Nabble - Everything List

3D Mandelbrot

2009-11-18T21:32:01Z

The Mandelbulb: first 'true' 3D image of famous fractal

enjoy

Kim Jones

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Re: The seven step series (november 2009)

2009-11-17T01:51:51Z

On 16 Nov 2009, at 17:45, Brent Meeker wrote:

> Bruno Marchal wrote:
>>
>> On 11 Nov 2009, at 19:52, Brent Meeker wrote:
>>
>>>
>>> But how is the "first person point of view" defined? Can this
>>> theory
>>> tell me how many persons exist at a given time?
>>
>>
>> I come back on this. The question "how many persons?" is a question
>> which remains very hard in the mechanist theory.
>>
>> To answer it, let me ask you a question. Suppose that old fashioned
>> time
>> travel is possible, and that Brent Meeker of the future decides to
>> travel in the past, and to say hello to the younger Brent Meeker.
>> They
>> met in a kitchen and drink coffee. Nobody else is present in the
>> kitchen. How many person are there in the kitchen? What would you
>> say?
>>
>> I think this: if you answer one, then I will tend to say that there
>> is
>> only one person in the multiverse, but it manifests itself in
>> different
>> overlapping contexts. If you answer "two", then I will tend to say
>> that
>> there are an infinity of persons in the multiverse.
>>
>> What do you think?
>
> I think closed time-like loops are probably impossible. But your
> answer
> just points to possible equivocation on "person". The time traveling
> Brent is a different person from the untraveled Brent because he has
> different memories just as the 70yr old Brent is a different person
> than
> the 10yr old Brent. But in another sense - causal continuity - they
> are
> the same person. It isn't necessary to introduce time travel to
> create this confusion of terms.
>
>
> But the first part of my question was about how a "first person
> view" is
> defined in this mathematical abstraction? What computations must my
> computer perform so that it has a first person view?

UDA has been constructed so that we don't have to answer this question
to understand that the physical laws emerge from numbers (assuming
comp).
It is just enough that we accept that there is a level of
substitution. Then we can prove that we cannot know-for-sure which
computations support consciousness, yet that we have to take into
account an infinity of those computations (below the substitution
level) to get the first person experiences measure.

But AUDA provides a hint of a more precise answer. Consciousness is
associated to the universal machine having the cognitive ability of a
Lobian machine(*). So PA and ZF are already conscious. Their
provability predicate obey Bp -> BBp. And their knowledge pseudo-
predicate defined by Kp = Bp & p, obeys it too: Kp -> KKp.

But remember that, by the movie graph (UDA step 8) consciousness is
not associated to the performance of a computer (= one computation/one
universal machine), but to the existence of the computations
(=infinity of computations and universal machines as defined in the
standard model of arithmetic). Consciousness is associated to the
logical relations between numbers which defined the alternate
consistent extensions of the "subject". You are, in that sense, the
same person as PA, and probably ZF, like you are the same person as
the young baby Brent.

And probably: rich qualia (like our owns) need long and deep stories
(very long computations capable of stabilizing on the interference of
the infinity of computations which exists below our level of
substitution).

Bruno

(*) Formally: it means they provability predicate obeys B(Bp -> p) ->
Bp (Löb Formula).
Bp -> BBp can be derived from this. It is actually done in Smullyan's
"Forever Undecided".

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

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Re: The seven step series (november 2009)

2009-11-16T08:45:04Z

Bruno Marchal wrote:

>
> On 11 Nov 2009, at 19:52, Brent Meeker wrote:
>
>>
>> But how is the "first person point of view" defined? Can this theory
>> tell me how many persons exist at a given time?
>
>
> I come back on this. The question "how many persons?" is a question
> which remains very hard in the mechanist theory.
>
> To answer it, let me ask you a question. Suppose that old fashioned time
> travel is possible, and that Brent Meeker of the future decides to
> travel in the past, and to say hello to the younger Brent Meeker. They
> met in a kitchen and drink coffee. Nobody else is present in the
> kitchen. How many person are there in the kitchen? What would you say?
>
> I think this: if you answer one, then I will tend to say that there is
> only one person in the multiverse, but it manifests itself in different
> overlapping contexts. If you answer "two", then I will tend to say that
> there are an infinity of persons in the multiverse.
>
> What do you think?

I think closed time-like loops are probably impossible. But your answer
just points to possible equivocation on "person". The time traveling
Brent is a different person from the untraveled Brent because he has
different memories just as the 70yr old Brent is a different person than
the 10yr old Brent. But in another sense - causal continuity - they are
the same person. It isn't necessary to introduce time travel to
create this confusion of terms.

But the first part of my question was about how a "first person view" is
defined in this mathematical abstraction? What computations must my
computer perform so that it has a first person view?

Brent
The person I was when I was 3 years old is dead. He died because
too much new information was added to his brain.
-- Saibal Mitra

>
> Note that in UDA, I use a definition of first person which identify a
> person with its personal memory, and so where many different persons can
> exist.
> But in AUDA, I use a more mathematical definition which eventually
> identify all persons. Then they can differentiate through a mixture of
> amnesia (they forget that they are the "universal person"), and personal
> memories (which they will use as self-identification means).
>
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
> --
>
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Re: The seven step series (november 2009)

2009-11-16T02:40:28Z

On 11 Nov 2009, at 19:52, Brent Meeker wrote:

But how is the "first person point of view" defined? Can this theory
tell me how many persons exist at a given time?

I come back on this. The question "how many persons?" is a question which remains very hard in the mechanist theory.

To answer it, let me ask you a question. Suppose that old fashioned time travel is possible, and that Brent Meeker of the future decides to travel in the past, and to say hello to the younger Brent Meeker. They met in a kitchen and drink coffee. Nobody else is present in the kitchen. How many person are there in the kitchen? What would you say?

I think this: if you answer one, then I will tend to say that there is only one person in the multiverse, but it manifests itself in different overlapping contexts. If you answer "two", then I will tend to say that there are an infinity of persons in the multiverse.

What do you think?

Note that in UDA, I use a definition of first person which identify a person with its personal memory, and so where many different persons can exist.

But in AUDA, I use a more mathematical definition which eventually identify all persons. Then they can differentiate through a mixture of amnesia (they forget that they are the "universal person"), and personal memories (which they will use as self-identification means).

Bruno

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

Re: Arguably The World's Greatest Woman

2009-11-15T07:14:40Z

On 15 Nov 2009, at 04:48, Brent Meeker wrote:

Science is neutral in the sense that science doesn't care what reality
is,

Fundamental science does care on what really is. But it is admitted by serious inquirer that there are alternative theories.

but science assumes that there is enough regularity in reality that
theories about it can be tested. The unprovable truths you refer to are
always relative to a particular set of axioms and rules of inference.

They are related to a self-referentially correct universal machine. Formal theories are just simple exemples of such machine.

So unless you have some way to limit "reality" to that set of axioms and
rules of inference, the truths are not unprovable "in reality".

The interest is that such machine discover that there is a "transcendent reality" above what they can prove. Already without making observation. Observation speed-up, like self-mulitiplication and confrontation speed up the "process".

Reality, nor meaning is never limited by the theory or machine. On the contrary, tha theory or machine is the tool by which "reality" can makes sense to pieces of reality and glue them together in the quest for the truth.

Religion = certain faith

It is just faith in a reality or in a truth. Religious text which tell that face has to be blind, can only be misunderstood poetical idea or cynical ways to manipulate people. To say to accept something with blind face is equivalent to say shup up and obeys me.

I am not talking on some pseudo-post blasphem human (too much human) terrestraial religion. I am talking of the the religion any universal machine, "before the fall of his soul", can infer by looking at herself.

- and makes a virtue of belief beyond or even contrary to
evidence. I agree with what you say about science, but I think you are
making up your own definition for religion.

Not really. It is the religion of the universal machine when she says
"yes" to the doctor, at her risk and peril. Or it is the religion
(truth) she can deduce from just imagining surviving such an experience.

That is what reminded me of the Bertrand Russell quotation - you seem
reluctant to give up the word "religion" while discarding the idea for
which it formerly stood: shared beliefs which were held on faith

I don't discard this. Shared beliefs hled by faith is already in science.

and
immune to experimental investigation

I can agree with this, but it should not be misinterpreted. It is the place where "things can be dangerous or close to the blasphem". It is the part of truth which is indeed beyond science. But this is not (although it is many time when religion "lives" a blasphemous period (say) wher the priest says "shut up and obey me", in is the place the teacher says now you have to look in yourself and trust yourself.

To feast, to private oneself of sleep, or taking some drug seems to provide some helps, but joke and circumstances can help too.

which explain human origins,
purpose, and morals.

So I agree with your definition of religion. And the only difference with science is that for one aspect of the truth it as asked to you to close the book and the eyes and look into yourself.

The gigantic revolution is that we know now that universal machine can already do the trick, and it is just fabulous what they can see.

It is a branch of math, and it is axiomatized by the modal logics G
and G*, and its intensional variants.

It is like opening our eyes and observing, and then trying to
figure a
mental coherent picture of what we see. But no one can prove that we
have find the last correct picture. No one. neither the scientist,
nor
the priest.
But some prove their picture in the sense of testing it and discarding
or modifying it if it fails. That's the scientist. Others avoid
testing their picture and cling to it in spite of its failures Those
are the priests.

Some scientist are bad too. It is not the problem of religion. It is the problem of humans sticking on wrong ideas. It is worth when the wrong idea are shared by coercion.

The problem is that if you confuse religion with bad or confused religion, you will prevent the possibility of better religion. So that confusion is maintained by the pseudo-religious people. Radical atheists are the best allies of the radical pseudo-religious. None one the coming back of the moderate and inquiring mind.

Religion is what extend science *by necessity*. It is indeed relative to any entity having self-referential abilities. But is may be shared by collection or organization of such machine relatively to probable histories.

I would say that religion (the truth) is the motor of science (the unending quest).

Any scientist who says that he does not religion is either a pure instrumentalist technician without conscience, or someone who has a blind faith religion and want to hide it from science or questioning.

Discarding religion, per se, result in transforming science into a religion, like equating proof and truth. This can lead only to problems. Theories, machine, beliefs are finite attempts to figure the "thing". Of course you have to have some faith in what you are searching.

The best idea like religion and democracy, can be perverted. But by dismissing attempts tpward serious modest theology, we make impossible to cure ourself of the perverted religions. And none religion is per se totally perverted. Humans are complex and is each group you have different tendencies, some may have the potential to "change their mind or evolve".

Religion is what results when science discover its modesty and limitations. Once you give the mimimal ability of self-inductive inference to a theory as simple as Peano Arithmetic, she get mystical, discover her limitations, and being 100% correct, she is mute on the proper theological part, but she can explain that by using interrogation mark.

In a nutshell, for the logician, in AUDA: science corresponds to G, and religion corresponds to G*. And pure religion, what you and only you can find in you (and especially not accept by blind faith) corresponds to G* minus G. It is a testable theology, given that its include the machine physics.

Bruno

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

Re: Arguably The World's Greatest Woman

2009-11-14T19:48:09Z

Bruno Marchal wrote:

> On 14 Nov 2009, at 22:33, Brent Meeker wrote:
>
>
>> Bruno Marchal wrote:
>>
>>> On 14 Nov 2009, at 01:33, Brent Meeker wrote:
>>>
>>>
>>>>> Why should we use the term "God" in the sense of those who clearly
>>>>> have confused science with temporal authoritative argument?
>>>>>
>>>> Because that's what most people who use the term mean. And if we
>>>> tell
>>>> them we're agnostic about God
>>>>
>>> Who them? Which Christians? There are many Christian theologians who
>>> have reasonable (with respect to comp, or to the scientific attitude)
>>> conception of God.
>>>
>> Many being a few thousand? But there are billions of Christians who
>> are
>> *not* theologians and a large fraction of them (at least in the U.S.)
>> use their votes and money to make Christian dogma public policy.
>>
>
> Yes, but if you use science 'against" them, you make science a pseudo-
> religion, and you give them more braids. If we don't get back to
> 'serious" (meaning hypothetical) theology, pseudo-religion will
> continue.
>
> Even if you take the 'theology' of the universal machine as a toy
> theology, it is remarkable how it explains the difference between
> science and theology. Science is *the* tool of those whose faith is
> not based on rumors.
>
>
>
>>> The difference between some american and european christians can be
>>> bigger than the difference between european atheists.
>>> But once we know some group does not argue, but use authoritatively
>>> some dogma, anyone with a scientific attitude should use its usual
>>> critical mind.
>>>
>>>
>>>
>>>
>>>> we will be telling them that we have no
>>>> good reason not to believe in their sky father and hence no good
>>>> reason
>>>> to resist the revealed morality they want to impose through laws.
>>>>
>>> Then it is like rejecting the "object" of a theory, because we
>>> disagree with a theory.
>>> It is like concluding that earth does not exist, because some people
>>> said it to be flat.
>>> There are no reasons to do that (except bad habits).
>>>
>> When we disagree with the Earth being flat it is because we have a
>> better theory about the shape of the Earth.
>>
>
> Exactly.
>
>
>
>> If I disagree with the theory that human events are controlled by
>> immortal beings living on top of Mt. Olympus, should I still entertain
>> the proposition that immortal beings live on Mt. Olympus as a
>> reasonable
>> scientific hypothesis.
>>
>
>
> Of course not. I am not aware such theory explains anything new, or
> actually anything at all.
>
>
>
>
>
>> Am I a dishonest atheist because I don't believe
>> in Zeus?
>>
>
> No. But as an atheist, who *believes there is a no God", you may hurt
> the sensibility of someone who find the idea or concept deep and
> interesting and may be some theologies are less wrong than other ...
>
> And most atheists are doubly believers. They believe in the
> inexistence of God, but many believe in the existence of Matter (some
> primitive matter "explaining everything").
>
> A a scientist I am completely agonstic:
>
> I don't believe in God
> I don't believe in the inexistence of God
> I don't believe in Matter (primary one)
> I don't believe in the non existence of Matter.
>
> I do find plausible that whatever I am, I may be Turing emulable, and
> all I say is that in that case the overall picture is No Matter but
> some 'truth' about a universal "dreamer". This includes (by UDA) its
> physical realities.
> Is it so astonishing that digital mechanism could make eventually
> physics a branch of Theoretical Computer science?
>
>
>
>
>
>
>
>>>
>>>
>>>>> The word and concept God have been used in all culture and
>>>>> tradition,
>>>>> and refer to to some projection of our ignorance, close to the
>>>>> idea of
>>>>> infinite, or inconceivable, in-something.
>>>>> May be this is due to the fact that many got a christian
>>>>> education. I
>>>>> did not. For me "God" refer to the all transcendant and ineffable
>>>>> things described by mystics and rationalized by the thinker who are
>>>>> searching.
>>>>> Like I said, atheists and christians defend the same concept of
>>>>> God,
>>>>> the first to believe in its non-existence, the second to believe in
>>>>> its existence. Why does atheist choose the definition of those in
>>>>> which they does not believe the theory. It is like to say
>>>>> "genetics is
>>>>> crap" because of Lyssenko.
>>>>>
>>>>>
>>>>> The agnostic search without prejudice and with a critical eyes on
>>>>> any
>>>>> theory.
>>>>>
>>>> Does your eye ever become so critical as to reject a theory - not
>>>> reject
>>>> for sure, but for all practical purposes you consider it false?
>>>>
>>> Yes. One refutation is enough (in principle). The refutation can be
>>> internal, like when the theory is shown inconsistent, or external,
>>> when the theory is contradicted by some experiment.
>>> Or we can reject a theory because we don't like it, if we want. taste
>>> and esthetic features can play a role.
>>> Without contradiction, it is hard to conclude a theory is "false".
>>> With comp "true" and "false" are by themselves very complex and
>>> delicate notions, in need of theories.
>>>
>> Then to say you uncertain about the existence of God when speaking to
>> non-theologian Christians or Muslims or Mormons you are being a
>> dishonest agnostic.
>>
>
>
> I don't understand. Be them Mormons, Muslims, Christians , ...
> atheists or Taoist, I told them, oh, look, if you say believe you can
> survive with a digital brain/body, then reality is described by the
> relation between Numbers, and the theology is of the type "Plotino-
> Pytagorean. Do you see why? If not read or that paper. I am pretty
> sure that those whose faith comes from inside may recognize feature.
>
>
>
>
>
>
>> This can be a very convenient position for academics
>> in the U.S. where the funding of research may depend on politicians
>> who
>> are sensitive to the votes of believers.
>>
>
> You loss me.
>
>
>
>
>>>
>>>>>> You say you are agnostic on (primitive) matter; but you usually
>>>>>> claim
>>>>>> to have proven that matter doesn't exist, because to assume it
>>>>>> does
>>>>>> leads to contradiction.
>>>>>>
>>>>> Not at all. I am entirely agnostic about Matter.
>>>>> What I am pretty sure of is that Matter is incompatible with
>>>>> Digital
>>>>> Mechanism. I do believe that Comp entails Matter makes no sense.
>>>>>
>>>>> I am agnostic on Matter, because I am agnostic on Digital
>>>>> Mechanism.
>>>>> And then diabolically enough, I have too, because none correct
>>>>> machine
>>>>> can know for sure Digital Mechanism is true (even after surviving a
>>>>> classical teleportation).
>>>>>
>>>> If not knowing for sure makes one an agnostic then I'm an agnostic
>>>> on
>>>> everything. But that definition implies science is no better than
>>>> guessing and all opinions are equal.
>>>> I think we need to keep a
>>>> distinction between knowing for sure and knowing in the sense of
>>>> having
>>>> good evidence for.
>>>>
>>> Well you right, and I just have insisted on this on the FOR list. But
>>> yes, I do believe that a scientist never know for sure, and that he
>>> does not commit *any* definitive ontological commitment. All theories
>>> are hypothetical. But this does not mean that all theories are equal.
>>> Some theories takes more time to be refuted. Some theories are more
>>> fertile, and can be more interestingly false.
>>> A scientist can judge a theory much better than another, without
>>> saying "I believe it to be true". He will say "I believe it to be
>>> more
>>> plausible than some other theories. We have to take our theory
>>> seriously until we find a better theory.
>>>
>>>
>>>
>>>
>>>> Scientific theories are never proved. That doesn't mean we're
>>>> agnostic
>>>> about whether the Earth is flat or spheroidal.
>>>>
>>> We can judge that "spheroidal" is far more plausible, and useful,
>>> given our current knowledge, but we can hardly say that science has
>>> proved that the earth is spheroidal, or that earth really exists. In
>>> science there are just no proof about anything concerning reality.
>>> Only radical atheists (unlike atheists like Carolyn Porco) can
>>> pretend
>>> that science has proved anything.
>>>
>> Depends on what you mean by "proved". There is "proven in court",
>> "proven by experiment", and "proven in mathematics" - remember the
>> base
>> meaning of "proven" is "tested". I would say Porco is a radical
>> agnostic
>> - one who doesn't want to reject popular religious ideas no matter how
>> much the evidence is against them because we can always reinterpret
>> them
>> in a way that they *might* be true.
>>
>
>
> I meant "proved about reality". Science is neutral about reality.
> Now Gödel's and Lob's theorems illustrates that universal machine can
> study its own limitation, and bet some unprovable truth (sometimes
> instinctively/automatically).
>

Science is neutral in the sense that science doesn't care what reality
is, but science assumes that there is enough regularity in reality that
theories about it can be tested. The unprovable truths you refer to are
always relative to a particular set of axioms and rules of inference.
So unless you have some way to limit "reality" to that set of axioms and
rules of inference, the truths are not unprovable "in reality".

> But Brent, I am critical on all non serious theology. In the human and
> applied human science we are still nowhere.
>
> I am not sure that Carolyn Porco does not reject popular religious
> ideas, like myself.
> And I am not sure how she would react when understanding that
> Mechanism Digital entails everything emerge from the story, described
> in elementary arithmetic of a universal machine looking at itself.
> Thanks to the Gödel-Löb-Solovay split, such a theory describes the
> provable and the unprovable part of the machines and this from its
> many different person points of view.
>
>
>
>
>
>>> Certainty is not among the goal of science. The goal of science is
>>> the
>>> "quest" of the truth, but it is a /quest/. I could say that religion
>>> is the goal, and science the means.
>>>
>> But every religion claims to have the truth - by tradition, by
>> visions,
>> by revelation
>>
>
> I am afraid that with the comp assumption, "claiming to have the
> truth" is a blasphem.
> It is human nature.
> Lesson: if someone claims to have the truth, run away.
>
> Science = doubt.
> Fundamental science = fundamental doubt.
>

Religion = certain faith

>
>
>
>
>> - and makes a virtue of belief beyond or even contrary to
>> evidence. I agree with what you say about science, but I think you are
>> making up your own definition for religion.
>>
>
>
> Not really. It is the religion of the universal machine when she says
> "yes" to the doctor, at her risk and peril. Or it is the religion
> (truth) she can deduce from just imagining surviving such an experience.
>

That is what reminded me of the Bertrand Russell quotation - you seem
reluctant to give up the word "religion" while discarding the idea for
which it formerly stood: shared beliefs which were held on faith and
immune to experimental investigation which explain human origins,
purpose, and morals.

> It is a branch of math, and it is axiomatized by the modal logics G
> and G*, and its intensional variants.
>
>
>
>>> It is like opening our eyes and observing, and then trying to
>>> figure a
>>> mental coherent picture of what we see. But no one can prove that we
>>> have find the last correct picture. No one. neither the scientist,
>>> nor
>>> the priest.

But some prove their picture in the sense of testing it and discarding
or modifying it if it fails. That's the scientist. Others avoid
testing their picture and cling to it in spite of its failures Those
are the priests.

>>> Only politicians behave like that sometimes, and usually
>>> for opportunist reasons. There is nothing more modest than science.
>>> But by opposing science to (honest) religion, we tend to make science
>>> into a pseudo (authoritative) religion.
>>>
>> No, we emphasize the difference between provisional belief
>> proportioned
>> to evidence and unquestionable belief in authoritarian revelations.
>>
>
> But the evidence are that after 1500 years of materialist theology,
> the human science have make only one progress (democracy) and continue
> to make the fundamental question out of the scientific method of
> investigation, like if only physics was, by definition, the
> fundamental science. "Matter" has been a fertile methodology, but it
> fails to explain its origin, its link with mathematics, and then it
> fails on the consciousness/reality problem.
>

I agree that matter fails to explain its origin, but I think its link
with mathematics is explained. Mathematics is just precise expression
and inference to avoid contradiction. If physics tried to use just
words or images in its theories it could more easily fall into
self-contradiction. Mathematics, in relation to physics, is just a
means of precise and consistent description of a theory.

> Classical Mechanism, once taken seriously, shows that the 'rational,
> elegant, and conceptually simpler picture could be different. In the
> tiny Sigma_1 part of arithmetical truth lives an incredibly creative
> creature, which behaviors and discourses needs mathematics which
> extends far away arithmetical if not mathematical truth.
>
> A universal machine is a bomb,yet a creative one.
>
>
>
>
>>> I said in different forums that the divorce between science and
>>> religion is a symptom of schizophrenia. A human temporary (I hope)
>>> laps of insanity. Religion can only extends science. The Islamic
>>> al-Ghazali (eleven century) did already explains this in great
>>> detail.
>>>
>> The Abrahamic religions conflict with science because they teach that
>> there are miracles (scientifically inexplicable events with are
>> answers
>> to pious prayers). Science has tested this theory and found no
>> evidence
>> for it and so scientists don't believe it; it is proven false to a
>> standard higher than courtrooms but less than mathematical.
>>
>
>
> Give time to people to get the things less literally. If we come back
> to seriousness in theology, even you may agree on some non literal
> interpretation of some old text.
>
> By its very nature, the "God intuition" is perverted by any use of
> that idea.
> God or truth is the last thing which needs authoritative argument.
>

I think you mean "authoritarian argument". Yet that is the kind of
argument used by all religions: "God commands it." Although you want to
define religion as a kind of betting on the truth of some mathematically
unprovable propositions, religion also has a definition in sociology.
Loyal Rue has written a very good book about religion from this
viewpoint called "Religion is Not About God"

> Discussion in the evening, or silence, may convey something, but
> someone whose faith is grounded, I guess he will let God presents
> itself, or not, instead of any other argument.
>
> Or he will build a theory, take some "theological" assumption
> seriously, like comp.
>

If everyone took their theology seriously there would be very few
Christians or Muslims - and no fundamentalist theists at all.

>
>
>
>>
>>
>>> A religion which fear science can only be based on bad faith.
>>>
>> All the religions I know of claim that science supports their beliefs
>> (with "interpretation") - unfortunately their beliefs are mutually
>> contrary.
>>
>
> But this is due because some make science a religion. Science cannot
> support religion, science can only refute the wrong theologies. A
> theology which asserts that science support her, is deadly wrong at
> the start, unless the support is given through hypothesis and (new)
> predictions in the usual way.
>

You must be aware that the latest form of this is called Intelligent
Design, a line of argument supported by research grants from the
Discovery Insitute in Seattle. It is a resurrection of William Paley's
argument from design which says that the world is to structured and
functional to have arisen by natural processes and that this is evidence
that the world was designed and created by a super-being. This has
given rise to many hypotheses which however are all of the form "Natural
processes can't explain THIS!" with various biochemical and cellular
structures substituted for "THIS".

> We are not talking about some human superstitutions. We search a
> theory which explains the origin of the physical laws, and which does
> not eliminate the person, and explain consciousness, or explain why we
> cannot explain consciousness, ... what could happen when we die, and
> many fundamental things like that, by reasoning from hypotheses.
>
> And not everything is necessarily wrong in the popular theologies
> either.
>
Unfortunately. If they were wrong about everything we could just
suppose the opposite.

> Well except, probably (cf UDA), the popular belief (assuming
> mechanism) in Matter.
>

So you are an a-matterist after all. :-)

Brent

> Now, it is a meta-theorem that if Mechanism is true, I will remain
> forever undecided about it.
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
> --
>
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>
>
>

Re: Arguably The World's Greatest Woman

2009-11-14T16:08:11Z

On 14 Nov 2009, at 17:48, John Mikes wrote:

> Bruno,
>
> you navigate into perillous waters.

I know, but that is the fun. Life and everything interesting apperas
on the border of the non controlable.

> Your statements are extremely smart and applicable - to a certain
> limit, at which they vanish into undecidedness.

Yes, indeed.

> You chose arithmetic thinking as your anchor to firmness - it is
> your choice and it works for you.

It is a theorem that is does not change the general idea. I have tried
the combinators, but the advantage of numbers is that their are taught
already in high school, and also, the most know Löbian machine, Peano
Arithmetic, has indeed those high school beliefs has only beliefs. It
is more simpler, and its chnage nothing for the comp reasoning.

> It does not work for me: I am still in the undecidedness and
> whatever I want to grab dissipates upon touching.

We have to be in undecidedness for reason of self-consistency.

> I do not state to be an atheist, for - as you correctly pointed out
> - it would necessitate a 'god' to deny and I do not get to such
> definition. I claim to be a "scientific" agnostic, questioning
> whatever traceable to a human 'mind's' (?) understanding and its
> limitations (including numbers - cf: David Bohm).
> In my approach we are limited and can extend our thinking only
> within our limits. I try to do my best - knowing that it is not
> enough.

It is *never* enough, for any honest universal machine/entity.

>
> The developing human 'mind' (= mental capabilities altogether) went
> through stepwise enwidenment including the religious faith and your
> extension into a universalized 'god' idea etc. This is why I cringe
> when accepting ancient ideas - definitely in an earlier stage of our
> development - to be applied to our 'later stage' (I almost wrote:
> more advanced - assuming we IMPROVE).

Why? I think that when we discover an error in a theory, or in case of
repeated failures, we may have to backtrack.

>
> I climb on the shoulders of giant oldies - not to see exactly as far
> as they do, but further.

Sometimes progress can blind you on older simpler ideas which suddenly
can get new interpretation. plotinus lacked the universal machine/
number, but was close (in its chapter on numbers).

> What do I see? something unexplainable - beyond my limitations.

OK.

> And definitely beyond the horizon of those whose shoulders I climbed
> onto.

You can't know that.

> What does not mean that I am smarter. I just have a vision I don't
> understand.

OK, but they may not understand too. Most mystics insists they don't
understand.

>
> I enjoyed your post - thank you - and warn you: going all the way
> may lead you into deep agnosticism and you may lose the grip on the
> assumed 'reality' that you are holding on today. I can afford it at
> my age, but you have work to do in a world that does not appreciate
> in science the "I DON'T KNOW" position.

I think people like David Deutsch, and many others agree that science
is the "don't know" per excellence. We try to make clear some beliefs
and pictures and to see the consequences. But I know some does not yet
know that (that science = doubt).

Kind regards,

Bruno

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

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Re: Arguably The World's Greatest Woman

2009-11-14T15:45:58Z

On 14 Nov 2009, at 22:33, Brent Meeker wrote:

> Bruno Marchal wrote:
>>
>> On 14 Nov 2009, at 01:33, Brent Meeker wrote:
>>
>>>> Why should we use the term "God" in the sense of those who clearly
>>>> have confused science with temporal authoritative argument?
>>>
>>> Because that's what most people who use the term mean. And if we
>>> tell
>>> them we're agnostic about God
>>
>> Who them? Which Christians? There are many Christian theologians who
>> have reasonable (with respect to comp, or to the scientific attitude)
>> conception of God.
> Many being a few thousand? But there are billions of Christians who
> are
> *not* theologians and a large fraction of them (at least in the U.S.)
> use their votes and money to make Christian dogma public policy.

Yes, but if you use science 'against" them, you make science a pseudo-
religion, and you give them more braids. If we don't get back to
'serious" (meaning hypothetical) theology, pseudo-religion will
continue.

Even if you take the 'theology' of the universal machine as a toy
theology, it is remarkable how it explains the difference between
science and theology. Science is *the* tool of those whose faith is
not based on rumors.

>
>> The difference between some american and european christians can be
>> bigger than the difference between european atheists.
>> But once we know some group does not argue, but use authoritatively
>> some dogma, anyone with a scientific attitude should use its usual
>> critical mind.
>>
>>
>>
>>> we will be telling them that we have no
>>> good reason not to believe in their sky father and hence no good
>>> reason
>>> to resist the revealed morality they want to impose through laws.
>>
>> Then it is like rejecting the "object" of a theory, because we
>> disagree with a theory.
>> It is like concluding that earth does not exist, because some people
>> said it to be flat.
>> There are no reasons to do that (except bad habits).
> When we disagree with the Earth being flat it is because we have a
> better theory about the shape of the Earth.

Exactly.

> If I disagree with the theory that human events are controlled by
> immortal beings living on top of Mt. Olympus, should I still entertain
> the proposition that immortal beings live on Mt. Olympus as a
> reasonable
> scientific hypothesis.

Of course not. I am not aware such theory explains anything new, or
actually anything at all.

> Am I a dishonest atheist because I don't believe
> in Zeus?

No. But as an atheist, who *believes there is a no God", you may hurt
the sensibility of someone who find the idea or concept deep and
interesting and may be some theologies are less wrong than other ...

And most atheists are doubly believers. They believe in the
inexistence of God, but many believe in the existence of Matter (some
primitive matter "explaining everything").

A a scientist I am completely agonstic:

I don't believe in God
I don't believe in the inexistence of God
I don't believe in Matter (primary one)
I don't believe in the non existence of Matter.

I do find plausible that whatever I am, I may be Turing emulable, and
all I say is that in that case the overall picture is No Matter but
some 'truth' about a universal "dreamer". This includes (by UDA) its
physical realities.
Is it so astonishing that digital mechanism could make eventually
physics a branch of Theoretical Computer science?

>>
>>
>>
>>>
>>>> The word and concept God have been used in all culture and
>>>> tradition,
>>>> and refer to to some projection of our ignorance, close to the
>>>> idea of
>>>> infinite, or inconceivable, in-something.
>>>> May be this is due to the fact that many got a christian
>>>> education. I
>>>> did not. For me "God" refer to the all transcendant and ineffable
>>>> things described by mystics and rationalized by the thinker who are
>>>> searching.
>>>> Like I said, atheists and christians defend the same concept of
>>>> God,
>>>> the first to believe in its non-existence, the second to believe in
>>>> its existence. Why does atheist choose the definition of those in
>>>> which they does not believe the theory. It is like to say
>>>> "genetics is
>>>> crap" because of Lyssenko.
>>>>
>>>>
>>>> The agnostic search without prejudice and with a critical eyes on
>>>> any
>>>> theory.
>>> Does your eye ever become so critical as to reject a theory - not
>>> reject
>>> for sure, but for all practical purposes you consider it false?
>>
>>
>> Yes. One refutation is enough (in principle). The refutation can be
>> internal, like when the theory is shown inconsistent, or external,
>> when the theory is contradicted by some experiment.
>> Or we can reject a theory because we don't like it, if we want. taste
>> and esthetic features can play a role.
>> Without contradiction, it is hard to conclude a theory is "false".
>> With comp "true" and "false" are by themselves very complex and
>> delicate notions, in need of theories.
>
> Then to say you uncertain about the existence of God when speaking to
> non-theologian Christians or Muslims or Mormons you are being a
> dishonest agnostic.

I don't understand. Be them Mormons, Muslims, Christians , ...
atheists or Taoist, I told them, oh, look, if you say believe you can
survive with a digital brain/body, then reality is described by the
relation between Numbers, and the theology is of the type "Plotino-
Pytagorean. Do you see why? If not read or that paper. I am pretty
sure that those whose faith comes from inside may recognize feature.

> This can be a very convenient position for academics
> in the U.S. where the funding of research may depend on politicians
> who
> are sensitive to the votes of believers.

You loss me.

>>
>>
>>>>> You say you are agnostic on (primitive) matter; but you usually
>>>>> claim
>>>>> to have proven that matter doesn't exist, because to assume it
>>>>> does
>>>>> leads to contradiction.
>>>>
>>>>
>>>> Not at all. I am entirely agnostic about Matter.
>>>> What I am pretty sure of is that Matter is incompatible with
>>>> Digital
>>>> Mechanism. I do believe that Comp entails Matter makes no sense.
>>>>
>>>> I am agnostic on Matter, because I am agnostic on Digital
>>>> Mechanism.
>>>> And then diabolically enough, I have too, because none correct
>>>> machine
>>>> can know for sure Digital Mechanism is true (even after surviving a
>>>> classical teleportation).
>>>
>>> If not knowing for sure makes one an agnostic then I'm an agnostic
>>> on
>>> everything. But that definition implies science is no better than
>>> guessing and all opinions are equal.
>>> I think we need to keep a
>>> distinction between knowing for sure and knowing in the sense of
>>> having
>>> good evidence for.
>>
>>
>> Well you right, and I just have insisted on this on the FOR list. But
>> yes, I do believe that a scientist never know for sure, and that he
>> does not commit *any* definitive ontological commitment. All theories
>> are hypothetical. But this does not mean that all theories are equal.
>> Some theories takes more time to be refuted. Some theories are more
>> fertile, and can be more interestingly false.
>> A scientist can judge a theory much better than another, without
>> saying "I believe it to be true". He will say "I believe it to be
>> more
>> plausible than some other theories. We have to take our theory
>> seriously until we find a better theory.
>>
>>
>>
>>>
>>> Scientific theories are never proved. That doesn't mean we're
>>> agnostic
>>> about whether the Earth is flat or spheroidal.
>>
>> We can judge that "spheroidal" is far more plausible, and useful,
>> given our current knowledge, but we can hardly say that science has
>> proved that the earth is spheroidal, or that earth really exists. In
>> science there are just no proof about anything concerning reality.
>> Only radical atheists (unlike atheists like Carolyn Porco) can
>> pretend
>> that science has proved anything.
> Depends on what you mean by "proved". There is "proven in court",
> "proven by experiment", and "proven in mathematics" - remember the
> base
> meaning of "proven" is "tested". I would say Porco is a radical
> agnostic
> - one who doesn't want to reject popular religious ideas no matter how
> much the evidence is against them because we can always reinterpret
> them
> in a way that they *might* be true.

I meant "proved about reality". Science is neutral about reality.
Now Gödel's and Lob's theorems illustrates that universal machine can
study its own limitation, and bet some unprovable truth (sometimes
instinctively/automatically).

But Brent, I am critical on all non serious theology. In the human and
applied human science we are still nowhere.

I am not sure that Carolyn Porco does not reject popular religious
ideas, like myself.
And I am not sure how she would react when understanding that
Mechanism Digital entails everything emerge from the story, described
in elementary arithmetic of a universal machine looking at itself.
Thanks to the Gödel-Löb-Solovay split, such a theory describes the
provable and the unprovable part of the machines and this from its
many different person points of view.

>
>> Certainty is not among the goal of science. The goal of science is
>> the
>> "quest" of the truth, but it is a /quest/. I could say that religion
>> is the goal, and science the means.
> But every religion claims to have the truth - by tradition, by
> visions,
> by revelation

I am afraid that with the comp assumption, "claiming to have the
truth" is a blasphem.
It is human nature.
Lesson: if someone claims to have the truth, run away.

Science = doubt.
Fundamental science = fundamental doubt.

> - and makes a virtue of belief beyond or even contrary to
> evidence. I agree with what you say about science, but I think you are
> making up your own definition for religion.

Not really. It is the religion of the universal machine when she says
"yes" to the doctor, at her risk and peril. Or it is the religion
(truth) she can deduce from just imagining surviving such an experience.

It is a branch of math, and it is axiomatized by the modal logics G
and G*, and its intensional variants.

>
>> It is like opening our eyes and observing, and then trying to
>> figure a
>> mental coherent picture of what we see. But no one can prove that we
>> have find the last correct picture. No one. neither the scientist,
>> nor
>> the priest. Only politicians behave like that sometimes, and usually
>> for opportunist reasons. There is nothing more modest than science.
>> But by opposing science to (honest) religion, we tend to make science
>> into a pseudo (authoritative) religion.
>
> No, we emphasize the difference between provisional belief
> proportioned
> to evidence and unquestionable belief in authoritarian revelations.

But the evidence are that after 1500 years of materialist theology,
the human science have make only one progress (democracy) and continue
to make the fundamental question out of the scientific method of
investigation, like if only physics was, by definition, the
fundamental science. "Matter" has been a fertile methodology, but it
fails to explain its origin, its link with mathematics, and then it
fails on the consciousness/reality problem.
Classical Mechanism, once taken seriously, shows that the 'rational,
elegant, and conceptually simpler picture could be different. In the
tiny Sigma_1 part of arithmetical truth lives an incredibly creative
creature, which behaviors and discourses needs mathematics which
extends far away arithmetical if not mathematical truth.

A universal machine is a bomb,yet a creative one.

>>
>> I said in different forums that the divorce between science and
>> religion is a symptom of schizophrenia. A human temporary (I hope)
>> laps of insanity. Religion can only extends science. The Islamic
>> al-Ghazali (eleven century) did already explains this in great
>> detail.
>
> The Abrahamic religions conflict with science because they teach that
> there are miracles (scientifically inexplicable events with are
> answers
> to pious prayers). Science has tested this theory and found no
> evidence
> for it and so scientists don't believe it; it is proven false to a
> standard higher than courtrooms but less than mathematical.

Give time to people to get the things less literally. If we come back
to seriousness in theology, even you may agree on some non literal
interpretation of some old text.

By its very nature, the "God intuition" is perverted by any use of
that idea.
God or truth is the last thing which needs authoritative argument.
Discussion in the evening, or silence, may convey something, but
someone whose faith is grounded, I guess he will let God presents
itself, or not, instead of any other argument.

Or he will build a theory, take some "theological" assumption
seriously, like comp.

>
>
>
>> A religion which fear science can only be based on bad faith.
> All the religions I know of claim that science supports their beliefs
> (with "interpretation") - unfortunately their beliefs are mutually
> contrary.

But this is due because some make science a religion. Science cannot
support religion, science can only refute the wrong theologies. A
theology which asserts that science support her, is deadly wrong at
the start, unless the support is given through hypothesis and (new)
predictions in the usual way.

We are not talking about some human superstitutions. We search a
theory which explains the origin of the physical laws, and which does
not eliminate the person, and explain consciousness, or explain why we
cannot explain consciousness, ... what could happen when we die, and
many fundamental things like that, by reasoning from hypotheses.

And not everything is necessarily wrong in the popular theologies
either.
Well except, probably (cf UDA), the popular belief (assuming
mechanism) in Matter.

Now, it is a meta-theorem that if Mechanism is true, I will remain
forever undecided about it.

Bruno

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

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Re: Arguably The World's Greatest Woman

2009-11-14T13:33:18Z

Bruno Marchal wrote:

>
> On 14 Nov 2009, at 01:33, Brent Meeker wrote:
>
>>> Why should we use the term "God" in the sense of those who clearly
>>> have confused science with temporal authoritative argument?
>>
>> Because that's what most people who use the term mean. And if we tell
>> them we're agnostic about God
>
> Who them? Which Christians? There are many Christian theologians who
> have reasonable (with respect to comp, or to the scientific attitude)
> conception of God.

Many being a few thousand? But there are billions of Christians who are
*not* theologians and a large fraction of them (at least in the U.S.)
use their votes and money to make Christian dogma public policy.

> The difference between some american and european christians can be
> bigger than the difference between european atheists.
> But once we know some group does not argue, but use authoritatively
> some dogma, anyone with a scientific attitude should use its usual
> critical mind.
>
>
>
>> we will be telling them that we have no
>> good reason not to believe in their sky father and hence no good reason
>> to resist the revealed morality they want to impose through laws.
>
> Then it is like rejecting the "object" of a theory, because we
> disagree with a theory.
> It is like concluding that earth does not exist, because some people
> said it to be flat.
> There are no reasons to do that (except bad habits).

When we disagree with the Earth being flat it is because we have a
better theory about the shape of the Earth.
If I disagree with the theory that human events are controlled by
immortal beings living on top of Mt. Olympus, should I still entertain
the proposition that immortal beings live on Mt. Olympus as a reasonable
scientific hypothesis. Am I a dishonest atheist because I don't believe
in Zeus?

>
>
>
>>
>>> The word and concept God have been used in all culture and tradition,
>>> and refer to to some projection of our ignorance, close to the idea of
>>> infinite, or inconceivable, in-something.
>>> May be this is due to the fact that many got a christian education. I
>>> did not. For me "God" refer to the all transcendant and ineffable
>>> things described by mystics and rationalized by the thinker who are
>>> searching.
>>> Like I said, atheists and christians defend the same concept of God,
>>> the first to believe in its non-existence, the second to believe in
>>> its existence. Why does atheist choose the definition of those in
>>> which they does not believe the theory. It is like to say "genetics is
>>> crap" because of Lyssenko.
>>>
>>>
>>> The agnostic search without prejudice and with a critical eyes on any
>>> theory.
>> Does your eye ever become so critical as to reject a theory - not reject
>> for sure, but for all practical purposes you consider it false?
>
>
> Yes. One refutation is enough (in principle). The refutation can be
> internal, like when the theory is shown inconsistent, or external,
> when the theory is contradicted by some experiment.
> Or we can reject a theory because we don't like it, if we want. taste
> and esthetic features can play a role.
> Without contradiction, it is hard to conclude a theory is "false".
> With comp "true" and "false" are by themselves very complex and
> delicate notions, in need of theories.

Then to say you uncertain about the existence of God when speaking to
non-theologian Christians or Muslims or Mormons you are being a
dishonest agnostic. This can be a very convenient position for academics
in the U.S. where the funding of research may depend on politicians who
are sensitive to the votes of believers.

>
>
>>>> You say you are agnostic on (primitive) matter; but you usually claim
>>>> to have proven that matter doesn't exist, because to assume it does
>>>> leads to contradiction.
>>>
>>>
>>> Not at all. I am entirely agnostic about Matter.
>>> What I am pretty sure of is that Matter is incompatible with Digital
>>> Mechanism. I do believe that Comp entails Matter makes no sense.
>>>
>>> I am agnostic on Matter, because I am agnostic on Digital Mechanism.
>>> And then diabolically enough, I have too, because none correct machine
>>> can know for sure Digital Mechanism is true (even after surviving a
>>> classical teleportation).
>>
>> If not knowing for sure makes one an agnostic then I'm an agnostic on
>> everything. But that definition implies science is no better than
>> guessing and all opinions are equal.
>> I think we need to keep a
>> distinction between knowing for sure and knowing in the sense of having
>> good evidence for.
>
>
> Well you right, and I just have insisted on this on the FOR list. But
> yes, I do believe that a scientist never know for sure, and that he
> does not commit *any* definitive ontological commitment. All theories
> are hypothetical. But this does not mean that all theories are equal.
> Some theories takes more time to be refuted. Some theories are more
> fertile, and can be more interestingly false.
> A scientist can judge a theory much better than another, without
> saying "I believe it to be true". He will say "I believe it to be more
> plausible than some other theories. We have to take our theory
> seriously until we find a better theory.
>
>
>
>>
>> Scientific theories are never proved. That doesn't mean we're agnostic
>> about whether the Earth is flat or spheroidal.
>
> We can judge that "spheroidal" is far more plausible, and useful,
> given our current knowledge, but we can hardly say that science has
> proved that the earth is spheroidal, or that earth really exists. In
> science there are just no proof about anything concerning reality.
> Only radical atheists (unlike atheists like Carolyn Porco) can pretend
> that science has proved anything.

Depends on what you mean by "proved". There is "proven in court",
"proven by experiment", and "proven in mathematics" - remember the base
meaning of "proven" is "tested". I would say Porco is a radical agnostic
- one who doesn't want to reject popular religious ideas no matter how
much the evidence is against them because we can always reinterpret them
in a way that they *might* be true.

> Certainty is not among the goal of science. The goal of science is the
> "quest" of the truth, but it is a /quest/. I could say that religion
> is the goal, and science the means.
But every religion claims to have the truth - by tradition, by visions,
by revelation - and makes a virtue of belief beyond or even contrary to
evidence. I agree with what you say about science, but I think you are
making up your own definition for religion.

> It is like opening our eyes and observing, and then trying to figure a
> mental coherent picture of what we see. But no one can prove that we
> have find the last correct picture. No one. neither the scientist, nor
> the priest. Only politicians behave like that sometimes, and usually
> for opportunist reasons. There is nothing more modest than science.
> But by opposing science to (honest) religion, we tend to make science
> into a pseudo (authoritative) religion.

No, we emphasize the difference between provisional belief proportioned
to evidence and unquestionable belief in authoritarian revelations.
>
> I said in different forums that the divorce between science and
> religion is a symptom of schizophrenia. A human temporary (I hope)
> laps of insanity. Religion can only extends science. The Islamic
> al-Ghazali (eleven century) did already explains this in great detail.

The Abrahamic religions conflict with science because they teach that
there are miracles (scientifically inexplicable events with are answers
to pious prayers). Science has tested this theory and found no evidence
for it and so scientists don't believe it; it is proven false to a
standard higher than courtrooms but less than mathematical.

> A religion which fear science can only be based on bad faith.
All the religions I know of claim that science supports their beliefs
(with "interpretation") - unfortunately their beliefs are mutually contrary.

Brent
“People are more unwilling to give up the word ‘God’ than to give up the
idea for which the word has hitherto stood”
--- Bertrand Russell

> A religion which fear the spirit of free research and free exam can
> only rely on lies and dishonest way to keep power. Some atheist today
> (in Europa) are acting like that, because they want to hide that
> atheism is a religion, actually a typically Aristotelian (easily
> anti-platonist) religion.
>
> As scientist we don't know, but can study and test different theories.
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
>
>
>
> --
>
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> Groups "Everything List" group.
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Re: Arguably The World's Greatest Woman

2009-11-14T08:48:04Z

Bruno,

you navigate into perillous waters. Your statements are extremely smart and applicable - to a certain limit, at which they vanish into undecidedness. You chose arithmetic thinking as your anchor to firmness - it is your choice and it works for you. It does not work for me: I am still in the undecidedness and whatever I want to grab dissipates upon touching.

I do not state to be an atheist, for - as you correctly pointed out - it would necessitate a 'god' to deny and I do not get to such definition. I claim to be a "scientific" agnostic, questioning whatever traceable to a human 'mind's' (?) understanding and its limitations (including numbers - cf: David Bohm).

In my approach we are limited and can extend our thinking only within our limits. I try to do my best - knowing that it is not enough.

The developing human 'mind' (= mental capabilities altogether) went through stepwise enwidenment including the religious faith and your extension into a universalized 'god' idea etc. This is why I cringe when accepting ancient ideas - definitely in an earlier stage of our development - to be applied to our 'later stage' (I almost wrote: more advanced - assuming we IMPROVE).

I climb on the shoulders of giant oldies - not to see exactly as far as they do, but further. What do I see? something unexplainable - beyond my limitations.

And definitely beyond the horizon of those whose shoulders I climbed onto.

What does not mean that I am smarter. I just have a vision I don't understand.

I enjoyed your post - thank you - and warn you: going all the way may lead you into deep agnosticism and you may lose the grip on the assumed 'reality' that you are holding on today. I can afford it at my age, but you have work to do in a world that does not appreciate in science the "I DON'T KNOW" position.

Best regards

John Mikes

On Fri, Nov 13, 2009 at 12:44 PM, Bruno Marchal <marchal@...> wrote:

Hi Kim,

Thank you very luch for the link to Carolyn Porco's presentation. Very nice talk. I appreciate a lot.

She is correct (even comp-correct) on the main thing: Science is agnostic.

"I believe in God" (Bg) is a religious statement. (B = I believe, g = 'God' exists", "~" = negation)

But B~g, the athesist statement, is a religious statement too. Atheism is a religion. (and doubly so for the materialist atheists).

Crazily enough, I note she shows this in the exact manner of the introductory chapter of "Conscience et Mécanisme"). So honest atheists exists.

Not so sure why she said she believes (religiously) in the non existence of God, without saying what she means by the word, especially that later she talk of science as the "quest for the truth", but with comp the mathematical notion of truth (relative to a machine and relative to the possible machine views) obeys literally to the notion of "God" in the Greek Theology of Plato (according to my own understanding of Plato, but confirmed by Plotinus and Hirschberger).

Mainly 'God' = the transcendent human-ineffable truth we are invited to search/explore/contemplate.

Making "Science", the quest of the truth, like Carrolyn Porko did (two times, at the two third of that video), is the basic axiom of Plato's theology. It makes science and reason (and mathematics, and music, ...) the most basic tools in the search of the admittedly religious (by science modesty!) truth.

* * *

Let me give you 3, (3! yes there is one more!) basic reasons to consider "Digital Mechanism" as a theology (actually a framework for variate theologies (Mechanism will not stop all possible religious conflicts, on the contrary given the existence of very different possible practices, like overlapping or not with the duplicate ... ).

- 1) To say "yes" to the doctor, even if some oracle guaranties the competence of the doctor and the accuracy of the comp substitution level, etc, is an irreductible act of faith in the possibility of a (relative) digital reincarnation.

- 2) It is a "scientific theology" in the following precise sense: To each machine, or machine's state, (or machine relative description) we associate the set of true arithmetical sentences concerning that machine (described in arithmetic, say). Roughly speaking:

Science = provability

Religion = truth (in the spirit, I am humble and modest, and I search)

Then, not only a universal machine can introspect itself and discover the gap between truth and provability. It can not only discover the unnameability of its own truth notion, but a very rich (in term of provability power) machine (like ZF) can study a big (not all) part of the theology of a more simpler Löbian machine, like Peano-Arithmetic. So although a machine cannot know that she is correct, she can lift the "invariant" theology of simpler lobian machine. Of course she cannot assert she has proved those statement, but she can assert that those are probably true as far as she is "correct", and comp is correct.

But there is a third reason.

-3) Church thesis. Also called Church Turing Thesis, and which I call sometimes Post law, or Gödel Miracle, or Post, Church, Turing, Markov thesis. Its truth entails the truth of the weaker thesis according to which there exists a universal machine. But do we know that? can we know that?

Do we know if there is a universal language, or a universal machine?

No one can prove that, of course. So here too you need to do a bet: an axiom, a thesis, an hypothesis. The miracle (Gödel) is that the set of partial computable functions is closed for the diagonalization, it cannot be transcended. As Gödel said, for the first time we get a mathematical definition of an epistemological concept. Gödel did hope that a similar thesis could exists for the notion of provability, but its own theorem, together with Church thesis prevents this (I think).

And then all attempts to define the computable functions leaded to the same class of partial computable functions. We get all the (total) computable functions, but they have to be situated in a non computable sequences among all the partial functions, as shown by Kleene's diagonalization (as shown in the last "seventh step serie thread", but I guess I have to come back on this). I recall that a total function is a partial function with subdomain equal to the whole N (N is included in N).

So comp, by Church thesis, is also a positive belief in a universal machine, despite the lack of proof of existence).

Of course Turing *did* prove its famous theorem saying that A Universal Turing machine exists. It is a theorem (even of arithmetic) that universal TURING machine exists, and that universal CHURCH lambda expression exists, and that universal SHOENFINKEL-CURRY combinators exists, etc.

For each universal language it can be shown a universal finite entity exists. But this does not prove that there is a universal machine for all computable functions, only that all those class have a relative universal entity. I mean Turing's theorem is not Turing's thesis. But Turing (Church)' thesis makes its universal machine "really" universal (with respect to digital computability).

What can arithmetic still prove is that TURING system, and CHURCH, one, and algol, fortran, lisp, etc. are all equivalent, making the universal TURING (or Church, ...) machine universal for all of CHURCH lambda expression, etc. They are all provably equivalent.

Now to prevent any misinterpretation, let us address the question:

Is the universal machine God?

I would say no. Sometimes I like to call it the baby god, though. In the arithmetical interpretation of the hypostasis the universal machine, once she knows that she is universal, (in a weak technical sense) can play the role of Plotinus' man, or discursive terrestrial intellect. It is man, not God. man means humans.

Universal machine are always finite entities, and exists always relatively to many other Universal machines (even if you can define the whole set of relations into arithmetic, or combinators, quantum topologies, ...).

I may refresh the arithmetical hypostases (cf AUDA). I limit myself to correct machines (they prove only correct arithmetical sentences, by definition). So when the machine says "p", it means that "p" is true. By Tarski theorem, it is the only way to say that "p is true". She just say p. So by "p" below, I mean the assertative proposition by the (correct) machine.

Plotinus one = arithmetical truth = p.

Plotinus divine Intellect (or intelligible) = Bp (Gödel's arithmetical "BEWEISBAR" provability predicate). But by incompleteness that INTELLECT admit an effective part borrowed by the machine: it is Plotinus' man.

That is, here, the INTELLECT splits into the true Intellect and the provable intellect. By Solovay theorem those two logics are axiomatised (at the propositional level) completely by G for the provable (by the machine) part, and by G* for the true but unprovable (by the machine) part. For exemple ~Bf (I will not assert a falsity) belongs to G* \ G. It is true, but not provable, by the correct machine.

Plotinus "universal soul" is the Theaetetical first person. It is the logic of the knower "inside the machine". It is given by the logic of the conjunction of Bp and p: Bp & p. It obeys, and is characterized by the modal logic S4Grz. Amazingly, it is not splitted by the incompleteness phenomenon= S4Grz = S4Grz*.

Then intelligible matter and sensible matter logics are given by the logic Bp & Dt, and Bp & p & Dt. respectfully. They both split by the Solovay "*" incompleteness results.

Plotinus admit at least this very precise arithmetical interpretation, and shows how incompleteness and insolubility structures the ignorance space of the (universal) machine.

Seen from inside, that space is *very* big, but incredibly richly structured, and the physical world, if the neoplatonist are correct, or if comp is correct, is given by the "mathematical bord of that ignorance space.

This is a verifiable (refutable) statement, making machine's theologies testable. Note that all correct Lobian machine (or even non machine, but still self-referentially correct entity) have the same abstract propositional theology (given by G and G* and their intensional variant).

***

Kim, thanks. I think I will send your Carolyn Porco's link to the salvia forum where discussion on atheism appears a lot. I was just abou trying to,explain the problem with *some* atheists.

Probably in the thread "Atheists, be nice!".

http://www.entheogen.com/forum/showthread.php?t=25489

(my username is "salvialover24", well sorry for that ...)

It will help me to explain that there is no problem with atheists, only with dishonest atheists (saying that atheism is not a religion, that science is on their side, etc.).

Of course, as a scientist, I am agnostic on ALL the Aristotelian Gods. This includes Matter (primitive matter).

Bruno

On 13 Nov 2009, at 12:17, Kim Jones wrote:

http://c0116791.cdn.cloudfiles.rackspacecloud.com/Carolyn-AAI09-720-web.mov

Carolyn Porco - the genius behind the Cassini mission. My favourite
female on the planet.

If you ever read Carl Sagan's only novel "Contact" (or saw the movie)
- this is the person on whom Sagan modelled Ellie Arroway (Jodie
Foster in the film)

Introduction by Richard Dawkins

cheers,

Kim Jones

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Re: Arguably The World's Greatest Woman

2009-11-14T01:20:54Z

On 14 Nov 2009, at 01:33, Brent Meeker wrote:

Why should we use the term "God" in the sense of those who clearly
have confused science with temporal authoritative argument?

Because that's what most people who use the term mean. And if we tell
them we're agnostic about God

Who them? Which Christians? There are many Christian theologians who have reasonable (with respect to comp, or to the scientific attitude) conception of God. The difference between some american and european christians can be bigger than the difference between european atheists.

But once we know some group does not argue, but use authoritatively some dogma, anyone with a scientific attitude should use its usual critical mind.

we will be telling them that we have no
good reason not to believe in their sky father and hence no good reason
to resist the revealed morality they want to impose through laws.

Then it is like rejecting the "object" of a theory, because we disagree with a theory.

It is like concluding that earth does not exist, because some people said it to be flat.

There are no reasons to do that (except bad habits).

The word and concept God have been used in all culture and tradition,
and refer to to some projection of our ignorance, close to the idea of
infinite, or inconceivable, in-something.
May be this is due to the fact that many got a christian education. I
did not. For me "God" refer to the all transcendant and ineffable
things described by mystics and rationalized by the thinker who are
searching.
Like I said, atheists and christians defend the same concept of God,
the first to believe in its non-existence, the second to believe in
its existence. Why does atheist choose the definition of those in
which they does not believe the theory. It is like to say "genetics is
crap" because of Lyssenko.

The agnostic search without prejudice and with a critical eyes on any
theory.
Does your eye ever become so critical as to reject a theory - not reject
for sure, but for all practical purposes you consider it false?

Yes. One refutation is enough (in principle). The refutation can be internal, like when the theory is shown inconsistent, or external, when the theory is contradicted by some experiment.

Or we can reject a theory because we don't like it, if we want. taste and esthetic features can play a role.

Without contradiction, it is hard to conclude a theory is "false".

With comp "true" and "false" are by themselves very complex and delicate notions, in need of theories.

You say you are agnostic on (primitive) matter; but you usually claim
to have proven that matter doesn't exist, because to assume it does
leads to contradiction.

Not at all. I am entirely agnostic about Matter.
What I am pretty sure of is that Matter is incompatible with Digital
Mechanism. I do believe that Comp entails Matter makes no sense.

I am agnostic on Matter, because I am agnostic on Digital Mechanism.
And then diabolically enough, I have too, because none correct machine
can know for sure Digital Mechanism is true (even after surviving a
classical teleportation).

If not knowing for sure makes one an agnostic then I'm an agnostic on
everything. But that definition implies science is no better than
guessing and all opinions are equal.

I think we need to keep a
distinction between knowing for sure and knowing in the sense of having
good evidence for.

Well you right, and I just have insisted on this on the FOR list. But yes, I do believe that a scientist never know for sure, and that he does not commit *any* definitive ontological commitment. All theories are hypothetical. But this does not mean that all theories are equal. Some theories takes more time to be refuted. Some theories are more fertile, and can be more interestingly false.

A scientist can judge a theory much better than another, without saying "I believe it to be true". He will say "I believe it to be more plausible than some other theories. We have to take our theory seriously until we find a better theory.

Scientific theories are never proved. That doesn't mean we're agnostic
about whether the Earth is flat or spheroidal.

We can judge that "spheroidal" is far more plausible, and useful, given our current knowledge, but we can hardly say that science has proved that the earth is spheroidal, or that earth really exists. In science there are just no proof about anything concerning reality. Only radical atheists (unlike atheists like Carolyn Porco) can pretend that science has proved anything. Certainty is not among the goal of science. The goal of science is the "quest" of the truth, but it is a quest. I could say that religion is the goal, and science the means. It is like opening our eyes and observing, and then trying to figure a mental coherent picture of what we see. But no one can prove that we have find the last correct picture. No one. neither the scientist, nor the priest. Only politicians behave like that sometimes, and usually for opportunist reasons. There is nothing more modest than science. But by opposing science to (honest) religion, we tend to make science into a pseudo (authoritative) religion.

I said in different forums that the divorce between science and religion is a symptom of schizophrenia. A human temporary (I hope) laps of insanity. Religion can only extends science. The Islamic al-Ghazali (eleven century) did already explains this in great detail. A religion which fear science can only be based on bad faith. A religion which fear the spirit of free research and free exam can only rely on lies and dishonest way to keep power. Some atheist today (in Europa) are acting like that, because they want to hide that atheism is a religion, actually a typically Aristotelian (easily anti-platonist) religion.

As scientist we don't know, but can study and test different theories.

Bruno

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

Re: Arguably The World's Greatest Woman

2009-11-13T16:33:53Z

Bruno Marchal wrote:

>
> On 13 Nov 2009, at 21:01, Brent Meeker wrote:
>>>
>>
>> I used to tell people who asked that I was an agnostic. But the
>> trouble with that was that they supposed I was uncertain about the
>> existence of *their* god: a supernatural immortal agent would loved
>> us but had an obsessive interest in our sex lives. So now I
>> generally tell people I'm an atheist, unless I think they are
>> interested in a philosophical answer, because I don't believe what
>> theists believe. So atheism is not a religion, it is a failure to
>> believe in the theist gods - those gods that are agents, omnipotent,
>> omniscient, and ominibenevolent. Thinking that such a god is does
>> not exist is a scientific theory, i.e. one supported by the evidence
>> and not contradicted by any credible evidence. I know you adopt a
>> very abstract and mathematical meaning for "theism", but we don't get
>> to define the meaning of words any more than I got to define "agnostic".
>
>
> Why should we use the term "God" in the sense of those who clearly
> have confused science with temporal authoritative argument?

Because that's what most people who use the term mean. And if we tell
them we're agnostic about God we will be telling them that we have no
good reason not to believe in their sky father and hence no good reason
to resist the revealed morality they want to impose through laws.

> The word and concept God have been used in all culture and tradition,
> and refer to to some projection of our ignorance, close to the idea of
> infinite, or inconceivable, in-something.
> May be this is due to the fact that many got a christian education. I
> did not. For me "God" refer to the all transcendant and ineffable
> things described by mystics and rationalized by the thinker who are
> searching.
> Like I said, atheists and christians defend the same concept of God,
> the first to believe in its non-existence, the second to believe in
> its existence. Why does atheist choose the definition of those in
> which they does not believe the theory. It is like to say "genetics is
> crap" because of Lyssenko.
>
>
> The agnostic search without prejudice and with a critical eyes on any
> theory.

Does your eye ever become so critical as to reject a theory - not reject
for sure, but for all practical purposes you consider it false?

>
>
>>
>> You say you are agnostic on (primitive) matter; but you usually claim
>> to have proven that matter doesn't exist, because to assume it does
>> leads to contradiction.
>
>
> Not at all. I am entirely agnostic about Matter.
> What I am pretty sure of is that Matter is incompatible with Digital
> Mechanism. I do believe that Comp entails Matter makes no sense.
>
> I am agnostic on Matter, because I am agnostic on Digital Mechanism.
> And then diabolically enough, I have too, because none correct machine
> can know for sure Digital Mechanism is true (even after surviving a
> classical teleportation).

If not knowing for sure makes one an agnostic then I'm an agnostic on
everything. But that definition implies science is no better than
guessing and all opinions are equal. I think we need to keep a
distinction between knowing for sure and knowing in the sense of having
good evidence for.

Brent

>
> Digital Mechanism is only my favorite working hypothesis, and also, I
> admit, I find it rather plausible given the quantum facts. But
> honestly, I don't know, and I gave reason why we cannot *know* that.
> It is part of the true but uncommunicable theological facts, and
> eventually it concerns only me and my doctor/shaman/priester/whatever.
>
> And then, as a computer scientist, I show also that the logic of
> self-reference by self-correct machine provides an arithmetical
> interpretation of Plotinus theology. But from this, comp is only made
> refutable, not proved.

Scientific theories are never proved. That doesn't mean we're agnostic
about whether the Earth is flat or spheroidal.

Brent

>
> Bruno
>
>
>
>>
>> Brent
>>>
>>>
>>>
>>>
>>>
>>>
>>> On 13 Nov 2009, at 12:17, Kim Jones wrote:
>>>
>>>> http://c0116791.cdn.cloudfiles.rackspacecloud.com/Carolyn-AAI09-720-web.mov
>>>>
>>>>
>>>> Carolyn Porco - the genius behind the Cassini mission. My favourite
>>>> female on the planet.
>>>>
>>>> If you ever read Carl Sagan's only novel "Contact" (or saw the movie)
>>>> - this is the person on whom Sagan modelled Ellie Arroway (Jodie
>>>> Foster in the film)
>>>>
>>>> Introduction by Richard Dawkins
>>>>
>>>> cheers,
>>>>
>>>> Kim Jones
>>>>
>>>>
>>>> --
>>>>
>>>> You received this message because you are subscribed to the Google
>>>> Groups "Everything List" group.
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>>>> everything-list+unsubscribe@....
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>>>> http://groups.google.com/group/everything-list?hl=.
>>>>
>>>>
>>>
>>> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
>>>
>>>
>>>
>>> --
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>>
>>
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>
> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
>
>
>
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Re: Arguably The World's Greatest Woman

2009-11-13T15:27:22Z

On 13 Nov 2009, at 21:01, Brent Meeker wrote:

I used to tell people who asked that I was an agnostic. But the trouble with that was that they supposed I was uncertain about the existence of *their* god: a supernatural immortal agent would loved us but had an obsessive interest in our sex lives. So now I generally tell people I'm an atheist, unless I think they are interested in a philosophical answer, because I don't believe what theists believe. So atheism is not a religion, it is a failure to believe in the theist gods - those gods that are agents, omnipotent, omniscient, and ominibenevolent. Thinking that such a god is does not exist is a scientific theory, i.e. one supported by the evidence and not contradicted by any credible evidence. I know you adopt a very abstract and mathematical meaning for "theism", but we don't get to define the meaning of words any more than I got to define "agnostic".

Why should we use the term "God" in the sense of those who clearly have confused science with temporal authoritative argument? The word and concept God have been used in all culture and tradition, and refer to to some projection of our ignorance, close to the idea of infinite, or inconceivable, in-something.

May be this is due to the fact that many got a christian education. I did not. For me "God" refer to the all transcendant and ineffable things described by mystics and rationalized by the thinker who are searching.

Like I said, atheists and christians defend the same concept of God, the first to believe in its non-existence, the second to believe in its existence. Why does atheist choose the definition of those in which they does not believe the theory. It is like to say "genetics is crap" because of Lyssenko.

The agnostic search without prejudice and with a critical eyes on any theory.

You say you are agnostic on (primitive) matter; but you usually claim to have proven that matter doesn't exist, because to assume it does leads to contradiction.

Not at all. I am entirely agnostic about Matter.

What I am pretty sure of is that Matter is incompatible with Digital Mechanism. I do believe that Comp entails Matter makes no sense.

I am agnostic on Matter, because I am agnostic on Digital Mechanism. And then diabolically enough, I have too, because none correct machine can know for sure Digital Mechanism is true (even after surviving a classical teleportation).

Digital Mechanism is only my favorite working hypothesis, and also, I admit, I find it rather plausible given the quantum facts. But honestly, I don't know, and I gave reason why we cannot *know* that. It is part of the true but uncommunicable theological facts, and eventually it concerns only me and my doctor/shaman/priester/whatever.

And then, as a computer scientist, I show also that the logic of self-reference by self-correct machine provides an arithmetical interpretation of Plotinus theology. But from this, comp is only made refutable, not proved.

Bruno

Brent

On 13 Nov 2009, at 12:17, Kim Jones wrote:

http://c0116791.cdn.cloudfiles.rackspacecloud.com/Carolyn-AAI09-720-web.mov

Carolyn Porco - the genius behind the Cassini mission. My favourite
female on the planet.

If you ever read Carl Sagan's only novel "Contact" (or saw the movie)
- this is the person on whom Sagan modelled Ellie Arroway (Jodie
Foster in the film)

Introduction by Richard Dawkins

cheers,

Kim Jones

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Re: Arguably The World's Greatest Woman

2009-11-13T12:01:28Z

Bruno Marchal wrote:

Hi Kim,

Thank you very luch for the link to Carolyn Porco's presentation. Very nice talk. I appreciate a lot.

She is correct (even comp-correct) on the main thing: Science is agnostic.

"I believe in God" (Bg) is a religious statement. (B = I believe, g = 'God' exists", "~" = negation)

But B~g, the athesist statement, is a religious statement too. Atheism is a religion. (and doubly so for the materialist atheists).

Crazily enough, I note she shows this in the exact manner of the introductory chapter of "Conscience et Mécanisme"). So honest atheists exists.

Not so sure why she said she believes (religiously) in the non existence of God, without saying what she means by the word, especially that later she talk of science as the "quest for the truth", but with comp the mathematical notion of truth (relative to a machine and relative to the possible machine views) obeys literally to the notion of "God" in the Greek Theology of Plato (according to my own understanding of Plato, but confirmed by Plotinus and Hirschberger).

Mainly 'God' = the transcendent human-ineffable truth we are invited to search/explore/contemplate.

Making "Science", the quest of the truth, like Carrolyn Porko did (two times, at the two third of that video), is the basic axiom of Plato's theology. It makes science and reason (and mathematics, and music, ...) the most basic tools in the search of the admittedly religious (by science modesty!) truth.

* * *

Let me give you 3, (3! yes there is one more!) basic reasons to consider "Digital Mechanism" as a theology (actually a framework for variate theologies (Mechanism will not stop all possible religious conflicts, on the contrary given the existence of very different possible practices, like overlapping or not with the duplicate ... ).

- 1) To say "yes" to the doctor, even if some oracle guaranties the competence of the doctor and the accuracy of the comp substitution level, etc, is an irreductible act of faith in the possibility of a (relative) digital reincarnation.

- 2) It is a "scientific theology" in the following precise sense: To each machine, or machine's state, (or machine relative description) we associate the set of true arithmetical sentences concerning that machine (described in arithmetic, say). Roughly speaking:

Science = provability

Religion = truth (in the spirit, I am humble and modest, and I search)

Then, not only a universal machine can introspect itself and discover the gap between truth and provability. It can not only discover the unnameability of its own truth notion, but a very rich (in term of provability power) machine (like ZF) can study a big (not all) part of the theology of a more simpler Löbian machine, like Peano-Arithmetic. So although a machine cannot know that she is correct, she can lift the "invariant" theology of simpler lobian machine. Of course she cannot assert she has proved those statement, but she can assert that those are probably true as far as she is "correct", and comp is correct.

But there is a third reason.

-3) Church thesis. Also called Church Turing Thesis, and which I call sometimes Post law, or Gödel Miracle, or Post, Church, Turing, Markov thesis. Its truth entails the truth of the weaker thesis according to which there exists a universal machine. But do we know that? can we know that?

Do we know if there is a universal language, or a universal machine?

No one can prove that, of course. So here too you need to do a bet: an axiom, a thesis, an hypothesis. The miracle (Gödel) is that the set of partial computable functions is closed for the diagonalization, it cannot be transcended. As Gödel said, for the first time we get a mathematical definition of an epistemological concept. Gödel did hope that a similar thesis could exists for the notion of provability, but its own theorem, together with Church thesis prevents this (I think).

And then all attempts to define the computable functions leaded to the same class of partial computable functions. We get all the (total) computable functions, but they have to be situated in a non computable sequences among all the partial functions, as shown by Kleene's diagonalization (as shown in the last "seventh step serie thread", but I guess I have to come back on this). I recall that a total function is a partial function with subdomain equal to the whole N (N is included in N).

So comp, by Church thesis, is also a positive belief in a universal machine, despite the lack of proof of existence).

Of course Turing *did* prove its famous theorem saying that A Universal Turing machine exists. It is a theorem (even of arithmetic) that universal TURING machine exists, and that universal CHURCH lambda expression exists, and that universal SHOENFINKEL-CURRY combinators exists, etc.

For each universal language it can be shown a universal finite entity exists. But this does not prove that there is a universal machine for all computable functions, only that all those class have a relative universal entity. I mean Turing's theorem is not Turing's thesis. But Turing (Church)' thesis makes its universal machine "really" universal (with respect to digital computability).

What can arithmetic still prove is that TURING system, and CHURCH, one, and algol, fortran, lisp, etc. are all equivalent, making the universal TURING (or Church, ...) machine universal for all of CHURCH lambda expression, etc. They are all provably equivalent.

Now to prevent any misinterpretation, let us address the question:

Is the universal machine God?

I would say no. Sometimes I like to call it the baby god, though. In the arithmetical interpretation of the hypostasis the universal machine, once she knows that she is universal, (in a weak technical sense) can play the role of Plotinus' man, or discursive terrestrial intellect. It is man, not God. man means humans.

Universal machine are always finite entities, and exists always relatively to many other Universal machines (even if you can define the whole set of relations into arithmetic, or combinators, quantum topologies, ...).

I may refresh the arithmetical hypostases (cf AUDA). I limit myself to correct machines (they prove only correct arithmetical sentences, by definition). So when the machine says "p", it means that "p" is true. By Tarski theorem, it is the only way to say that "p is true". She just say p. So by "p" below, I mean the assertative proposition by the (correct) machine.

Plotinus one = arithmetical truth = p.

Plotinus divine Intellect (or intelligible) = Bp (Gödel's arithmetical "BEWEISBAR" provability predicate). But by incompleteness that INTELLECT admit an effective part borrowed by the machine: it is Plotinus' man.

That is, here, the INTELLECT splits into the true Intellect and the provable intellect. By Solovay theorem those two logics are axiomatised (at the propositional level) completely by G for the provable (by the machine) part, and by G* for the true but unprovable (by the machine) part. For exemple ~Bf (I will not assert a falsity) belongs to G* \ G. It is true, but not provable, by the correct machine.

Plotinus "universal soul" is the Theaetetical first person. It is the logic of the knower "inside the machine". It is given by the logic of the conjunction of Bp and p: Bp & p. It obeys, and is characterized by the modal logic S4Grz. Amazingly, it is not splitted by the incompleteness phenomenon= S4Grz = S4Grz*.

Then intelligible matter and sensible matter logics are given by the logic Bp & Dt, and Bp & p & Dt. respectfully. They both split by the Solovay "*" incompleteness results.

Plotinus admit at least this very precise arithmetical interpretation, and shows how incompleteness and insolubility structures the ignorance space of the (universal) machine.

Seen from inside, that space is *very* big, but incredibly richly structured, and the physical world, if the neoplatonist are correct, or if comp is correct, is given by the "mathematical bord of that ignorance space.

This is a verifiable (refutable) statement, making machine's theologies testable. Note that all correct Lobian machine (or even non machine, but still self-referentially correct entity) have the same abstract propositional theology (given by G and G* and their intensional variant).

***

Kim, thanks. I think I will send your Carolyn Porco's link to the salvia forum where discussion on atheism appears a lot. I was just abou trying to,explain the problem with *some* atheists.

Probably in the thread "Atheists, be nice!".

http://www.entheogen.com/forum/showthread.php?t=25489

(my username is "salvialover24", well sorry for that ...)

It will help me to explain that there is no problem with atheists, only with dishonest atheists (saying that atheism is not a religion, that science is on their side, etc.).

Of course, as a scientist, I am agnostic on ALL the Aristotelian Gods. This includes Matter (primitive matter).

Bruno

I used to tell people who asked that I was an agnostic. But the trouble with that was that they supposed I was uncertain about the existence of *their* god: a supernatural immortal agent would loved us but had an obsessive interest in our sex lives. So now I generally tell people I'm an atheist, unless I think they are interested in a philosophical answer, because I don't believe what theists believe. So atheism is not a religion, it is a failure to believe in the theist gods - those gods that are agents, omnipotent, omniscient, and ominibenevolent. Thinking that such a god is does not exist is a scientific theory, i.e. one supported by the evidence and not contradicted by any credible evidence. I know you adopt a very abstract and mathematical meaning for "theism", but we don't get to define the meaning of words any more than I got to define "agnostic".

You say you are agnostic on (primitive) matter; but you usually claim to have proven that matter doesn't exist, because to assume it does leads to contradiction.

Brent

On 13 Nov 2009, at 12:17, Kim Jones wrote:

http://c0116791.cdn.cloudfiles.rackspacecloud.com/Carolyn-AAI09-720-web.mov

Carolyn Porco - the genius behind the Cassini mission. My favourite
female on the planet.

If you ever read Carl Sagan's only novel "Contact" (or saw the movie)
- this is the person on whom Sagan modelled Ellie Arroway (Jodie
Foster in the film)

Introduction by Richard Dawkins

cheers,

Kim Jones

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Re: Arguably The World's Greatest Woman

2009-11-13T09:44:02Z

Hi Kim,

Thank you very luch for the link to Carolyn Porco's presentation. Very nice talk. I appreciate a lot.

She is correct (even comp-correct) on the main thing: Science is agnostic.

"I believe in God" (Bg) is a religious statement. (B = I believe, g = 'God' exists", "~" = negation)

But B~g, the athesist statement, is a religious statement too. Atheism is a religion. (and doubly so for the materialist atheists).

Crazily enough, I note she shows this in the exact manner of the introductory chapter of "Conscience et Mécanisme"). So honest atheists exists.

Not so sure why she said she believes (religiously) in the non existence of God, without saying what she means by the word, especially that later she talk of science as the "quest for the truth", but with comp the mathematical notion of truth (relative to a machine and relative to the possible machine views) obeys literally to the notion of "God" in the Greek Theology of Plato (according to my own understanding of Plato, but confirmed by Plotinus and Hirschberger).

Mainly 'God' = the transcendent human-ineffable truth we are invited to search/explore/contemplate.

Making "Science", the quest of the truth, like Carrolyn Porko did (two times, at the two third of that video), is the basic axiom of Plato's theology. It makes science and reason (and mathematics, and music, ...) the most basic tools in the search of the admittedly religious (by science modesty!) truth.

* * *

Let me give you 3, (3! yes there is one more!) basic reasons to consider "Digital Mechanism" as a theology (actually a framework for variate theologies (Mechanism will not stop all possible religious conflicts, on the contrary given the existence of very different possible practices, like overlapping or not with the duplicate ... ).

- 1) To say "yes" to the doctor, even if some oracle guaranties the competence of the doctor and the accuracy of the comp substitution level, etc, is an irreductible act of faith in the possibility of a (relative) digital reincarnation.

- 2) It is a "scientific theology" in the following precise sense: To each machine, or machine's state, (or machine relative description) we associate the set of true arithmetical sentences concerning that machine (described in arithmetic, say). Roughly speaking:

Science = provability

Religion = truth (in the spirit, I am humble and modest, and I search)

Then, not only a universal machine can introspect itself and discover the gap between truth and provability. It can not only discover the unnameability of its own truth notion, but a very rich (in term of provability power) machine (like ZF) can study a big (not all) part of the theology of a more simpler Löbian machine, like Peano-Arithmetic. So although a machine cannot know that she is correct, she can lift the "invariant" theology of simpler lobian machine. Of course she cannot assert she has proved those statement, but she can assert that those are probably true as far as she is "correct", and comp is correct.

But there is a third reason.

-3) Church thesis. Also called Church Turing Thesis, and which I call sometimes Post law, or Gödel Miracle, or Post, Church, Turing, Markov thesis. Its truth entails the truth of the weaker thesis according to which there exists a universal machine. But do we know that? can we know that?

Do we know if there is a universal language, or a universal machine?

No one can prove that, of course. So here too you need to do a bet: an axiom, a thesis, an hypothesis. The miracle (Gödel) is that the set of partial computable functions is closed for the diagonalization, it cannot be transcended. As Gödel said, for the first time we get a mathematical definition of an epistemological concept. Gödel did hope that a similar thesis could exists for the notion of provability, but its own theorem, together with Church thesis prevents this (I think).

And then all attempts to define the computable functions leaded to the same class of partial computable functions. We get all the (total) computable functions, but they have to be situated in a non computable sequences among all the partial functions, as shown by Kleene's diagonalization (as shown in the last "seventh step serie thread", but I guess I have to come back on this). I recall that a total function is a partial function with subdomain equal to the whole N (N is included in N).

So comp, by Church thesis, is also a positive belief in a universal machine, despite the lack of proof of existence).

Of course Turing *did* prove its famous theorem saying that A Universal Turing machine exists. It is a theorem (even of arithmetic) that universal TURING machine exists, and that universal CHURCH lambda expression exists, and that universal SHOENFINKEL-CURRY combinators exists, etc.

For each universal language it can be shown a universal finite entity exists. But this does not prove that there is a universal machine for all computable functions, only that all those class have a relative universal entity. I mean Turing's theorem is not Turing's thesis. But Turing (Church)' thesis makes its universal machine "really" universal (with respect to digital computability).

What can arithmetic still prove is that TURING system, and CHURCH, one, and algol, fortran, lisp, etc. are all equivalent, making the universal TURING (or Church, ...) machine universal for all of CHURCH lambda expression, etc. They are all provably equivalent.

Now to prevent any misinterpretation, let us address the question:

Is the universal machine God?

I would say no. Sometimes I like to call it the baby god, though. In the arithmetical interpretation of the hypostasis the universal machine, once she knows that she is universal, (in a weak technical sense) can play the role of Plotinus' man, or discursive terrestrial intellect. It is man, not God. man means humans.

Universal machine are always finite entities, and exists always relatively to many other Universal machines (even if you can define the whole set of relations into arithmetic, or combinators, quantum topologies, ...).

I may refresh the arithmetical hypostases (cf AUDA). I limit myself to correct machines (they prove only correct arithmetical sentences, by definition). So when the machine says "p", it means that "p" is true. By Tarski theorem, it is the only way to say that "p is true". She just say p. So by "p" below, I mean the assertative proposition by the (correct) machine.

Plotinus one = arithmetical truth = p.

Plotinus divine Intellect (or intelligible) = Bp (Gödel's arithmetical "BEWEISBAR" provability predicate). But by incompleteness that INTELLECT admit an effective part borrowed by the machine: it is Plotinus' man.

That is, here, the INTELLECT splits into the true Intellect and the provable intellect. By Solovay theorem those two logics are axiomatised (at the propositional level) completely by G for the provable (by the machine) part, and by G* for the true but unprovable (by the machine) part. For exemple ~Bf (I will not assert a falsity) belongs to G* \ G. It is true, but not provable, by the correct machine.

Plotinus "universal soul" is the Theaetetical first person. It is the logic of the knower "inside the machine". It is given by the logic of the conjunction of Bp and p: Bp & p. It obeys, and is characterized by the modal logic S4Grz. Amazingly, it is not splitted by the incompleteness phenomenon= S4Grz = S4Grz*.

Then intelligible matter and sensible matter logics are given by the logic Bp & Dt, and Bp & p & Dt. respectfully. They both split by the Solovay "*" incompleteness results.

Plotinus admit at least this very precise arithmetical interpretation, and shows how incompleteness and insolubility structures the ignorance space of the (universal) machine.

Seen from inside, that space is *very* big, but incredibly richly structured, and the physical world, if the neoplatonist are correct, or if comp is correct, is given by the "mathematical bord of that ignorance space.

This is a verifiable (refutable) statement, making machine's theologies testable. Note that all correct Lobian machine (or even non machine, but still self-referentially correct entity) have the same abstract propositional theology (given by G and G* and their intensional variant).

***

Kim, thanks. I think I will send your Carolyn Porco's link to the salvia forum where discussion on atheism appears a lot. I was just abou trying to,explain the problem with *some* atheists.

Probably in the thread "Atheists, be nice!".

http://www.entheogen.com/forum/showthread.php?t=25489

(my username is "salvialover24", well sorry for that ...)

It will help me to explain that there is no problem with atheists, only with dishonest atheists (saying that atheism is not a religion, that science is on their side, etc.).

Of course, as a scientist, I am agnostic on ALL the Aristotelian Gods. This includes Matter (primitive matter).

Bruno

On 13 Nov 2009, at 12:17, Kim Jones wrote:

http://c0116791.cdn.cloudfiles.rackspacecloud.com/Carolyn-AAI09-720-web.mov

Carolyn Porco - the genius behind the Cassini mission. My favourite
female on the planet.

If you ever read Carl Sagan's only novel "Contact" (or saw the movie)
- this is the person on whom Sagan modelled Ellie Arroway (Jodie
Foster in the film)

Introduction by Richard Dawkins

cheers,

Kim Jones

--

You received this message because you are subscribed to the Google Groups "Everything List" group.
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http://iridia.ulb.ac.be/~marchal/

Arguably The World's Greatest Woman

2009-11-13T03:17:42Z

http://c0116791.cdn.cloudfiles.rackspacecloud.com/Carolyn-AAI09-720-web.mov

Carolyn Porco - the genius behind the Cassini mission. My favourite
female on the planet.

If you ever read Carl Sagan's only novel "Contact" (or saw the movie)
- this is the person on whom Sagan modelled Ellie Arroway (Jodie
Foster in the film)

Introduction by Richard Dawkins

cheers,

Kim Jones

--

You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to everything-list@....
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Re: The seven step series (november 2009)

2009-11-11T14:45:37Z

On 11 Nov 2009, at 19:52, Brent Meeker wrote:

>
> Bruno Marchal wrote:
>>
>> On 10 Nov 2009, at 19:29, Brent Meeker wrote:
>>
>>
>>>>
>>> But this seems like creating a problem where none existed. The
>>> factorial is a certain function, the brain performs a certain
>>> function.
>>> Now you say we will formalize the concept of function in order to
>>> study
>>> what the brain does and perhaps understand what is consciousness.
>>> But
>>> there is nothing that requires that you start over with all possible
>>> computations. That is like explaining the factorial function by
>>> considering all possible computations that produce it (like the
>>> above).
>>> It's not wrong, but it doesn't follow from saying that the
>>> factorial is
>>> a function. That's why I say I take it as an ansatz - "Let's
>>> consider
>>> all possible computations and see if we can pick out physics and the
>>> brain and consciousness from them."
>>
>>
>> Hmm... The seventh step comes after six other steps. I think you
>> confuse UDA and Tegmark or Egan speculation on the mathematical
>> nature
>> of physics. But when we assume comp,
>
> But it seems there is a shift the meaning of "assume comp" here. We
> start with comp = "Consciousness is something a brain does. A brain
> does a lot of things (metabolizes, takes up space,...) but the thing
> it
> does that produces consciousness is a kind of computation, i.e.
> information processing. " Almost all scientists and philosophers
> think
> that is good hypothesis and one they would assume. But then it seems
> you use comp2 = "We - our stream of consciousness - IS a computation
> that exists in the Platonic sense." This seems slightly different.

When some materialists, like some neuroscientists, assume the brain
does computations at some high level, like with neuronal processing. I
am not sure all are aware of the digitality assumption needed for
making sense to the word computation.
But if we assume the brain obeys to the physical laws, then we assume
comp already, given that the physical laws are, as far as we know,
Turing emulable.

Comp is NOT the hypothesis that "consciousness is something brain
does". This is not even a precise definition of comp, given that
strictly speaking we don't know what a brain is, nor what
consciousness. But that's ok, because comp is very close to that,
perhaps equivalent deending of what you mean by "consciousness is
something brain does".

Comp is two things: "yes doctor", which means: there is a level such
that I survive (or feel nothing) when may brain is substitute for
digital part made at that level". This does not use any neither a
definition of brain, except it is something which can be described by
some machine (but not necessarily the one in the skull), nor any idea
of consciousness, above what we can ask to a doctor (will I make it
Doc?).

And then I believe you did understand the seventh step. In a "concrete
universe with a UD running in it (even materially), well, if my comp
state is S, my future subjective experience is given by a sum on all
computations going through S. So if the laws of physics still applies,
they have to be recover from the mathematics of computations, which is
a branch of math. In physics the notion does not admit definition
which is different from the one by mathematicians. And quantum
computation, actually a mathematical notion, is already close to the
idea of sum on infinities of computations.

After the seven step, you can still invoke, to save both comp and
materialist, that we live in a universe which is too little for a
universal dovetailing to be executed integrally or on some large
portion.

That is why there is an eight step, which shows that the universal
machine (that we all provably are, even if comp is false) cannot, once
comp is true, make the difference, for a short time on which bear the
probabilities, distinguish between any implementations made below its
substitution level, notably between "physically implemented" or
"arithmetically implemented". Step 8 shows that consciousness is not
produced by the brain. Consciousness is "produced" by the arithmetical
relation (or XYZ-ical relation with XXX being a first order
specification of any universal system.
In that case the move to a little universe can not work, and reality,
or more aptly the realities (corresponding to each points of view)
have to emerge from the XYZ-relations.

I don't need any more "platonic reality" than I need to explain what
is Church thesis, what is a universal machine or number, etc. No book
of physics assume less.

>
>> the physical appearance cannot be describe by *any* computation a
>> priori:
> But the main evidence for the comp hypothesis is that physics is so
> successfully described by computations.

Not necessarily. If you take Old QM (SWE + Collapse), the collapse of
the wave, and its result, IS NOT the output of a computation.
If you take the "new" QM, which assumes comp, the physical appearance
is already described by infinities of computations. The only problem
is that by assuming comp and taking it seriously into account (meaning
taking the first and third person distinction into account) the UDA-
MGA argument shows that the SWE has to be derived from comp, that is
from number theory (or the XYZ-theory).

I take XYZ = Arithmetic, just because Arithmetic is already universal,
and is already taught in high school.

As I said, it would help if you could say where in SANE04 you have a
problem. I will send to the list a new version of MGA quite close to
the one already sent. (MGA is just sketched in SANE04).

>
>
>> it *has* to be retrieve from all computation. Roughly speaking, if we
>> are universal machine,
>
> But assuming "we are a universal machine" is assuming more than "our
> brains do computations and that produces consciousness."

No, it is less. I can prove to you that you are at least a universal
machine.
Comp is that you are Turing emulable, and this means that you are not
MORE than a universal machine.
Universal here is used in respect of computability, or emulability,
not in the sense of provability or anything else.

>
>> we do belong to an infinity of computation, and matter, or anything
>> below our substitution level, has to be described by "all
>> computations". It is an open problem if that sum converge toward
>> something we could describe by "one" computation.
> If it is proven that it doesn't, would that refute comp2?

Why? Not necessarily. Unless you mean that all physical result is
given by that "one" computation, which is already not the case with
"new QM".

> Would we be
> left with no explanation of the perceived unity of individual
> consciousness?

Consciousness is when (universal) machine bets (instinctively at
first) on "transcending realities", like their parents, their local
neighborhood (to begin with), up to things like "physical universe",
"Gods" or the Number Realm.
It is always hypothetical. It is not always consciously "hypothetical".

>
>
>> It is the whole point of the reasoning. It is "theorem" in the comp
>> theory that matter emerges from all computations. From this you can
>> prove that comp implies the non-cloning of any piece of matter, like
>> it proves the existence of a strong form of indeterminacy, etc.
>
> What's the non-cloning proof?

UDA1--7 is enough. To predict the exact state of any object, you have
to run the whole dovetailer. This is not possible, so the exact state
of any piece of matter, although it may be simulated quickly with a
big accuracy, would need the whole running of the UD to be emulated.

>
>>
>>
>>>>>>
>>>>> Could you remind me what the phi_i are? The enumerated partial
>>>>> functions?
>>>>
>>>>
>>>> The enumerated so called "partial /computable/ functions".
>>>>
>>>> To get them, take your favorite universal system (fortran, lisp, c
>>>> ++,
>>>> java, whatever), write down the grammatically correct description
>>>> of
>>>> function (of one argument, say, that is, from N to N). Put those
>>>> codes
>>>> in lexicographical order, and you get the corresponding phi_i:
>>>> phi_1,
>>>> phi_2, ..., and their domain W_1, W_2, W_3, ...
>>>>
>>>> With Church thesis, all the computable functions (having the
>>>> domain N)
>>>> will belong to that list, but there will be no algorithm capable of
>>>> telling in advance for any phi_i if it compute partial computable
>>>> function or a computable functions.
>>>>
>>>> Given that this is a key point for everything which will follow, I
>>>> have to be sure that most people understand exactly why this has to
>>>> be so.
>>>
>>> Ok, I think I understand. It's probably not relevant here, but
>>> physicist usually think of functions which can be computed
>>> approximately
>>> by a uniformly convergent algorithm as computable (e.g. compute
>>> pi) but
>>> I think in the above you mean computable in the Turing sense that
>>> the
>>> computation stops with the answer (e.g. compute pi to 100 decimal
>>> places). Right?
>>
>>
>> Right. There is a vocabulary problem about what is a function, and
>> unfortunately english speaker and french speaker have different
>> conventions, and sometimes I slip from one to other, and this does
>> not
>> help. Usually a function from N to N is supposed to be defined on all
>> element of N. And thus a computable function will have an algorithm
>> which does stop on all of its input.
>> But the Kleene diagonalization shows that there is no computable list
>> of all computable functions, so if a language is universal, it means
>> that the computable functions can only belong to a list of something
>> else. That something else are called partial computable function:
>> they
>> are allowed to be not necessarily define on some natural number. So
>> to
>> get ALL functions, in some computable way, we have to take something
>> larger: all partial functions, and to get all execution of all
>> algorithm, we will have to dovetail,
> Thanks, I did understand, but sometimes I need reassurance that I've
> grasped it.

Tanks for telling. I think many does not grasp it, or does grasp it
since a longer time.
I will sum up, but people would help by telling if they have grasped
Cantor diagonalization proof of the non enumerability of N^N. Then I
can explain with more assurance Kleene very similar, yet completely
different result and their consequence.

People should reread perhaps the "coffee bar machine" thread, or the
"combinator" thread, or learn some programming language to familiarize
themselves with example of universal system. But all what I need does
not depend on any particular system. I refer to the numbers because
everyone know them, but once a universal system is very simple, it
becomes rather long and tedious to show that is universal. There is an
hard pedagogical dilemma here.

>
>> and from the first person point of view, there is an emerging
>> continuum of computations, and it plays the role of the background
>> roots of the physical laws, below our substitution level.
>
> But how is the "first person point of view" defined? Can this theory
> tell me how many persons exist at a given time?

In the UDA, the first person view is defined very simply by the
personal memory, or the personal diary of the teleported candidate.
The key is that such a memory is annihilated and reconstituted when
the experiencer is annihilated or reconstituted. (Which explain what
the first person will not "feel the split" (to talk like Everett).
The third person description is given by what is not annihilated, like
a local observer, or eventually the number theoretical relations
themselves.

IN QM, roughly speaking the third person view can be described by
Everett universal wave, or Deutsch (Heisenbergian) universal matrix.
And the first person views are given by what the machine observer
memories in each branch of that differentiating waves.

But with comp, eventually the third person description is given by the
relation between number (and definable with + and *), and the "Everett
wave" is retrievable as a first person (plural) point of view.

Thanks to Everett QM, we have very strong evidence, assuming comp,
that we are multiple (infinities) but share deep and long
computations. QM saves comp from solipsism, but matter, well Matter,
does not go through.

That's a good thing because no one really can defined it, nor provide
evidence that it exists, beyond a naïve extrapolation of the boolean
mind from its local neighborhood.
And once you assume Matter, the mind body problem become non
resoluble, you can even get divorce between human and exact science,
leading to people having no idea what is going on, yet having all
means of destruction/creation at their disposal ... Brrr...

Bruno

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

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Re: The seven step series (november 2009)

2009-11-11T10:52:45Z

Bruno Marchal wrote:

>
> On 10 Nov 2009, at 19:29, Brent Meeker wrote:
>
>
>>>
>> But this seems like creating a problem where none existed. The
>> factorial is a certain function, the brain performs a certain function.
>> Now you say we will formalize the concept of function in order to study
>> what the brain does and perhaps understand what is consciousness. But
>> there is nothing that requires that you start over with all possible
>> computations. That is like explaining the factorial function by
>> considering all possible computations that produce it (like the above).
>> It's not wrong, but it doesn't follow from saying that the factorial is
>> a function. That's why I say I take it as an ansatz - "Let's consider
>> all possible computations and see if we can pick out physics and the
>> brain and consciousness from them."
>
>
> Hmm... The seventh step comes after six other steps. I think you
> confuse UDA and Tegmark or Egan speculation on the mathematical nature
> of physics. But when we assume comp,

But it seems there is a shift the meaning of "assume comp" here. We
start with comp = "Consciousness is something a brain does. A brain
does a lot of things (metabolizes, takes up space,...) but the thing it
does that produces consciousness is a kind of computation, i.e.
information processing. " Almost all scientists and philosophers think
that is good hypothesis and one they would assume. But then it seems
you use comp2 = "We - our stream of consciousness - IS a computation
that exists in the Platonic sense." This seems slightly different.

> the physical appearance cannot be describe by *any* computation a priori:
But the main evidence for the comp hypothesis is that physics is so
successfully described by computations.

> it *has* to be retrieve from all computation. Roughly speaking, if we
> are universal machine,

But assuming "we are a universal machine" is assuming more than "our
brains do computations and that produces consciousness."

> we do belong to an infinity of computation, and matter, or anything
> below our substitution level, has to be described by "all
> computations". It is an open problem if that sum converge toward
> something we could describe by "one" computation.
If it is proven that it doesn't, would that refute comp2? Would we be
left with no explanation of the perceived unity of individual consciousness?

> It is the whole point of the reasoning. It is "theorem" in the comp
> theory that matter emerges from all computations. From this you can
> prove that comp implies the non-cloning of any piece of matter, like
> it proves the existence of a strong form of indeterminacy, etc.

What's the non-cloning proof?

>
>
>>>>>
>>>> Could you remind me what the phi_i are? The enumerated partial
>>>> functions?
>>>
>>>
>>> The enumerated so called "partial /computable/ functions".
>>>
>>> To get them, take your favorite universal system (fortran, lisp, c++,
>>> java, whatever), write down the grammatically correct description of
>>> function (of one argument, say, that is, from N to N). Put those codes
>>> in lexicographical order, and you get the corresponding phi_i: phi_1,
>>> phi_2, ..., and their domain W_1, W_2, W_3, ...
>>>
>>> With Church thesis, all the computable functions (having the domain N)
>>> will belong to that list, but there will be no algorithm capable of
>>> telling in advance for any phi_i if it compute partial computable
>>> function or a computable functions.
>>>
>>> Given that this is a key point for everything which will follow, I
>>> have to be sure that most people understand exactly why this has to
>>> be so.
>>
>> Ok, I think I understand. It's probably not relevant here, but
>> physicist usually think of functions which can be computed approximately
>> by a uniformly convergent algorithm as computable (e.g. compute pi) but
>> I think in the above you mean computable in the Turing sense that the
>> computation stops with the answer (e.g. compute pi to 100 decimal
>> places). Right?
>
>
> Right. There is a vocabulary problem about what is a function, and
> unfortunately english speaker and french speaker have different
> conventions, and sometimes I slip from one to other, and this does not
> help. Usually a function from N to N is supposed to be defined on all
> element of N. And thus a computable function will have an algorithm
> which does stop on all of its input.
> But the Kleene diagonalization shows that there is no computable list
> of all computable functions, so if a language is universal, it means
> that the computable functions can only belong to a list of something
> else. That something else are called partial computable function: they
> are allowed to be not necessarily define on some natural number. So to
> get ALL functions, in some computable way, we have to take something
> larger: all partial functions, and to get all execution of all
> algorithm, we will have to dovetail,

Thanks, I did understand, but sometimes I need reassurance that I've
grasped it.

> and from the first person point of view, there is an emerging
> continuum of computations, and it plays the role of the background
> roots of the physical laws, below our substitution level.

But how is the "first person point of view" defined? Can this theory
tell me how many persons exist at a given time?

Brent

>
> The physical world is not just a mathematical space among mathematical
> spaces, it is really a sort of summary of the whole border of the
> whole set of "mathematical spaces" as seen by mean universal machines.
> That the laws of physics seems computable is a mystery now.
>
> I am just showing that the comp theory reduces the mind-body problem
> to a pure arithmetical (or combinatorial, ...) body problem.
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
>
>
>
>
> >

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Re: The seven step series (november 2009)

2009-11-11T10:29:52Z

Rex Allen wrote:

> On Tue, Nov 10, 2009 at 1:29 PM, Brent Meeker <meekerdb@... wrote:
>
>> That's why I say I take it as an ansatz - "Let's consider
>> all possible computations and see if we can pick out physics and the
>> brain and consciousness from them."
>>
>
> I would think that it's pretty much a given that out of all possible
> computations, we surely will be able to find some way of representing
> physics, the brain, and the contents of conscious experience.
>

But it's the "picking out" that's problem. That's the generic problem
with the everything-theories. Sure the UD generates all possible
strings and physics must be in there somewhere - so what. Tegmark
hypothesizes all possible mathematical structures exist - so yeah
physics must be in there too.

> If we can't find some way to symbolically/logically represent these
> things...what would that mean? Wouldn't it mean that we ourselves
> aren't capable of grasping them?
>
> So, I don't think I see the significance of success in this
> project...I would think that success in finding some
> logico-mathematical representation of physics
IF you can *find* it among all the detritus.

> and the rest is the
> expected outcome, and that conclusive failure would be big news.
>
> So with computationalism, you can't see beneath the substitution level
> to the underlying "processor" substrate of what really exists. The
> conscious experience that results from the computation doesn't have to
> reveal anything about the nature of the computer...below the
> substitution level could be neurons, transistors, falling dominoes,
> dust clouds (a la Egan), numbers, platonic objects, alien matter
> existing in some alternate universe, Wang's Carpet (Egan again),
> ROCKS...basically anything capable of supporting computation...who
> knows? It would all look the same to us above the substitution level,
> right?
>
> If we were to go with Bruno's proposal, wouldn't it be because a
> substrate of platonically existing numbers seemed like a more
> plausible substrate than a contingently existing physical universe of
> matter and energy and laws which sprang from...nothing? Has existed
> eternally? What?

Platonic existence seems like a very thin concept to me and it's not
very plausible (to me) that it can provide the ontology of the
universe. I see numbers part of the description. That the universe
sprang from nothing is a going theory in cosmogony supported by the
observation that whatever conserved quantities are evaluated, energy,
momentum, charge, entropy,..., the total for the universe comes out
zero. The philosophical difference that seems to divide people is that
some are happy to accept that some things are contingent and others feel
it better to hypothesize infinities in order to secure determinism.

Brent

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Re: The seven step series (november 2009)

2009-11-11T01:16:05Z

On 11 Nov 2009, at 08:48, Rex Allen wrote:

>
> On Tue, Nov 10, 2009 at 1:29 PM, Brent Meeker
> <meekerdb@... wrote:
>>
>> That's why I say I take it as an ansatz - "Let's consider
>> all possible computations and see if we can pick out physics and the
>> brain and consciousness from them."
>
> I would think that it's pretty much a given that out of all possible
> computations, we surely will be able to find some way of representing
> physics, the brain, and the contents of conscious experience.
>
> If we can't find some way to symbolically/logically represent these
> things...what would that mean? Wouldn't it mean that we ourselves
> aren't capable of grasping them?
>
> So, I don't think I see the significance of success in this
> project...I would think that success in finding some
> logico-mathematical representation of physics and the rest is the
> expected outcome, and that conclusive failure would be big news.
>
> So with computationalism, you can't see beneath the substitution level
> to the underlying "processor" substrate of what really exists. The
> conscious experience that results from the computation doesn't have to
> reveal anything about the nature of the computer...below the
> substitution level could be neurons, transistors, falling dominoes,
> dust clouds (a la Egan), numbers, platonic objects, alien matter
> existing in some alternate universe, Wang's Carpet (Egan again),
> ROCKS...basically anything capable of supporting computation...who
> knows? It would all look the same to us above the substitution level,
> right?

No, as i said to Brent, comp says exactly what is below our
substitution level: all computations. If our consciousness supervenes
on state S, it means we have to take all computations going through
state S.
If we look below our computational substitution level, and find a
computation, like in classical physics, then we know that either we
are not machine, or that we are in some simulation (and this has
probability zero from our first person perspective, so that if we see
classical computable laws, from our first person perspective we can no
more be machine). Here, of course the quantum data confirms that we
could be machine. QM is an ally of digital mechanism. If the physical
truth was classical physics, UDA would be a proof that we are not
digital machine.

>
> If we were to go with Bruno's proposal, wouldn't it be because a
> substrate of platonically existing numbers seemed like a more
> plausible substrate than a contingently existing physical universe of
> matter and energy and laws which sprang from...nothing? Has existed
> eternally? What?

I agree with you. A physical universe is a bit like a creationist
concept, it does not explain neither consciousness nor matter. But
with comp, the point is that it is not a proposal, but a logical
consequence, if I may insist. It is the UDA point.

Bruno

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

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Re: The seven step series (november 2009)

2009-11-11T01:07:31Z

On 10 Nov 2009, at 19:29, Brent Meeker wrote:

But this seems like creating a problem where none existed. The
factorial is a certain function, the brain performs a certain function.
Now you say we will formalize the concept of function in order to study
what the brain does and perhaps understand what is consciousness. But
there is nothing that requires that you start over with all possible
computations. That is like explaining the factorial function by
considering all possible computations that produce it (like the above).
It's not wrong, but it doesn't follow from saying that the factorial is
a function. That's why I say I take it as an ansatz - "Let's consider
all possible computations and see if we can pick out physics and the
brain and consciousness from them."

Hmm... The seventh step comes after six other steps. I think you confuse UDA and Tegmark or Egan speculation on the mathematical nature of physics. But when we assume comp, the physical appearance cannot be describe by *any* computation a priori: it *has* to be retrieve from all computation. Roughly speaking, if we are universal machine, we do belong to an infinity of computation, and matter, or anything below our substitution level, has to be described by "all computations". It is an open problem if that sum converge toward something we could describe by "one" computation. It is the whole point of the reasoning. It is "theorem" in the comp theory that matter emerges from all computations. From this you can prove that comp implies the non-cloning of any piece of matter, like it proves the existence of a strong form of indeterminacy, etc.

Could you remind me what the phi_i are? The enumerated partial
functions?

The enumerated so called "partial /computable/ functions".

To get them, take your favorite universal system (fortran, lisp, c++,
java, whatever), write down the grammatically correct description of
function (of one argument, say, that is, from N to N). Put those codes
in lexicographical order, and you get the corresponding phi_i: phi_1,
phi_2, ..., and their domain W_1, W_2, W_3, ...

With Church thesis, all the computable functions (having the domain N)
will belong to that list, but there will be no algorithm capable of
telling in advance for any phi_i if it compute partial computable
function or a computable functions.

Given that this is a key point for everything which will follow, I
have to be sure that most people understand exactly why this has to be so.

Ok, I think I understand. It's probably not relevant here, but
physicist usually think of functions which can be computed approximately
by a uniformly convergent algorithm as computable (e.g. compute pi) but
I think in the above you mean computable in the Turing sense that the
computation stops with the answer (e.g. compute pi to 100 decimal
places). Right?

Right. There is a vocabulary problem about what is a function, and unfortunately english speaker and french speaker have different conventions, and sometimes I slip from one to other, and this does not help. Usually a function from N to N is supposed to be defined on all element of N. And thus a computable function will have an algorithm which does stop on all of its input.

But the Kleene diagonalization shows that there is no computable list of all computable functions, so if a language is universal, it means that the computable functions can only belong to a list of something else. That something else are called partial computable function: they are allowed to be not necessarily define on some natural number. So to get ALL functions, in some computable way, we have to take something larger: all partial functions, and to get all execution of all algorithm, we will have to dovetail, and from the first person point of view, there is an emerging continuum of computations, and it plays the role of the background roots of the physical laws, below our substitution level.

The physical world is not just a mathematical space among mathematical spaces, it is really a sort of summary of the whole border of the whole set of "mathematical spaces" as seen by mean universal machines. That the laws of physics seems computable is a mystery now.

I am just showing that the comp theory reduces the mind-body problem to a pure arithmetical (or combinatorial, ...) body problem.

Bruno

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

Re: The seven step series (november 2009)

2009-11-10T23:48:28Z

On Tue, Nov 10, 2009 at 1:29 PM, Brent Meeker <meekerdb@... wrote:
>
> That's why I say I take it as an ansatz - "Let's consider
> all possible computations and see if we can pick out physics and the
> brain and consciousness from them."

I would think that it's pretty much a given that out of all possible
computations, we surely will be able to find some way of representing
physics, the brain, and the contents of conscious experience.

If we can't find some way to symbolically/logically represent these
things...what would that mean? Wouldn't it mean that we ourselves
aren't capable of grasping them?

So, I don't think I see the significance of success in this
project...I would think that success in finding some
logico-mathematical representation of physics and the rest is the
expected outcome, and that conclusive failure would be big news.

So with computationalism, you can't see beneath the substitution level
to the underlying "processor" substrate of what really exists. The
conscious experience that results from the computation doesn't have to
reveal anything about the nature of the computer...below the
substitution level could be neurons, transistors, falling dominoes,
dust clouds (a la Egan), numbers, platonic objects, alien matter
existing in some alternate universe, Wang's Carpet (Egan again),
ROCKS...basically anything capable of supporting computation...who
knows? It would all look the same to us above the substitution level,
right?

If we were to go with Bruno's proposal, wouldn't it be because a
substrate of platonically existing numbers seemed like a more
plausible substrate than a contingently existing physical universe of
matter and energy and laws which sprang from...nothing? Has existed
eternally? What?

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Re: The seven step series (november 2009)

2009-11-10T10:29:09Z

Bruno Marchal wrote:

>
> On 09 Nov 2009, at 20:43, Brent Meeker wrote:
>
>>
>> Bruno Marchal wrote:
>>>
>>> Hi,
>>>
>>> Let us come back on the "seven step" thread.
>>>
>>> Let me recall the initial motivation. The movie graph argument (cf the
>>> MGA thread) shows that it is senseless to attach consciousness to the
>>> physical activity of a brain or a computer.
>>>
>>> If we keep the computational thesis for the cognitive process, we have
>>> to associate consciousness to the computation, and not to its physical
>>> realization. Actually we have to explain what is a "physical
>>> realization" from the existence of computations.
>>>
>>> But then we have to understand better what we mean by computation, in
>>> the mathematical sense, given that we cannot use any physics, at this
>>> stage.
>>>
>>> Luckily, the notion of computation has been discovered last century by
>>> mathematicians. They were motivated by the foundation of mathematics
>>> after the "crisis" of set theory.
>>>
>>> So what is a computation? Let us try some definitions.
>>>
>>> Attempt 1: A computation is a sequence of computational states.
>>>
>>> If we agree with this, it remains to define what is a computational
>>> states. But the definition above misses something important. I suspect
>>> everything can be "recoded" as a sequence of computational states, and
>>> this could be the reason why some are willing to say that rock and
>>> thinks like that are conscious.
>>>
>>> A physicist could say that what is lacking is a genuine causality
>>> relation which links the states from the sequence of computational
>>> states. But:
>>> - in the context of the MGA argument, this should be seen as a red
>>> herring
>>> - the notion of causality is extremely vague, even for a materialist.
>>>
>>> So:
>>>
>>> Attempt 2: A computation is a sequence of computational states
>>> obtained sequentially through the activity of some machine.
>>>
>>> This is actually a good definition, except that we have to define
>>> (without using physics) what we mean by activity, and machine. This
>>> may be problematic because we want to define activity by a sequence of
>>> state of some machine ... So:
>>
>> I don't think it's very good since it depends on the notion of
>> "computational states" to define computation. It is not clear that any
>> sequence of states cannot be "computational states". It seems to me
>> that we really take as primitive the concept of a function, something
>> that is given some information and transforms it into some other
>> information. That's what we think brains do - and they do a lot of it
>> which is not conscious. When we have abstracted away what the
>> information is about, we can regard it just as a string or number and
>> apply the ideas of Turing, Church, et al to the transformation as a
>> computation. But we have left behind the idea that the information was
>> about something or represented something. In the context of a
>> computation as a consciousness this representation is a relation between
>> the information being transformed and the world of which one is
>> conscious. So it seems you have ignored physics rather than explained
>> it. However, I can accept it as an ansatz in hope that the explanation
>> will emerge in the end.
>
>
> The problem which appears taking only the function is that a function
> can be computed in many different way. For example here is a way to
> compute the factorial function:
>
> BEGIN
> READ INPUT N
> SIMULATE BRENT MEEKER DRINKING COFFEE
> IF BRENT SAYS "GOOD" OUTPUT N*(N-1)* ... *1
> IF BRENT SAYS "BAD" OUTPUT N*(N-1)* ... *1
> IF BRENT SAYS NOTHING, AFTER AWHILE, OUTPUT N*(N-1)* ... *1
> END
>
> That program will go through the right computational state
> corresponding to you drinking coffee, yet compute the same function
> that any more reasonable way to compute the factorial.
> It will be impossible to dismiss those "computational states" if we
> want a comp supervenience thesis.
>

But this seems like creating a problem where none existed. The
factorial is a certain function, the brain performs a certain function.
Now you say we will formalize the concept of function in order to study
what the brain does and perhaps understand what is consciousness. But
there is nothing that requires that you start over with all possible
computations. That is like explaining the factorial function by
considering all possible computations that produce it (like the above).
It's not wrong, but it doesn't follow from saying that the factorial is
a function. That's why I say I take it as an ansatz - "Let's consider
all possible computations and see if we can pick out physics and the
brain and consciousness from them."

>
>
>
>
>
>>>
>>> Attempt 3: a computation is a sequence of states such that it exists a
>>> machine going through that sequence of states when computed by ...
>>>
>>> Well, we cannot refer to activity or to a physical implementation, so
>>> what?
>>>
>>> Attempt 4
>>>
>>> A computation is a sequence of states of some machine when executed by
>>> some Universal Machine.
>>>
>>> That is a progress, in case we succeed in defining "executed by some
>>> universal machine", without using physics. But now we have the problem
>>>
>>> Does a universal machine exist? And what is the mathematical meaning
>>> of "execution".
>>>
>>> But now, Church Thesis (Post, Church, Turing, Markov Thesis) is a
>>> strengthening of the following weaker thesis: It exists a universal
>>> machine.
>>>
>>> And, all those machines, for Post, Turing, were mathematical
>>> construction, right at the beginning.
>>>
>>> Church thesis is strictly speaking the statement that his formal
>>> (mathematical) system, known as Lambda Calculus, is universal with
>>> respect to computability. The basic entity there are the lambda
>>> expressions (those little cousins of the combinators, for those who
>>> remembers old threads).
>>>
>>> Turing thesis is that the language describing Turing machines is
>>> universal with respect of that same class, and soon it will be proved
>>> that they are equivalent indeed, making Church thesis equivalent to
>>> Turing thesis, (and equivalent to "Post law").
>>>
>>> Then Turing proved the existence of the "universal Turing Machine",
>>> and indeed, since we know now that for each such universal system for
>>> such system the "understanding of the language" can be encoded in the
>>> language itself. So there is a universal lambda expression. There is a
>>> universal Turing Machine. A universal Post production system, or a
>>> Fortran interpreter (or compiled) in Fortran, or a Lisp intepreter in
>>> Lisp.
>>>
>>> Some may ask "which universal machine?". But the whole point of
>>> classical computationalism (and UDA) consists in showing that below
>>> your (our common) substitution level, we have to take account of all
>>> universal machines. Any universal dovetailer dovetails on all of them.
>>> So even if only one computation "wins", it has to be justify by a
>>> (relative) sum on all computations.
>>>
>>> I have suggested to take the combinators, without success, so I will
>>> suggest later to take Robinson Arithmetic, which is Turing Universal,
>>> as seen as a computer. It is really very elementary arithmetic.
>>> Very simple cellular automata rules leads to universality, in this
>>> Church Turing sense, like the "game of life" by Conway. Universality
>>> is somehow cheap, and it happens that elementary arithmetic (with
>>> zero, the successor rule, addition and multiplication) is already
>>> Turing universal.
>>>
>>> "being a piece of computations" is equivalent with "being executed by
>>> the universal dovetailer", and such a proposition can be translated
>>> into elementary arithmetic. This is equivalent with Gödel's showing
>>> how to translated statements about propositions, theories, machines,
>>> into statement about numbers.
>>>
>>> But be careful to understand what happen here. It is not that the laws
>>> of computations or universal machine dream are so easy that we can
>>> represent them by number relation, the real discovery is that the
>>> relation among numbers can be very complex.
>>>
>>> That is why I insist so much that an understanding already of just
>>> Church thesis makes you modest, even just about what you can prove
>>> about numbers.
>>>
>>> OK? Any question about the diagonalizations of Cantor and Kleene?
>>>
>>> I need this for the understanding of what the phi_i are. A universal
>>> number will be a number u such that phi_u(x, y) = phi_x(y). (with
>>> "(x,y)" represents a number through a computable bijection).
>> Could you remind me what the phi_i are? The enumerated partial
>> functions?
>
>
> The enumerated so called "partial /computable/ functions".
>
> To get them, take your favorite universal system (fortran, lisp, c++,
> java, whatever), write down the grammatically correct description of
> function (of one argument, say, that is, from N to N). Put those codes
> in lexicographical order, and you get the corresponding phi_i: phi_1,
> phi_2, ..., and their domain W_1, W_2, W_3, ...
>
> With Church thesis, all the computable functions (having the domain N)
> will belong to that list, but there will be no algorithm capable of
> telling in advance for any phi_i if it compute partial computable
> function or a computable functions.
>
> Given that this is a key point for everything which will follow, I
> have to be sure that most people understand exactly why this has to be so.

Ok, I think I understand. It's probably not relevant here, but
physicist usually think of functions which can be computed approximately
by a uniformly convergent algorithm as computable (e.g. compute pi) but
I think in the above you mean computable in the Turing sense that the
computation stops with the answer (e.g. compute pi to 100 decimal
places). Right?

Brent

>
> So I will come back on this.
>
> Thanks for the feedback,
>
> Bruno
>
>
>
>
>
>
>
>>
>> Brent
>>>
>>> The key point is that the notion of computation can be defined in
>>> arithmetic. By Church thesis, limiting the computations to those
>>> definable in arithmetic does not eliminate any computations.
>>>
>>> So the computational supervenience thesis is also equivalent with the
>>> arithmetical supervenience thesis.
>>>
>>> Another important mathematical point is that Universality for
>>> computations entails non universality for provability. That is
>>> incompleteness. Universal machine have capabilities far beyond what
>>> they can prove and known. The universal machine can lost itself in his
>>> own creation. And, ASSUMING Church thesis, the existence of the
>>> universal machine is a theorem of elementary arithmetic.
>>>
>>> It reminds me Aurobindo:
>>>
>>>
>>> /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/
>>>
>>>
>>> Any questions, remarks, comments?
>>>
>>> Bruno
>>>
>>>
>>>
>>>
>>>
>>>
>>> On 11 Oct 2009, at 19:53, Bruno Marchal wrote:
>>>
>>>> Hi John, hi Marty,
>>>> On 10 Oct 2009, at 21:47, John Mikes wrote:
>>>>
>>>>> Bruno, we had similar puzzles in middle school in the 30s.
>>>>> The barber could not shave himself because he shaved only those who
>>>>> did not shave themselves (and shaved all). So for (Q #1) in the 1st
>>>>> vriant
>>>>> *she(?)* was a female, unless *he(?)* was a beardless male
>>>>
>>>>
>>>> You are right. The barber gender is female. I don't see why you add
>>>> that he could be a beardless male. It is part of the problem that we
>>>> are in a tyrannic country where no man can have a beard.
>>>>
>>>>
>>>>
>>>>
>>>>> (and the 'all' refers to only the *bearded* males requiring a
>>>>> shave).
>>>>> *
>>>>> Q#2 is beyond me, I do not resort to a QM-pattern like Schrodinger's
>>>>> cat.
>>>>> (Sh/H)e is either-or, not both.
>>>>
>>>> I am not sure I understand, except that Q#2 remains unanswered, OK. I
>>>> will first comment Marty's posts.
>>>>
>>>>
>>>> On 11 Oct 2009, at 01:30, m.a. wrote:
>>>>
>>>>> *Or the barber is a special exception to the group designated
>>>>> as "men" and exists on a higher level of being. Therefore he can
>>>>> shave himself without transgressing the rule as stated in the
>>>>> premise. Isn't this one of Russell's paradoxes? marty a.*
>>>>
>>>> Well, if the barber is not human, there is indeed no problem. But
>>>> here the fact that it can be a woman, and that usually a barber is a
>>>> human being, and that the question refer to a gender strongly suggest
>>>> that the solution "the barber is a woman" is more reasonable that
>>>> "the barber is an extraterrestrial". I think.
>>>>
>>>>> And didn't Russell decide that this type of paradox should be
>>>>> outlawed from allowable statements within the practice of
>>>>> logic? m.a.
>>>>
>>>> Nice you see the relation with Russel's paradox. This is a very deep
>>>> paradox which shows we have to handle the notion of sets with some
>>>> care. Torgny Tholerus already mentionned this, and he defended the
>>>> idea this is an argument for ultrafinitism, which in my opinion is
>>>> like throwing the baby (the infinite sets) with the water of the bath.
>>>>
>>>> If we dare to consider that the collection of *all* sets is itself a
>>>> set, we have a nice example of a set which contains itself as an
>>>> element.
>>>> This is not problematical in itself, and in some axiomatic set
>>>> theories, some sets can belong to themselves.
>>>>
>>>> What becomes problematical is the idea of defining a set in intension
>>>> by using *any* criteria.
>>>> Indeed, let us call *universe*, U, the set of all sets. U belongs-to
>>>> U. But {1, 2} does not belongs to {1, 2}, so some sets belong to
>>>> themselves and some sets don't. So it looks like we could define a
>>>> new set E of which contains all the sets which does not belongs to
>>>> themselves. For example clearly the set {1, 2} is an element of E,
>>>> and U is not an element of E.
>>>> But then we are in trouble. Does E belongs to E?
>>>> If E belongs to E, then he contradicts the definition of E, which
>>>> contains only those set which does not belong to themselves. So E has
>>>> to not belong to E. But then E does verify its own definition, so
>>>> that he does belong to E. So E belongs to E and E does not belong to
>>>> E. Damned.
>>>>
>>>> Well, this proves that the intuitive idea of set is inconsistent. We
>>>> do have to make the notion more precise to avoid such kind of
>>>> reasoning. All the many very different attempts to make the notion of
>>>> set precise have lead toward interesting mathematics, philosophy and
>>>> even religion (i think). But this would lead us far away of the
>>>> topic. We will have opportunity to come back on this. With the most
>>>> usual axiomatic set theories, the set of all sets is not a set, and
>>>> the criteria to defined set in intension is usually weakened. So much
>>>> that some axioms have to be added to get a reasonably rich theory.
>>>>
>>>>
>>>> Question 2.
>>>>
>>>>> 2) What the hell has all this to do with diagonalization, ... and
>>>>> universal machine?
>>>>>
>>>>
>>>> Let us write (x y) to say that some relation between x and y exists.
>>>> In the problem, for example, (x y) means that x shaves y, and x and y
>>>> are supposed to be humans.
>>>> In Russel's paradox (x y) means that x belongs to y, that is X
>>>> contains y as an element, and x and y are supposed to be sets.
>>>>
>>>> Argument by diagonalization always proceeds by using the diagonal
>>>> twice. Which diagonal?
>>>>
>>>> 1) the first diagonal:
>>>>
>>>> Well (x y) is a couple, and so belongs to the cartesian product of
>>>> the set (of those x, y) with itself. Put in another way, if you look
>>>> at all (x y) you get a matrix of pair of things (humans in the
>>>> problem, sets in the paradox).
>>>>
>>>> OK?
>>>>
>>>> Well, the (x x) will constituted the diagonal of that matrix. x is
>>>> supposed to vary in their respective domain (the humans in the
>>>> village, the set, in the universe of all sets.
>>>>
>>>> In the village, this gives something like (Sophie Sophie) (Claude
>>>> Claude) (Arthur Arthur) etc. As long as there are inhabitants in the
>>>> village. With the sets, the diagonal is any couple (x x) with x an
>>>> arbitrary set.
>>>>
>>>> The barber, let us call it B, and the paradoxical set E from above
>>>> are defined in a very similar way, said "by diagonalization", because
>>>> it involves the diagonal (x, x).
>>>>
>>>> The barber is defined by the condition that he shaves all and only
>>>> the men who does not shave themselves.
>>>>
>>>> B shaves x
>>>> if and only if
>>>> x is a man and NOT (x x). "NOT (x,x)" means that x does not shave
>>>> x. OK?
>>>>
>>>> E is defined by the condition that it contains all and only the sets
>>>> which does not contain themselves as element.
>>>>
>>>> E contain x as element
>>>> if and only if
>>>> NOT(x x)
>>>>
>>>> 2) The second diagonal:
>>>>
>>>> Consist in looking what happen to the barber B, or the set E, when
>>>> applied to itself.
>>>>
>>>> The second diagonalisation is the question (B B)?, or the question
>>>> (E E)?
>>>>
>>>> (B B)? = Does B shaves B?
>>>>
>>>> And then, by definition of the barber B, if it is a man, we get a
>>>> contradiction. Fortunately no contradiction occurs in case the barber
>>>> is a woman. If he is a man, he has to shave himself if and only if he
>>>> does not shave himself. If she is a woman, then she does not shave
>>>> herself and has no obligation to do given that the barber shaves
>>>> *only* men, by definition. So here, we have just proved that in that
>>>> village the barber is a woman. Or, taking Marty's remark into
>>>> account; we have proved that IF the barber is a human, THEN it is a
>>>> woman. No contradiction occurs if the barber is a god, an
>>>> extraterrestrial or a machine, with or without gender. It can be
>>>> anything not shaving itself, and shaving by definition only the men
>>>> of the village.
>>>>
>>>> (E E)? = Does the set E contains itself as an element?
>>>>
>>>> If yes: then it violates its own definition.
>>>> If no: well, it violates again its definition.
>>>>
>>>> With (B B), we "prove a theorem", thanks to the saving condition
>>>> excluding the possibility that (B B) is true in advance.
>>>> With (E E) we get a genuine difficulty showing that the naïve idea of
>>>> sets is inconsistent.
>>>>
>>>> And what if we delete the saving condition in the Barber problem,
>>>> leading us to the "usual" Barber paradox. What if we say, with x
>>>> varying on all humans (making barber shaving all womans, unless using
>>>> John's proposal for the notion of "not shaving").
>>>>
>>>> First diagonalisation:
>>>>
>>>> B shaves x
>>>> if and only if
>>>> NOT (x x).
>>>>
>>>> Well, second diagonalisation, we get:
>>>>
>>>> (B B)
>>>> if and only if
>>>> NOT(B B)
>>>>
>>>> A contradiction. Is it catastrophical? Not at all, it is a
>>>> contradiction only assuming such a village exists. So it is only a
>>>> proof that nowhere in any consistent reality or galaxies,
>>>> multiverses, whatsoever you will ever find a barber, inhabiting a
>>>> village and shaving all and only all the inhabitants who don't shave
>>>> themselves. You will not find it for the same reason you will never
>>>> find a square with only three sides, (unless dreaming or
>>>> hallucinating or something?).
>>>>
>>>> Do you see the two diagonalisations in Cantor theorem's proof? And in
>>>> Kleene's proof?
>>>>
>>>> We suppose there is a bijection between N and some set of functions.
>>>> So we suppose there is an indexing of the functions, f_i available.
>>>> The first diagonalisation is in the definition of g:
>>>>
>>>> g(n) = f_n(n) + 1
>>>>
>>>>
>>>> Then, for "good" or "bad" reasons, according of the context, we
>>>> suppose g belongs to the set of f_n, so that we can apply g on its
>>>> own index, that is the second diagonalization, and get wonderful
>>>> variate results according again the context.
>>>>
>>>> Actually
>>>>
>>>> 1) when f_i are supposed to be a bijection between N and N^N, we get
>>>> a contradiction. Showing that N^N are not enumerable.
>>>> 2) when f_i are supposed to be a computable bijection between N and
>>>> N^N-comp, we get a contradiction. Showing that, although enumerable,
>>>> 2^N-comp and N^N-comp are not computably enumerable.
>>>> 3) when f_i are supposed to belong to an universal sequence of
>>>> N^N-comp, we ... crash the universal machine, and find ourself unable
>>>> to prevent by any means such crashing without destroying the machine
>>>> universality. Showing that if we want *all*l total computable
>>>> functions in the universal sequence N^N-partial-comp, they will be
>>>> hidden in a non solvable ways (Pi-2 complete) among the partial
>>>> functions. Partial function are like ignorance tunnels, or abysses,
>>>> in the reality with which universal machines can be confronted.
>>>>
>>>> I will come back on this, and develop, but this could make sense for
>>>> those who have followed the last posts, in this thread.
>>>>
>>>> Precisely N^N-comp is the set of functions from N to N which are
>>>> computable.
>>>> N^N-partial-comp is the set of partial functions from N to N which
>>>> are computable on their domains. Those partial functions are either
>>>> defined on all N, and called total functions, or they are not defined
>>>> for some number, and which, strictly speaking are functions from a
>>>> subset of N to N.
>>>>
>>>> Take it easy. I intend to summarize and come back on some crucial
>>>> points, soon or a bit later.
>>>>
>>>> Bruno
>>>>
>>>>
>>>>
>>>>> On Fri, Oct 9, 2009 at 12:00 PM, Bruno Marchal <marchal@...
>>>>> <mailto:marchal@...>
>>>>> <mailto:marchal@...>> wrote:
>>>>>
>>>>>
>>>>> Hi,
>>>>>
>>>>> I am so buzy that I have not the time to give long explanations,
>>>>> so I
>>>>> give here a short exercise and a subject of reflexion instead.
>>>>>
>>>>> Exercise:
>>>>>
>>>>> There is Tyrannic country where by law it was forbidden for any
>>>>> man to
>>>>> have a beard.
>>>>> And there is village, in that country, and it is said that there
>>>>> is a
>>>>> barber in that village, who shaves all and only the men who don't
>>>>> shave themselves.
>>>>>
>>>>> Two questions:
>>>>>
>>>>> 1) What is the gender of the barber?
>>>>> 2) What the hell has all this to do with diagonalization, ... and
>>>>> universal machine?
>>>>>
>>>>> Have a good day,
>>>>>
>>>>> Bruno
>>>>>
>>>>> http://iridia.ulb.ac.be/~marchal/
>>>>> <http://iridia.ulb.ac.be/%7Emarchal/>
>>>>> <http://iridia.ulb.ac.be/%7Emarchal/>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>
>>>> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>
>>> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
>>>
>>>
>>>
>>> t?hl=en
>>> -~----------~----~----~----~------~----~------~--~---
>>>
>>
>>
>>
>>
>
> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
>
>
>
>
> >

Re: The seven step series (november 2009)

2009-11-10T00:56:59Z

On 09 Nov 2009, at 20:43, Brent Meeker wrote:

Bruno Marchal wrote:

Hi,

Let us come back on the "seven step" thread.

Let me recall the initial motivation. The movie graph argument (cf the
MGA thread) shows that it is senseless to attach consciousness to the
physical activity of a brain or a computer.

If we keep the computational thesis for the cognitive process, we have
to associate consciousness to the computation, and not to its physical
realization. Actually we have to explain what is a "physical
realization" from the existence of computations.

But then we have to understand better what we mean by computation, in
the mathematical sense, given that we cannot use any physics, at this
stage.

Luckily, the notion of computation has been discovered last century by
mathematicians. They were motivated by the foundation of mathematics
after the "crisis" of set theory.

So what is a computation? Let us try some definitions.

Attempt 1: A computation is a sequence of computational states.

If we agree with this, it remains to define what is a computational
states. But the definition above misses something important. I suspect
everything can be "recoded" as a sequence of computational states, and
this could be the reason why some are willing to say that rock and
thinks like that are conscious.

A physicist could say that what is lacking is a genuine causality
relation which links the states from the sequence of computational
states. But:
- in the context of the MGA argument, this should be seen as a red herring
- the notion of causality is extremely vague, even for a materialist.

So:

Attempt 2: A computation is a sequence of computational states
obtained sequentially through the activity of some machine.

This is actually a good definition, except that we have to define
(without using physics) what we mean by activity, and machine. This
may be problematic because we want to define activity by a sequence of
state of some machine ... So:

I don't think it's very good since it depends on the notion of
"computational states" to define computation. It is not clear that any
sequence of states cannot be "computational states". It seems to me
that we really take as primitive the concept of a function, something
that is given some information and transforms it into some other
information. That's what we think brains do - and they do a lot of it
which is not conscious. When we have abstracted away what the
information is about, we can regard it just as a string or number and
apply the ideas of Turing, Church, et al to the transformation as a
computation. But we have left behind the idea that the information was
about something or represented something. In the context of a
computation as a consciousness this representation is a relation between
the information being transformed and the world of which one is
conscious. So it seems you have ignored physics rather than explained
it. However, I can accept it as an ansatz in hope that the explanation
will emerge in the end.

The problem which appears taking only the function is that a function can be computed in many different way. For example here is a way to compute the factorial function:

BEGIN

READ INPUT N

SIMULATE BRENT MEEKER DRINKING COFFEE

IF BRENT SAYS "GOOD" OUTPUT N*(N-1)* ... *1

IF BRENT SAYS "BAD" OUTPUT N*(N-1)* ... *1

IF BRENT SAYS NOTHING, AFTER AWHILE, OUTPUT N*(N-1)* ... *1

END

That program will go through the right computational state corresponding to you drinking coffee, yet compute the same function that any more reasonable way to compute the factorial.

It will be impossible to dismiss those "computational states" if we want a comp supervenience thesis.

Attempt 3: a computation is a sequence of states such that it exists a
machine going through that sequence of states when computed by ...

Well, we cannot refer to activity or to a physical implementation, so
what?

Attempt 4

A computation is a sequence of states of some machine when executed by
some Universal Machine.

That is a progress, in case we succeed in defining "executed by some
universal machine", without using physics. But now we have the problem

Does a universal machine exist? And what is the mathematical meaning
of "execution".

But now, Church Thesis (Post, Church, Turing, Markov Thesis) is a
strengthening of the following weaker thesis: It exists a universal
machine.

And, all those machines, for Post, Turing, were mathematical
construction, right at the beginning.

Church thesis is strictly speaking the statement that his formal
(mathematical) system, known as Lambda Calculus, is universal with
respect to computability. The basic entity there are the lambda
expressions (those little cousins of the combinators, for those who
remembers old threads).

Turing thesis is that the language describing Turing machines is
universal with respect of that same class, and soon it will be proved
that they are equivalent indeed, making Church thesis equivalent to
Turing thesis, (and equivalent to "Post law").

Then Turing proved the existence of the "universal Turing Machine",
and indeed, since we know now that for each such universal system for
such system the "understanding of the language" can be encoded in the
language itself. So there is a universal lambda expression. There is a
universal Turing Machine. A universal Post production system, or a
Fortran interpreter (or compiled) in Fortran, or a Lisp intepreter in
Lisp.

Some may ask "which universal machine?". But the whole point of
classical computationalism (and UDA) consists in showing that below
your (our common) substitution level, we have to take account of all
universal machines. Any universal dovetailer dovetails on all of them.
So even if only one computation "wins", it has to be justify by a
(relative) sum on all computations.

I have suggested to take the combinators, without success, so I will
suggest later to take Robinson Arithmetic, which is Turing Universal,
as seen as a computer. It is really very elementary arithmetic.
Very simple cellular automata rules leads to universality, in this
Church Turing sense, like the "game of life" by Conway. Universality
is somehow cheap, and it happens that elementary arithmetic (with
zero, the successor rule, addition and multiplication) is already
Turing universal.

"being a piece of computations" is equivalent with "being executed by
the universal dovetailer", and such a proposition can be translated
into elementary arithmetic. This is equivalent with Gödel's showing
how to translated statements about propositions, theories, machines,
into statement about numbers.

But be careful to understand what happen here. It is not that the laws
of computations or universal machine dream are so easy that we can
represent them by number relation, the real discovery is that the
relation among numbers can be very complex.

That is why I insist so much that an understanding already of just
Church thesis makes you modest, even just about what you can prove
about numbers.

OK? Any question about the diagonalizations of Cantor and Kleene?

I need this for the understanding of what the phi_i are. A universal
number will be a number u such that phi_u(x, y) = phi_x(y). (with
"(x,y)" represents a number through a computable bijection).
Could you remind me what the phi_i are? The enumerated partial functions?

The enumerated so called "partial computable functions".

To get them, take your favorite universal system (fortran, lisp, c++, java, whatever), write down the grammatically correct description of function (of one argument, say, that is, from N to N). Put those codes in lexicographical order, and you get the corresponding phi_i: phi_1, phi_2, ..., and their domain W_1, W_2, W_3, ...

With Church thesis, all the computable functions (having the domain N) will belong to that list, but there will be no algorithm capable of telling in advance for any phi_i if it compute partial computable function or a computable functions.

Given that this is a key point for everything which will follow, I have to be sure that most people understand exactly why this has to be so.

So I will come back on this.

Thanks for the feedback,

Bruno

Brent

The key point is that the notion of computation can be defined in
arithmetic. By Church thesis, limiting the computations to those
definable in arithmetic does not eliminate any computations.

So the computational supervenience thesis is also equivalent with the
arithmetical supervenience thesis.

Another important mathematical point is that Universality for
computations entails non universality for provability. That is
incompleteness. Universal machine have capabilities far beyond what
they can prove and known. The universal machine can lost itself in his
own creation. And, ASSUMING Church thesis, the existence of the
universal machine is a theorem of elementary arithmetic.

It reminds me Aurobindo:

/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/

Any questions, remarks, comments?

Bruno

On 11 Oct 2009, at 19:53, Bruno Marchal wrote:

Hi John, hi Marty,
On 10 Oct 2009, at 21:47, John Mikes wrote:

Bruno, we had similar puzzles in middle school in the 30s.
The barber could not shave himself because he shaved only those who
did not shave themselves (and shaved all). So for (Q #1) in the 1st
vriant
*she(?)* was a female, unless *he(?)* was a beardless male

You are right. The barber gender is female. I don't see why you add
that he could be a beardless male. It is part of the problem that we
are in a tyrannic country where no man can have a beard.

(and the 'all' refers to only the *bearded* males requiring a shave).
*
Q#2 is beyond me, I do not resort to a QM-pattern like Schrodinger's
cat.
(Sh/H)e is either-or, not both.

I am not sure I understand, except that Q#2 remains unanswered, OK. I
will first comment Marty's posts.

On 11 Oct 2009, at 01:30, m.a. wrote:

*Or the barber is a special exception to the group designated
as "men" and exists on a higher level of being. Therefore he can
shave himself without transgressing the rule as stated in the
premise. Isn't this one of Russell's paradoxes?       marty a.*

Well, if the barber is not human, there is indeed no problem. But
here the fact that it can be a woman, and that usually a barber is a
human being, and that the question refer to a gender strongly suggest
that the solution "the barber is a woman" is more reasonable that
"the barber is an extraterrestrial". I think.

And didn't Russell decide that this type of paradox should be
outlawed from allowable statements within the practice of
logic?      m.a.

Nice you see the relation with Russel's paradox. This is a very deep
paradox which shows we have to handle the notion of sets with some
care. Torgny Tholerus already mentionned this, and he defended the
idea this is an argument for ultrafinitism, which in my opinion is
like throwing the baby (the infinite sets) with the water of the bath.

If we dare to consider that the collection of *all* sets is itself a
set, we have a nice example of a set which contains itself as an
element.
This is not problematical in itself, and in some axiomatic set
theories, some sets can belong to themselves.

What becomes problematical is the idea of defining a set in intension
by using *any* criteria.
Indeed, let us call *universe*, U, the set of all sets. U belongs-to
U. But {1, 2} does not belongs to {1, 2}, so some sets belong to
themselves and some sets don't. So it looks like we could define a
new set E of which contains all the sets which does not belongs to
themselves. For example clearly the set {1, 2} is an element of E,
and U is not an element of E.
But then we are in trouble. Does E belongs to E?
If E belongs to E, then he contradicts the definition of E, which
contains only those set which does not belong to themselves. So E has
to not belong to E. But then E does verify its own definition, so
that he does belong to E. So E belongs to E and E does not belong to
E. Damned.

Well, this proves that the intuitive idea of set is inconsistent. We
do have to make the notion more precise to avoid such kind of
reasoning. All the many very different attempts to make the notion of
set precise have lead toward interesting mathematics, philosophy and
even religion (i think). But this would lead us far away of the
topic. We will have opportunity to come back on this. With the most
usual axiomatic set theories, the set of all sets is not a set, and
the criteria to defined set in intension is usually weakened. So much
that some axioms have to be added to get a reasonably rich theory.

Question 2.

   2) What the hell has all this to do with diagonalization, ... and
   universal machine?

Let us write (x y) to say that some relation between x and y exists.
In the problem, for example, (x y) means that x shaves y, and x and y
are supposed to be humans.
In Russel's paradox (x y) means that x belongs to y, that is X
contains y as an element, and x and y are supposed to be sets.

Argument by diagonalization always proceeds by using the diagonal
twice. Which diagonal?

1) the first diagonal:

Well (x y) is a couple, and so belongs to the cartesian product of
the set (of those x, y) with itself. Put in another way, if you look
at all (x y) you get a matrix of pair of things (humans in the
problem, sets in the paradox).

OK?

Well, the (x x) will constituted the diagonal of that matrix. x is
supposed to vary in their respective domain (the humans in the
village, the set, in the universe of all sets.

In the village, this gives something like (Sophie Sophie) (Claude
Claude) (Arthur Arthur) etc. As long as there are inhabitants in the
village. With the sets, the diagonal is any couple (x x) with x an
arbitrary set.

The barber, let us call it B, and the paradoxical set E from above
are defined in a very similar way, said "by diagonalization", because
it involves the diagonal (x, x).

The barber is defined by the condition that he shaves all and only
the men who does not shave themselves.

B shaves x
if and only if
x is a man and NOT (x x).    "NOT (x,x)" means that x does not shave
x. OK?

E is defined by the condition that it contains all and only the sets
which does not contain themselves as element.

E contain x as element
if and only if
NOT(x x)

2) The second diagonal:

Consist in looking what happen to the barber B, or the set E, when
applied to itself.

The second diagonalisation is the question (B B)?, or the question (E E)?

(B B)? = Does B shaves B?

And then, by definition of the barber B, if it is a man, we get a
contradiction. Fortunately no contradiction occurs in case the barber
is a woman. If he is a man, he has to shave himself if and only if he
does not shave himself. If she is a woman, then she does not shave
herself and has no obligation to do given that the barber shaves
*only* men, by definition. So here, we have just proved that in that
village the barber is a woman. Or, taking Marty's remark into
account; we have proved that IF the barber is a human, THEN it is a
woman. No contradiction occurs if the barber is a god, an
extraterrestrial or a machine, with or without gender. It can be
anything not shaving itself, and shaving by definition only the men
of the village.

(E E)? = Does the set E contains itself as an element?

If yes: then it violates its own definition.
If no: well, it violates again its definition.

With (B B), we "prove a theorem", thanks to the saving condition
excluding the possibility that (B B) is true in advance.
With (E E) we get a genuine difficulty showing that the naïve idea of
sets is inconsistent.

And what if we delete the saving condition in the Barber problem,
leading us to the "usual" Barber paradox. What if we say, with x
varying on all humans (making barber shaving all womans, unless using
John's proposal for the notion of "not shaving").

First diagonalisation:

B shaves x
if and only if
NOT (x x).

Well, second diagonalisation, we get:

(B B)
if and only if
NOT(B B)

A contradiction. Is it catastrophical? Not at all, it is a
contradiction only assuming such a village exists. So it is only a
proof that nowhere in any consistent reality or galaxies,
multiverses, whatsoever you will ever find a barber, inhabiting a
village and shaving all and only all the inhabitants who don't shave
themselves. You will not find it for the same reason you will never
find a square with only three sides, (unless dreaming or
hallucinating or something?).

Do you see the two diagonalisations in Cantor theorem's proof? And in
Kleene's proof?

We suppose there is a bijection between N and some set of functions.
So we suppose there is an indexing of the functions, f_i available.
The first diagonalisation is in the definition of g:

g(n) = f_n(n) + 1

Then, for "good" or "bad" reasons, according of the context, we
suppose g belongs to the set of f_n, so that we can apply g on its
own index, that is the second diagonalization, and get wonderful
variate results according again the context.

Actually

1) when f_i are supposed to be a bijection between N and N^N, we get
a contradiction. Showing that N^N are not enumerable.
2) when f_i are supposed to be a computable bijection between N and
N^N-comp, we get a contradiction. Showing that, although enumerable,
2^N-comp and N^N-comp are not computably enumerable.
3) when f_i are supposed to belong to an universal sequence of
N^N-comp, we ... crash the universal machine, and find ourself unable
to prevent by any means such crashing without destroying the machine
universality. Showing that if we want *all*l total computable
functions in the universal sequence N^N-partial-comp, they will be
hidden in a non solvable ways (Pi-2 complete) among the partial
functions. Partial function are like ignorance tunnels, or abysses,
in the reality with which universal machines can be confronted.

I will come back on this, and develop, but this could make sense for
those who have followed the last posts, in this thread.

Precisely N^N-comp is the set of functions from N to N which are
computable.
N^N-partial-comp is the set of partial functions from N to N which
are computable on their domains. Those partial functions are either
defined on all N, and called total functions, or they are not defined
for some number, and which, strictly speaking are functions from a
subset of N to N.

Take it easy. I intend to summarize and come back on some crucial
points, soon or a bit later.

Bruno

On Fri, Oct 9, 2009 at 12:00 PM, Bruno Marchal <marchal@...
<marchal@...>> wrote:

   Hi,

   I am so buzy that I have not the time to give long explanations,
   so I
   give here a short exercise and a subject of reflexion instead.

   Exercise:

   There is Tyrannic country where by law it was forbidden for any
   man to
   have a beard.
   And there is village, in that country, and it is said that there
   is a
   barber in that village, who shaves all and only the men who don't
   shave themselves.

   Two questions:

   1) What is the gender of the barber?
   2) What the hell has all this to do with diagonalization, ... and
   universal machine?

   Have a good day,

   Bruno

   http://iridia.ulb.ac.be/~marchal/
   <http://iridia.ulb.ac.be/%7Emarchal/>

http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>

http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>

t?hl=en
-~----------~----~----~----~------~----~------~--~---

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

Re: The seven step series (november 2009)

2009-11-09T11:43:16Z

Bruno Marchal wrote:

>
> Hi,
>
> Let us come back on the "seven step" thread.
>
> Let me recall the initial motivation. The movie graph argument (cf the
> MGA thread) shows that it is senseless to attach consciousness to the
> physical activity of a brain or a computer.
>
> If we keep the computational thesis for the cognitive process, we have
> to associate consciousness to the computation, and not to its physical
> realization. Actually we have to explain what is a "physical
> realization" from the existence of computations.
>
> But then we have to understand better what we mean by computation, in
> the mathematical sense, given that we cannot use any physics, at this
> stage.
>
> Luckily, the notion of computation has been discovered last century by
> mathematicians. They were motivated by the foundation of mathematics
> after the "crisis" of set theory.
>
> So what is a computation? Let us try some definitions.
>
> Attempt 1: A computation is a sequence of computational states.
>
> If we agree with this, it remains to define what is a computational
> states. But the definition above misses something important. I suspect
> everything can be "recoded" as a sequence of computational states, and
> this could be the reason why some are willing to say that rock and
> thinks like that are conscious.
>
> A physicist could say that what is lacking is a genuine causality
> relation which links the states from the sequence of computational
> states. But:
> - in the context of the MGA argument, this should be seen as a red herring
> - the notion of causality is extremely vague, even for a materialist.
>
> So:
>
> Attempt 2: A computation is a sequence of computational states
> obtained sequentially through the activity of some machine.
>
> This is actually a good definition, except that we have to define
> (without using physics) what we mean by activity, and machine. This
> may be problematic because we want to define activity by a sequence of
> state of some machine ... So:

I don't think it's very good since it depends on the notion of
"computational states" to define computation. It is not clear that any
sequence of states cannot be "computational states". It seems to me
that we really take as primitive the concept of a function, something
that is given some information and transforms it into some other
information. That's what we think brains do - and they do a lot of it
which is not conscious. When we have abstracted away what the
information is about, we can regard it just as a string or number and
apply the ideas of Turing, Church, et al to the transformation as a
computation. But we have left behind the idea that the information was
about something or represented something. In the context of a
computation as a consciousness this representation is a relation between
the information being transformed and the world of which one is
conscious. So it seems you have ignored physics rather than explained
it. However, I can accept it as an ansatz in hope that the explanation
will emerge in the end.

>
> Attempt 3: a computation is a sequence of states such that it exists a
> machine going through that sequence of states when computed by ...
>
> Well, we cannot refer to activity or to a physical implementation, so
> what?
>
> Attempt 4
>
> A computation is a sequence of states of some machine when executed by
> some Universal Machine.
>
> That is a progress, in case we succeed in defining "executed by some
> universal machine", without using physics. But now we have the problem
>
> Does a universal machine exist? And what is the mathematical meaning
> of "execution".
>
> But now, Church Thesis (Post, Church, Turing, Markov Thesis) is a
> strengthening of the following weaker thesis: It exists a universal
> machine.
>
> And, all those machines, for Post, Turing, were mathematical
> construction, right at the beginning.
>
> Church thesis is strictly speaking the statement that his formal
> (mathematical) system, known as Lambda Calculus, is universal with
> respect to computability. The basic entity there are the lambda
> expressions (those little cousins of the combinators, for those who
> remembers old threads).
>
> Turing thesis is that the language describing Turing machines is
> universal with respect of that same class, and soon it will be proved
> that they are equivalent indeed, making Church thesis equivalent to
> Turing thesis, (and equivalent to "Post law").
>
> Then Turing proved the existence of the "universal Turing Machine",
> and indeed, since we know now that for each such universal system for
> such system the "understanding of the language" can be encoded in the
> language itself. So there is a universal lambda expression. There is a
> universal Turing Machine. A universal Post production system, or a
> Fortran interpreter (or compiled) in Fortran, or a Lisp intepreter in
> Lisp.
>
> Some may ask "which universal machine?". But the whole point of
> classical computationalism (and UDA) consists in showing that below
> your (our common) substitution level, we have to take account of all
> universal machines. Any universal dovetailer dovetails on all of them.
> So even if only one computation "wins", it has to be justify by a
> (relative) sum on all computations.
>
> I have suggested to take the combinators, without success, so I will
> suggest later to take Robinson Arithmetic, which is Turing Universal,
> as seen as a computer. It is really very elementary arithmetic.
> Very simple cellular automata rules leads to universality, in this
> Church Turing sense, like the "game of life" by Conway. Universality
> is somehow cheap, and it happens that elementary arithmetic (with
> zero, the successor rule, addition and multiplication) is already
> Turing universal.
>
> "being a piece of computations" is equivalent with "being executed by
> the universal dovetailer", and such a proposition can be translated
> into elementary arithmetic. This is equivalent with Gödel's showing
> how to translated statements about propositions, theories, machines,
> into statement about numbers.
>
> But be careful to understand what happen here. It is not that the laws
> of computations or universal machine dream are so easy that we can
> represent them by number relation, the real discovery is that the
> relation among numbers can be very complex.
>
> That is why I insist so much that an understanding already of just
> Church thesis makes you modest, even just about what you can prove
> about numbers.
>
> OK? Any question about the diagonalizations of Cantor and Kleene?
>
> I need this for the understanding of what the phi_i are. A universal
> number will be a number u such that phi_u(x, y) = phi_x(y). (with
> "(x,y)" represents a number through a computable bijection).

Could you remind me what the phi_i are? The enumerated partial functions?

Brent

>
> The key point is that the notion of computation can be defined in
> arithmetic. By Church thesis, limiting the computations to those
> definable in arithmetic does not eliminate any computations.
>
> So the computational supervenience thesis is also equivalent with the
> arithmetical supervenience thesis.
>
> Another important mathematical point is that Universality for
> computations entails non universality for provability. That is
> incompleteness. Universal machine have capabilities far beyond what
> they can prove and known. The universal machine can lost itself in his
> own creation. And, ASSUMING Church thesis, the existence of the
> universal machine is a theorem of elementary arithmetic.
>
> It reminds me Aurobindo:
>
>
> /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/
>
>
> Any questions, remarks, comments?
>
> Bruno
>
>
>
>
>
>
> On 11 Oct 2009, at 19:53, Bruno Marchal wrote:
>
>> Hi John, hi Marty,
>> On 10 Oct 2009, at 21:47, John Mikes wrote:
>>
>>> Bruno, we had similar puzzles in middle school in the 30s.
>>> The barber could not shave himself because he shaved only those who
>>> did not shave themselves (and shaved all). So for (Q #1) in the 1st
>>> vriant
>>> *she(?)* was a female, unless *he(?)* was a beardless male
>>
>>
>> You are right. The barber gender is female. I don't see why you add
>> that he could be a beardless male. It is part of the problem that we
>> are in a tyrannic country where no man can have a beard.
>>
>>
>>
>>
>>> (and the 'all' refers to only the *bearded* males requiring a shave).
>>> *
>>> Q#2 is beyond me, I do not resort to a QM-pattern like Schrodinger's
>>> cat.
>>> (Sh/H)e is either-or, not both.
>>
>> I am not sure I understand, except that Q#2 remains unanswered, OK. I
>> will first comment Marty's posts.
>>
>>
>> On 11 Oct 2009, at 01:30, m.a. wrote:
>>
>>> *Or the barber is a special exception to the group designated
>>> as "men" and exists on a higher level of being. Therefore he can
>>> shave himself without transgressing the rule as stated in the
>>> premise. Isn't this one of Russell's paradoxes? marty a.*
>>
>> Well, if the barber is not human, there is indeed no problem. But
>> here the fact that it can be a woman, and that usually a barber is a
>> human being, and that the question refer to a gender strongly suggest
>> that the solution "the barber is a woman" is more reasonable that
>> "the barber is an extraterrestrial". I think.
>>
>>> And didn't Russell decide that this type of paradox should be
>>> outlawed from allowable statements within the practice of
>>> logic? m.a.
>>
>> Nice you see the relation with Russel's paradox. This is a very deep
>> paradox which shows we have to handle the notion of sets with some
>> care. Torgny Tholerus already mentionned this, and he defended the
>> idea this is an argument for ultrafinitism, which in my opinion is
>> like throwing the baby (the infinite sets) with the water of the bath.
>>
>> If we dare to consider that the collection of *all* sets is itself a
>> set, we have a nice example of a set which contains itself as an
>> element.
>> This is not problematical in itself, and in some axiomatic set
>> theories, some sets can belong to themselves.
>>
>> What becomes problematical is the idea of defining a set in intension
>> by using *any* criteria.
>> Indeed, let us call *universe*, U, the set of all sets. U belongs-to
>> U. But {1, 2} does not belongs to {1, 2}, so some sets belong to
>> themselves and some sets don't. So it looks like we could define a
>> new set E of which contains all the sets which does not belongs to
>> themselves. For example clearly the set {1, 2} is an element of E,
>> and U is not an element of E.
>> But then we are in trouble. Does E belongs to E?
>> If E belongs to E, then he contradicts the definition of E, which
>> contains only those set which does not belong to themselves. So E has
>> to not belong to E. But then E does verify its own definition, so
>> that he does belong to E. So E belongs to E and E does not belong to
>> E. Damned.
>>
>> Well, this proves that the intuitive idea of set is inconsistent. We
>> do have to make the notion more precise to avoid such kind of
>> reasoning. All the many very different attempts to make the notion of
>> set precise have lead toward interesting mathematics, philosophy and
>> even religion (i think). But this would lead us far away of the
>> topic. We will have opportunity to come back on this. With the most
>> usual axiomatic set theories, the set of all sets is not a set, and
>> the criteria to defined set in intension is usually weakened. So much
>> that some axioms have to be added to get a reasonably rich theory.
>>
>>
>> Question 2.
>>
>>> 2) What the hell has all this to do with diagonalization, ... and
>>> universal machine?
>>>
>>
>> Let us write (x y) to say that some relation between x and y exists.
>> In the problem, for example, (x y) means that x shaves y, and x and y
>> are supposed to be humans.
>> In Russel's paradox (x y) means that x belongs to y, that is X
>> contains y as an element, and x and y are supposed to be sets.
>>
>> Argument by diagonalization always proceeds by using the diagonal
>> twice. Which diagonal?
>>
>> 1) the first diagonal:
>>
>> Well (x y) is a couple, and so belongs to the cartesian product of
>> the set (of those x, y) with itself. Put in another way, if you look
>> at all (x y) you get a matrix of pair of things (humans in the
>> problem, sets in the paradox).
>>
>> OK?
>>
>> Well, the (x x) will constituted the diagonal of that matrix. x is
>> supposed to vary in their respective domain (the humans in the
>> village, the set, in the universe of all sets.
>>
>> In the village, this gives something like (Sophie Sophie) (Claude
>> Claude) (Arthur Arthur) etc. As long as there are inhabitants in the
>> village. With the sets, the diagonal is any couple (x x) with x an
>> arbitrary set.
>>
>> The barber, let us call it B, and the paradoxical set E from above
>> are defined in a very similar way, said "by diagonalization", because
>> it involves the diagonal (x, x).
>>
>> The barber is defined by the condition that he shaves all and only
>> the men who does not shave themselves.
>>
>> B shaves x
>> if and only if
>> x is a man and NOT (x x). "NOT (x,x)" means that x does not shave
>> x. OK?
>>
>> E is defined by the condition that it contains all and only the sets
>> which does not contain themselves as element.
>>
>> E contain x as element
>> if and only if
>> NOT(x x)
>>
>> 2) The second diagonal:
>>
>> Consist in looking what happen to the barber B, or the set E, when
>> applied to itself.
>>
>> The second diagonalisation is the question (B B)?, or the question (E E)?
>>
>> (B B)? = Does B shaves B?
>>
>> And then, by definition of the barber B, if it is a man, we get a
>> contradiction. Fortunately no contradiction occurs in case the barber
>> is a woman. If he is a man, he has to shave himself if and only if he
>> does not shave himself. If she is a woman, then she does not shave
>> herself and has no obligation to do given that the barber shaves
>> *only* men, by definition. So here, we have just proved that in that
>> village the barber is a woman. Or, taking Marty's remark into
>> account; we have proved that IF the barber is a human, THEN it is a
>> woman. No contradiction occurs if the barber is a god, an
>> extraterrestrial or a machine, with or without gender. It can be
>> anything not shaving itself, and shaving by definition only the men
>> of the village.
>>
>> (E E)? = Does the set E contains itself as an element?
>>
>> If yes: then it violates its own definition.
>> If no: well, it violates again its definition.
>>
>> With (B B), we "prove a theorem", thanks to the saving condition
>> excluding the possibility that (B B) is true in advance.
>> With (E E) we get a genuine difficulty showing that the naïve idea of
>> sets is inconsistent.
>>
>> And what if we delete the saving condition in the Barber problem,
>> leading us to the "usual" Barber paradox. What if we say, with x
>> varying on all humans (making barber shaving all womans, unless using
>> John's proposal for the notion of "not shaving").
>>
>> First diagonalisation:
>>
>> B shaves x
>> if and only if
>> NOT (x x).
>>
>> Well, second diagonalisation, we get:
>>
>> (B B)
>> if and only if
>> NOT(B B)
>>
>> A contradiction. Is it catastrophical? Not at all, it is a
>> contradiction only assuming such a village exists. So it is only a
>> proof that nowhere in any consistent reality or galaxies,
>> multiverses, whatsoever you will ever find a barber, inhabiting a
>> village and shaving all and only all the inhabitants who don't shave
>> themselves. You will not find it for the same reason you will never
>> find a square with only three sides, (unless dreaming or
>> hallucinating or something?).
>>
>> Do you see the two diagonalisations in Cantor theorem's proof? And in
>> Kleene's proof?
>>
>> We suppose there is a bijection between N and some set of functions.
>> So we suppose there is an indexing of the functions, f_i available.
>> The first diagonalisation is in the definition of g:
>>
>> g(n) = f_n(n) + 1
>>
>>
>> Then, for "good" or "bad" reasons, according of the context, we
>> suppose g belongs to the set of f_n, so that we can apply g on its
>> own index, that is the second diagonalization, and get wonderful
>> variate results according again the context.
>>
>> Actually
>>
>> 1) when f_i are supposed to be a bijection between N and N^N, we get
>> a contradiction. Showing that N^N are not enumerable.
>> 2) when f_i are supposed to be a computable bijection between N and
>> N^N-comp, we get a contradiction. Showing that, although enumerable,
>> 2^N-comp and N^N-comp are not computably enumerable.
>> 3) when f_i are supposed to belong to an universal sequence of
>> N^N-comp, we ... crash the universal machine, and find ourself unable
>> to prevent by any means such crashing without destroying the machine
>> universality. Showing that if we want *all*l total computable
>> functions in the universal sequence N^N-partial-comp, they will be
>> hidden in a non solvable ways (Pi-2 complete) among the partial
>> functions. Partial function are like ignorance tunnels, or abysses,
>> in the reality with which universal machines can be confronted.
>>
>> I will come back on this, and develop, but this could make sense for
>> those who have followed the last posts, in this thread.
>>
>> Precisely N^N-comp is the set of functions from N to N which are
>> computable.
>> N^N-partial-comp is the set of partial functions from N to N which
>> are computable on their domains. Those partial functions are either
>> defined on all N, and called total functions, or they are not defined
>> for some number, and which, strictly speaking are functions from a
>> subset of N to N.
>>
>> Take it easy. I intend to summarize and come back on some crucial
>> points, soon or a bit later.
>>
>> Bruno
>>
>>
>>
>>> On Fri, Oct 9, 2009 at 12:00 PM, Bruno Marchal <marchal@...
>>> <mailto:marchal@...>> wrote:
>>>
>>>
>>> Hi,
>>>
>>> I am so buzy that I have not the time to give long explanations,
>>> so I
>>> give here a short exercise and a subject of reflexion instead.
>>>
>>> Exercise:
>>>
>>> There is Tyrannic country where by law it was forbidden for any
>>> man to
>>> have a beard.
>>> And there is village, in that country, and it is said that there
>>> is a
>>> barber in that village, who shaves all and only the men who don't
>>> shave themselves.
>>>
>>> Two questions:
>>>
>>> 1) What is the gender of the barber?
>>> 2) What the hell has all this to do with diagonalization, ... and
>>> universal machine?
>>>
>>> Have a good day,
>>>
>>> Bruno
>>>
>>> http://iridia.ulb.ac.be/~marchal/
>>> <http://iridia.ulb.ac.be/%7Emarchal/>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>
>> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
>>
>>
>>
>>
>>
>>
>
> http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
>
>
>
> t?hl=en
> -~----------~----~----~----~------~----~------~--~---
>

The seven step series (november 2009)

2009-11-09T10:04:01Z

Hi,

Let us come back on the "seven step" thread.

Let me recall the initial motivation. The movie graph argument (cf the MGA thread) shows that it is senseless to attach consciousness to the physical activity of a brain or a computer.

If we keep the computational thesis for the cognitive process, we have to associate consciousness to the computation, and not to its physical realization. Actually we have to explain what is a "physical realization" from the existence of computations.

But then we have to understand better what we mean by computation, in the mathematical sense, given that we cannot use any physics, at this stage.

Luckily, the notion of computation has been discovered last century by mathematicians. They were motivated by the foundation of mathematics after the "crisis" of set theory.

So what is a computation? Let us try some definitions.

Attempt 1: A computation is a sequence of computational states.

If we agree with this, it remains to define what is a computational states. But the definition above misses something important. I suspect everything can be "recoded" as a sequence of computational states, and this could be the reason why some are willing to say that rock and thinks like that are conscious.

A physicist could say that what is lacking is a genuine causality relation which links the states from the sequence of computational states. But:

- in the context of the MGA argument, this should be seen as a red herring

- the notion of causality is extremely vague, even for a materialist.

So:

Attempt 2: A computation is a sequence of computational states obtained sequentially through the activity of some machine.

This is actually a good definition, except that we have to define (without using physics) what we mean by activity, and machine. This may be problematic because we want to define activity by a sequence of state of some machine ... So:

Attempt 3: a computation is a sequence of states such that it exists a machine going through that sequence of states when computed by ...

Well, we cannot refer to activity or to a physical implementation, so what?

Attempt 4

A computation is a sequence of states of some machine when executed by some Universal Machine.

That is a progress, in case we succeed in defining "executed by some universal machine", without using physics. But now we have the problem

Does a universal machine exist? And what is the mathematical meaning of "execution".

But now, Church Thesis (Post, Church, Turing, Markov Thesis) is a strengthening of the following weaker thesis: It exists a universal machine.

And, all those machines, for Post, Turing, were mathematical construction, right at the beginning.

Church thesis is strictly speaking the statement that his formal (mathematical) system, known as Lambda Calculus, is universal with respect to computability. The basic entity there are the lambda expressions (those little cousins of the combinators, for those who remembers old threads).

Turing thesis is that the language describing Turing machines is universal with respect of that same class, and soon it will be proved that they are equivalent indeed, making Church thesis equivalent to Turing thesis, (and equivalent to "Post law").

Then Turing proved the existence of the "universal Turing Machine", and indeed, since we know now that for each such universal system for such system the "understanding of the language" can be encoded in the language itself. So there is a universal lambda expression. There is a universal Turing Machine. A universal Post production system, or a Fortran interpreter (or compiled) in Fortran, or a Lisp intepreter in Lisp.

Some may ask "which universal machine?". But the whole point of classical computationalism (and UDA) consists in showing that below your (our common) substitution level, we have to take account of all universal machines. Any universal dovetailer dovetails on all of them. So even if only one computation "wins", it has to be justify by a (relative) sum on all computations.

I have suggested to take the combinators, without success, so I will suggest later to take Robinson Arithmetic, which is Turing Universal, as seen as a computer. It is really very elementary arithmetic.

Very simple cellular automata rules leads to universality, in this Church Turing sense, like the "game of life" by Conway. Universality is somehow cheap, and it happens that elementary arithmetic (with zero, the successor rule, addition and multiplication) is already Turing universal.

"being a piece of computations" is equivalent with "being executed by the universal dovetailer", and such a proposition can be translated into elementary arithmetic. This is equivalent with Gödel's showing how to translated statements about propositions, theories, machines, into statement about numbers.

But be careful to understand what happen here. It is not that the laws of computations or universal machine dream are so easy that we can represent them by number relation, the real discovery is that the relation among numbers can be very complex.

That is why I insist so much that an understanding already of just Church thesis makes you modest, even just about what you can prove about numbers.

OK? Any question about the diagonalizations of Cantor and Kleene?

I need this for the understanding of what the phi_i are. A universal number will be a number u such that phi_u(x, y) = phi_x(y). (with "(x,y)" represents a number through a computable bijection).

The key point is that the notion of computation can be defined in arithmetic. By Church thesis, limiting the computations to those definable in arithmetic does not eliminate any computations.

So the computational supervenience thesis is also equivalent with the arithmetical supervenience thesis.

Another important mathematical point is that Universality for computations entails non universality for provability. That is incompleteness. Universal machine have capabilities far beyond what they can prove and known. The universal machine can lost itself in his own creation. And, ASSUMING Church thesis, the existence of the universal machine is a theorem of elementary arithmetic.

It reminds me Aurobindo:

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

Any questions, remarks, comments?

Bruno

On 11 Oct 2009, at 19:53, Bruno Marchal wrote:

Hi John, hi Marty,
On 10 Oct 2009, at 21:47, John Mikes wrote:

Bruno, we had similar puzzles in middle school in the 30s.

The barber could not shave himself because he shaved only those who did not shave themselves (and shaved all). So for  (Q #1) in the 1st vriant

she(?) was a female, unless he(?) was a beardless male

You are right. The barber gender is female. I don't see why you add that he could be a beardless male. It is part of the problem that we are in a tyrannic country where no man can have a beard.

(and the 'all' refers to only the bearded males requiring a shave).

*

Q#2 is beyond me, I do not resort to a QM-pattern like Schrodinger's cat.

(Sh/H)e is either-or, not both.

I am not sure I understand, except that Q#2 remains unanswered, OK. I will first comment Marty's posts.

On 11 Oct 2009, at 01:30, m.a. wrote:

Or the barber is a special exception to the group designated as "men" and exists on a higher level of being. Therefore he can shave himself without transgressing the rule as stated in the premise. Isn't this one of Russell's paradoxes?       marty a.

Well, if the barber is not human, there is indeed no problem. But here the fact that it can be a woman, and that usually a barber is a human being, and that the question refer to a gender strongly suggest that the solution "the barber is a woman" is more reasonable that "the barber is an extraterrestrial". I think.

And didn't Russell decide that this type of paradox should be outlawed from allowable statements within the practice of logic?      m.a.

Nice you see the relation with Russel's paradox. This is a very deep paradox which shows we have to handle the notion of sets with some care. Torgny Tholerus already mentionned this, and he defended the idea this is an argument for ultrafinitism, which in my opinion is like throwing the baby (the infinite sets) with the water of the bath.

If we dare to consider that the collection of *all* sets is itself a set, we have a nice example of a set which contains itself as an element.
This is not problematical in itself, and in some axiomatic set theories, some sets can belong to themselves.

What becomes problematical is the idea of defining a set in intension by using *any* criteria.
Indeed, let us call *universe*, U, the set of all sets. U belongs-to U. But {1, 2} does not belongs to {1, 2}, so some sets belong to themselves and some sets don't. So it looks like we could define a new set E of which contains all the sets which does not belongs to themselves. For example clearly the set {1, 2} is an element of E, and U is not an element of E.
But then we are in trouble. Does E belongs to E?
If E belongs to E, then he contradicts the definition of E, which contains only those set which does not belong to themselves. So E has to not belong to E. But then E does verify its own definition, so that he does belong to E. So E belongs to E and E does not belong to E. Damned.

Well, this proves that the intuitive idea of set is inconsistent. We do have to make the notion more precise to avoid such kind of reasoning. All the many very different attempts to make the notion of set precise have lead toward interesting mathematics, philosophy and even religion (i think). But this would lead us far away of the topic. We will have opportunity to come back on this. With the most usual axiomatic set theories, the set of all sets is not a set, and the criteria to defined set in intension is usually weakened. So much that some axioms have to be added to get a reasonably rich theory.

Question 2.

2) What the hell has all this to do with diagonalization, ... and
universal machine?

Let us write (x y) to say that some relation between x and y exists.
In the problem, for example, (x y) means that x shaves y, and x and y are supposed to be humans.
In Russel's paradox (x y) means that x belongs to y, that is X contains y as an element, and x and y are supposed to be sets.

Argument by diagonalization always proceeds by using the diagonal twice. Which diagonal?

1) the first diagonal:

Well (x y) is a couple, and so belongs to the cartesian product of the set (of those x, y) with itself. Put in another way, if you look at all (x y) you get a matrix of pair of things (humans in the problem, sets in the paradox).

OK?

Well, the (x x) will constituted the diagonal of that matrix. x is supposed to vary in their respective domain (the humans in the village, the set, in the universe of all sets.

In the village, this gives something like (Sophie Sophie) (Claude Claude) (Arthur Arthur) etc. As long as there are inhabitants in the village. With the sets, the diagonal is any couple (x x) with x an arbitrary set.

The barber, let us call it B, and the paradoxical set E from above are defined in a very similar way, said "by diagonalization", because it involves the diagonal (x, x).

The barber is defined by the condition that he shaves all and only the men who does not shave themselves.

B shaves x
if and only if
x is a man and NOT (x x). "NOT (x,x)" means that x does not shave x. OK?

E is defined by the condition that it contains all and only the sets which does not contain themselves as element.

E contain x as element
if and only if
NOT(x x)

2) The second diagonal:

Consist in looking what happen to the barber B, or the set E, when applied to itself.

The second diagonalisation is the question (B B)?, or the question (E E)?

(B B)? = Does B shaves B?

And then, by definition of the barber B, if it is a man, we get a contradiction. Fortunately no contradiction occurs in case the barber is a woman. If he is a man, he has to shave himself if and only if he does not shave himself. If she is a woman, then she does not shave herself and has no obligation to do given that the barber shaves *only* men, by definition. So here, we have just proved that in that village the barber is a woman. Or, taking Marty's remark into account; we have proved that IF the barber is a human, THEN it is a woman. No contradiction occurs if the barber is a god, an extraterrestrial or a machine, with or without gender. It can be anything not shaving itself, and shaving by definition only the men of the village.

(E E)? = Does the set E contains itself as an element?

If yes: then it violates its own definition.
If no: well, it violates again its definition.

With (B B), we "prove a theorem", thanks to the saving condition excluding the possibility that (B B) is true in advance.
With (E E) we get a genuine difficulty showing that the naïve idea of sets is inconsistent.

And what if we delete the saving condition in the Barber problem, leading us to the "usual" Barber paradox. What if we say, with x varying on all humans (making barber shaving all womans, unless using John's proposal for the notion of "not shaving").

First diagonalisation:

B shaves x
if and only if
NOT (x x).

Well, second diagonalisation, we get:

(B B)
if and only if
NOT(B B)

A contradiction. Is it catastrophical? Not at all, it is a contradiction only assuming such a village exists. So it is only a proof that nowhere in any consistent reality or galaxies, multiverses, whatsoever you will ever find a barber, inhabiting a village and shaving all and only all the inhabitants who don't shave themselves. You will not find it for the same reason you will never find a square with only three sides, (unless dreaming or hallucinating or something?).

Do you see the two diagonalisations in Cantor theorem's proof? And in Kleene's proof?

We suppose there is a bijection between N and some set of functions. So we suppose there is an indexing of the functions, f_i available. The first diagonalisation is in the definition of g:

g(n) = f_n(n) + 1

Then, for "good" or "bad" reasons, according of the context, we suppose g belongs to the set of f_n, so that we can apply g on its own index, that is the second diagonalization, and get wonderful variate results according again the context.

Actually

1) when f_i are supposed to be a bijection between N and N^N, we get a contradiction. Showing that N^N are not enumerable.
2) when f_i are supposed to be a computable bijection between N and N^N-comp, we get a contradiction. Showing that, although enumerable, 2^N-comp and N^N-comp are not computably enumerable.
3) when f_i are supposed to belong to an universal sequence of N^N-comp, we ... crash the universal machine, and find ourself unable to prevent by any means such crashing without destroying the machine universality. Showing that if we want *all*l total computable functions in the universal sequence N^N-partial-comp, they will be hidden in a non solvable ways (Pi-2 complete) among the partial functions. Partial function are like ignorance tunnels, or abysses, in the reality with which universal machines can be confronted.

I will come back on this, and develop, but this could make sense for those who have followed the last posts, in this thread.

Precisely N^N-comp is the set of functions from N to N which are computable.
N^N-partial-comp is the set of partial functions from N to N which are computable on their domains. Those partial functions are either defined on all N, and called total functions, or they are not defined for some number, and which, strictly speaking are functions from a subset of N to N.

Take it easy. I intend to summarize and come back on some crucial points, soon or a bit later.

Bruno

On Fri, Oct 9, 2009 at 12:00 PM, Bruno Marchal <marchal@...> wrote:

Hi,

I am so buzy that I have not the time to give long explanations, so I
give here a short exercise and a subject of reflexion instead.

Exercise:

There is Tyrannic country where by law it was forbidden for any man to
have a beard.
And there is village, in that country, and it is said that there is a
barber in that village, who shaves all and only the men who don't
shave themselves.

Two questions:

1) What is the gender of the barber?
2) What the hell has all this to do with diagonalization, ... and
universal machine?

Have a good day,

Bruno

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

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

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

Re: request for glossary + announcement that the seventh step series thread will soon be resumed

2009-11-08T05:09:48Z

I think that's the question Bruno's proof is designed to answer in the negative, a conclusion of which I have difficulty convincing myself. m.a.

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

From: jamikes@...

To: everything-list@...

Sent: Saturday, November 07, 2009 11:16 AM

Subject: Re: request for glossary + announcement that the seventh step series thread will soon be resumed

Marty,

how about my weird question: "and if 1 is wrong and what he 'sees' as OA is only a replica of the OA and is WRONG? Is 'being a replica' a human priviledge?

(Forget it!)

John M

On Fri, Nov 6, 2009 at 7:04 PM, m.a. <marty684@...> wrote:

Bruno,

Good to see you back! I have a question with reference to the experiment described in the first person indeterminacy paper. If, before the teleportation, the omniscient authority tells the subject that he will find a zero in his envelope, both subjects will expect to find a zero after the procedure, no? The subject who finds the 1, must inevitably conclude that he is in fact a duplicate since he trusts the OA implicitly and reasons that if he were the original (real) subject, he would be seeing a zero. Where is the flaw in my logic? marty a.

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

From: marchal@...

To: everything-list@...

Sent: Friday, November 06, 2009 11:45 AM

Subject: Re: request for glossary + announcement that the seventh step series thread will soon be resumed

Hi all,

Welcome to fcy

"Universal Dance Association" is quite cute :) A universal dance could be a Universal Dovetailer if "digital dance" could make sense.

UDA (in this list) is for Universal Dovetailer Argument. You should google on this term, on the net or on the everything-list archive. You may look here also for references:

http://groups.google.com/group/everything-list/web/auda

A universal dovetailer is a program which generates and execute all possible programs. It is a mathematical object and its existence follows from the Post-Church-Turing thesis.

The universal dovetailer argument is an argument which shows that the mechanist hypothesis leads to a notion of strong first person indeterminacy, and that eventually the laws of both physics and psychology/theology (quanta and qualia) have to be derived from "pure" number theory/computer science.

If I succeed to explain UDA sufficiently well, I will be able to give some account of AUDA which is far more sophisticated, and useful only to get already quantitative physical information from numbers/computer science (as opposed to UDA which "just" show that physics has to be given by a first person measure on the computations occurring in the universal dovetailing).

----

Elsevier has asked me to write some topics on its SciTopics. You may take a look at

http://www.scitopics.com/The_first_person_computationalist_indeterminacy.html

http://www.scitopics.com/Godel_Mind_and_Machine.html

Comments are welcomed.

I let you know that I will have some more time for now (October was very heavy!). So it is time to ask questions for the thread "the seven step series" (which is about the seventh step of the UDA) before I proceed. I will make a little sum up next week. There has been more than five versions of UDA already send to the list, but I am not sure everyone understand, so please ask questions. All questions are allowed on this non moderate list, so feel free, to ask anything (related) to the everything-like approach in the search of a "TOE" (Theory of everything-including-consciousness-and-person (as opposed to the TOE of the physicians which search to unify only what is observable and third person describable).

Marty, Kim, are you still there? Have you a problem with Cantor diagonal proof of the non enumerability of the set of functions from N to N (N^N)? Or do you prefer I explain this again in the sum up?

On 05 Nov 2009, at 06:03, fcy wrote:

As a newcomer to this group, there are many things I'm unable to
follow, in detail, due to unfamiliarity with many of the acronyms.

For instance, googling UDA turns up links related to the Ulster
Defense Association, the Universal Dance Association, Urban Design
Associates, and the United Dairymen of Arizona, none of which seem to
be what's being discussed here.

Thanks in advance,

fcy

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

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You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to everything-list@...
To unsubscribe from this group, send email to everything-list+unsubscribe@...
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Re: request for glossary + announcement that the seventh step series thread will soon be resumed

2009-11-07T08:16:49Z

Marty,

how about my weird question: "and if 1 is wrong and what he 'sees' as OA is only a replica of the OA and is WRONG? Is 'being a replica' a human priviledge?

(Forget it!)

John M

On Fri, Nov 6, 2009 at 7:04 PM, m.a. <marty684@...> wrote:

Bruno,

Good to see you back! I have a question with reference to the experiment described in the first person indeterminacy paper. If, before the teleportation, the omniscient authority tells the subject that he will find a zero in his envelope, both subjects will expect to find a zero after the procedure, no? The subject who finds the 1, must inevitably conclude that he is in fact a duplicate since he trusts the OA implicitly and reasons that if he were the original (real) subject, he would be seeing a zero. Where is the flaw in my logic? marty a.

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

From: marchal@...

To: everything-list@...

Sent: Friday, November 06, 2009 11:45 AM

Subject: Re: request for glossary + announcement that the seventh step series thread will soon be resumed

Hi all,

Welcome to fcy

"Universal Dance Association" is quite cute :) A universal dance could be a Universal Dovetailer if "digital dance" could make sense.

UDA (in this list) is for Universal Dovetailer Argument. You should google on this term, on the net or on the everything-list archive. You may look here also for references:

http://groups.google.com/group/everything-list/web/auda

A universal dovetailer is a program which generates and execute all possible programs. It is a mathematical object and its existence follows from the Post-Church-Turing thesis.

The universal dovetailer argument is an argument which shows that the mechanist hypothesis leads to a notion of strong first person indeterminacy, and that eventually the laws of both physics and psychology/theology (quanta and qualia) have to be derived from "pure" number theory/computer science.

If I succeed to explain UDA sufficiently well, I will be able to give some account of AUDA which is far more sophisticated, and useful only to get already quantitative physical information from numbers/computer science (as opposed to UDA which "just" show that physics has to be given by a first person measure on the computations occurring in the universal dovetailing).

----

Elsevier has asked me to write some topics on its SciTopics. You may take a look at

http://www.scitopics.com/The_first_person_computationalist_indeterminacy.html

http://www.scitopics.com/Godel_Mind_and_Machine.html

Comments are welcomed.

I let you know that I will have some more time for now (October was very heavy!). So it is time to ask questions for the thread "the seven step series" (which is about the seventh step of the UDA) before I proceed. I will make a little sum up next week. There has been more than five versions of UDA already send to the list, but I am not sure everyone understand, so please ask questions. All questions are allowed on this non moderate list, so feel free, to ask anything (related) to the everything-like approach in the search of a "TOE" (Theory of everything-including-consciousness-and-person (as opposed to the TOE of the physicians which search to unify only what is observable and third person describable).

Marty, Kim, are you still there? Have you a problem with Cantor diagonal proof of the non enumerability of the set of functions from N to N (N^N)? Or do you prefer I explain this again in the sum up?

On 05 Nov 2009, at 06:03, fcy wrote:

As a newcomer to this group, there are many things I'm unable to
follow, in detail, due to unfamiliarity with many of the acronyms.

For instance, googling UDA turns up links related to the Ulster
Defense Association, the Universal Dance Association, Urban Design
Associates, and the United Dairymen of Arizona, none of which seem to
be what's being discussed here.

Thanks in advance,

fcy

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

--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to everything-list@...
To unsubscribe from this group, send email to everything-list+unsubscribe@...
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
-~----------~----~----~----~------~----~------~--~---

Re: request for glossary + announcement that the seventh step series thread will soon be resumed

2009-11-07T04:54:12Z

Sorry, I misunderstood the premise. Thanks for the quick reply. marty a.

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

From: marchal@...

To: everything-list@...

Sent: Saturday, November 07, 2009 2:16 AM

Subject: Re: request for glossary + announcement that the seventh step series thread will soon be resumed

On 07 Nov 2009, at 01:04, m.a. wrote:

Bruno,

Good to see you back! I have a question with reference to the experiment described in the first person indeterminacy paper. If, before the teleportation, the omniscient authority tells the subject that he will find a zero in his envelope, both subjects will expect to find a zero after the procedure, no? The subject who finds the 1, must inevitably conclude that he is in fact a duplicate since he trusts the OA implicitly and reasons that if he were the original (real) subject, he would be seeing a zero. Where is the flaw in my logic? marty a.

The subject of the experience believe in comp, and knows the protocol of the experience. So he knows the "original" will be destroyed or annihilated after the scanning procedure. He know in advance that both subject are duplicate, and so "I am the duplicate" does not make sense.

Even if he decides to trust the OA, and then to abandon comp if he is in front of the "one" in the envelop, he will feel as being the original person (we still assume comp), with the memory that the OA told him that he will find "zero", which will make him rightly say "for me right now the OA was wrong, whatever I am".

The experience here was symmetrical. From the first person perspective it makes no sense at all to say "I am the duplicate". We know, and he knows, and the OA knows, in advance, that they are both "duplicate".

Bruno

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

From: marchal@...

To: everything-list@...

Sent: Friday, November 06, 2009 11:45 AM

Subject: Re: request for glossary + announcement that the seventh step series thread will soon be resumed

Hi all,

Welcome to fcy

"Universal Dance Association" is quite cute :) A universal dance could be a Universal Dovetailer if "digital dance" could make sense.

UDA (in this list) is for Universal Dovetailer Argument. You should google on this term, on the net or on the everything-list archive. You may look here also for references:

http://groups.google.com/group/everything-list/web/auda

A universal dovetailer is a program which generates and execute all possible programs. It is a mathematical object and its existence follows from the Post-Church-Turing thesis.

The universal dovetailer argument is an argument which shows that the mechanist hypothesis leads to a notion of strong first person indeterminacy, and that eventually the laws of both physics and psychology/theology (quanta and qualia) have to be derived from "pure" number theory/computer science.

If I succeed to explain UDA sufficiently well, I will be able to give some account of AUDA which is far more sophisticated, and useful only to get already quantitative physical information from numbers/computer science (as opposed to UDA which "just" show that physics has to be given by a first person measure on the computations occurring in the universal dovetailing).

----

Elsevier has asked me to write some topics on its SciTopics. You may take a look at

http://www.scitopics.com/The_first_person_computationalist_indeterminacy.html

http://www.scitopics.com/Godel_Mind_and_Machine.html

Comments are welcomed.

I let you know that I will have some more time for now (October was very heavy!). So it is time to ask questions for the thread "the seven step series" (which is about the seventh step of the UDA) before I proceed. I will make a little sum up next week. There has been more than five versions of UDA already send to the list, but I am not sure everyone understand, so please ask questions. All questions are allowed on this non moderate list, so feel free, to ask anything (related) to the everything-like approach in the search of a "TOE" (Theory of everything-including-consciousness-and-person (as opposed to the TOE of the physicians which search to unify only what is observable and third person describable).

Marty, Kim, are you still there? Have you a problem with Cantor diagonal proof of the non enumerability of the set of functions from N to N (N^N)? Or do you prefer I explain this again in the sum up?

On 05 Nov 2009, at 06:03, fcy wrote:

As a newcomer to this group, there are many things I'm unable to
follow, in detail, due to unfamiliarity with many of the acronyms.

For instance, googling UDA turns up links related to the Ulster
Defense Association, the Universal Dance Association, Urban Design
Associates, and the United Dairymen of Arizona, none of which seem to
be what's being discussed here.

Thanks in advance,

fcy

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

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

--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to everything-list@...
To unsubscribe from this group, send email to everything-list+unsubscribe@...
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
-~----------~----~----~----~------~----~------~--~---

Re: request for glossary + announcement that the seventh step series thread will soon be resumed

2009-11-06T23:16:21Z

On 07 Nov 2009, at 01:04, m.a. wrote:

Bruno,
Good to see you back! I have a question with reference to the experiment described in the first person indeterminacy paper. If, before the teleportation, the omniscient authority tells the subject that he will find a zero in his envelope, both subjects will expect to find a zero after the procedure, no? The subject who finds the 1, must inevitably conclude that he is in fact a duplicate since he trusts the OA implicitly and reasons that if he were the original (real) subject, he would be seeing a zero. Where is the flaw in my logic? marty a.

The subject of the experience believe in comp, and knows the protocol of the experience. So he knows the "original" will be destroyed or annihilated after the scanning procedure. He know in advance that both subject are duplicate, and so "I am the duplicate" does not make sense.

Even if he decides to trust the OA, and then to abandon comp if he is in front of the "one" in the envelop, he will feel as being the original person (we still assume comp), with the memory that the OA told him that he will find "zero", which will make him rightly say "for me right now the OA was wrong, whatever I am".

The experience here was symmetrical. From the first person perspective it makes no sense at all to say "I am the duplicate". We know, and he knows, and the OA knows, in advance, that they are both "duplicate".

Bruno

----- Original Message -----
From: marchal@...
To: everything-list@...
Sent: Friday, November 06, 2009 11:45 AM
Subject: Re: request for glossary + announcement that the seventh step series thread will soon be resumed

Hi all,

Welcome to fcy

"Universal Dance Association" is quite cute :) A universal dance could be a Universal Dovetailer if "digital dance" could make sense.

UDA (in this list) is for Universal Dovetailer Argument. You should google on this term, on the net or on the everything-list archive. You may look here also for references:

http://groups.google.com/group/everything-list/web/auda

A universal dovetailer is a program which generates and execute all possible programs. It is a mathematical object and its existence follows from the Post-Church-Turing thesis.

The universal dovetailer argument is an argument which shows that the mechanist hypothesis leads to a notion of strong first person indeterminacy, and that eventually the laws of both physics and psychology/theology (quanta and qualia) have to be derived from "pure" number theory/computer science.

If I succeed to explain UDA sufficiently well, I will be able to give some account of AUDA which is far more sophisticated, and useful only to get already quantitative physical information from numbers/computer science (as opposed to UDA which "just" show that physics has to be given by a first person measure on the computations occurring in the universal dovetailing).

----

Elsevier has asked me to write some topics on its SciTopics. You may take a look at

http://www.scitopics.com/The_first_person_computationalist_indeterminacy.html

http://www.scitopics.com/Godel_Mind_and_Machine.html

Comments are welcomed.

I let you know that I will have some more time for now (October was very heavy!). So it is time to ask questions for the thread "the seven step series" (which is about the seventh step of the UDA) before I proceed. I will make a little sum up next week. There has been more than five versions of UDA already send to the list, but I am not sure everyone understand, so please ask questions. All questions are allowed on this non moderate list, so feel free, to ask anything (related) to the everything-like approach in the search of a "TOE" (Theory of everything-including-consciousness-and-person (as opposed to the TOE of the physicians which search to unify only what is observable and third person describable).

Marty, Kim, are you still there? Have you a problem with Cantor diagonal proof of the non enumerability of the set of functions from N to N (N^N)? Or do you prefer I explain this again in the sum up?

On 05 Nov 2009, at 06:03, fcy wrote:

As a newcomer to this group, there are many things I'm unable to
follow, in detail, due to unfamiliarity with many of the acronyms.

For instance, googling UDA turns up links related to the Ulster
Defense Association, the Universal Dance Association, Urban Design
Associates, and the United Dairymen of Arizona, none of which seem to
be what's being discussed here.

Thanks in advance,

fcy

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

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

Re: request for glossary + announcement that the seventh step series thread will soon be resumed

2009-11-06T16:04:22Z

Bruno,

Good to see you back! I have a question with reference to the experiment described in the first person indeterminacy paper. If, before the teleportation, the omniscient authority tells the subject that he will find a zero in his envelope, both subjects will expect to find a zero after the procedure, no? The subject who finds the 1, must inevitably conclude that he is in fact a duplicate since he trusts the OA implicitly and reasons that if he were the original (real) subject, he would be seeing a zero. Where is the flaw in my logic? marty a.

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

From: marchal@...

To: everything-list@...

Sent: Friday, November 06, 2009 11:45 AM

Subject: Re: request for glossary + announcement that the seventh step series thread will soon be resumed

Hi all,

Welcome to fcy

"Universal Dance Association" is quite cute :) A universal dance could be a Universal Dovetailer if "digital dance" could make sense.

UDA (in this list) is for Universal Dovetailer Argument. You should google on this term, on the net or on the everything-list archive. You may look here also for references:

http://groups.google.com/group/everything-list/web/auda

A universal dovetailer is a program which generates and execute all possible programs. It is a mathematical object and its existence follows from the Post-Church-Turing thesis.

The universal dovetailer argument is an argument which shows that the mechanist hypothesis leads to a notion of strong first person indeterminacy, and that eventually the laws of both physics and psychology/theology (quanta and qualia) have to be derived from "pure" number theory/computer science.

If I succeed to explain UDA sufficiently well, I will be able to give some account of AUDA which is far more sophisticated, and useful only to get already quantitative physical information from numbers/computer science (as opposed to UDA which "just" show that physics has to be given by a first person measure on the computations occurring in the universal dovetailing).

----

Elsevier has asked me to write some topics on its SciTopics. You may take a look at

http://www.scitopics.com/The_first_person_computationalist_indeterminacy.html

http://www.scitopics.com/Godel_Mind_and_Machine.html

Comments are welcomed.

I let you know that I will have some more time for now (October was very heavy!). So it is time to ask questions for the thread "the seven step series" (which is about the seventh step of the UDA) before I proceed. I will make a little sum up next week. There has been more than five versions of UDA already send to the list, but I am not sure everyone understand, so please ask questions. All questions are allowed on this non moderate list, so feel free, to ask anything (related) to the everything-like approach in the search of a "TOE" (Theory of everything-including-consciousness-and-person (as opposed to the TOE of the physicians which search to unify only what is observable and third person describable).

Marty, Kim, are you still there? Have you a problem with Cantor diagonal proof of the non enumerability of the set of functions from N to N (N^N)? Or do you prefer I explain this again in the sum up?

On 05 Nov 2009, at 06:03, fcy wrote:

As a newcomer to this group, there are many things I'm unable to
follow, in detail, due to unfamiliarity with many of the acronyms.

For instance, googling UDA turns up links related to the Ulster
Defense Association, the Universal Dance Association, Urban Design
Associates, and the United Dairymen of Arizona, none of which seem to
be what's being discussed here.

Thanks in advance,

fcy

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

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Re: request for glossary + announcement that the seventh step series thread will soon be resumed

2009-11-06T08:45:30Z

Hi all,

Welcome to fcy

"Universal Dance Association" is quite cute :) A universal dance could be a Universal Dovetailer if "digital dance" could make sense.

UDA (in this list) is for Universal Dovetailer Argument. You should google on this term, on the net or on the everything-list archive. You may look here also for references:

http://groups.google.com/group/everything-list/web/auda

A universal dovetailer is a program which generates and execute all possible programs. It is a mathematical object and its existence follows from the Post-Church-Turing thesis.

The universal dovetailer argument is an argument which shows that the mechanist hypothesis leads to a notion of strong first person indeterminacy, and that eventually the laws of both physics and psychology/theology (quanta and qualia) have to be derived from "pure" number theory/computer science.

If I succeed to explain UDA sufficiently well, I will be able to give some account of AUDA which is far more sophisticated, and useful only to get already quantitative physical information from numbers/computer science (as opposed to UDA which "just" show that physics has to be given by a first person measure on the computations occurring in the universal dovetailing).

----

Elsevier has asked me to write some topics on its SciTopics. You may take a look at

http://www.scitopics.com/The_first_person_computationalist_indeterminacy.html

http://www.scitopics.com/Godel_Mind_and_Machine.html

Comments are welcomed.

I let you know that I will have some more time for now (October was very heavy!). So it is time to ask questions for the thread "the seven step series" (which is about the seventh step of the UDA) before I proceed. I will make a little sum up next week. There has been more than five versions of UDA already send to the list, but I am not sure everyone understand, so please ask questions. All questions are allowed on this non moderate list, so feel free, to ask anything (related) to the everything-like approach in the search of a "TOE" (Theory of everything-including-consciousness-and-person (as opposed to the TOE of the physicians which search to unify only what is observable and third person describable).

Marty, Kim, are you still there? Have you a problem with Cantor diagonal proof of the non enumerability of the set of functions from N to N (N^N)? Or do you prefer I explain this again in the sum up?

On 05 Nov 2009, at 06:03, fcy wrote:

As a newcomer to this group, there are many things I'm unable to
follow, in detail, due to unfamiliarity with many of the acronyms.

For instance, googling UDA turns up links related to the Ulster
Defense Association, the Universal Dance Association, Urban Design
Associates, and the United Dairymen of Arizona, none of which seem to
be what's being discussed here.

Thanks in advance,

fcy

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

Re: request for glossary

2009-11-05T23:26:18Z

Try http://everythingwiki.gcn.cx/wiki/index.php?title=Main_Page

It could do with some work, though :).

Cheers

On Wed, Nov 04, 2009 at 09:03:10PM -0800, fcy wrote:

>
> As a newcomer to this group, there are many things I'm unable to
> follow, in detail, due to unfamiliarity with many of the acronyms.
>
> For instance, googling UDA turns up links related to the Ulster
> Defense Association, the Universal Dance Association, Urban Design
> Associates, and the United Dairymen of Arizona, none of which seem to
> be what's being discussed here.
>
> Thanks in advance,
>
> fcy
>
>

--

----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpcoder@...
Australia http://www.hpcoders.com.au
----------------------------------------------------------------------------

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Re: Many-Worlds iPhone app!

2009-11-05T00:48:25Z

On 05 Nov 2009, at 04:11, Dr. John Yates wrote:

Bruno wrote

The question is then: where does that continuous information come
from? ...

I could not locate the intriguingly titled "Many-Worlds iPhone appl"
heading in this group, from which it seems to have somehow come, so
I added a copy to the bottom of this post, sorry if this duplicates but
it should interest readers here anyway.

It was a reply to the FOR list (Fabric of Reality list). But it concerns many points discussed on the everything list, so I put it in "cc".

The original "Many-Worlds iphone app" was a sort of advertising for a gadget to manage your quantum alternate future. Here:

Split the universe with this quantum-based iPhone app:

Universe Splitter <http://cheapuniverses.com/universesplitter>

Enjoy!

-- Eric Daniels

Hm, http://arxiv.org/abs/quant-ph/0104033 is interesting , though the
copy I looked up at Arxiv does not seem to have Abstract or
Conclusions.Also, interestingly, it still seems to leave many options
open.

I understood it in general terms and was also interested in the
Mandelbrot set approach of Bruno. I have several books of a
techie/coffee table approach at hand on the Mandelbrot set - as most of
us do - and I also looked at the Bruno videos
http://www.youtube.com/watch?v=RTuP02b_a7Y and
http://www.youtube.com/watch?v=-lFT4H7E7Ac

I would agree that there Bruno has something to say. However the fact is
also that neither conventional nor quantum computing cover all the real
options available - experimentally my own blog
http://ttjohn.blogspot.com/ mentions the fact that nowadays even the
so-called 'Libet half-second' is experimentally naive by the standards
of 2009. I'm thinking that there now needs to be an advance in the
Godel/Chaitin theorem approach to more theorems of a similar kind.

Could and will say more on this if and when we progress on the diagonalization technics.

By the way we are hoping to have a conference in Goa in 2010 at my
Institute for Fundamental Studies (in Goa) which I hope may help to
clarify these matters, some preliminary details on blog
http://ttjohn.blogspot.com/ .

Thanks to keep us informed.

Bruno

---------------------------------------------------------------
On 18 Oct 2009, at 01:13, Alan Forrester wrote:

The universes, are just part of a more complex structure as
explained here

http://arxiv.org/abs/quant-ph/0104033

part of that more complex structure is loads of continuous
information that is not copied and cannot be copied although we can
get access to some information about it because it affects the
probabilities of the things we can observe.

The question is then: where does that continuous information come from?
But it is easy to explain this when we assume the hypothesis that
"we", at some genuine third person description level, are Turing
emulable. In that case we get a continuous explosion of histories
(computations) going through our states already defined in arithmetic.
Our consciousness can stabilize only on the deep histories which are
also stable for a continuum of random fluctuations. Why? Because those
exists as defined by the law of elementary arithmetic, which is indeed
already Turing universal.

If the Mandelbrot set(*) M is Turing universal (or Post creative),
then it constitutes a good third person view of the multiverse. It is
constituted of an infinite but enumerable collection of tiny sub-
Mandelbrot sets, each of which is surrendered by a continuum of
histories (if you agree with the rule Y = II, that is, bifurcations of
the futures are differentiation of the pasts). You can literally see
the "histories" bifurcating infinitely often when converging on the
border of a sub-Mandelbrot set. The results of the bifurcations
organize themselves into converging "polygonal rings" with 2^n sides
(n going to the infinite).

(*) By Mandelbrot set I mean the rational Mandelbrot set: I mean his
intersection with Q X Q (Q = the rational number). See this to have a
look on 4 nices zoom (enlargement) on it. Obviously, no machines can
distinguish a zoom on M from a zoom on M intersected with Q X Q.

Here is just one video with four nice zooms on M (or M intersected
with Q X Q). The third and fifth one illustrates the convergence of
"bifurcating histories" on the border of M.

http://www.youtube.com/watch?v=RTuP02b_a7Y

If comp is true, and if M is creative, "you" are there. Each of your
possible states is dense on the border of M. There is always an
infinity of "3-you" between two "3-you". But from your own personal
perspective, it is far more complex, and a priori the M set don't
provide the information, I think you need to introduce the self-
reference logics to pursue the kind of analysis Everett has done on
the universal wave function.
Normally the quantum wave should be justified here, from M + a notion
of internal relative view.

Hmm... This de-zoom (followed by a zoom) illustrates very well too:

http://www.youtube.com/watch?v=-lFT4H7E7Ac

The relation with arithmetic is that the question of 'rational
belongness to rational M' is expressible in elementary arithmetic, as
you can guess from the existence of those zooms, if you know how a
computer functions and and what is its relation with arithmetic.

Bruno

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

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

request for glossary

2009-11-04T21:03:10Z

As a newcomer to this group, there are many things I'm unable to
follow, in detail, due to unfamiliarity with many of the acronyms.

For instance, googling UDA turns up links related to the Ulster
Defense Association, the Universal Dance Association, Urban Design
Associates, and the United Dairymen of Arizona, none of which seem to
be what's being discussed here.

Thanks in advance,

fcy

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You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to everything-list@...
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