On 24 Aug 2012, at 02:17, Alberto G. Corona wrote:

Honestly I do not find the Gödel theorem a limitation for computers.

Indeed, as Judson Webb showed the anti-mechanism argument based on Gödel is double edged, when made precise enough it becomes a tool making possible to the machine to overcome it.

I think that Penrose and other did a right translation from the Gódel theorem to a problem of a Turing machine,. But this translation can be done in a different way.

Penrose was wrong, but eventually got the main point: Gödel's incompleteness does not show that we are not machine, but does show that we cannot consistently kno which machine we are, as the duplication thought experience can also explain more easily. This is exploited in AUDA, as it leads to the arithmetical form of the indeterminacy.

Gödel already knew in 1931 that theories like his Principia Mathematica, or ZF, PA, etc. can prove their own incompleteness theorem. PA proves consistent(PA) -> non-provable-by-PA(consistent(PA)).
Consistent(PA) is non-provable-by-PA('0 = 1').

The diagonalization is a useful tool to show that non computable things exists, and non-provable-by-X or Y, but those diagonalization are mostly constructive and computable.

It is possible to design a program that modify itself by adding new axioms, included the diagonalizations, so that the number of axioms can grow for any need.


This is rutinely done for equivalent problems in rule-based expert systems or in ordinary interpreters (aided by humans) in complex domains. But reduced to integer aritmetics, A turing machine that implements a math proof system at the deep level, that is, in an interpreter where new axioms can be automatically added trough diagonalizations, may expand the set of know deductions by incorporating new axioms trough diagonalization. This is not prohibited by the Gódel theorem. What is prohibited is to know all true statements on this domain. But this also apply to humans. So a computer can realize that a new axiom is absent in his initial set and to add it, Just like humans.

Right. G* can be emulated by G. At the propositional modal level, this makes a machine able to find all its true but non provable sentences. That makes the machine an excellent mystic subject.

I do not see in this a limitation for human free will. I wrote about this before.

It helps it. And it gives a role to consciousness as a sort of universal accelerator of computations. This relies more on the length of proof theorem than incompleteness, but all those things can be related precisely.


The notion of free will based on the deterministc nature of the phisics or computation is a degenerated, false problem which is an obsession of the Positivists. Look form "degenerated" and "Positivism" to find mi opinion about that in this list if you are interested.

2012/8/24 Jason Resch <jasonre...@gmail.com>

On Thu, Aug 23, 2012 at 1:18 PM, benjayk <benjamin.jaku...@googlemail.com > wrote:

Jason Resch-2 wrote:
>> Taking the universal dovetailer, it could really mean everything (or >> nothing), just like the sentence "You can interpret whatever you want
>> into
>> this sentence..." or like the stuff that monkeys type on typewriters.
> A sentence (any string of information) can be interpreted in any possible > way, but a computation defines/creates its own meaning. If you see a > particular step in an algorithm adds two numbers, it can pretty clearly be
> interpreted as addition, for example.
A computation can't define its own meaning, since it only manipulates
symbols (that is the definition of a computer),

I think it is a rather poor definition of a computer. Some have tried to define the entire field of mathematics as nothing more than a game of symbol manipulation (see http://en.wikipedia.org/wiki/Formalism_(mathematics) ). But if mathematics can be viewed as nothing but symbol manipulation, and everything can be described in terms of mathematics, then what is not symbol manipulation?

and symbols need a meaning
outside of them to make sense.

The meaning of a symbol derives from the context of the machine which processes it.

Jason Resch-2 wrote:
>> Jason Resch-2 wrote:
>> >
>> >>
>> >> Also, the universal dovetailer can't select a computation. So if I
>> write
>> >> a
>> >> program that computes something specific, I do something that the UD
>> >> doesn't
>> >> do.
>> >>
>> >
>> > But you, as the one writing a specific program, is an element of the
>> UD.
>> First, you presuppose that I am a contained in a computation.
>> Secondly, that's not true. There are no specific programs in the UD. The
>> UD
>> itself is a specifc program and in it there is nothing in it that
>> dilineates
>> on program from the others.
> Each program has its own separate, non-overlapping, contiguous memory
> space.
This may be true from your perspective, but if you actually run the UD it
just uses its own memory space.

Is your computer only running one program right now or many?

Jason Resch-2 wrote:
>> Jason Resch-2 wrote:
>> >
>> > The UD contains an entity who believes it writes a single program. >> No! The UD doesn't contain entities at all. It is just a computation. You
>> can only interpret entities into it.
> Why do I have to? As Bruno often asks, does anyone have to watch your
> brain through an MRI and interpret what it is doing for you to be
> conscious?
Because there ARE no entities in the UD per its definition. It only contains
symbols that are manipulated in a particular way.

You forgot the processes, which are interpreting those symbols.

The spikes of neural activity in your optic nerve are just symbols, but given an interpreter (your visual cortex and brain) those symbols become quite meaningful.

The definitions of the UD
or a universal turing machine or of computers in general don't contain a
reference to entities.

The definition of this universe doesn't contain a reference to human beings either.

So you can only add that to its working in your own imagination.

I think I would still be able to experience meaning even if no one was looking at me.

It is like 1+1=2 doesn't say anything about putting an apple into a bowl with an apple already in it. You can interpret that into it, and its not
necessarily wrong, but it is not part of the equation.
Similarily you can interpret entities into the UD and that is also not
necessarily wrong, put the entities then still are not part of the UD.

Jason Resch-2 wrote:
>> Jason Resch-2 wrote:
>> >
>> >> It is similar to claiming that it is hard to find a text that is not
>> >> derived
>> >> from monkeys bashing on type writers, just because they will produce
>> >> every
>> >> possible output some day.
>> >>
>> >> Intelligence is not simply blindly going through every possibility but
>> >> also
>> >> encompasses organizing them meaningfully and selecting specific ones
>> and
>> >> producing them in a certain order and producing them within a certain
>> >> time
>> >> limit.
>> >>
>> >
>> > And there are processes that do this, within the UD.
>> No. It can't select a computation because it includes all computations.
>> To
>> select a computation you must exclude some compuations, and the UD can't
>> do
>> that (since it is precisely going through all computations)
> So it selects them all, and excludes nothing. How is this a meaningful
> limitation?
> If you look at two entities, X, and Y. X can do everything Y can do, and > more, but Y can only do a subset of what X does. You say that X is more
> limited than Y because it can't do only what Y does.
That's absolutely correct. A human that (tries to) eat all of the food in the supermarket is more limited (and dumb) than a human that just does a subset of this, picking the food it wants and eat that. The former human is dead, or at least will have to visit the hospital, the latter is well and

Less is indeed more, in many cases.

Jason Resch-2 wrote:
>> Jason Resch-2 wrote:
>> >
>> >   The UD is an example
>> > that programs can grow beyond the intentions of the creator.
>> I don't dispute that at all. I very much agree that computer rise beyond
>> the
>> intention of their users (because we don't actually know what the program
>> will actually do).
> Okay.
> Do you believe a computer program could evolve to be more intelligent than
> its programmer?
No, not in every way. Yes, in many ways. Computer already have, to some
degree. If we take IQ as a measure of intelligence, there are already
computers that score better than the vast majority of humans.


Interesting. Although my suspicion is they just programmed the http://oeis.org/ database into it, and sorted the sequences by how well known they were.

Really it is not at all about intelligence in this sense. It is more about
awareness or universal intelligence.

Jason Resch-2 wrote:
>> Jason Resch-2 wrote:
>> >
>> >  The UD itself
>> > isn't intelligent, but it contains intelligences.
>> I am not even saying that the UD isn't intelligent. I am just saying that >> humans are intelligent in a way that the UD is not (and actually the
>> opposite is true as well).
> Okay, could you clarify in what ways we are more intelligent?
> For example, could you show a problem that can a human solve that a
> computer with unlimited memory and time could not?
Say you have a universal turing machine with the alphabet {0, 1}
The problem is: Change one of the symbols of this turing machine to 2.

Your example is defining a problem to not be solvable by a specific entity, not turing machines in general. Let's say there were an android next to this other turing machine with a tape with 1's and 0's on it. The android could write a 2 on it just as easily as any human could. Now of course the turing machine with the tape might not lack this capability, but that is a limitation of that particular incarnation of a Turing machine.

Equivalent example: You may be unable to conduct brain surgery on yourself, but this does not mean humans (or Turing machines) are incapable of performing brain surgery.

Given that it is a universal turing machine, it is supposed to be able to solve that problem. Yet because it doesn't have access to the right level,
it cannot do it.
It is an example of direct self-manipulation, which turing machines are not
capable of (with regards to their alphabet in this case).

Neither can humans change fundamental properties of our physical incarnation. You can't decide to turn one of your neurons into a magnetic monopole, for instance, but this is not the kind of problem I was referring to.

To avoid issues of level confusion, it is better to think of problems with informational solutions, since information can readily cross levels. That is, some question is asked and some answer is provided. Can you think of any question that is only solvable by human brains, but not solvable by computers?

You could of course create a model of that turing machine within that turing machine and change their alphabet in the model, but since this was not the
problem in question this is not the right solution.

Or the problem "manipulate the code of yourself if you are a program, solve 1+1 if you are human (computer and human meaning what the average humans
considers computer and human)" towards a program written in a turing
universal programming language without the ability of self- modification. The best it could do is manipulate a model of its own code (but this wasn't the
Yet we can simply solve the problem by answering 1+1=2 (since we are human
and not computers by the opinion of the majority).

These are certainly creative examples, but they are games of language. I haven't seen any fundamental limitation that can't be trivially reflected back and applied as an equivalent limitation of humans.


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