Hi Steve,

A few comments...

Nobody is trying to implement Hutter's AIXI design, it's a mathematical
design intended as a "proof of principle"

Within Hutter's framework, one calculates the shortest program that explains
the data, where "shortest" is measured on Turing  machine M.   Given a
sufficient number of observations, the choice of M doesn't matter and AIXI
will eventually learn any computable reward pattern.  However, choosing the
right M can greatly accelerate learning.  In the case of a physical AGI
system, choosing M to incorporate the correct laws of physics would
obviously accelerate learning considerably.

Many AGI designs try to incorporate prior understanding of the structure &
properties of the physical world, in various ways.  I have a whole chapter
on this in my forthcoming book on OpenCog....  E.g. OpenCog's design
includes a physics-engine, which is used directly and to aid with
inferential extrapolations...

So I agree with most of your points, but I don't find them original except
in phrasing ;)

... ben

On Sun, Jun 27, 2010 at 2:30 PM, Steve Richfield

> Ben, et al,
> *I think I may finally grok the fundamental misdirection that current AGI
> thinking has taken!
> *This is a bit subtle, and hence subject to misunderstanding. Therefore I
> will first attempt to explain what I see, WITHOUT so much trying to convince
> you (or anyone) that it is necessarily correct. Once I convey my vision,
> then let the chips fall where they may.
> On Sun, Jun 27, 2010 at 6:35 AM, Ben Goertzel <b...@goertzel.org> wrote:
>> Hutter's AIXI for instance works [very roughly speaking] by choosing the
>> most compact program that, based on historical data, would have yielded
>> maximum reward
> ... and there it is! What did I see?
> Example applicable to the lengthy following discussion:
> 1 - 2
> 2 - 2
> 3 - 2
> 4 - 2
> 5 - ?
> What is "?".
> Now, I'll tell you that the left column represents the distance along a 4.5
> unit long table, and the right column represents the distance above the
> floor that you will be as your walk the length of the table. Knowing this,
> without ANY supporting physical experience, I would guess "?" to be zero, or
> maybe a little more if I were to step off of the table and land onto
> something lower, like the shoes that I left there.
> In an imaginary world where a GI boots up with a complete understanding of
> physics, etc., we wouldn't prefer the simplest "program" at all, but rather
> the simplest representation of the real world that is not physics/math *in
> *consistent with our observations. All observations would be presumed to
> be consistent with the response curves of our sensors, showing a world in
> which Newton's laws prevail, etc. Armed with these presumptions, our
> physics-complete AGI would look for the simplest set of *UN*observed
> phenomena that explained the observed phenomena. This theory of a
> physics-complete AGI seems undeniable, but of course, we are NOT born
> physics-complete - or are we?!
> This all comes down to the limits of representational math. At great risk
> of hand-waving on a keyboard, I'll try to explain by pseudo-translating the
> concepts into NN/AGI terms.
> We all know about layering and columns in neural systems, and understand
> Bayesian math. However, let's dig a little deeper into exactly what is being
> represented by the "outputs" (or "terms" for died-in-the-wool AGIers). All
> physical quantities are well known to have value, significance, and
> dimensionality. Neurons/Terms (N/T) could easily be protein-tagged as to the
> dimensionality that their functionality is capable of producing, so that
> only compatible N/Ts could connect to them. However, let's dig a little
> deeper into "dimensionality"
> Physicists think we live in an MKS (Meters, Kilograms, Seconds) world, and
> that all dimensionality can be reduced to MKS. For physics purposes they may
> be right (see challenge below), but maybe for information processing
> purposes, they are missing some important things.
> *Challenge to MKS:* Note that some physicists and most astronomers utilize
> "*dimensional analysis*" where they experimentally play with the
> dimensions of observations to inductively find manipulations that would
> yield the dimensions of unobservable quantities, e.g. the mass of a star,
> and then run the numbers through the same manipulation to see if the results
> at least have the right exponent. However, many/most such manipulations
> produce nonsense, so they simply use this technique to jump from
> observations to a list of prospective results with wildly different
> exponents, and discard the results with the ridiculous exponents to find the
> correct result. The frequent failures of this process indirectly
> demonstrates that there is more to dimensionality (and hence physics) than
> just MKS. Let's accept that, and presume that neurons must have already
> dealt with whatever is missing from current thought.
> Consider, there is some (hopefully finite) set of reasonable manipulations
> that could be done to Bayesian measures, with the various competing theories
> of recognition representing part of that set. The reasonable mathematics to
> perform on spacial features is probably different than the reasonable
> mathematics to perform on recognized objects, or the recognition of
> impossible observations, the manipulation of ideas, etc. Hence, N/Ts could
> also be tagged for this deeper level of dimensionality, so that ideas don't
> get mixed up with spacial features, etc.
> Note that we may not have perfected this process, and further, that this
> process need not be perfected. Somewhere around the age of 12, many of our
> neurons DIE. Perhaps these were just the victims of insufficiently precise
> dimensional tagging?
> Once things can ONLY connect up in mathematically reasonable ways, what
> remains between a newborn and a physics-complete AGI? Obviously, the
> physics, which can be quite different on land than in the water. Hence, the
> physics must also be learned.
> My point here is that if we impose a fragile requirement for mathematical
> correctness against a developing system of physics and REJECT simplistic
> explanations (not observations) that would violate either the mathematics or
> the physics, then we don't end up with overly simplistic and useless
> "programs", but rather we find more complex explanations that are physics
> and mathematically believable.
> we should REJECT the concept of "pattern matching" UNLESS the discovered
> pattern is both physics and mathematically correct. In short, the next
> number in the "2, 2, 2, 2, ?" example sequence would *obviously* (by this
> methodology) not be "2".
> OK, the BIG question here is whether a carefully-designed (or evolved over
> 100 million years) system of representation can FORCE the construction of
> systems (like us) that work this way, so that our "programs" aren't "simple"
> at all, but rather are maximally correct?
> Anyway, I hope you grok the question above, and agree that the search for
> the simplest "program" (without every possible reasonable physics and math
> constraint that can be found) may be a considerable misdirection. Once you
> impose physics and math constraints, which could potentially be done with
> simplistic real-world mechanisms like protein tagging in neurons, the
> problems then shifts to finding ANY solution that fits the complex
> constraints, rather than finding the SIMPLEST solution without such
> constraints.
> Once we can get past the questions, hopefully we can discuss prospective
> answers.
> Are we in agreement here?
> Any thoughts?
> Steve
>    *agi* | Archives <https://www.listbox.com/member/archive/303/=now>
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Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
CTO, Genescient Corp
Vice Chairman, Humanity+
Advisor, Singularity University and Singularity Institute
External Research Professor, Xiamen University, China

“When nothing seems to help, I go look at a stonecutter hammering away at
his rock, perhaps a hundred times without as much as a crack showing in it.
Yet at the hundred and first blow it will split in two, and I know it was
not that blow that did it, but all that had gone before.”

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