On 19 Aug 2011, at 20:18, Evgenii Rudnyi wrote:

On 18.08.2011 16:24 Bruno Marchal said the following:

On 17 Aug 2011, at 20:07, meekerdb wrote:

On 8/17/2011 10:36 AM, Evgenii Rudnyi wrote:
On 16.08.2011 20:47 meekerdb said the following:
On 8/16/2011 11:03 AM, Evgenii Rudnyi wrote:
Yes, this is why in my first post, I said consider God's
Turing machine (free from our limitations). Then it is
obvious that with the appropriate tape, a physical system
can be approximated to any desired level of accuracy so
long as it is predictable. Colin said such models of
physics or chemistry are impossible, so I hope he
elaborates on what makes these systems unpredictable.

I have to repeat that the current simulation technology just
does not scale. With it even God will not help. The only way
that I could imagine is that God's Turing machine is based on
completely different simulation technology (this however
means that our current knowledge of physical laws and/or
numerics is wrong).

Scale doesn't matter at the level of theoretical possibility.
Bruno's UD is the most inefficient possible way to compute this
universe - but he only cares that it's possible. All universal
Turing machines are equivalent so it doesn't matter what God's
is based on. Maybe you just mean the world is not computable in
the sense that it is nomologically impossible to compute it
faster than just letting it happen.

I understand what you say. On the other hand however, it is still
good to look at the current level of simulation technology,
especially when people make predictions on what happens in the
future (in other messages the possibility of brain simulation and
talk about physico-chemical processes).

From such a viewpoint, even a level of one-cell simulation is not
reachable in the foreseeable future. Hence, in my view, after
the discussion about theoretical limits it would be good to look
at the reality. It might probably help to think the assumptions

I would say that it is small practical things that force us to
reconsider our conceptions.


I agree with that sentiment. That's why I often try to think of
consciousness in terms of what it would mean to provide a Mars
Rover with consciousness. According to Bruno the ones we've sent to
Mars were already conscious, since their computers were capable of
Lobian logic.

I don't remember having said this. I even doubt that Mars Rover is
universal, although that might be serendipitously possible
(universality is very cheap), in which case it would be as conscious
as a human being under a high dose of salvia (a form of consciousness
quite disconnected from terrestrial realities). But it is very
probable that it is not Löbian. I don't see why they would have given
the induction axioms to Mars Rover (the induction axioms is what
gives the Löbian self-referential power).

But clearly they did not have human-like consciousness (or
intelligence). I think it much more likely that we could make a
Mars Rover with consciousness and intelligence somewhat similar to
humans using von Neumann computers or artificial neural nets than
by trying to actually simulate a brain.

I think consciousness might be attributed to the virgin (non
programmed) universal machine, but such consciousness is really the
basic consciousness of everyone, before the contingent
differentiation on the histories. LUMs, on the contrary, have a
self-consciousness, even when basically virgin: they makes a
distinction between them and some possible independent or
transcendental reality.

No doubt the truth is a bit far more subtle, if only because there
are intermediate stage between UMs and LUMs.

When I search on Google Scholar

lobian robot

then there is only one hit (I guess that this is Bruno's thesis). When I search however

loebian robot

there are some more hits with for example Loebian embodiment. I do not not know what it means but in my view it would be interesting to build a robot with a Loebian logic and research it. In my view, it is not enough to state that there is already some consciousness there. It would be rather necessary to research on what it actually means. Say it has visual consciousness experience, it feels pain or something else.

It would be interesting to see what people do in this area. For example, "Loebian embodiment" sounds interesting and it would be nice to find some review about it.

"Löbian machine" is an idiosyncrasy that I use as a shorter expression for what the logicians usually describes by "a sufficiently rich theory".
I have not yet decide on how to exactly define them.

I hesitate between a very weak sense, like any belief system (machine, theory) close for the Löb rule (which says that you can deduce p from Bp -> p). A stronger sense is : any belief system having the Löb's formula in it. So it contains the "formal Löb rule": B(Bp -> p) -> Bp.

But my current favorite definition is: any universal machine which can prove p -> Bp for p sigma_1 (or equivalent). This I paraphrase in layman's language by: any universal machine which knows that she is universal. Sigma_1 proposition are those having the shape ExP(x) with P decidable. You can intuit that *you* can do, by testing P(0), P(1), P(2), ... until you find a n such that P(n).

A theorem prover which can prove all true sigma_1 proposition is provably equivalent with a universal machine, and all universal machine can prove (modulo modification of the language) the true sigma_1 propositions.

PA and ZF are Löbian machine in that last sense (which implies the weaker senses). They are emulated in the human brain of those who study them, although they are easy to implement on computers.

A long time ago I concluded that some theorem prover, written by Chang, also by Boyer and Moore, are Löbian. When a child grasp notion like "anniversary", "death", "forever", "potentially infinite", they show Löbianity.

Are humans Löbian? Hard to say, because they have a non monotonical layer (they can retrieve old beliefs), but it is clear they have a Löbian machine (or entity) living inside. Fear of death, fear of the unknown and fear of the others are typically Löbian.

Another definition: a Löbian entity is an entity whose 3-self- referential beliefs obeys to the logics G and G*. Then you can apply the Theaetetus theory to get the 1-knower logic, and the 1-physics, etc. They have all the same theology, but the personal arithmetical content of the "Bp" can vary a lot.



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