Pei Wang wrote:
In my opinion, one of the most common mistakes made by people is to think AI
in terms of computability and computational complexity, using concepts like
Turing machine, algorithm, and so on. For a long argument, see
http://www.cis.temple.edu/~pwang/551-PT/Lecture/Computation.pdf.
Shane Legg wrote, responding to Pei Wang:
> Perhaps where our difference is best highlighted is in the
> following quote that you use:
>
> “something can be computational at one level,
> but not at another level” [Hofstadter, 1985]
>
> To this I would say: "Something can LOOK like compu
you
are trying to solve is to reply my current email. Is this problem
computable? Do you follow an algorithm in solving it? What is the
computational complexity of this process?
Pei
- Original Message -
From: "Shane Legg" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]&
Pei:
> For that "level" issue, one way to see it is through the concept
> of "virtual
> machine". We all know that at a low level computer only has procedural
> language and binary data, but at a high level it has
> non-procedural language
> (such as functional or logical languages) and decimal d
OTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Saturday, January 11, 2003 8:43 PM
Subject: RE: [agi] AI and computation (was: The Next Wave)
> Pei:
>
> > For that "level" issue, one way to see it is through the concept
> > of "virtual
> > machine".
pei wrote:
> "M1 and M2 can simulate each other" doesn't mean "M1 and M2 are
> identical",
> nor that the two should be analyzed in the same way.
I agree, of course
> Efficiency is one
> issue, the suitability of concepts is another.
>
The two issues are closely linked though. If M1 and M2 can
Hi Ben,
Ahhh, all this brings back memories of the good old days
at Webmind... :)
It's just a pitty that Jeff isn't here :(
Shane, i think you and pei are using different language to say very
similar things...
I thought that too. But then decided that either his use of terms
was so out of
Hi Pei,
One issue that make that version of the paper controversial is the term
"computation", which actually has two senses: (1) "whatever computer
does",and (2) "what defined as `computation' in computability theory". In
the paper I'm using the second sense of the term. (I'm revising the pape
hi,
>
> Ahhh, all this brings back memories of the good old days
> at Webmind... :)
>
> It's just a pitty that Jeff isn't here :(
>
You know, I've felt that SO often and so intensely lately, as Izabela and I
have been working out all the kinks in PTL
[a note to outsiders: Jeff pressing was a c
- Original Message -
From: "Shane Legg" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Saturday, January 11, 2003 9:42 PM
Subject: Re: [agi] AI and computation (was: The Next Wave)
> Hi Pei,
>
> > One issue that make that version of t
Pei wrote:
> Right. Again let's use NARS as a concrete example. It can answer
> questions,
> but if you ask the same question twice to the system at different
> time, you
> may get different answers. In this sense, there is no algorithm that takes
> the question as input, and produces an unique
> I think my reply to this is similar in nature to Ben's (however I think
> Ben's example of a push down automaton is a bit misleading as it's
> really the abilty to carry state between system cycles not during a
> cycle of that is important)
Yeah, you're right mr. legg ... I should have stuck wi
On 1/11/03 5:31 PM, "Pei Wang" <[EMAIL PROTECTED]> wrote:
>
> My argument, briefly speaking, is that it is quite possible, in the current
> computer, to solve problems in such a way that is non-deterministic (i.e.,
> context-sensitive) and open-ended (as in anytime algorithms). Such a
> process d
> Note that this particular property is more-or-less how our system
> cheats the
> halting problem, infinite loops, and similar. When you run an program
> instance that ends up in this state, the algorithms (in a generic sense)
> tend to rewrite themselves such that they jump to a conclusion and
On 1/11/03 9:39 PM, "Ben Goertzel" <[EMAIL PROTECTED]> wrote:
> But you can't escape the halting problem on the lower level.
>
> Using randomness you can escape the halting problem, in a sense. But, you
> can't get true randomness in your virtual machine, only simulated
> randomness. So you are
Hi James,
Interesting, as I make a similar argument. I'm using an unconventional
model of universal computation on finite state machinery that, among other
and from your other email,
There is still a halting problem, just not a practical halting
problem for most intents and purposes.
As t
James Rogers wrote:
> Obviously this is something of an oversimplification; I think I see your
> point. There is still a halting problem, just not a practical halting
> problem for most intents and purposes. Or at least it has been
> pushed to a
> level of abstraction where we don't really wor
Shane wrote (responding to James)
> > We implement a virtual machine on top of a standard
> > computer architecture that is designed around a fundamentally different
> > model of a universal computer.
>
> I doubt that your model is really all that fundamentally different.
> Either your model isn't
Pei Wang wrote:
> Again, I'm not saying that NARS is not a TM in any sense, but
> that it is not
> a TM at the questing-answering level. As I said in the paper, if you
> consider the life-long history of input and output of the whole
> system, NARS
> is a TM. Also, if you check each individual
- Original Message -
From: "Ben Goertzel" <[EMAIL PROTECTED]>
> So let's look at NARS over the time-interval [s,t] corresponding to the
> answering of an individual question...
>
> Over this time-interval
>
> "The NARS program plus its internal state at the time point s"
>
> is still mode
- Original Message -
From: "Shane Legg" <[EMAIL PROTECTED]>
> I think my reply to this is similar in nature to Ben's (however I think
> Ben's example of a push down automaton is a bit misleading as it's
> really the abilty to carry state between system cycles not during a
> cycle of that
> Once again, the interesting question is not "Is NARS a TM?", but
> "Is NARS a
> TM with respect to problem P?" If the problem is "To answer
> Ben's email on
> `AI and compuation'", then the system is not a TM (though it may
> be a TM in
> many other senses). For this reason, to discuss the comp
icted from the current problem alone.
I'm afraid I just opened another can of worm.
Pei
- Original Message -
From: "James Rogers" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Sunday, January 12, 2003 12:26 AM
Subject: Re: [agi] AI and computation (was:
- Original Message -
From: "Ben Goertzel" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Sunday, January 12, 2003 10:50 AM
Subject: RE: [agi] AI and computation (was: The Next Wave)
> > Once again, the interesting question is not "Is NARS a TM?
-
> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On
> Behalf Of Pei Wang
> Sent: Sunday, January 12, 2003 11:05 AM
> To: [EMAIL PROTECTED]
> Subject: Re: [agi] AI and computation (was: The Next Wave)
>
>
> James,
>
> I basically agree with your points.
>
&g
> > I'm sorry but I still don't understand exactly what you mean by "Is
> computer
> > program-instance X a TM with respect to problem P"
>
> Each TM (or algorithm) is defined with respect to a "problem",
> which is set
> of valid input strings. Each string in the set is a problem instance, ans
>
On Sun, Jan 12, 2003 at 09:38:26AM -0500, Ben Goertzel wrote:
> To me, the question of what a computational model can do with moderately
> small space and time resource constraints is at least equally "fundamental"
Computability theory: can this be computed?
Complexibility theory: does it take po
On Sun, Jan 12, 2003 at 10:37:13AM -0500, Pei Wang wrote:
> See my replies to Ben. As soon as the final answer (not intermidiate
> answer) depends on internal state, we are not talking about the same Turing
> Machine anymore. Of course you can build a thoery in this way, but it is
> already not
On Sun, Jan 12, 2003 at 11:05:15AM -0500, Pei Wang wrote:
> another related topic: the final state. In my paper I said that my system is
> not a TM, also because it doesn't have a set of predetermined final states
A system using S and K combinators isn't a TM at all; totally different
mechanism o
On 1/12/03 9:43 AM, "Damien Sullivan" <[EMAIL PROTECTED]> wrote:
>
> I'll take the risk of replying to other messages here without reading the 2
> dozen other replies first. It sounds like James is using primitive recursive
> functions, equivalent to Hofstadter's BLoop in _GEB_. Those are a subs
> And just to be clear, its obviously a Turing machine since it
> runs on Turing
> machines and you can run any Turing machine on it. It is just very
> different from normal conceptions of universal computers. But
> then, I could
> say the exact same thing about the human brain.
>
> Cheers,
>
>
On Sun, Jan 12, 2003 at 03:25:08PM -0500, Ben Goertzel wrote:
> It is clear that traditional formal computing theory, though in principle
> *applicable* to AGI programs, is pretty much useless to the AGI theorist...
Is this anything unique to AGI? Does computing theory have much relevance for
Li
bject: Re: [agi] AI and computation (was: The Next Wave)
>
>
> On Sun, Jan 12, 2003 at 03:25:08PM -0500, Ben Goertzel wrote:
>
> > It is clear that traditional formal computing theory, though in
> principle
> > *applicable* to AGI programs, is pretty much useless to the AGI
>
Hi Ben,
If two computational models can solve radically different problems *under
realistic space and time constraints*, then are they "fundamentally
different" or not??
You seem to want call two models "fundamentally the same" if they can solve
the same problems under infinite time and space c
Shane wrote:
> Two systems are fundamentally equivalent if it's possible for them to
> simulate each other given any finite amount of resources. They are
> fundamentally different if this is impossible no matter how much
> resource is made available. Clearly this is a very deep and
> fundamenta
Pei Wang wrote:
Again, I'm not saying that NARS is not a TM in any sense, but that it is not
a TM at the questing-answering level. As I said in the paper, if you
consider the life-long history of input and output of the whole system, NARS
is a TM. Also, if you check each individual inference st
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