It all depends on what definition of number you are using. If it's
constructive, then it must be a finite set of numbers. If it's based on
full Number Theory, then it's either incomplete or inconsistent. If
it's based on any of several subsets of Number Theory that don't allow
One more time: the proof of Occam's Razor depends on whether the universe is
computable by a Turing machine. It does not depend on whether the universe is
computable by a machine that we could actually build. I never claimed it was
practical to do all of science by simulating physics.
-- Matt
Hutter's proof that Occam's Razor (in a certain form) is key to intelligence
depends on
1) a specific definition of what intelligence is
2) a restriction to intelligent systems with a huge amount of computational
resources
as well as
3) an assumption that the universe is in-principle
--- On Fri, 10/31/08, Ben Goertzel [EMAIL PROTECTED] wrote:
Hutter's proof that Occam's Razor (in a certain form) is key to intelligence
depends on
1) a specific definition of what intelligence is
2) a restriction to intelligent systems with a huge amount of computational
resources
as well
I was referring to AIXItl which is also contained in Hutter's papers/book
and operates with merely infeasibly huge rather than infinite resources...
Hutter's theorems say *nothing* about the optimal way to achieve
intelligence (according to his definition, and under the assumption of a
computable
The question that worries me is: **What does it matter if AIXI __is__
optimal, given that it uses infinitely many resources**??
And, what does it matter if AIXI-tl is near-optimal, given that it uses
infeasibly much resources?
These are nice theoretical systems addressing nice math problems ...
Right, but I am not talking about AIXI^tl. I agree AIXI^tl is not a practical
approach to AGI because it has exponential time complexity. The important
results are the non-computability of AIXI and its proof of Occam's Razor as a
general principle (if physics is Turing computable).
-- Matt
--- On Fri, 10/31/08, Ben Goertzel [EMAIL PROTECTED] wrote:
The question that worries me is: **What does it matter if AIXI __is__
optimal, given that it uses infinitely many resources**??
Because it puts machine learning research on a firmer theoretical foundation.
For example, we know from
I would like to state a middle ground between the viewpoints cited in the
email below:
It seems to me that if one had a man-made computer capable of computing all
the astronically-large and planks-length-fine state information and
computations that take place in all of reality at the level
In classical logic programming, there is the concept of unification,
where one expression is matched against another, and one or both
expressions may contain variables. For example, (FOO ?A) unifies with
(FOO 42) by setting the variable ?A = 42.
Suppose you have a database of N expressions, and
On Fri, Oct 31, 2008 at 8:00 PM, Pei Wang [EMAIL PROTECTED] wrote:
The closest thing I can think of is Rete algorithm --- see
http://en.wikipedia.org/wiki/Rete_algorithm
Thanks! If I'm understanding correctly, the Rete algorithm only
handles lists of constants and variables, not general
I didn't directly code it myself, but as far as I know, nested lists
should be fine, though the N expressions probably should remain
constant.
Pei
On Fri, Oct 31, 2008 at 4:44 PM, Russell Wallace
[EMAIL PROTECTED] wrote:
On Fri, Oct 31, 2008 at 8:00 PM, Pei Wang [EMAIL PROTECTED] wrote:
The
Let's try this . . . .
In Universal Algorithmic Intelligence on page 20, Hutter uses Occam's razor
in the definition of .
Then, at the bottom of the page, he merely claims that using as an
estimate for ? may be a reasonable thing to do
That's not a proof of Occam's Razor.
= = = = = =
I think Hutter is being modest.
-- Matt Mahoney, [EMAIL PROTECTED]
--- On Fri, 10/31/08, Mark Waser [EMAIL PROTECTED] wrote:
From: Mark Waser [EMAIL PROTECTED]
Subject: Re: [agi] Occam's Razor and its abuse
To: agi@v2.listbox.com
Date: Friday, October 31, 2008, 5:41 PM
Let's try this . .
I think Hutter is being modest.
Huh?
So . . . . are you going to continue claiming that Occam's Razor is proved
or are you going to stop (or are you going to point me to the proof)?
- Original Message -
From: Matt Mahoney [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Friday,
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