Re: [agi] Cloud Intelligence

[Russell Wallace]

On Thu, Oct 30, 2008 at 6:45 AM,  <[EMAIL PROTECTED]> wrote:
> It sure seems to me that the availability of cloud computing is valuable
> to the AGI project.  There are some claims that maybe intelligent programs
> are still waiting on sufficient computer power, but with something like
> this, anybody who really thinks that and has some real software in mind
> has no excuse.  They can get whatever cpu horsepower they need, I'm pretty
> sure even to the theoretical levels predicted by, say, Moravec and
> Kurzweil.  It takes away that particular excuse.

Indeed, that's been the most important effect of computing power
limitations. It's not that we've ever been able to say "this program
would do great things, if only we had the hardware to run it". It's
that we learn to flinch away from the good designs, the workable
approaches, because they won't fit on the single cheap beige box we
have on our desks. The key benefit of cloud computing is one that can
be had before the first line of code is written: don't think in terms
of how your design will run on one box, think in terms of how it will
run on 10,000.


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RE: [agi] Cloud Intelligence

[John G. Rose]

> From: Russell Wallace [mailto:[EMAIL PROTECTED]
> On Thu, Oct 30, 2008 at 6:45 AM,  <[EMAIL PROTECTED]> wrote:
> > It sure seems to me that the availability of cloud computing is
> valuable
> > to the AGI project.  There are some claims that maybe intelligent
> programs
> > are still waiting on sufficient computer power, but with something
> like
> > this, anybody who really thinks that and has some real software in
> mind
> > has no excuse.  They can get whatever cpu horsepower they need, I'm
> pretty
> > sure even to the theoretical levels predicted by, say, Moravec and
> > Kurzweil.  It takes away that particular excuse.
> 
> Indeed, that's been the most important effect of computing power
> limitations. It's not that we've ever been able to say "this program
> would do great things, if only we had the hardware to run it". It's
> that we learn to flinch away from the good designs, the workable
> approaches, because they won't fit on the single cheap beige box we
> have on our desks. The key benefit of cloud computing is one that can
> be had before the first line of code is written: don't think in terms
> of how your design will run on one box, think in terms of how it will
> run on 10,000.
> 

My suspicion though is that say you had 100 physical servers and then 100
physical cloud servers. You could hand tailor your distributed application
so that it is extremely more efficient not running on the cloud substrate.
Even if you took the grid substrate that the cloud is running on and hand
tweaked your app to utilize that I suspect that it would still be way less
efficient than a 100% native written.

The advantage of using cloud or grid substrate is that it makes writing the
application much easier. Hand coded distributed applications take a
particular expertise to develop. Eliminating that helps from a bootstrap
perspective.

Also when you have control over your server you can manipulate topology. It
is possible to enhance inter-server communication by creating custom
physical and virtual network topology.

I assume as grid and cloud computing matures the software substrate will
become more efficient and adaptable to the application. To be sure though on
the efficiencies, some tests would need to be run. Unless someone here
understands cloud/grid enough to know what the deal is or has already run
tests.

John





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Re: [agi] Cloud Intelligence

[Russell Wallace]

On Thu, Oct 30, 2008 at 3:07 PM, John G. Rose <[EMAIL PROTECTED]> wrote:
> My suspicion though is that say you had 100 physical servers and then 100
> physical cloud servers. You could hand tailor your distributed application
> so that it is extremely more efficient not running on the cloud substrate.

Why would you suspect that? My understanding of cloud computing is
that the servers are perfectly ordinary Linux boxes, with perfectly
ordinary network connections, it's just that you rent them instead of
buying them.


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Re: [agi] Cloud Intelligence

[Ben Goertzel]

Unless you are going to hand-wire some special processor-to-processor
interconnect fabric, this seems probably not to be true...

ben g

On Thu, Oct 30, 2008 at 11:15 AM, Russell Wallace <[EMAIL PROTECTED]
> wrote:

> On Thu, Oct 30, 2008 at 3:07 PM, John G. Rose <[EMAIL PROTECTED]>
> wrote:
> > My suspicion though is that say you had 100 physical servers and then 100
> > physical cloud servers. You could hand tailor your distributed
> application
> > so that it is extremely more efficient not running on the cloud
> substrate.
>
> Why would you suspect that? My understanding of cloud computing is
> that the servers are perfectly ordinary Linux boxes, with perfectly
> ordinary network connections, it's just that you rent them instead of
> buying them.
>
>
> ---
> agi
> Archives: https://www.listbox.com/member/archive/303/=now
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> Modify Your Subscription:
> https://www.listbox.com/member/?&;
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>



-- 
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
Director of Research, SIAI
[EMAIL PROTECTED]

"A human being should be able to change a diaper, plan an invasion, butcher
a hog, conn a ship, design a building, write a sonnet, balance accounts,
build a wall, set a bone, comfort the dying, take orders, give orders,
cooperate, act alone, solve equations, analyze a new problem, pitch manure,
program a computer, cook a tasty meal, fight efficiently, die gallantly.
Specialization is for insects."  -- Robert Heinlein



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RE: [agi] Cloud Intelligence

[John G. Rose]

> From: Ben Goertzel [mailto:[EMAIL PROTECTED]
> Sent: Thursday, October 30, 2008 9:18 AM
> To: agi@v2.listbox.com
> Subject: Re: [agi] Cloud Intelligence
> 
> 
> Unless you are going to hand-wire some special processor-to-processor
> interconnect fabric, this seems probably not to be true...
> 
> ben g
> On Thu, Oct 30, 2008 at 11:15 AM, Russell Wallace
> <[EMAIL PROTECTED]> wrote:
> On Thu, Oct 30, 2008 at 3:07 PM, John G. Rose <[EMAIL PROTECTED]>
> wrote:
> > My suspicion though is that say you had 100 physical servers and then
> 100
> > physical cloud servers. You could hand tailor your distributed
> application
> > so that it is extremely more efficient not running on the cloud
> substrate.
> Why would you suspect that? My understanding of cloud computing is
> that the servers are perfectly ordinary Linux boxes, with perfectly
> ordinary network connections, it's just that you rent them instead of
> buying them.
> 

Not talking custom hardware, when you take your existing app and apply it to
the distributed resource and network topology (your 100 servers) you can
structure it to maximize its "execution" reward. And the design of the app
should take the topology into account. Just creating an app and uploading it
to a cloud and assuming the cloud will be smart enough to figure it out?
There's gonna be layers there man and resource task switching with other
customers.

Cloud substrate software is probably good but not that good.

You could understand how the cloud processes and structure your app towards
that. I have no idea how these clouds are implemented.

John



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Re: [agi] Cloud Intelligence

[Russell Wallace]

On Thu, Oct 30, 2008 at 3:42 PM, John G. Rose <[EMAIL PROTECTED]> wrote:
> Not talking custom hardware, when you take your existing app and apply it to
> the distributed resource and network topology (your 100 servers) you can
> structure it to maximize its "execution" reward. And the design of the app
> should take the topology into account.

That would be a very bad idea, even if there were no such thing as
cloud computing. Even if there was a significant efficiency gain to be
had that way (which there isn't, in the usual scenario where you're
talking about ethernet not some custom grid fabric), as soon as the
next hardware purchase comes along, the design over which you sweated
so hard is now useless or worse than useless.


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RE: [agi] Cloud Intelligence

[John G. Rose]

> From: Russell Wallace [mailto:[EMAIL PROTECTED]
> On Thu, Oct 30, 2008 at 3:42 PM, John G. Rose <[EMAIL PROTECTED]>
> wrote:
> > Not talking custom hardware, when you take your existing app and
> apply it to
> > the distributed resource and network topology (your 100 servers) you
> can
> > structure it to maximize its "execution" reward. And the design of
> the app
> > should take the topology into account.
> 
> That would be a very bad idea, even if there were no such thing as
> cloud computing. Even if there was a significant efficiency gain to be
> had that way (which there isn't, in the usual scenario where you're
> talking about ethernet not some custom grid fabric), as soon as the
> next hardware purchase comes along, the design over which you sweated
> so hard is now useless or worse than useless.
> 

No, you don't lock it into an instance in time. You make it selectively
scalable. 

When your app or your application's resources span more than one machine you
need to organize that. The choice on how you do so effects execution
efficiency. You could have an app now that needs 10 machines to run and 5
years from now will run on one machine yes. That is true. 

John



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Re: [agi] Cloud Intelligence

[Russell Wallace]

On Thu, Oct 30, 2008 at 4:04 PM, John G. Rose <[EMAIL PROTECTED]> wrote:
> No, you don't lock it into an instance in time. You make it selectively
> scalable.
>
> When your app or your application's resources span more than one machine you
> need to organize that. The choice on how you do so effects execution
> efficiency. You could have an app now that needs 10 machines to run and 5
> years from now will run on one machine yes. That is true.

Okay, when you said "design", I thought you meant making design
decisions about the architecture. If you're talking tweaking
configuration files, sure; but you can do that on a cloud, too.


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[agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Pei Wang]

On Wed, Oct 29, 2008 at 10:44 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote:
>
> My assumption is that the physics of the observable universe is computable 
> (which is widely believed to be true).

To me, this is another topic where several different claims tangled together.

[A]. "Every law or model proposed in physics is computable and
therefore can be calculated by a Turing Machine."

This is what Zuse argued in his original paper, which started this
whole discussion.

Given my limited knowledge of physics, it sounds correct, and I have
no problem here.

[B]. "Because of A, all laws and models in physics can be calculated
by a Turing Machine."

This is Zuse's hypothesis. He didn't really argue for it, but
suggested it as a possibility. I think that this is theoretically
possible, but practically very unlikely to happen. Physics, like any
science, consists of incompatible theories each focusing on one aspect
of the world. A consistent "Theory of Physics" is very hard to get, if
not impossible.

I don't have a high expectation for B to be realized, though do accept
it as a meaningful and interesting possibility to consider, or even as
an ultimate goal of research for a physicist.

[C]. "Because of B, the universe can be simulated in Turing Machine".

This is where I start to feel uncomfortable. Even if someone has got a
theory can explains all observed physical phenomena, and formulated it
in a Turing machine, it is still only a description of the universe at
a certain level of description. To claim it describes "the universe",
rather than just "all observed physical phenomena", you need to assume
a strong version of Physicalism and Reductionism, so that all
phenomena can be reduced into physical phenomena with no information
loss.

To me, this claim is philosophically incorrect. There is no single
language or level of description that describes "the true world",
while all the other descriptions are just its approximation.

[D]. "Because of C, the universe is a Turing Machine".

To me, this is a confusion between an object and a
description/simulation of an object. Even if C is true, a simulated
universe is still not a universe itself, just as a simulated hurricane
in a computer is not a real hurricane itself, because it does not have
the defining property of "hurricane" in our world (which is different
from the simulated world in the computer).

Of course, some people will go to the extreme to say that I'm really
living in a simulated world, it is just that I haven't realize it yet.
This is a reasonable argument, but since I don't see what difference
it will make if I accept it, it won't be considered here.

In summary, what I cannot accept in AGI research is the assumption
that there is a real/true/object description of the universe, and all
theories or knowledge are partial approximation of it. Turing Machine
is just one form of this "objective truth". To me, though this opinion
is acceptable in many situations in everyday life, it will lead the
research of AGI to a wrong direction.

Pei


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RE: [agi] Cloud Intelligence

[John G. Rose]

> From: Russell Wallace [mailto:[EMAIL PROTECTED]
> 
> On Thu, Oct 30, 2008 at 4:04 PM, John G. Rose <[EMAIL PROTECTED]>
> wrote:
> > No, you don't lock it into an instance in time. You make it
> selectively
> > scalable.
> >
> > When your app or your application's resources span more than one
> machine you
> > need to organize that. The choice on how you do so effects execution
> > efficiency. You could have an app now that needs 10 machines to run
> and 5
> > years from now will run on one machine yes. That is true.
> 
> Okay, when you said "design", I thought you meant making design
> decisions about the architecture. If you're talking tweaking
> configuration files, sure; but you can do that on a cloud, too.
> 
> 

I AM talking about design decision in the architecture. I assume that AGI is
so resource constrained at this time that the architecture has to be molded
to conventional hardware for the next several years. It would be nice not to
worry about that and just design AGI based on theory assuming infinite
resources.

Take the brain for example. It's not one homogenous mass of entangled
neurons. It is partitioned up. This evolved design is partially based on
efficiency. If the electrochemical communication metrics were different the
brain would be partitioned up differently.

John





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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Matt Mahoney]

--- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:
> [C]. "Because of B, the universe can be simulated in
> Turing Machine".
> 
> This is where I start to feel uncomfortable.

The theory cannot be tested directly because there is no such thing as a real 
Turing machine. But we can show that the observable universe has finite 
information content according to the known laws of physics and cosmology, which 
assumes finite age, size, and mass. In particular, the Bekenstein bound of the 
Hubble radius gives an exact number (2.91 x 10^122 bits).

http://en.wikipedia.org/wiki/Bekenstein_bound
http://en.wikipedia.org/wiki/Age_of_the_universe

This does not mean you could model the universe. It would be impossible to 
build a memory this large. Any physically realizable computer would have to be 
built inside our observable universe. But that is not a requirement for Occam's 
Razor to hold.

I realize we don't have a complete theory of physics. In particular, quantum 
mechanics has not been unified with general relativity. I also realize that 
even if we did have a complete theory, we couldn't prove it.

-- Matt Mahoney, [EMAIL PROTECTED]




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RE: [agi] Cloud Intelligence

[Matt Mahoney]

Cloud computing is compatible with my proposal for distributed AGI. It's just 
not big enough. I would need 10^10 processors, each 10^3 to 10^6 times more 
powerful than a PC.

-- Matt Mahoney, [EMAIL PROTECTED]



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Pei Wang]

Matt,

I understand your explanation, but you haven't answered my main
problem here: why to simulate the universe we only need physics, but
not chemistry, biology, psychology, history, philosophy, ...? Why not
to say "all human knowledge"?

Pei

On Thu, Oct 30, 2008 at 1:51 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote:
> --- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:
>> [C]. "Because of B, the universe can be simulated in
>> Turing Machine".
>>
>> This is where I start to feel uncomfortable.
>
> The theory cannot be tested directly because there is no such thing as a real 
> Turing machine. But we can show that the observable universe has finite 
> information content according to the known laws of physics and cosmology, 
> which assumes finite age, size, and mass. In particular, the Bekenstein bound 
> of the Hubble radius gives an exact number (2.91 x 10^122 bits).
>
> http://en.wikipedia.org/wiki/Bekenstein_bound
> http://en.wikipedia.org/wiki/Age_of_the_universe
>
> This does not mean you could model the universe. It would be impossible to 
> build a memory this large. Any physically realizable computer would have to 
> be built inside our observable universe. But that is not a requirement for 
> Occam's Razor to hold.
>
> I realize we don't have a complete theory of physics. In particular, quantum 
> mechanics has not been unified with general relativity. I also realize that 
> even if we did have a complete theory, we couldn't prove it.
>
> -- Matt Mahoney, [EMAIL PROTECTED]
>
>
>
>
> ---
> agi
> Archives: https://www.listbox.com/member/archive/303/=now
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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Matt Mahoney]

--- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:

> I understand your explanation, but you haven't answered my main
> problem here: why to simulate the universe we only need physics, but
> not chemistry, biology, psychology, history, philosophy, ...? Why not
> to say "all human knowledge"?

An exact description of the quantum state of the universe gives you everything 
else. There is no requirement that the computation be tractable for Occam's 
Razor to hold. AIXI only requires that the environment have a probability 
distribution that is computable by a Turing machine.

-- Matt Mahoney, [EMAIL PROTECTED]



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Ben Goertzel]

>
> An exact description of the quantum state of the universe gives you
> everything else. There is no requirement that the computation be tractable
> for Occam's Razor to hold. AIXI only requires that the environment have a
> probability distribution that is computable by a Turing machine.
>
> -- Matt Mahoney, [EMAIL PROTECTED]
>


And of course that requirement is a philosophical assumption which seems
reasonable, but can never be empirically validated in any definitive way ;-)

ben g



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Pei Wang]

On Thu, Oct 30, 2008 at 3:07 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote:
>
> An exact description of the quantum state of the universe gives you 
> everything else.

Why? Just because it is the smallest object we know? Is this a
self-evident commonsense, or a conclusion from physics?

As I said before, this is a very strong version of reductionism. It
was widely accepted in the time of Newton and Laplace, but I don't
think it is still considered as a valid theory in philosophy of
science. This position is not only unjustifiable, but also lead the
research to wrong directions. It is like to suggest an architect to
analyze the structure of a building at atom level, because all
building materials are made by atoms, after all. The fact that all
building materials are indeed made by atoms only makes the suggestion
even more harmful than a suggestion based on false statements.

Pei


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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Ben Goertzel]

On Thu, Oct 30, 2008 at 4:50 PM, Pei Wang <[EMAIL PROTECTED]> wrote:

> On Thu, Oct 30, 2008 at 3:07 PM, Matt Mahoney <[EMAIL PROTECTED]>
> wrote:
> >
> > An exact description of the quantum state of the universe gives you
> everything else.
>
> Why? Just because it is the smallest object we know? Is this a
> self-evident commonsense, or a conclusion from physics?
>


It's an implication of quantum theory.

However, it's not yet fully validated experimentally or theoretically.

No one has ever, for instance,
derived the periodic table of the elements from the laws of physics, without
making a
lot of hacky assumptions that amount to using known facts of chemistry to
tune various
constants in the derivations.

ben g


>
> As I said before, this is a very strong version of reductionism. It
> was widely accepted in the time of Newton and Laplace, but I don't
> think it is still considered as a valid theory in philosophy of
> science. This position is not only unjustifiable, but also lead the
> research to wrong directions. It is like to suggest an architect to
> analyze the structure of a building at atom level, because all
> building materials are made by atoms, after all. The fact that all
> building materials are indeed made by atoms only makes the suggestion
> even more harmful than a suggestion based on false statements.
>
> Pei
>
>
> ---
> agi
> Archives: https://www.listbox.com/member/archive/303/=now
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-- 
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
Director of Research, SIAI
[EMAIL PROTECTED]

"A human being should be able to change a diaper, plan an invasion, butcher
a hog, conn a ship, design a building, write a sonnet, balance accounts,
build a wall, set a bone, comfort the dying, take orders, give orders,
cooperate, act alone, solve equations, analyze a new problem, pitch manure,
program a computer, cook a tasty meal, fight efficiently, die gallantly.
Specialization is for insects."  -- Robert Heinlein



---
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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Pei Wang]

On Thu, Oct 30, 2008 at 4:53 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
>
>
> On Thu, Oct 30, 2008 at 4:50 PM, Pei Wang <[EMAIL PROTECTED]> wrote:
>>
>> On Thu, Oct 30, 2008 at 3:07 PM, Matt Mahoney <[EMAIL PROTECTED]>
>> wrote:
>> >
>> > An exact description of the quantum state of the universe gives you
>> > everything else.
>>
>> Why? Just because it is the smallest object we know? Is this a
>> self-evident commonsense, or a conclusion from physics?
>
>
> It's an implication of quantum theory.

So there are physicists who think in principle the stock market can be
accurately predicated from quantum theory alone? I'd like to get a
reference on that. ;-)

Pei

> However, it's not yet fully validated experimentally or theoretically.
>
> No one has ever, for instance,
> derived the periodic table of the elements from the laws of physics, without
> making a
> lot of hacky assumptions that amount to using known facts of chemistry to
> tune various
> constants in the derivations.
>
> ben g
>
>>
>> As I said before, this is a very strong version of reductionism. It
>> was widely accepted in the time of Newton and Laplace, but I don't
>> think it is still considered as a valid theory in philosophy of
>> science. This position is not only unjustifiable, but also lead the
>> research to wrong directions. It is like to suggest an architect to
>> analyze the structure of a building at atom level, because all
>> building materials are made by atoms, after all. The fact that all
>> building materials are indeed made by atoms only makes the suggestion
>> even more harmful than a suggestion based on false statements.
>>
>> Pei
>>
>>
>> ---
>> agi
>> Archives: https://www.listbox.com/member/archive/303/=now
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>
>
>
> --
> Ben Goertzel, PhD
> CEO, Novamente LLC and Biomind LLC
> Director of Research, SIAI
> [EMAIL PROTECTED]
>
> "A human being should be able to change a diaper, plan an invasion, butcher
> a hog, conn a ship, design a building, write a sonnet, balance accounts,
> build a wall, set a bone, comfort the dying, take orders, give orders,
> cooperate, act alone, solve equations, analyze a new problem, pitch manure,
> program a computer, cook a tasty meal, fight efficiently, die gallantly.
> Specialization is for insects."  -- Robert Heinlein
>
>
> 
> agi | Archives | Modify Your Subscription


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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Ben Goertzel]

On Thu, Oct 30, 2008 at 4:59 PM, Pei Wang <[EMAIL PROTECTED]> wrote:

> On Thu, Oct 30, 2008 at 4:53 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
> >
> >
> > On Thu, Oct 30, 2008 at 4:50 PM, Pei Wang <[EMAIL PROTECTED]>
> wrote:
> >>
> >> On Thu, Oct 30, 2008 at 3:07 PM, Matt Mahoney <[EMAIL PROTECTED]>
> >> wrote:
> >> >
> >> > An exact description of the quantum state of the universe gives you
> >> > everything else.
> >>
> >> Why? Just because it is the smallest object we know? Is this a
> >> self-evident commonsense, or a conclusion from physics?
> >
> >
> > It's an implication of quantum theory.
>
> So there are physicists who think in principle the stock market can be
> accurately predicated from quantum theory alone? I'd like to get a
> reference on that. ;-)


Pei, I think a majority -- or at least a substantial plurality -- of
physicists think that.  Really.

ben



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Pei Wang]

On Thu, Oct 30, 2008 at 5:00 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
>
>> So there are physicists who think in principle the stock market can be
>> accurately predicated from quantum theory alone? I'd like to get a
>> reference on that. ;-)
>
> Pei, I think a majority -- or at least a substantial plurality -- of
> physicists think that.  Really.
>
> ben

Too bad --- they all should take a course in philosophy of science.

Even if that is the case, I don't accept it as a reason to tolerant
this opinion in AGI research.

Pei


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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Mike Tintner]

Matt: An exact description of the quantum state of the universe gives you 
everything else.



Pei:> Why? Just because it is the smallest object we know? Is this a

self-evident commonsense, or a conclusion from physics?

As I said before, this is a very strong version of reductionism. It
was widely accepted in the time of Newton and Laplace, but I don't
think it is still considered as a valid theory in philosophy of
science. This position is not only unjustifiable, but also lead the
research to wrong directions. It is like to suggest an architect to
analyze the structure of a building at atom level, because all
building materials are made by atoms, after all. The fact that all
building materials are indeed made by atoms only makes the suggestion
even more harmful than a suggestion based on false statements.


The real flaw in physics-based reductionism is that you cannot explain 
*evolution*/*creativity*. Your quantum explanation will not explain for a 
start how new molecules - elements - compounds evolved.


Now in principle it might be possible to have a quantum account that 
explained the capacity for some level of evolutionary emergence - some level 
of element-ary evolution. But it's hardly going to explain higher levels. 
Different kinds of wholes - different kinds of clouds and stars and planets 
and black holes.


And it's certainly not going to explain how life evolved - how cells came to 
be, how, for example, different kinds of sensing and perception and 
consciousness and reflection and conscience emerged.


In sum, a physics explanation cannot explain how the different levels of 
forms and behaviour of matter - of which the world consists - evolved - and 
*could/will evolve in the future*. Physics is very low-level.stuff.


This is why I keep banging on about Kauffman's Reinventing the Sacred.It 
deals precisely with this.  And it makes the connection - as AI/AGI-ers 
completely fail to do between all kinds of creativity - from low-level 
evolutionary creativity to high-level human and social creativity. (BTW 
evolution and creativity have themselves evolved and taken on new forms - 
and will continue to do so).


The challenge for science generally is to develop a new mechanistic 
worldview that can incorporate the creativity of the world - just as the 
challenge for AGI is to explain and instantiate high-level creativity (and 
even start talking about it).





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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Matt Mahoney]

--- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:
> So there are physicists who think in principle the stock
> market can be
> accurately predicated from quantum theory alone? I'd
> like to get a
> reference on that. ;-)

If you had a Turing machine, yes.

It also assumes you know which of the possible 2^(2^409) possible states the 
universe is in. (2^409 ~ 2.9 x 10^122 bits = entropy of the universe). So don't 
expect any experimental verification.

However, AIXI suggests a simpler explanation for our existence. Consider an 
enumeration of Turing machines, such that the n'th machine is run for n steps 
until a universe containing intelligent life is found. In this case, our 
universe could have been computed in 2^818 steps.

-- Matt Mahoney, [EMAIL PROTECTED]



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Matt Mahoney]

--- On Thu, 10/30/08, Mike Tintner <[EMAIL PROTECTED]> wrote:

> The real flaw in physics-based reductionism is that you
> cannot explain *evolution*/*creativity*.

The explanation is the anthropic principle. If the physics of our universe did 
not allow for evolution of intelligent life, then we wouldn't be here to ask 
the question.

-- Matt Mahoney, [EMAIL PROTECTED]



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Ben Goertzel]

 The anthropic principle does not prove reductionism -- it just proves that
physics is *consistent* with our existence, not that physics *determines*
our existence without the participation of other factors.

ben g

On Thu, Oct 30, 2008 at 5:24 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote:

> --- On Thu, 10/30/08, Mike Tintner <[EMAIL PROTECTED]> wrote:
>
> > The real flaw in physics-based reductionism is that you
> > cannot explain *evolution*/*creativity*.
>
> The explanation is the anthropic principle. If the physics of our universe
> did not allow for evolution of intelligent life, then we wouldn't be here to
> ask the question.
>
> -- Matt Mahoney, [EMAIL PROTECTED]
>
>
>
> ---
> agi
> Archives: https://www.listbox.com/member/archive/303/=now
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-- 
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
Director of Research, SIAI
[EMAIL PROTECTED]

"A human being should be able to change a diaper, plan an invasion, butcher
a hog, conn a ship, design a building, write a sonnet, balance accounts,
build a wall, set a bone, comfort the dying, take orders, give orders,
cooperate, act alone, solve equations, analyze a new problem, pitch manure,
program a computer, cook a tasty meal, fight efficiently, die gallantly.
Specialization is for insects."  -- Robert Heinlein



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Pei Wang]

On Thu, Oct 30, 2008 at 5:18 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote:
> --- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:
>> So there are physicists who think in principle the stock
>> market can be
>> accurately predicated from quantum theory alone? I'd
>> like to get a
>> reference on that. ;-)
>
> If you had a Turing machine, yes.
>
> It also assumes you know which of the possible 2^(2^409) possible states the 
> universe is in. (2^409 ~ 2.9 x 10^122 bits = entropy of the universe). So 
> don't expect any experimental verification.

Matt,

Even if all of our models of the universe can be put into a Turing
Machine, your conclusion still doesn't follow, because you need to
further assume the model is perfect, that is, it describes the
universe *as it is*. This is another conclusion that conflict with the
current understanding of science.

Pei


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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Ben Goertzel]

>
>
> This is why I keep banging on about Kauffman's Reinventing the Sacred.It
> deals precisely with this.  And it makes the connection - as AI/AGI-ers
> completely fail to do between all kinds of creativity - from low-level
> evolutionary creativity to high-level human and social creativity. (BTW
> evolution and creativity have themselves evolved and taken on new forms -
> and will continue to do so).



I'm not sure why you're so pumped about Kauffman as regards creativity ... I
like his work, but it's not as though he gives any kind of detailed
explanation  of how specific acts of human creativity come about

Your big argument against my approach to AGI seems to be that I haven't give
detailed, step-by-step explanations of how human-level-AI-type acts of
creativity would come about in a system built according to my designs...

My counterargument is that in a system like OpenCogPrime, any substantial
creative act is going to arise via the combination of a huge number of small
cognitive acts interrelating in complex ways.  So there is no reason to
expect it to be simple to give a detailed explanation of how a substantial
creative act will come about in the system ...

I think it might take weeks  of effort to chart out the possible dynamics of
a single substantial creative act within the OpenCogPrime system.  This
might well be an interesting exercise to carry out, but I haven't yet done
it.

Now, what does Kauffman do?  Does he explain in detail how some particular,
substantial creative act might emerge in a human brain, or an AI system?
No.  He lays out some general principles and ideas, and then gives examples
from much simpler systems, whose resemblance to AGI systems is highly
theory-dependent.

In short, he -- like me -- thinks that any substantial creative act is going
to arise via the combination of a huge number of small cognitive acts
interrelating in complex ways ... so that there is no reason to expect it to
be simple to give a detailed explanation of how a substantial creative act
will come about in a complex system like the human brain ...

ben g



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Matt Mahoney]

--- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:

> Even if that is the case, I don't accept it as a reason
> to tolerant this opinion in AGI research.

The point is not that AGI should model things at the level of atoms. The point 
is that we should apply the principle of Occam's Razor to machine learning and 
AGI. We already do that in all practical learning algorithms. For example in 
NARS, a link between two concepts like (if X then Y) has a probability and a 
confidence that depends on the counts of (X,Y) and (X, not Y). This model is a 
simplification from a sequence of n events (with algorithmic complexity 2n) to 
two small integers (with algorithmic complexity 2 log n). The reason this often 
works in practice is Occam's Razor. That might not be the case if physics were 
not computable.

-- Matt Mahoney, [EMAIL PROTECTED]





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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Ben Goertzel]

I note that physicists have frequently, throughout the last few hundred
years, expressed confidence in their understanding of the whole universe ...
and then been proven wrong by later generations of physicists...

Personally I find it highly unlikely that the current physical understanding
of the universe as a whole is going to survive the next century ...
especially with the Singularity looming and all that.  Most likely,
superintelligent AGIs will tell us why our current physics ideas are very
limited.

Fortunately, we don't seem to need to understand the physical universe very
completely in order to build AGIs at the human level and beyond.

-- Ben G

On Thu, Oct 30, 2008 at 5:29 PM, Pei Wang <[EMAIL PROTECTED]> wrote:

> On Thu, Oct 30, 2008 at 5:18 PM, Matt Mahoney <[EMAIL PROTECTED]>
> wrote:
> > --- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:
> >> So there are physicists who think in principle the stock
> >> market can be
> >> accurately predicated from quantum theory alone? I'd
> >> like to get a
> >> reference on that. ;-)
> >
> > If you had a Turing machine, yes.
> >
> > It also assumes you know which of the possible 2^(2^409) possible states
> the universe is in. (2^409 ~ 2.9 x 10^122 bits = entropy of the universe).
> So don't expect any experimental verification.
>
> Matt,
>
> Even if all of our models of the universe can be put into a Turing
> Machine, your conclusion still doesn't follow, because you need to
> further assume the model is perfect, that is, it describes the
> universe *as it is*. This is another conclusion that conflict with the
> current understanding of science.
>
> Pei
>
>
> ---
> agi
> Archives: https://www.listbox.com/member/archive/303/=now
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-- 
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
Director of Research, SIAI
[EMAIL PROTECTED]

"A human being should be able to change a diaper, plan an invasion, butcher
a hog, conn a ship, design a building, write a sonnet, balance accounts,
build a wall, set a bone, comfort the dying, take orders, give orders,
cooperate, act alone, solve equations, analyze a new problem, pitch manure,
program a computer, cook a tasty meal, fight efficiently, die gallantly.
Specialization is for insects."  -- Robert Heinlein



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Ben Goertzel]

While I am actually a fan of Occam's Razor as a guiding principle for AGI, I
really don't think AGI should base itself on assumptions like "physics is
computable"

In fact, this assumption seems to me an egregious *violation* of Occam's
Razor!!

Occam's Razor says we should make the minimum hypotheses needed.
Hypothesizing a computable universe is almost *surely* nowhere near the
minimum hypothesis needed to guide the creation of an AGI

-- Ben G

On Thu, Oct 30, 2008 at 5:36 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote:

> --- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:
>
> > Even if that is the case, I don't accept it as a reason
> > to tolerant this opinion in AGI research.
>
> The point is not that AGI should model things at the level of atoms. The
> point is that we should apply the principle of Occam's Razor to machine
> learning and AGI. We already do that in all practical learning algorithms.
> For example in NARS, a link between two concepts like (if X then Y) has a
> probability and a confidence that depends on the counts of (X,Y) and (X, not
> Y). This model is a simplification from a sequence of n events (with
> algorithmic complexity 2n) to two small integers (with algorithmic
> complexity 2 log n). The reason this often works in practice is Occam's
> Razor. That might not be the case if physics were not computable.
>
> -- Matt Mahoney, [EMAIL PROTECTED]
>
>
>
>
>
> ---
> agi
> Archives: https://www.listbox.com/member/archive/303/=now
> RSS Feed: https://www.listbox.com/member/archive/rss/303/
> Modify Your Subscription:
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-- 
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
Director of Research, SIAI
[EMAIL PROTECTED]

"A human being should be able to change a diaper, plan an invasion, butcher
a hog, conn a ship, design a building, write a sonnet, balance accounts,
build a wall, set a bone, comfort the dying, take orders, give orders,
cooperate, act alone, solve equations, analyze a new problem, pitch manure,
program a computer, cook a tasty meal, fight efficiently, die gallantly.
Specialization is for insects."  -- Robert Heinlein



---
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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Matt Mahoney]

--- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:

> Matt,
> 
> Even if all of our models of the universe can be put into a Turing
> Machine, your conclusion still doesn't follow, because you need to
> further assume the model is perfect, that is, it describes the
> universe *as it is*. This is another conclusion that conflict with the
> current understanding of science.

If I can assume that Turing machines exist, then I can assume perfect knowledge 
of the state of the universe. It doesn't change my conclusion that the universe 
is computable.

-- Matt Mahoney, [EMAIL PROTECTED]



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Mike Tintner]

Ben,

Kauffman does not provide a new worldview, certainly - he merely identifies the 
need for one - and he shows how this is necessary at every level from basic 
physics to economics and our psychology of thinking. He crucially shows that 
this worldview must incorporate the creative principle which is evident at 
every level of evolution - and which is of central importance for AGI.

I don't think, as I said, that his is a major work,  precisely because he 
doesn't have any new theory about the creative principle. But it's an important 
valuable work - a stepping stone - because our worldview is about to change 
(much as our economic-and-poltical world order is about to change!).

Thanks for your more detailed points in answer to my criticisms of AGI's "lack 
of creativity." But if I may, I'll reply in a more considered way another time 
- the criticisms still hold :).



  Ben/MT:




This is why I keep banging on about Kauffman's Reinventing the Sacred.It 
deals precisely with this.  And it makes the connection - as AI/AGI-ers 
completely fail to do between all kinds of creativity - from low-level 
evolutionary creativity to high-level human and social creativity. (BTW 
evolution and creativity have themselves evolved and taken on new forms - and 
will continue to do so).


  I'm not sure why you're so pumped about Kauffman as regards creativity ... I 
like his work, but it's not as though he gives any kind of detailed explanation 
 of how specific acts of human creativity come about

  Your big argument against my approach to AGI seems to be that I haven't give 
detailed, step-by-step explanations of how human-level-AI-type acts of 
creativity would come about in a system built according to my designs...

  My counterargument is that in a system like OpenCogPrime, any substantial 
creative act is going to arise via the combination of a huge number of small 
cognitive acts interrelating in complex ways.  So there is no reason to expect 
it to be simple to give a detailed explanation of how a substantial creative 
act will come about in the system ...

  I think it might take weeks  of effort to chart out the possible dynamics of 
a single substantial creative act within the OpenCogPrime system.  This might 
well be an interesting exercise to carry out, but I haven't yet done it.

  Now, what does Kauffman do?  Does he explain in detail how some particular, 
substantial creative act might emerge in a human brain, or an AI system?  No.  
He lays out some general principles and ideas, and then gives examples from 
much simpler systems, whose resemblance to AGI systems is highly 
theory-dependent.

  In short, he -- like me -- thinks that any substantial creative act is going 
to arise via the combination of a huge number of small cognitive acts 
interrelating in complex ways ... so that there is no reason to expect it to be 
simple to give a detailed explanation of how a substantial creative act will 
come about in a complex system like the human brain ...

  ben g











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agi | Archives  | Modify Your Subscription  



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Ben Goertzel]

>
>
> If I can assume that Turing machines exist, then I can assume perfect
> knowledge of the state of the universe. It doesn't change my conclusion that
> the universe is computable.
>
> -- Matt Mahoney, [EMAIL PROTECTED]
>


1)
Turing machines are mathematical abstractions and don't physically exist

2)
I thought **I** had a lot of hubris but ... wow!  Color me skeptical that
you possess perfect knowledge of the state of the universe ;-)


ben g



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Re: [agi] "the universe is computable" ..PS

[Mike Tintner]

Matt:>> An exact description of the quantum state of the universe gives you 
everything else.




I want to take what I said a little further, because, though basically 
true, it was a little too ethereal.


A physics approach - reducing all things to their fundamental parts/ 
particles - cannot, I said, explain the evolutionary/creative capacity of 
things.


To make this more concrete - a physics/reductionist approach cannot explain 
the *plasticity* of matter.  Natural objects are not like artificial 
objects - like a brick wall that can be deconstructed both analytically and 
physically into precise, discrete parts/bricks.


Natural objects are all to varying degrees plastic. They can be reshaped, 
reforged in an infinity of possible ways to create an infinity of possible 
new materials.


And not only can their form be changed, but also their function and 
behaviour and movement.


Especially organic materials. Soft tissue can become bones. Limbs. 
Sensors.And so on.


And the functions of parts can be changed. Tongues can be made to see.  Feet 
can be made to grasp. Bent backs can be made to stand up erect. And so on.


So, to sum up more precisely,  a physics/ reductionist approach - reducing 
things to their parts - can explain the basic *nature of things, including 
their' plasticity* - how it is that plasticine is so plastic.


What it can't do is explain or define the *potential* of things, including 
their  *spectrum of plasticity*. It cannot explain the infinite variety of 
shapes you can create with plasticine and other things,  and the infinity of 
new forms that you can create by an infinity of operations such as 
baking/burning/freezing/barbecuing etc etc.


(Or to put that another way, science which tells you the basic nature of 
things,  is distinct from technology which is in the continuous process of 
piling up an infinity of things that you can do with, and make out of 
things).


The current mechanistic worldview is essentially a rigid, rational, 
discrete-parts picture of things and the world generally - in which the 
creativity of matter has no place, and is largely ignored. The new 
mechanistic worldview that is emerging is a plastic, creative, fluid-parts/ 
shapeshifting picture of things - which will embrace creativity.


Narrow AI (and current AGI)  basically embody a rigid, rational, 
"crystallised" intelligence. True AGI involves a flexible, creative, "fluid" 
intelligence. (The crystallised/fluid distinction is part of sci. 
psychology).





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RE: [agi] Cloud Intelligence

[John G. Rose]

> From: Matt Mahoney [mailto:[EMAIL PROTECTED]
> 
> Cloud computing is compatible with my proposal for distributed AGI.
> It's just not big enough. I would need 10^10 processors, each 10^3 to
> 10^6 times more powerful than a PC.
> 

The only thing we have that come close to those numbers are insect brains.
Maybe something can be biogenetically engineered :) Somehow wire billions of
insect brains together modified in such a way that they are peer 2 peer and
emerge a greater intelligence :)

John



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Matt Mahoney]

Ben, you missed my point. We use Turing machines in all kinds of computer 
science proofs, even though you can't build one. Turing machines have infinite 
memory, so it is not unreasonable to assume that if Turing machines did exist, 
then one could store the 2^409 bits needed to describe the quantum state of the 
observable universe and then perform computations on that data to predict the 
future.

I described how a Turing machine could obtain that knowledge in about 2^818 
steps by enumerating all possible universes until intelligent life is found. As 
evidence, I suggest that the algorithmic complexity of the free parameters in 
string theory, general relativity, and the initial state of the Big Bang is on 
the order of a few hundred bits.

-- Matt Mahoney, [EMAIL PROTECTED]

--- On Thu, 10/30/08, Ben Goertzel <[EMAIL PROTECTED]> wrote:
From: Ben Goertzel <[EMAIL PROTECTED]>
Subject: Re: [agi] "the universe is computable" [Was: Occam's Razor and its 
abuse]
To: agi@v2.listbox.com
Date: Thursday, October 30, 2008, 6:02 PM






If I can assume that Turing machines exist, then I can assume perfect knowledge 
of the state of the universe. It doesn't change my conclusion that the universe 
is computable.



-- Matt Mahoney, [EMAIL PROTECTED]



1)
Turing machines are mathematical abstractions and don't physically exist

2)
I thought **I** had a lot of hubris but ... wow!  Color me skeptical that you 
possess perfect knowledge of the state of the universe ;-) 



ben g





  

  
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Re: [agi] "the universe is computable" ..PS

[Matt Mahoney]

--- On Thu, 10/30/08, Mike Tintner <[EMAIL PROTECTED]> wrote:

> To make this more concrete - a physics/reductionist
> approach cannot explain 
> the *plasticity* of matter.  Natural objects are not like
> artificial 
> objects - like a brick wall that can be deconstructed both
> analytically and 
> physically into precise, discrete parts/bricks.

Yes it can. You could derive the fact that atoms can move relative to one 
another from their quantum wave equations. What you can't do is explain the 
universe in enough detail that you could predict all of the future events that 
matter to you. That's because you need 10^122 bits to describe the state of the 
observable universe in a deterministic model, and your brain only has 10^9 bits 
of memory.

-- Matt Mahoney, [EMAIL PROTECTED]



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RE: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[John G. Rose]

You can't compute the universe within this universe because the computation
would have to include itself.

Also there's not enough energy to power the computation.

But if the universe is not what we think it is, perhaps it is computable
since all kinds of assumptions are made about it, structurally and so forth.

John



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RE: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Matt Mahoney]

--- On Thu, 10/30/08, John G. Rose <[EMAIL PROTECTED]> wrote:

> You can't compute the universe within this universe
> because the computation
> would have to include itself.

Exactly. That is why our model of physics must be probabilistic (quantum 
mechanics).

-- Matt Mahoney, [EMAIL PROTECTED]



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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Pei Wang]

Agree.

As I mentioned before, science was used to be seen as the pursuing of
"truth", and its theories aimed at describing the aspects of world "as
it is". Now it has been taken as a wrong view. Science is organized
human experience, which is fundamentally based on human cognitive
capability and human experience, so its description of the world never
perfectly matches the world itself.

Actually this is what makes science an everlasting enterprise.
Otherwise there will be a day when science really tells us everything
about the world --- as a Turing Machine or not --- then it will stop
there. Now we know that it will never happen. There will always be
phenomena that no existing theory can explain or predict --- this is
the "insufficient knowledge and resources" situation at the level of
whole human society.

Obviously many people working in science still hold the old
("classical"?) view of science, which usually does not cause too big a
difference in what they do in their research. However, if the subject
of the research is science itself or the human cognition process, then
the old view is not even good enough as an approximation or
idealization.

For people who think the above is just my personal bias, I recommend
the following readings:

*. any textbook in philosophy of science, as far as it include Kuhn and Lakatos
*. Philosophy in the Flesh : The Embodied Mind and Its Challenge to
Western Thought,
by George Lakoff and Mark Johnson
*. Why We See What We Do: An Empirical Theory of Vision, by Dale
Purves and R. Beau Lotto

Pei

On Thu, Oct 30, 2008 at 5:35 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
>
> I note that physicists have frequently, throughout the last few hundred
> years, expressed confidence in their understanding of the whole universe ...
> and then been proven wrong by later generations of physicists...
>
> Personally I find it highly unlikely that the current physical understanding
> of the universe as a whole is going to survive the next century ...
> especially with the Singularity looming and all that.  Most likely,
> superintelligent AGIs will tell us why our current physics ideas are very
> limited.
>
> Fortunately, we don't seem to need to understand the physical universe very
> completely in order to build AGIs at the human level and beyond.
>
> -- Ben G
>
> On Thu, Oct 30, 2008 at 5:29 PM, Pei Wang <[EMAIL PROTECTED]> wrote:
>>
>> On Thu, Oct 30, 2008 at 5:18 PM, Matt Mahoney <[EMAIL PROTECTED]>
>> wrote:
>> > --- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:
>> >> So there are physicists who think in principle the stock
>> >> market can be
>> >> accurately predicated from quantum theory alone? I'd
>> >> like to get a
>> >> reference on that. ;-)
>> >
>> > If you had a Turing machine, yes.
>> >
>> > It also assumes you know which of the possible 2^(2^409) possible states
>> > the universe is in. (2^409 ~ 2.9 x 10^122 bits = entropy of the universe).
>> > So don't expect any experimental verification.
>>
>> Matt,
>>
>> Even if all of our models of the universe can be put into a Turing
>> Machine, your conclusion still doesn't follow, because you need to
>> further assume the model is perfect, that is, it describes the
>> universe *as it is*. This is another conclusion that conflict with the
>> current understanding of science.
>>
>> Pei
>>
>>
>> ---
>> agi
>> Archives: https://www.listbox.com/member/archive/303/=now
>> RSS Feed: https://www.listbox.com/member/archive/rss/303/
>> Modify Your Subscription: https://www.listbox.com/member/?&;
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>
>
>
> --
> Ben Goertzel, PhD
> CEO, Novamente LLC and Biomind LLC
> Director of Research, SIAI
> [EMAIL PROTECTED]
>
> "A human being should be able to change a diaper, plan an invasion, butcher
> a hog, conn a ship, design a building, write a sonnet, balance accounts,
> build a wall, set a bone, comfort the dying, take orders, give orders,
> cooperate, act alone, solve equations, analyze a new problem, pitch manure,
> program a computer, cook a tasty meal, fight efficiently, die gallantly.
> Specialization is for insects."  -- Robert Heinlein
>
>
> 
> agi | Archives | Modify Your Subscription


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Re: [agi] constructivist issues

[Charles Hixson]

If you were talking about something actual, then you would have a valid 
point.  Numbers, though, only exist in so far as they exist in the 
theory that you are using to define them.  E.g., if I were to claim that 
no number larger than the power-set of energy states within the universe 
were valid, it would not be disprovable.  That would immediately mean 
that only finite numbers were valid.


P.S.:  Just because you have a rule that could generate a particular 
number given a larger than possible number of steps doesn't mean that it 
is a valid number, as you can't actually ever generate it.  I suspect 
that infinity is primarily a computational convenience.  But one 
shouldn't mistake the fact that it's very convenient for meaning that 
it's true.  Or, given Occam's Razor, should one?  But Occam's Razor only 
detects provisional truths, not actual ones.


If you're going to be constructive, then you must restrict yourself to 
finitely many steps, each composed of finitely complex reasoning.  And 
this means that you must give up both infinite numbers and irrational 
numbers.  To do otherwise means assuming that you can make infinitely 
precise measurements (which would, at any rate, allow irrational numbers 
back in).


Therefore, I would assert that it isn't that it leaves "*even more* 
about numbers left undefined", but that those characteristics aren't in 
such a case properties of numbers.  Merely of the simplifications an 
abstractions made to ease computation.


Abram Demski wrote:

Charles,

Interesting point-- but, all of these theories would be weaker then
the standard axioms, and so there would be *even more* about numbers
left undefined in them.

--Abram

On Tue, Oct 28, 2008 at 10:46 PM, Charles Hixson
<[EMAIL PROTECTED]> wrote:
  

Excuse me, but I thought there were subsets of Number theory which were
strong enough to contain all the integers, and perhaps all the rational, but
which weren't strong enough to prove Gödel's incompleteness theorem in.  I
seem to remember, though, that you can't get more than a finite number of
irrationals in such a theory.  And I think that there are limitations on
what operators can be defined.

Still, depending on what you mean my Number, that would seem to mean that
Number was well-defined.  Just not in Number Theory, but that's because
Number Theory itself wasn't well-defined.





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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Pei Wang]

On Thu, Oct 30, 2008 at 5:36 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote:
>
> The point is not that AGI should model things at the level of atoms.

I didn't blame anyone for doing that. What I said is: to predict the
environment as a Turing Machine (symbol by symbol) is just like to
construct a building atom by atom. The problem is not merely in
complexity, but in the level of description.

> The point is that we should apply the principle of Occam's Razor to machine 
> learning and AGI.

If by "Occam's Razor" you mean "the learning mechanism should prefer
simpler result", I don't think anyone has disagreed (though people may
not use that term, or may justify it differently), but if by "Occam's
Razor" you mean "learning should start by giving simpler hypotheses
higher prior probability", I still don't see why.

> We already do that in all practical learning algorithms. For example in NARS, 
> a link between two concepts like (if X then Y) has a probability and a 
> confidence that depends on the counts of (X,Y) and (X, not Y).

Yes, except it is not a "probability" in the sense of "limit of frequency".

> This model is a simplification from a sequence of n events (with algorithmic 
> complexity 2n) to two small integers (with algorithmic complexity 2 log n).

This is your interpretation, which is fine, though I don't see why I
must see it the same way, though I do agree that it is a summary of
experience.

> The reason this often works in practice is Occam's Razor. That might not be 
> the case if physics were not computable.

Again, this is a description of your belief, not a justification of this belief.

Pei


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RE: [agi] Cloud Intelligence

[Matt Mahoney]

--- On Thu, 10/30/08, John G. Rose <[EMAIL PROTECTED]> wrote:

> > From: Matt Mahoney [mailto:[EMAIL PROTECTED]
> > 
> > Cloud computing is compatible with my proposal for distributed AGI.
> > It's just not big enough. I would need 10^10 processors, each 10^3 to
> > 10^6 times more powerful than a PC.
> > 
> 
> The only thing we have that come close to those numbers are
> insect brains.
> Maybe something can be biogenetically engineered :) Somehow
> wire billions of
> insect brains together modified in such a way that they are
> peer 2 peer and
> emerge a greater intelligence :)

Or molecular computing. The Earth has about 10^37 bits of data encoded in DNA*. 
Evolution executes a parallel algorithm that runs at 10^33 operations per 
second**. This far exceeds the 10^25 bits of memory and 10^27 OPS needed to 
simulate all the human brains on Earth as neural networks***.

*Human DNA has 6 x 10^9 base pairs (diploid count) at 2 bits each ~ 10^10 bits. 
The human body has ~ 10^14 cells = 10^24 bits. There are ~ 10^10 humans ~ 10^34 
bits. Humans make up 0.1% of the biomass ~ 10^37 bits.

**Cell replication ranges from 20 minutes in bacteria to ~ 1 year in human 
tissue. Assume 10^-4 replications per second on average ~ 10^33 OPS. The figure 
would be much higher if you include RNA and protein synthesis.

***Assume 10^15 synapses per brain at 1 bit each and 10 ms resolution times 
10^10 humans.

-- Matt Mahoney, [EMAIL PROTECTED]



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Re: [agi] "the universe is computable" ..PS

[Mike Tintner]

Matt:MT>

To make this more concrete - a physics/reductionist
approach cannot explain
the *plasticity* of matter.  Natural objects are not like
artificial
objects - like a brick wall that can be deconstructed both
analytically and
physically into precise, discrete parts/bricks.


Yes it can. You could derive the fact that atoms can move relative to one 
another from their quantum wave equations. What you can't do is explain 
the universe in enough detail that you could predict all of the future 
events that matter to you. That's because you need 10^122 bits to describe 
the state of the observable universe in a deterministic model, and your 
brain only has 10^9 bits of memory.


Matt,

What are the shapes/forms (and range of shapes/forms) of atoms?  And the 
range of shapes/forms of fundamental particles? And what are the range of 
possible forms of any of those ranges of  forms?


And how would you or physics derive the properties of different materials 
from these shapes? Why is it that rigidity is a collective property of an 
iron bar, but not an iron atom?


IOW how do you know what can and can't be predicted from atoms and 
fundamental particles?  And doesn't your (and science's) Lego picture of the 
world have a great deal of v. fundamental holes, and involve a great deal of 
assumed parts and frameworks which may be - indeed are almost certainly, 
given the history of science - false?


P.S. Can you please explain how computation itself is computable  - given 
that it doesn't have to be instantiated on any particular physical 
substrate - and can be on everything from silicon chips to buckets of water 
and abaci?  It would be a bit silly if you can't, no?.


But if you can't do that, please give one example of how *any* form of 
emergence in the history of the world is explicable by physics. It would be 
even sillier if you can't do that, no, and yet are still making mindblowing 
claims about what can be explained re the universe?


You have, as Ben has pointed out, been repeatedly assuming more or less 
divine knowledge of the world. [Who else could know that it takes exactly 
10^122 bits to describe the state of the observable universe,  or $1 
quadrillion to create AGI? Such awesome precision and certainty). It 
shouldn't be too much to ask you to enlighten us lesser mortals as to just 
one or two of the world's other secrets here ).  And where will the S&P 500 
be at the end of Tuesday?






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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Pei Wang]

Matt,

How about the following argument:

A. "Since in principle all human knowledge about the universe can be
expressed in English, we say that the universe exists as a English
essay --- though we don't know which one yet".

B. "Because of A, the ultimate scientific research method is to
exhaustively produce all possible English essays, test each of them
against the universe, and keep the best --- since there are infinite
number of them, the process won't terminate, but it can be used as an
idealized model of scientific research, and the best scientific theory
will always be produced in this way."

C. "As a practical version of B, we can limit the length of the essay,
in characters, to a constant N. Then this algorithm will surely find
the best scientific theory within length N in finite time. Now
everyone doing science should approximate this process as closely as
possible, and the only remaining issue is computational power to reach
larger and larger N."

Of course, I don't mean that your argument is this silly --- the
research paradigm you argued for is interesting and valuable in
certain aspects --- though I do feel some similarity between the two
cases.

Pei


On Thu, Oct 30, 2008 at 7:30 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote:
> Ben, you missed my point. We use Turing machines in all kinds of computer
> science proofs, even though you can't build one. Turing machines have
> infinite memory, so it is not unreasonable to assume that if Turing machines
> did exist, then one could store the 2^409 bits needed to describe the
> quantum state of the observable universe and then perform computations on
> that data to predict the future.
>
> I described how a Turing machine could obtain that knowledge in about 2^818
> steps by enumerating all possible universes until intelligent life is found.
> As evidence, I suggest that the algorithmic complexity of the free
> parameters in string theory, general relativity, and the initial state of
> the Big Bang is on the order of a few hundred bits.
>
> -- Matt Mahoney, [EMAIL PROTECTED]
>
> --- On Thu, 10/30/08, Ben Goertzel <[EMAIL PROTECTED]> wrote:
>
> From: Ben Goertzel <[EMAIL PROTECTED]>
> Subject: Re: [agi] "the universe is computable" [Was: Occam's Razor and its
> abuse]
> To: agi@v2.listbox.com
> Date: Thursday, October 30, 2008, 6:02 PM
>
>
>>
>>
>> If I can assume that Turing machines exist, then I can assume perfect
>> knowledge of the state of the universe. It doesn't change my conclusion that
>> the universe is computable.
>>
>> -- Matt Mahoney, [EMAIL PROTECTED]
>
>
> 1)
> Turing machines are mathematical abstractions and don't physically exist
>
> 2)
> I thought **I** had a lot of hubris but ... wow!  Color me skeptical that
> you possess perfect knowledge of the state of the universe ;-)
>
>
> ben g
> 
> agi | Archives | Modify Your Subscription
>
> 
> agi | Archives | Modify Your Subscription


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Re: [agi] Machine Consciousness Workshop, Hong Kong, June 2009

[Colin Hales]

Hi,
I was wondering as to the formatwho does what, how...speaking etc 
etc.. what sort of airing do the contributors get for their material?

regards
colin


Ben Goertzel wrote:

Hi all,

I wanted to let you know that Gino Yu and I are co-organizing  a 
Workshop on Machine

Consciousness, which will be held in  Hong Kong in June 2008: see

http://novamente.net/machinecs/index.html

for details. 

It is colocated with a larger, interdisciplinary conference on 
consciousness research,

which has previously been announced:

http://www.consciousness.arizona.edu/

As an aside, I also note that the date for submitting papers to
AGI-09 has been extended, by popular demand, till November 12;
see

http://agi-09.org/

AGI-09 will welcome quality papers on any strong-AI
related topics.

thanks!
ben

--
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
Director of Research, SIAI
[EMAIL PROTECTED] 


"A human being should be able to change a diaper, plan an invasion, 
butcher a hog, conn a ship, design a building, write a sonnet, balance 
accounts, build a wall, set a bone, comfort the dying, take orders, 
give orders, cooperate, act alone, solve equations, analyze a new 
problem, pitch manure, program a computer, cook a tasty meal, fight 
efficiently, die gallantly. Specialization is for insects."  -- Robert 
Heinlein




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Re: [agi] Machine Consciousness Workshop, Hong Kong, June 2009

[Ben Goertzel]

Accepted papers will be in two categories

-- oral presentation
-- poster presentation

Oral presentations will be relatively brief and then followed by
discussions, similar to the format of AGI-08

-- Ben G


On Thu, Oct 30, 2008 at 9:09 PM, Colin Hales
<[EMAIL PROTECTED]>wrote:

>  Hi,
> I was wondering as to the formatwho does what, how...speaking etc etc..
> what sort of airing do the contributors get for their material?
> regards
> colin
>
>
> Ben Goertzel wrote:
>
> Hi all,
>
> I wanted to let you know that Gino Yu and I are co-organizing  a Workshop
> on Machine
> Consciousness, which will be held in  Hong Kong in June 2008: see
>
> http://novamente.net/machinecs/index.html
>
> for details.
>
> It is colocated with a larger, interdisciplinary conference on
> consciousness research,
> which has previously been announced:
>
> http://www.consciousness.arizona.edu/
>
> As an aside, I also note that the date for submitting papers to
> AGI-09 has been extended, by popular demand, till November 12;
> see
>
> http://agi-09.org/
>
> AGI-09 will welcome quality papers on any strong-AI
> related topics.
>
> thanks!
> ben
>
> --
> Ben Goertzel, PhD
> CEO, Novamente LLC and Biomind LLC
> Director of Research, SIAI
> [EMAIL PROTECTED]
>
>
> "A human being should be able to change a diaper, plan an invasion, butcher
> a hog, conn a ship, design a building, write a sonnet, balance accounts,
> build a wall, set a bone, comfort the dying, take orders, give orders,
> cooperate, act alone, solve equations, analyze a new problem, pitch manure,
> program a computer, cook a tasty meal, fight efficiently, die gallantly.
> Specialization is for insects."  -- Robert Heinlein
>
>
>  --
>*agi* | Archives 
>  | 
> ModifyYour Subscription
> 
>
>  --
>   *agi* | Archives 
>  | 
> ModifyYour Subscription
> 
>



-- 
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
Director of Research, SIAI
[EMAIL PROTECTED]

"A human being should be able to change a diaper, plan an invasion, butcher
a hog, conn a ship, design a building, write a sonnet, balance accounts,
build a wall, set a bone, comfort the dying, take orders, give orders,
cooperate, act alone, solve equations, analyze a new problem, pitch manure,
program a computer, cook a tasty meal, fight efficiently, die gallantly.
Specialization is for insects."  -- Robert Heinlein



---
agi
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Re: [agi] "the universe is computable" [Was: Occam's Razor and its abuse]

[Matt Mahoney]

I am not suggesting that we model the universe by an exact computation. That is 
impossible (as John Rose pointed out) because the computer would have to be 
inside the universe it is modeling.

I am suggesting that Occam's Razor holds in the observable universe because the 
only requirement for the proof of AIXI is that the environment have a 
probability distribution that is computable by a Turing machine. That is the 
case for the laws of physics as they are currently understood.

-- Matt Mahoney, [EMAIL PROTECTED]


--- On Thu, 10/30/08, Pei Wang <[EMAIL PROTECTED]> wrote:

> From: Pei Wang <[EMAIL PROTECTED]>
> Subject: Re: [agi] "the universe is computable" [Was: Occam's Razor and its 
> abuse]
> To: agi@v2.listbox.com
> Date: Thursday, October 30, 2008, 8:28 PM
> Matt,
> 
> How about the following argument:
> 
> A. "Since in principle all human knowledge about the
> universe can be
> expressed in English, we say that the universe exists as a
> English
> essay --- though we don't know which one yet".
> 
> B. "Because of A, the ultimate scientific research
> method is to
> exhaustively produce all possible English essays, test each
> of them
> against the universe, and keep the best --- since there are
> infinite
> number of them, the process won't terminate, but it can
> be used as an
> idealized model of scientific research, and the best
> scientific theory
> will always be produced in this way."
> 
> C. "As a practical version of B, we can limit the
> length of the essay,
> in characters, to a constant N. Then this algorithm will
> surely find
> the best scientific theory within length N in finite time.
> Now
> everyone doing science should approximate this process as
> closely as
> possible, and the only remaining issue is computational
> power to reach
> larger and larger N."
> 
> Of course, I don't mean that your argument is this
> silly --- the
> research paradigm you argued for is interesting and
> valuable in
> certain aspects --- though I do feel some similarity
> between the two
> cases.
> 
> Pei
> 
> 
> On Thu, Oct 30, 2008 at 7:30 PM, Matt Mahoney
> <[EMAIL PROTECTED]> wrote:
> > Ben, you missed my point. We use Turing machines in
> all kinds of computer
> > science proofs, even though you can't build one.
> Turing machines have
> > infinite memory, so it is not unreasonable to assume
> that if Turing machines
> > did exist, then one could store the 2^409 bits needed
> to describe the
> > quantum state of the observable universe and then
> perform computations on
> > that data to predict the future.
> >
> > I described how a Turing machine could obtain that
> knowledge in about 2^818
> > steps by enumerating all possible universes until
> intelligent life is found.
> > As evidence, I suggest that the algorithmic complexity
> of the free
> > parameters in string theory, general relativity, and
> the initial state of
> > the Big Bang is on the order of a few hundred bits.
> >
> > -- Matt Mahoney, [EMAIL PROTECTED]
> >
> > --- On Thu, 10/30/08, Ben Goertzel
> <[EMAIL PROTECTED]> wrote:
> >
> > From: Ben Goertzel <[EMAIL PROTECTED]>
> > Subject: Re: [agi] "the universe is
> computable" [Was: Occam's Razor and its
> > abuse]
> > To: agi@v2.listbox.com
> > Date: Thursday, October 30, 2008, 6:02 PM
> >
> >
> >>
> >>
> >> If I can assume that Turing machines exist, then I
> can assume perfect
> >> knowledge of the state of the universe. It
> doesn't change my conclusion that
> >> the universe is computable.
> >>
> >> -- Matt Mahoney, [EMAIL PROTECTED]
> >
> >
> > 1)
> > Turing machines are mathematical abstractions and
> don't physically exist
> >
> > 2)
> > I thought **I** had a lot of hubris but ... wow! 
> Color me skeptical that
> > you possess perfect knowledge of the state of the
> universe ;-)
> >
> >
> > ben g
> > 
> > agi | Archives | Modify Your Subscription
> >
> > 
> > agi | Archives | Modify Your Subscription
> 
> 
> ---
> agi
> Archives: https://www.listbox.com/member/archive/303/=now
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Re: [agi] "the universe is computable" ..PS

[Matt Mahoney]

--- On Thu, 10/30/08, Mike Tintner <[EMAIL PROTECTED]> wrote:

> What are the shapes/forms (and range of shapes/forms) of
> atoms?

The shapes are given by solving Schrodinger's equation.
http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

> And how would you or physics derive the properties of
> different materials from these shapes?

By solving the equation for millions of atoms on a very large computer. 
Computing chemical and physical properties has never been done this way because 
unfortunately the computation time increases exponentially with the number of 
particles.

> where will the S&P 500 
> be at the end of Tuesday?

Sorry, I would need a computer much bigger than the universe to compute that 
(and it probably wouldn't finish running by Tuesday).

-- Matt Mahoney, [EMAIL PROTECTED]



---
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Re: [agi] constructivist issues

[Abram Demski]

Charles,

OK, but if you argue in that manner, then your original point is a
little strange, doesn't it? Why worry about Godelian incompleteness if
you think incompleteness is just fine?

"Therefore, I would assert that it isn't that it leaves "*even more*
about numbers left undefined", but that those characteristics aren't
in such a case properties of numbers.  Merely of the simplifications
an abstractions made to ease computation."

In this language, what I'm saying is that it is important to examine
the "simplifications and abstractions", and discover how they work, so
that we can "ease computation" in our implementations.

--Abram

On Thu, Oct 30, 2008 at 7:58 PM, Charles Hixson
<[EMAIL PROTECTED]> wrote:
> If you were talking about something actual, then you would have a valid
> point.  Numbers, though, only exist in so far as they exist in the theory
> that you are using to define them.  E.g., if I were to claim that no number
> larger than the power-set of energy states within the universe were valid,
> it would not be disprovable.  That would immediately mean that only finite
> numbers were valid.
>
> P.S.:  Just because you have a rule that could generate a particular number
> given a larger than possible number of steps doesn't mean that it is a valid
> number, as you can't actually ever generate it.  I suspect that infinity is
> primarily a computational convenience.  But one shouldn't mistake the fact
> that it's very convenient for meaning that it's true.  Or, given Occam's
> Razor, should one?  But Occam's Razor only detects provisional truths, not
> actual ones.
>
> If you're going to be constructive, then you must restrict yourself to
> finitely many steps, each composed of finitely complex reasoning.  And this
> means that you must give up both infinite numbers and irrational numbers.
>  To do otherwise means assuming that you can make infinitely precise
> measurements (which would, at any rate, allow irrational numbers back in).
>
> Therefore, I would assert that it isn't that it leaves "*even more* about
> numbers left undefined", but that those characteristics aren't in such a
> case properties of numbers.  Merely of the simplifications an abstractions
> made to ease computation.


---
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Re: [agi] "the universe is computable" ..PS

[Abram Demski]

Matt,

What Mike is saying here may sound odd, but I think there is a
reasonable way of interpreting it in light of the article Richard
Loosemore posted in a recent thread (New Scientist: "Why nature can't
be reduced to mathematical laws"). So, Mike is entirely correct here
if we interpret the "potential" he is referring to as the abstractions
that engineers *must* use to explore the space of possible designs. In
other words: facts about the concrete universe could be entirely
determinate, yet even the most concrete-seeming abstract model could
contain logical indeterminacy. (How you *interpret* this
indeterminacy, that is, constructively or classically, is of course
another issue.)

--Abram

On Thu, Oct 30, 2008 at 10:57 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote:
> --- On Thu, 10/30/08, Mike Tintner <[EMAIL PROTECTED]> wrote:
>
>> What are the shapes/forms (and range of shapes/forms) of
>> atoms?
>
> The shapes are given by solving Schrodinger's equation.
> http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation
>
>> And how would you or physics derive the properties of
>> different materials from these shapes?
>
> By solving the equation for millions of atoms on a very large computer. 
> Computing chemical and physical properties has never been done this way 
> because unfortunately the computation time increases exponentially with the 
> number of particles.
>
>> where will the S&P 500
>> be at the end of Tuesday?
>
> Sorry, I would need a computer much bigger than the universe to compute that 
> (and it probably wouldn't finish running by Tuesday).
>
> -- Matt Mahoney, [EMAIL PROTECTED]
>
>
>
> ---
> agi
> Archives: https://www.listbox.com/member/archive/303/=now
> RSS Feed: https://www.listbox.com/member/archive/rss/303/
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>


---
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Re: [agi] "the universe is computable" ..PS

[Eric Burton]

I actually emailed a gentleman at Sandia one time asking why don't
they use their molecular dynamics setup to extrapolate novel instances
and classes of high-temperature superconductor etc. What I came away
with is you really want to be simulating sub-molecular interactions in
order to extrapolate thermodynamic properties of unknown compounds. I
don't know if this is do-able. Does anyone know anything about it :|


---
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Re: [agi] constructivist issues

[Charles Hixson]

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 
incompleteness to be proven (or even described) then the numbers are 
precisely this which is included in that subset of the theory.


Number Theory is the one with the largest (i.e., and infinite number) of 
unprovable theories about numbers of the variations that I have been 
considering.   My point in the just prior post is that numbers are 
precisely that item which the theory you are using to describe them says 
they are, since they are artifacts created for computational 
convenience, as opposed to direct sensory experiences of the universe.


As such, it doesn't make sense to say that a subset of number theory 
leaves more facts about numbers undefined.  In the subsets those aren't 
facts about numbers.


Abram Demski wrote:

Charles,

OK, but if you argue in that manner, then your original point is a
little strange, doesn't it? Why worry about Godelian incompleteness if
you think incompleteness is just fine?

"Therefore, I would assert that it isn't that it leaves "*even more*
about numbers left undefined", but that those characteristics aren't
in such a case properties of numbers.  Merely of the simplifications
an abstractions made to ease computation."

In this language, what I'm saying is that it is important to examine
the "simplifications and abstractions", and discover how they work, so
that we can "ease computation" in our implementations.

--Abram

On Thu, Oct 30, 2008 at 7:58 PM, Charles Hixson
<[EMAIL PROTECTED]> wrote:
  

If you were talking about something actual, then you would have a valid
point.  Numbers, though, only exist in so far as they exist in the theory
that you are using to define them.  E.g., if I were to claim that no number
larger than the power-set of energy states within the universe were valid,
it would not be disprovable.  That would immediately mean that only finite
numbers were valid.

P.S.:  Just because you have a rule that could generate a particular number
given a larger than possible number of steps doesn't mean that it is a valid
number, as you can't actually ever generate it.  I suspect that infinity is
primarily a computational convenience.  But one shouldn't mistake the fact
that it's very convenient for meaning that it's true.  Or, given Occam's
Razor, should one?  But Occam's Razor only detects provisional truths, not
actual ones.

If you're going to be constructive, then you must restrict yourself to
finitely many steps, each composed of finitely complex reasoning.  And this
means that you must give up both infinite numbers and irrational numbers.
 To do otherwise means assuming that you can make infinitely precise
measurements (which would, at any rate, allow irrational numbers back in).

Therefore, I would assert that it isn't that it leaves "*even more* about
numbers left undefined", but that those characteristics aren't in such a
case properties of numbers.  Merely of the simplifications an abstractions
made to ease computation.





---
agi
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