, and a Russian guy who wrote papers that nobody understands (as far as I know).

Bruno

On 02 Jun 2009, at 20:29, Jesse Mazer wrote:

> Date: Tue, 2 Jun 2009 19:43:59 +0200
> From: torgny@...
> To: everything-list@...
> Subject: Re: The seven step-Mathematical preliminaries
> 
> 
> Bruno Marchal skrev:
>> 4) The set of all natural numbers. This set is hard to define, yet I 
>> hope you agree we can describe it by the infinite quasi exhaustion by 
>> {0, 1, 2, 3, ...}.
>> 
> 
> Let N be the biggest number in the set {0, 1, 2, 3, ...}.
> 
> Exercise: does the number N+1 belongs to the set of natural numbers, 
> that is does N+1 belongs to {0, 1, 2, 3, ...}?

Not every well-ordered set has a largest member. Every well-ordered set has a "size" represented by an ordinal (see http://en.wikipedia.org/wiki/Ordinal_number ) and there is a particular type of ordinal called a "limit ordinal" which has no largest member, as discussed in the section of that article at http://en.wikipedia.org/wiki/Ordinal_number#Successor_and_limit_ordinals 

Of course this is just how it works in set theory, I think you have said you are some type of finitist so unlike a set theorist you may not want to "allow" sets with no largest member, but in this case you shouldn't even use notation like {0, 1, 2, 3, ...} that does not specify the largest member. I suppose instead you could write something like {0, 1, 2, 3, ..., N} but in this case you should specify what N is supposed to represent...the largest finite number that any human has conceived of up to the present date? The number of distinct physical entities in the universe (or the observable universe)? For a finitist what defines "largest", and can it change over time?

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

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[Brian Tenneson]

Thanks for the links.  I'll look over them and hopefully I'll understand
what I see.  At least if I have questions I can ask though maybe not in
this thread.

I don't yet know precisely what you mean by a machine but I do have
superficial knowledge of Turing machines; I'm assuming there is a
resemblance between the two concepts.  I surmise that a machine can have
an input like a question and if it halts then the question has a
decidable answer, else it has no decidable answer.

What about posing the following question "am I a machine" or the
statement "I am a machine" and maybe some machines halt on an answer and
some don't.  Ie, if X is a machine, then have it attempt to compute the
statement "X is a machine."  (I know I'm a bit fuzzy on the details.)  
For machines X that return "X is a machine" I would be inclined to think
such machines possess at least some form of self-awareness, a kind of
abstract self-awareness devoid of sensation (or so it would appear).

-Brian

Bruno Marchal wrote:

> On 02 Jun 2009, at 18:54, Brian Tenneson wrote:
>
>  
>> Thank you for starting this discussion.  I have only joined recently  
>> and
>> have little knowledge of your research.  To see it laid out in the
>> sequence you describe should make it clear to me what it is all about.
>>
>> I'm particularly interested in the interaction between consciousness  
>> and
>> computation.  In Max Tegmark's Ensemble TOE paper he alludes to a
>> self-aware structure.  I take structure to be an object of study in
>> logic (model theory, in particular) but am not at all sure how
>> consciousness, which I envision self-awareness to be deeply tied to,
>> connects to mathematics.  It seems you're going to build up to a
>> statement such as "consciousness is computable" OR "consciousness is  
>> not
>> computable," or something about consciousness, at least.
>>    
>
>
>
> In UDA, I avoid the use of consciousness. I just use the hypothesis  
> that consciousness, or first person experience remains unchanged for a  
> functional substitution made at the correct comp substitution level  
> (this is the comp hypothesis).
> Then the UD Argument  is supposed to show, that physicalism cannot be  
> maintained and that physics is a branch of computer science, or even  
> just number theory.
> In AUDA, I refine the constructive feature of UDA to begin the  
> extraction of physics.
> You can read my paper here, and print the UD slides, because I  
> currently refer often to the steps of that reasoning:
>
> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
>
> I have written a better one, but I must still put it in my webapge.
>
> It seems to me that Tegmark is a bit fuzzy about the way he attaches  
> the first person experience with the "universes"/bodies. Like many  
> physicists, he is a bit naive about the mind-body problem. The  
> computationalist hypothesis is not a solution per se, just a tool  
> making it possible to reformulate the problem. Indeed it forces a  
> reduction of the mind-body problem to a highly non trivial body  
> problem. It is my whole point.
>
> UDA shows that if I am a machine then the universe, whatever it may  
> be, cannot be a machine. An apparent physical universe can, and  
> actually must emerge, from inside, but this one too cannot be entirely  
> described by a machine.
>
>
>
>
>  
>> In light of that it seems a prudent fundamental step would be to  
>> define
>> what it means for one structure to be aware of another.
>>    
>
>
>
> In AUDA, the arithmetical and more constructive version of UDA,  
> consciousness, like truth, will appear to be undefinable, except by  
> some fixed point of the doubting procedure. It is then show equivalent  
> to an instinctive bet on a reality. It has a relative self-speeding  
> role.
>
>
>
>
>
>  
>> This would
>> apparently be some relation on the aggregate of all structures (which
>> may be the entire level 4 multiverse in Tegmark's theory).  Perhaps  
>> some
>> basic fundamental step would be to provide some axioms on what this
>> relation could be but I'm almost convinced this can't be done in a
>> non-controversial way.
>>    
>
>
> Computationalism is not controversal, nor is my deduction, but few  
> people get both the quantum difficulties and the mathematical logic. I  
> am more ignored than misunderstood, and then I don't publish so much.  
> But I love to explain to people with a genuine interest in those issues.
>
>
>
>  
>> I know I'm putting the cart before the horse here so I don't expect  
>> all
>> to be revealed for some time when it occurs in your exposition.  If
>> there is some literature by yourself or others on the particular
>> subjects and issues I mentioned, I'd appreciate links to them.
>>    
>
>
> Almost all my papers dig on that issue. See my url
>
> http://iridia.ulb.ac.be/~marchal/
>
> or search in this list for explanations. What is new, and  
> counterintuitive is that computationalism entails a reversal between  
> physics and machine's biology/psychology/theology .... See my paper on  
> Plotinus for a presentation of AUDA in term of Plotinus (neo)platonist  
> theology.
>
> We cannot define consciousness (nor the notion of natural numbers),  
> but we don't have to define those things to reason about, once we  
> agree on some principles (like the "yes doctor" and Church thesis).
>
> Welcome aboard on the train Brian,
>
> Bruno
>
> >
>
>  

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[Bruno Marchal]

The beauty of all this, Brian, is that the correct (arithmetically)  
universal machine will never been able to answer the question "are you  
a machine?", but she (it) will be able to bet she is a (unknown)  
machine. She will never know which one, and she will refute all  
theories saying which machine she could be, unless she decided to  
identify herself with the virgin, never programmed, universal one.

There is a way to attribute a first person view to a machine, but  
then, from that first person view, the machine will be correct in  
saying "I am not a machine".

The consequence of computationalism are so much counterintuitive that  
"even" machines cannot really believe in comp. Yet, those machine  
which believe in the numbers and induction will be able to explain  
exactly all this. Machines can prove that if they are a correct  
machine, then they cannot "believe" that they are a correct machine.

It is related to the incompleteness phenomenon and the logic of self-
reference which is exploited in the AUDA.

Actually it works also for Turing hypermachines, and a vast collection  
of machine extensions, and even self-aware structures completly  
unrelated to machine, which unfortunately needs a lot of model theory  
to be described (like "truth in all transitive model of ZF", if this  
rings a bell).

But here we anticipate a lot. Hope this can open your appetite.

Bruno



On 02 Jun 2009, at 21:08, Brian Tenneson wrote:

>
> Thanks for the links.  I'll look over them and hopefully I'll  
> understand
> what I see.  At least if I have questions I can ask though maybe not  
> in
> this thread.
>
> I don't yet know precisely what you mean by a machine but I do have
> superficial knowledge of Turing machines; I'm assuming there is a
> resemblance between the two concepts.  I surmise that a machine can  
> have
> an input like a question and if it halts then the question has a
> decidable answer, else it has no decidable answer.
>
> What about posing the following question "am I a machine" or the
> statement "I am a machine" and maybe some machines halt on an answer  
> and
> some don't.  Ie, if X is a machine, then have it attempt to compute  
> the
> statement "X is a machine."  (I know I'm a bit fuzzy on the details.)
> For machines X that return "X is a machine" I would be inclined to  
> think
> such machines possess at least some form of self-awareness, a kind of
> abstract self-awareness devoid of sensation (or so it would appear).
>
> -Brian
>
> Bruno Marchal wrote:
>> On 02 Jun 2009, at 18:54, Brian Tenneson wrote:
>>
>>
>>> Thank you for starting this discussion.  I have only joined recently
>>> and
>>> have little knowledge of your research.  To see it laid out in the
>>> sequence you describe should make it clear to me what it is all  
>>> about.
>>>
>>> I'm particularly interested in the interaction between consciousness
>>> and
>>> computation.  In Max Tegmark's Ensemble TOE paper he alludes to a
>>> self-aware structure.  I take structure to be an object of study in
>>> logic (model theory, in particular) but am not at all sure how
>>> consciousness, which I envision self-awareness to be deeply tied to,
>>> connects to mathematics.  It seems you're going to build up to a
>>> statement such as "consciousness is computable" OR "consciousness is
>>> not
>>> computable," or something about consciousness, at least.
>>>
>>
>>
>>
>> In UDA, I avoid the use of consciousness. I just use the hypothesis
>> that consciousness, or first person experience remains unchanged  
>> for a
>> functional substitution made at the correct comp substitution level
>> (this is the comp hypothesis).
>> Then the UD Argument  is supposed to show, that physicalism cannot be
>> maintained and that physics is a branch of computer science, or even
>> just number theory.
>> In AUDA, I refine the constructive feature of UDA to begin the
>> extraction of physics.
>> You can read my paper here, and print the UD slides, because I
>> currently refer often to the steps of that reasoning:
>>
>> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
>>
>> I have written a better one, but I must still put it in my webapge.
>>
>> It seems to me that Tegmark is a bit fuzzy about the way he attaches
>> the first person experience with the "universes"/bodies. Like many
>> physicists, he is a bit naive about the mind-body problem. The
>> computationalist hypothesis is not a solution per se, just a tool
>> making it possible to reformulate the problem. Indeed it forces a
>> reduction of the mind-body problem to a highly non trivial body
>> problem. It is my whole point.
>>
>> UDA shows that if I am a machine then the universe, whatever it may
>> be, cannot be a machine. An apparent physical universe can, and
>> actually must emerge, from inside, but this one too cannot be  
>> entirely
>> described by a machine.
>>
>>
>>
>>
>>
>>> In light of that it seems a prudent fundamental step would be to
>>> define
>>> what it means for one structure to be aware of another.
>>>
>>
>>
>>
>> In AUDA, the arithmetical and more constructive version of UDA,
>> consciousness, like truth, will appear to be undefinable, except by
>> some fixed point of the doubting procedure. It is then show  
>> equivalent
>> to an instinctive bet on a reality. It has a relative self-speeding
>> role.
>>
>>
>>
>>
>>
>>
>>> This would
>>> apparently be some relation on the aggregate of all structures  
>>> (which
>>> may be the entire level 4 multiverse in Tegmark's theory).  Perhaps
>>> some
>>> basic fundamental step would be to provide some axioms on what this
>>> relation could be but I'm almost convinced this can't be done in a
>>> non-controversial way.
>>>
>>
>>
>> Computationalism is not controversal, nor is my deduction, but few
>> people get both the quantum difficulties and the mathematical  
>> logic. I
>> am more ignored than misunderstood, and then I don't publish so much.
>> But I love to explain to people with a genuine interest in those  
>> issues.
>>
>>
>>
>>
>>> I know I'm putting the cart before the horse here so I don't expect
>>> all
>>> to be revealed for some time when it occurs in your exposition.  If
>>> there is some literature by yourself or others on the particular
>>> subjects and issues I mentioned, I'd appreciate links to them.
>>>
>>
>>
>> Almost all my papers dig on that issue. See my url
>>
>> http://iridia.ulb.ac.be/~marchal/
>>
>> or search in this list for explanations. What is new, and
>> counterintuitive is that computationalism entails a reversal between
>> physics and machine's biology/psychology/theology .... See my paper  
>> on
>> Plotinus for a presentation of AUDA in term of Plotinus  
>> (neo)platonist
>> theology.
>>
>> We cannot define consciousness (nor the notion of natural numbers),
>> but we don't have to define those things to reason about, once we
>> agree on some principles (like the "yes doctor" and Church thesis).
>>
>> Welcome aboard on the train Brian,
>>
>> Bruno
>>
>>>
>>
>>
>
> >

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




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[James Rose-5]

What is the definition of  "a machine"?  I have a sense that there
is an intuitive one but not an explicit one, appropriate to the
discussions here.

James



----- Original Message ----
From: Bruno Marchal <marchal@...>
To: everything-list@...
Sent: Tuesday, June 2, 2009 12:29:47 PM
Subject: Re: The seven step-Mathematical preliminaries


The beauty of all this, Brian, is that the correct (arithmetically) 
universal machine will never been able to answer the question "are you 
a machine?", but she (it) will be able to bet she is a (unknown) 
machine. She will never know which one, and she will refute all 
theories saying which machine she could be, unless she decided to 
identify herself with the virgin, never programmed, universal one.

There is a way to attribute a first person view to a machine, but 
then, from that first person view, the machine will be correct in 
saying "I am not a machine".

The consequence of computationalism are so much counterintuitive that 
"even" machines cannot really believe in comp. Yet, those machine 
which believe in the numbers and induction will be able to explain 
exactly all this. Machines can prove that if they are a correct 
machine, then they cannot "believe" that they are a correct machine.

It is related to the incompleteness phenomenon and the logic of self-
reference which is exploited in the AUDA.

Actually it works also for Turing hypermachines, and a vast collection 
of machine extensions, and even self-aware structures completly 
unrelated to machine, which unfortunately needs a lot of model theory 
to be described (like "truth in all transitive model of ZF", if this 
rings a bell).

But here we anticipate a lot. Hope this can open your appetite.

Bruno



On 02 Jun 2009, at 21:08, Brian Tenneson wrote:

>
> Thanks for the links.  I'll look over them and hopefully I'll 
> understand
> what I see.  At least if I have questions I can ask though maybe not 
> in
> this thread.
>
> I don't yet know precisely what you mean by a machine but I do have
> superficial knowledge of Turing machines; I'm assuming there is a
> resemblance between the two concepts.  I surmise that a machine can 
> have
> an input like a question and if it halts then the question has a
> decidable answer, else it has no decidable answer.
>
> What about posing the following question "am I a machine" or the
> statement "I am a machine" and maybe some machines halt on an answer 
> and
> some don't.  Ie, if X is a machine, then have it attempt to compute 
> the
> statement "X is a machine."  (I know I'm a bit fuzzy on the details.)
> For machines X that return "X is a machine" I would be inclined to 
> think
> such machines possess at least some form of self-awareness, a kind of
> abstract self-awareness devoid of sensation (or so it would appear).
>
> -Brian
>
> Bruno Marchal wrote:
>> On 02 Jun 2009, at 18:54, Brian Tenneson wrote:
>>
>>
>>> Thank you for starting this discussion.  I have only joined recently
>>> and
>>> have little knowledge of your research.  To see it laid out in the
>>> sequence you describe should make it clear to me what it is all 
>>> about.
>>>
>>> I'm particularly interested in the interaction between consciousness
>>> and
>>> computation.  In Max Tegmark's Ensemble TOE paper he alludes to a
>>> self-aware structure.  I take structure to be an object of study in
>>> logic (model theory, in particular) but am not at all sure how
>>> consciousness, which I envision self-awareness to be deeply tied to,
>>> connects to mathematics.  It seems you're going to build up to a
>>> statement such as "consciousness is computable" OR "consciousness is
>>> not
>>> computable," or something about consciousness, at least.
>>>
>>
>>
>>
>> In UDA, I avoid the use of consciousness. I just use the hypothesis
>> that consciousness, or first person experience remains unchanged 
>> for a
>> functional substitution made at the correct comp substitution level
>> (this is the comp hypothesis).
>> Then the UD Argument  is supposed to show, that physicalism cannot be
>> maintained and that physics is a branch of computer science, or even
>> just number theory.
>> In AUDA, I refine the constructive feature of UDA to begin the
>> extraction of physics.
>> You can read my paper here, and print the UD slides, because I
>> currently refer often to the steps of that reasoning:
>>
>> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
>>
>> I have written a better one, but I must still put it in my webapge.
>>
>> It seems to me that Tegmark is a bit fuzzy about the way he attaches
>> the first person experience with the "universes"/bodies. Like many
>> physicists, he is a bit naive about the mind-body problem. The
>> computationalist hypothesis is not a solution per se, just a tool
>> making it possible to reformulate the problem. Indeed it forces a
>> reduction of the mind-body problem to a highly non trivial body
>> problem. It is my whole point.
>>
>> UDA shows that if I am a machine then the universe, whatever it may
>> be, cannot be a machine. An apparent physical universe can, and
>> actually must emerge, from inside, but this one too cannot be 
>> entirely
>> described by a machine.
>>
>>
>>
>>
>>
>>> In light of that it seems a prudent fundamental step would be to
>>> define
>>> what it means for one structure to be aware of another.
>>>
>>
>>
>>
>> In AUDA, the arithmetical and more constructive version of UDA,
>> consciousness, like truth, will appear to be undefinable, except by
>> some fixed point of the doubting procedure. It is then show 
>> equivalent
>> to an instinctive bet on a reality. It has a relative self-speeding
>> role.
>>
>>
>>
>>
>>
>>
>>> This would
>>> apparently be some relation on the aggregate of all structures 
>>> (which
>>> may be the entire level 4 multiverse in Tegmark's theory).  Perhaps
>>> some
>>> basic fundamental step would be to provide some axioms on what this
>>> relation could be but I'm almost convinced this can't be done in a
>>> non-controversial way.
>>>
>>
>>
>> Computationalism is not controversal, nor is my deduction, but few
>> people get both the quantum difficulties and the mathematical 
>> logic. I
>> am more ignored than misunderstood, and then I don't publish so much.
>> But I love to explain to people with a genuine interest in those 
>> issues.
>>
>>
>>
>>
>>> I know I'm putting the cart before the horse here so I don't expect
>>> all
>>> to be revealed for some time when it occurs in your exposition.  If
>>> there is some literature by yourself or others on the particular
>>> subjects and issues I mentioned, I'd appreciate links to them.
>>>
>>
>>
>> Almost all my papers dig on that issue. See my url
>>
>> http://iridia.ulb.ac.be/~marchal/
>>
>> or search in this list for explanations. What is new, and
>> counterintuitive is that computationalism entails a reversal between
>> physics and machine's biology/psychology/theology .... See my paper 
>> on
>> Plotinus for a presentation of AUDA in term of Plotinus 
>> (neo)platonist
>> theology.
>>
>> We cannot define consciousness (nor the notion of natural numbers),
>> but we don't have to define those things to reason about, once we
>> agree on some principles (like the "yes doctor" and Church thesis).
>>
>> Welcome aboard on the train Brian,
>>
>> Bruno
>>
>>>
>>
>>
>
> >

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





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[Bruno Marchal]

On 02 Jun 2009, at 18:46, Kelly Harmon wrote:




>
>> First, in the multiplication experience, the question of your choice
>> is not addressed, nor needed.
>> The question is really: what will happen to you. You give the right
>> answer above.
>>
>
> You're saying that there are no low probability worlds?  Or only that
> they're outnumbered by the high probability worlds?

The last. Low probability world exists but not only it is rare to  
access them, but it super-rare to remain in them, well, if comp  
succeeds!


>
>
> I guess I'm not clear on what you're getting at with this pixel
> thought-experiment.

The UD is the many-world, or many-histories. The 2^big movies  
multiplication is a tiny trivial part of the UD, and being  
immaterialist you should understand that we are doing all the time  
this "thought" experiment. If we don't succeed in justifying why  
things look normal, comp has to be abandoned. We have to explain why  
the computational histories win when the UD plays the trick of  
generating a continuum of non computational histories. The  
computational histories which will "win" are those who entangled with  
the non computational histories so as to make normality inherited by  
the computational one. Somehow.

>
>
>
>> Have you understand UDA1-6?, because I think most get those steps. I
>> will soon explain in all details UDA-7, which is not entirely  
>> obvious.
>> If you take your own philosophy seriously, you don't need UDA8. But  
>> it
>> can be useful to convince others, of the necessity of that
>> "philosophy", once we bet on the comp hyp.
>>
>
> I think I have a good grasp of 1 through 6.

Cool, I am just explaining UDA-7, in all details, from scratch.

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,

            I appreciate the simplicity of the examples. My answers follow the questions.    marty a.

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

From: "Bruno Marchal" <marchal@...>

>

>
> ============================================= begin 
> ===============================
>
> 1) SET
>
> Informal definition: a set is a collection of object, called elements, 
> with the idea that it, the collection or set, can be considered itself 
> as an object. It is a many seen as a one, if you want. If the set is 
> not to big, we can describe it exhaustively by listing the elements, 
> if the set is bigger, we can describe it by some other way. Usually we 
> use accolades "{", followed by the elements, separated by commas, and 
> then "}", in the exhaustive description of a set.
>
> Example/exercise:
>
> 1) The set of odd natural numbers which are little than 10. This is a 
> well defined, and not to big set, so we can describe it exhaustively by
> {1, 3, 5, 7, 9}. In this case we say that 7 belongs to  {1, 3, 5, 7, 9}.
> Exercise 1: does the number 24 belongs to the set {1, 3, 5, 7, 9}?    NO
>
> 2) the set of even natural number  which are little than 13. It is {0, 
> 2, 4, 6, 8, 10, 12}. OK? Some people can have a difficulty which is 
> not related to the notion of set, for example they can ask themselves 
> if zero (0) is really an even number. We will come back to this.         
>
> 3) The set of odd natural numbers which are little than 100. This set 
> is already too big to describe exhaustively. We will freely describe 
> such a set by a quasi exhaustion like {1, 3, 5, 7, 9, 11, ... 95, 97, 
> 99}.
> Exercise 2: does the number 93 belongs to the set of odd natural 
> numbers which are little than 100, that is: does 93 belongs to {1, 3, 
> 5, 7, 9, 11, ... 95, 97, 99}?                                                               YES
>
> 4) The set of all natural numbers. This set is hard to define, yet I 
> hope you agree we can describe it by the infinite quasi exhaustion by 
> {0, 1, 2, 3, ...}.
> Exercise 3: does the number 666 belongs to the set of natural numbers, 
> that is does 666 belongs to {0, 1, 2, 3, ...}.                                         YES
> Exercice 4: does the real number square-root(2) belongs to {0, 1, 2, 
> 3, ...}?                                                                                              NO (a guess)
>
>
> 5) When a set is too big or cumbersome, mathematician like to give 
> them a name. They will usually say: let S be the set {14, 345, 78}. 
> Then we can say that 14 belongs to S, for example.
> Exercise 5: does 345 belongs to S?                                                    YES
>
> A set is entirely defined by its elements. Put in another way, we will 
> say that two sets are equal if they have the same elements.
> Exercise 6. Let S be the set {0, 1, 45} and let M be the set described 
> by {45, 0, 1}. Is it true or false that S is equal to M?                              YES
> Exercise 7. Let S be the set {666} and M be the set {6, 6, 6}. Is is 
> true or false that S is equal to M?                                                        NO                                                      
>
> Seven exercises are enough. Are you ready to answer them. I hope you 
> don't find them too much easy, because I intend to proceed in a way 
> such that all exercise will be as easy, despite we will climb toward 
> very much deeper notion. Feel free to ask question, comments, etc. I 
> will try to adapt myself.                                                                       SO FAR SO GOOD
>
> Next: we will see some operation on sets (union, intersection), and 
> the notion of subset. If all this work, I will build a latex document, 
> and make it the standard reference for the seventh step for the non 
> mathematician, or for the beginners in mathematics.
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/

>
>
>
>
>
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[Brent Meeker-2]

Bruno Marchal wrote:
> ...
> A set is entirely defined by its elements. Put in another way, we will  
> say that two sets are equal if they have the same elements.
> Exercise 6. Let S be the set {0, 1, 45} and let M be the set described  
> by {45, 0, 1}. Is it true or false that S is equal to M?
> Exercise 7. Let S be the set {666} and M be the set {6, 6, 6}. Is is  
> true or false that S is equal to M?
>  

But there are no duplicates in sets; so {6,6,6} is either not a set
(instead it's a triple) or it's just strange notation for {6}.  Right?

Brent

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[Kim Jones-2]

On Wed Jun  3  0:39 , Bruno Marchal <marchal@...> sent:

>
>Hi Kim, Hi Marty and others,
>
>So it is perhaps time to do some math.


It is


>Obviously this is a not a course in math, but it is an explanation  
>from scratch of the seven step of the universal dovetailer argument.  
>It is a shortcut, and most probably we will make some digression from  
>time to time, but let us try not to digress too much.
>
>Kim, you are OK with this?


I am




I have to take into account the problem you  
>did have with math, and which makes this lesson a bit challenging for  
>me, and I guess for you too.


Hopefully my innocence will allow me to bypass the pedantry and orthodoxies of the field and allow a
shortcut to a high level of understanding of the UDA. Only a complete neophyte would have the gall to
say something like that!

>
>I begin with the very useful and elementary notion of set, as  
>explained in what is called "naive set theory", and which is the base  
>of almost all part of math.
>
>============================================= begin  
>===============================
>
>1) SET
>
>Informal definition: a set is a collection of object, called elements,  
>with the idea that it, the collection or set, can be considered itself  
>as an object. It is a many seen as a one, if you want. If the set is  
>not to big, we can describe it exhaustively by listing the elements,  
>if the set is bigger, we can describe it by some other way. Usually we  
>use accolades "{", followed by the elements, separated by commas, and  
>then "}", in the exhaustive description of a set.
>
>Example/exercise:
>
>1) The set of odd natural numbers which are little than 10. This is a  
>well defined, and not to big set, so we can describe it exhaustively by
>{1, 3, 5, 7, 9}. In this case we say that 7 belongs to  {1, 3, 5, 7, 9}.
>Exercise 1: does the number 24 belongs to the set {1, 3, 5, 7, 9}?

No

>
>2) the set of even natural number  which are little than 13. It is {0,  
>2, 4, 6, 8, 10, 12}. OK? Some people can have a difficulty which is  
>not related to the notion of set, for example they can ask themselves  
>if zero (0) is really an even number. We will come back to this.
>
>3) The set of odd natural numbers which are little than 100. This set  
>is already too big to describe exhaustively. We will freely describe  
>such a set by a quasi exhaustion like {1, 3, 5, 7, 9, 11, ... 95, 97,  
>99}.
>Exercise 2: does the number 93 belongs to the set of odd natural  
>numbers which are little than 100, that is: does 93 belongs to {1, 3,  
>5, 7, 9, 11, ... 95, 97, 99}?

Yes



>
>4) The set of all natural numbers. This set is hard to define, yet I  
>hope you agree we can describe it by the infinite quasi exhaustion by  
>{0, 1, 2, 3, ...}.
>Exercise 3: does the number 666 belongs to the set of natural numbers,  
>that is does 666 belongs to {0, 1, 2, 3, ...}.


Yes


>Exercice 4: does the real number square-root(2) belongs to {0, 1, 2,  
>3, ...}?


No idea what square-root(2) means. When I said I was innumerate I wasn't kidding! I could of course look
it up or ask my mathematics teacher friends but I just know your explanation will make theirs seem trite.


>
>
>5) When a set is too big or cumbersome, mathematician like to give  
>them a name. They will usually say: let S be the set {14, 345, 78}.  
>Then we can say that 14 belongs to S, for example.
>Exercise 5: does 345 belongs to S?


Clearly, yes



>A set is entirely defined by its elements. Put in another way, we will  
>say that two sets are equal if they have the same elements.
>Exercise 6. Let S be the set {0, 1, 45} and let M be the set described  
>by {45, 0, 1}. Is it true or false that S is equal to M?


True - unless integer position within a given sequence in a set plays a role. I will guess that it does not



>Exercise 7. Let S be the set {666} and M be the set {6, 6, 6}. Is is  
>true or false that S is equal to M?


False - the commas separate each natural number


>
>Seven exercises are enough. Are you ready to answer them.


Done - apart from the square root question


 I hope you  
>don't find them too much easy, because I intend to proceed in a way  
>such that all exercise will be as easy, despite we will climb toward  
>very much deeper notion. Feel free to ask question, comments, etc. I  
>will try to adapt myself.


Very excited about doing this. If you can make it all as approachable as this I am over the moon!



>
>Next: we will see some operation on sets (union, intersection), and  
>the notion of subset. If all this work, I will build a latex document,  
>and make it the standard reference for the seventh step for the non  
>mathematician, or for the beginners in mathematics.


What a wonderful idea!

Kim


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


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[Bruno Marchal]

On 02 Jun 2009, at 21:41, James Rose wrote:

>
>
> What is the definition of  "a machine"?  I have a sense that there
> is an intuitive one but not an explicit one, appropriate to the
> discussions here.

It is part of the goal of the seven step thread to define what is a  
mathematical machine.
Part of this will consist in showing that such a notion is everything  
but obvious.

Here Brian was anticipating on what will follow, actually. I have no  
problem with anticipation like that, to sustain the motivation, but of  
course they does not belong to the pedagogical sequences, and people  
should not worry if they don't understand them.

Bruno

>
>
> James
>
>
>
> ----- Original Message ----
> From: Bruno Marchal <marchal@...>
> To: everything-list@...
> Sent: Tuesday, June 2, 2009 12:29:47 PM
> Subject: Re: The seven step-Mathematical preliminaries
>
>
> The beauty of all this, Brian, is that the correct (arithmetically)
> universal machine will never been able to answer the question "are you
> a machine?", but she (it) will be able to bet she is a (unknown)
> machine. She will never know which one, and she will refute all
> theories saying which machine she could be, unless she decided to
> identify herself with the virgin, never programmed, universal one.
>
> There is a way to attribute a first person view to a machine, but
> then, from that first person view, the machine will be correct in
> saying "I am not a machine".
>
> The consequence of computationalism are so much counterintuitive that
> "even" machines cannot really believe in comp. Yet, those machine
> which believe in the numbers and induction will be able to explain
> exactly all this. Machines can prove that if they are a correct
> machine, then they cannot "believe" that they are a correct machine.
>
> It is related to the incompleteness phenomenon and the logic of self-
> reference which is exploited in the AUDA.
>
> Actually it works also for Turing hypermachines, and a vast collection
> of machine extensions, and even self-aware structures completly
> unrelated to machine, which unfortunately needs a lot of model theory
> to be described (like "truth in all transitive model of ZF", if this
> rings a bell).
>
> But here we anticipate a lot. Hope this can open your appetite.
>
> Bruno
>
>
>
> On 02 Jun 2009, at 21:08, Brian Tenneson wrote:
>
>>
>> Thanks for the links.  I'll look over them and hopefully I'll
>> understand
>> what I see.  At least if I have questions I can ask though maybe not
>> in
>> this thread.
>>
>> I don't yet know precisely what you mean by a machine but I do have
>> superficial knowledge of Turing machines; I'm assuming there is a
>> resemblance between the two concepts.  I surmise that a machine can
>> have
>> an input like a question and if it halts then the question has a
>> decidable answer, else it has no decidable answer.
>>
>> What about posing the following question "am I a machine" or the
>> statement "I am a machine" and maybe some machines halt on an answer
>> and
>> some don't.  Ie, if X is a machine, then have it attempt to compute
>> the
>> statement "X is a machine."  (I know I'm a bit fuzzy on the details.)
>> For machines X that return "X is a machine" I would be inclined to
>> think
>> such machines possess at least some form of self-awareness, a kind of
>> abstract self-awareness devoid of sensation (or so it would appear).
>>
>> -Brian
>>
>> Bruno Marchal wrote:
>>> On 02 Jun 2009, at 18:54, Brian Tenneson wrote:
>>>
>>>
>>>> Thank you for starting this discussion.  I have only joined  
>>>> recently
>>>> and
>>>> have little knowledge of your research.  To see it laid out in the
>>>> sequence you describe should make it clear to me what it is all
>>>> about.
>>>>
>>>> I'm particularly interested in the interaction between  
>>>> consciousness
>>>> and
>>>> computation.  In Max Tegmark's Ensemble TOE paper he alludes to a
>>>> self-aware structure.  I take structure to be an object of study in
>>>> logic (model theory, in particular) but am not at all sure how
>>>> consciousness, which I envision self-awareness to be deeply tied  
>>>> to,
>>>> connects to mathematics.  It seems you're going to build up to a
>>>> statement such as "consciousness is computable" OR "consciousness  
>>>> is
>>>> not
>>>> computable," or something about consciousness, at least.
>>>>
>>>
>>>
>>>
>>> In UDA, I avoid the use of consciousness. I just use the hypothesis
>>> that consciousness, or first person experience remains unchanged
>>> for a
>>> functional substitution made at the correct comp substitution level
>>> (this is the comp hypothesis).
>>> Then the UD Argument  is supposed to show, that physicalism cannot  
>>> be
>>> maintained and that physics is a branch of computer science, or even
>>> just number theory.
>>> In AUDA, I refine the constructive feature of UDA to begin the
>>> extraction of physics.
>>> You can read my paper here, and print the UD slides, because I
>>> currently refer often to the steps of that reasoning:
>>>
>>> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
>>>
>>> I have written a better one, but I must still put it in my webapge.
>>>
>>> It seems to me that Tegmark is a bit fuzzy about the way he attaches
>>> the first person experience with the "universes"/bodies. Like many
>>> physicists, he is a bit naive about the mind-body problem. The
>>> computationalist hypothesis is not a solution per se, just a tool
>>> making it possible to reformulate the problem. Indeed it forces a
>>> reduction of the mind-body problem to a highly non trivial body
>>> problem. It is my whole point.
>>>
>>> UDA shows that if I am a machine then the universe, whatever it may
>>> be, cannot be a machine. An apparent physical universe can, and
>>> actually must emerge, from inside, but this one too cannot be
>>> entirely
>>> described by a machine.
>>>
>>>
>>>
>>>
>>>
>>>> In light of that it seems a prudent fundamental step would be to
>>>> define
>>>> what it means for one structure to be aware of another.
>>>>
>>>
>>>
>>>
>>> In AUDA, the arithmetical and more constructive version of UDA,
>>> consciousness, like truth, will appear to be undefinable, except by
>>> some fixed point of the doubting procedure. It is then show
>>> equivalent
>>> to an instinctive bet on a reality. It has a relative self-speeding
>>> role.
>>>
>>>
>>>
>>>
>>>
>>>
>>>> This would
>>>> apparently be some relation on the aggregate of all structures
>>>> (which
>>>> may be the entire level 4 multiverse in Tegmark's theory).  Perhaps
>>>> some
>>>> basic fundamental step would be to provide some axioms on what this
>>>> relation could be but I'm almost convinced this can't be done in a
>>>> non-controversial way.
>>>>
>>>
>>>
>>> Computationalism is not controversal, nor is my deduction, but few
>>> people get both the quantum difficulties and the mathematical
>>> logic. I
>>> am more ignored than misunderstood, and then I don't publish so  
>>> much.
>>> But I love to explain to people with a genuine interest in those
>>> issues.
>>>
>>>
>>>
>>>
>>>> I know I'm putting the cart before the horse here so I don't expect
>>>> all
>>>> to be revealed for some time when it occurs in your exposition.  If
>>>> there is some literature by yourself or others on the particular
>>>> subjects and issues I mentioned, I'd appreciate links to them.
>>>>
>>>
>>>
>>> Almost all my papers dig on that issue. See my url
>>>
>>> http://iridia.ulb.ac.be/~marchal/
>>>
>>> or search in this list for explanations. What is new, and
>>> counterintuitive is that computationalism entails a reversal between
>>> physics and machine's biology/psychology/theology .... See my paper
>>> on
>>> Plotinus for a presentation of AUDA in term of Plotinus
>>> (neo)platonist
>>> theology.
>>>
>>> We cannot define consciousness (nor the notion of natural numbers),
>>> but we don't have to define those things to reason about, once we
>>> agree on some principles (like the "yes doctor" and Church thesis).
>>>
>>> Welcome aboard on the train Brian,
>>>
>>> Bruno
>>>
>>>>
>>>
>>>
>>
>>>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
>
> >

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




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[Bruno Marchal]

On 02 Jun 2009, at 22:00, Brent Meeker wrote:

>
> Bruno Marchal wrote:
>> ...
>> A set is entirely defined by its elements. Put in another way, we  
>> will
>> say that two sets are equal if they have the same elements.
>> Exercise 6. Let S be the set {0, 1, 45} and let M be the set  
>> described
>> by {45, 0, 1}. Is it true or false that S is equal to M?
>> Exercise 7. Let S be the set {666} and M be the set {6, 6, 6}. Is is
>> true or false that S is equal to M?
>>
>
> But there are no duplicates in sets; so {6,6,6} is either not a set
> (instead it's a triple) or it's just strange notation for {6}.  Right?

Right. I was not well inspired with this exercise. At least it should  
have been given AFTER having said that a set is determined only by its  
elements. So {6, 6, 6} is really the same as the set {6}. Something  
like {6, 6, 6} is usually called a bag, and will never been used.
Of course {666} is different from {6}.

Apology. This will probably happen again, when I am distracted, so if  
an exercise seems weird or senseless, please don't panic!

Bruno

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




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