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Sunday, September 18, 2011

A Mind-World Correspondence Principle

I had some more ideas, working toward a general theory of general intelligence, which I wrote in a paper posted online at Dynamical Psychology.

(Please note: it's fairly abstract theoretical/mathematical material, so if you're solely interested in current AGI engineering work, don't bother! The hope is that this theory will be able to help guide engineering work once it's further developed, but it's not at that stage yet. So for now my abstract mathematical AGI theory work and practical AGI engineering work are only loosely coupled.)

The crux of the paper is:

MIND-WORLD CORRESPONDENCE PRINCIPLE: For an organism with a reasonably high level of intelligence in a certain world, relative to a certain set of goals, the mind-world path transfer function is a goal-weighted approximate functor

To see what those terms mean and why it might be a useful notion, you'll have to read the paper.

A cruder expression of the same idea, with fewer special defined terms is:

MIND-WORLD CORRESPONDENCE-PRINCIPLE: For a mind to work intelligently toward certain goals in a certain world, there should be a nice mapping from goal-directed sequences of world-states into sequences of mind-states, where “nice” means that a world-state-sequence W composed of two parts W1 and W2, gets mapped into a mind-state-sequence M composed of two corresponding parts M1 and M2.

As noted toward the end of the paper, this principle gives us systematic way to approach questions like: Why do real-world minds seem to be full of hierarchical structures? The answer is probably that the real world is full of goal-relevant hierarchical structures. The Mind-World Correspondence Principle explains exactly why these hierarchical structures in the world have to be reflected by hierarchical structures in the mind of any system that's intelligent in the world.

As an aside, it also occurred to me that these ideas might give us a nice way to formalize the notion of a "good mind upload," in category-theoretic terms.

I.e., if we characterize minds via transition graphs in the way done in the paper, then we can argue that mind X is a valid upload of mind Y if there is a fairly accurate approximate functor from X's transition graph to Y's.

And, if Y is a nondestructive upload (so X still exists after the uploading), it would remain a good upload of X over time if, as X and Y both changed, there was a natural transformation governing the functors between them. Of course, your upload might not WANT to remain aligned with you in this manner, but that's a different issue...

11 comments:

Favorite said...

On Intelligence by J.Hawkins, p. 125
A Model of the World
Why is the neocortex built as a hierarchy?
You can think about the world, move around in the world, and make predictions of the future because your cortex has built a model of the world. One of the most important concepts in this book is that the cortex's hierarchical structure stores a model of the hierarchical structure of the real world. The real world's nested structure is mirrored by the nested structure of your cortex.

Ben Goertzel said...

Favorite: Indeed, that's a commonplace observation in neuroscience, not original to Hawkins & at all. But I wanted to derive this idea from a solid theoretical framework, rather than just making it as an intuitive one-off observation.

Jef Allbright said...

It appears you may be almost ready to continue our conversation from Convergence08 on possible methods to estimate the relative hierarchical coherence of a mind's states (or flows) mapped onto relevant features of the environment of interaction.

Related is Ulanowicz's notion of ascendency, the "organized power" of an ecological system in terms of the coherence of its trophic flows.

Also, Holland's "building block hypothesis", however flawed (supported by schema of increasingly improbable description length, but neglecting multilevel selection of weak linkages *between* building blocks.)

And of course we have our observations of nature's widespread, hierarchical (perhaps more correctly "fractal") reuse of building blocks over cosmic range of scale.

Looking forward to your further thoughts on the tractability of calculating, modeling, or (most likely) simply assessing inequality of the coherence over context of systems exercising "organized power" within their environment.

David said...

Favorite,

Could it not be the reverse? It is hierarchical structure of the cortex that makes us see the world in a hierarchical way, not a property of the world itself.

I think Hawkins has argued later that hierarchy is merely a requirement for efficiency and reuse, not a functionally essential aspect, though my memory is a bit vague here.

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