I guess I haven't read those papers, so sorry if I was leading you up
the garden path re GTMs.
It sounds interesting that the universal prior could work for
generalisation of the Turing machine, although I'm not sure what the
implications would be. Anyway, it sounds like you've got a research
On Wed, Nov 26, 2008 at 02:55:08PM -0500, Abram Demski wrote:
Russel,
I do not see why some appropriately modified version of that theorem
couldn't be proven for other settings. As a concrete example let's
just use Schmidhuber's GTMs. There would be universal GTMs and a
constant cost for
Russel,
Hmm, can't we simply turn any coding into a prefix-free-coding by
prefacing each code for a GTM with a number of 1s indicating the
length of the following description, and then a 0 signaling the
beginning of the actual description? I am not especially familiar with
the prefix issue, so
On Thu, Nov 27, 2008 at 02:40:04PM -0500, Abram Demski wrote:
Russel,
Hmm, can't we simply turn any coding into a prefix-free-coding by
prefacing each code for a GTM with a number of 1s indicating the
length of the following description, and then a 0 signaling the
beginning of the actual
Russel,
I just went to look at the paper Hierarchies of generalized
Kolmogorov complexities and nonenumerable universal measures
computable in the limit-- to find a quote showing that GTMs were a
generalization of Turing Machines rather then a restriction. I found
such a quote as soon as page 2:
Russel,
The paper does indeed showcase one example of a universal prior that
includes non-computable universes... Theorem 4.1. So it's *possible*.
Of course it then proceeds to dash hopes for a universal prior over a
broader domain, defined by GTMs. So, it would be interesting to know
more about
Hi Abram,
On 26 Nov 2008, at 00:01, Abram Demski wrote:
Bruno,
Yes, I have encountered the provability logics before, but I am no
expert.
We will perhaps have opportunity to talk about this.
In any given
generation, the entity who can represent the truth-predicate of the
most
Russel,
I do not see why some appropriately modified version of that theorem
couldn't be proven for other settings. As a concrete example let's
just use Schmidhuber's GTMs. There would be universal GTMs and a
constant cost for conversion and everything else needed for a version
of the theorem,
Bruno,
I am glad for the opportunity to discuss these things with someone who
knows something about these issues.
In my opinion, revision theories are useful when a machine begins to
bet on an universal environment independent of herself. Above her
Godel-Lob-Solovay correct self-reference
Russel,
Can you point me to any references? I am curious to hear why the
universality goes away, and what crucially depends means, et cetera.
-Abram Demski
On Tue, Nov 25, 2008 at 5:44 AM, Russell Standish [EMAIL PROTECTED] wrote:
On Mon, Nov 24, 2008 at 11:52:55AM -0500, Abram Demski wrote:
On Tue, Nov 25, 2008 at 04:58:41PM -0500, Abram Demski wrote:
Russel,
Can you point me to any references? I am curious to hear why the
universality goes away, and what crucially depends means, et cetera.
-Abram Demski
This is sort of discussed in my book Theory of Nothing, but not in
Bruno,
Yes, I have encountered the provability logics before, but I am no expert.
In any given
generation, the entity who can represent the truth-predicate of the
most other entities will dominate.
Why?
The notion of the entities adapting their logics in order to better
reason about each
really means. Again there was some recent discussion on
this... I was very tempted to comment, but I wanted to lurk a while to
get the idea of the group before posting my join post.
Following is my view on what the big questions are when it comes to
specifying the correct logic.
The first two big
Hi Abram, welcome.
On 24 Nov 2008, at 17:52, Abram Demski wrote (in part):
The little puzzle is this: Godel's theorem tells us that any
sufficiently strong logic does not have a complete set of deduction
rules; the axioms will fail to capture all truths about the logical
entities we're
Hi Bruno,
I am not sure I follow you here. All what Godel's incompleteness
proves is that no machine, or no axiomatisable theory can solve all
halting problems.
The undecidability is always relative to such or such theory or
machine prover. For self-modifying theorem prover, the undecidable
On 24 Nov 2008, at 21:52, Abram Demski wrote:
Hi Bruno,
I am not sure I follow you here. All what Godel's incompleteness
proves is that no machine, or no axiomatisable theory can solve all
halting problems.
The undecidability is always relative to such or such theory or
machine prover.
contribute the future
discussion. i had just sent a post before i notice the 'JOIN
POST' convention. i hope that's not a serious violation :)
i am currently interesting on logic, computability,
evolution, as well as complex adapt system in general. i am
not a physics major, so i always found quantum
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