182 10 A Mind-World Correspondence Principle
Via pursuing to the mind-world correspondence property in this context, I believe we will find that world-paths reflecting successive refinement correspond to mind-paths embodying suc- cessive refinement. This will be found to relate to the hierarchical structures found so frequently in both the physical world and the human mind-brain. Hierarchical structures allow many rel- evant goals to be approached via successive refinement, which I believe is the ultimate reason why hierarchical structures are so common in the human mind-brain.
Another next step would be exploring what mind-world correspondence means for the struc- ture and dynamics of a limited-resources intelligence. If an organism O has limited resources and, to be intelligent, needs to make
P(o(O, M(A), t(7))]o(O, M(B), T))
high for particular world state-sets A and B, then what’s the organism’s best approach? Arguably, it should represent (/(A) and M(B) internally in such a way that very little compu- tational effort is required for it to transition between M(A) and M(B). For instance, this could be done by coding its knowledge in such a way that 17(A) and M(B) share many common bits; or it could be done in other more complicated ways.
If, for instance, A is a subset of B, then it may prove beneficial for the organism to represent M(A) physically as a subset of its representation of M(B).
Pursuing this line of thinking, one could likely derive specific properties of an intelligent organism’s internal information-flow, from properties of the environment and goals with respect to which it’s supposed to be intelligent.
This would allow us to achieve the holy grail of intelligence theory as I understand it: given a description of an environment and goals, to be able to derive an architectural description for an organism that will display a high level of intelligence relative to those goals, given limited computational resources.
While this “holy grail” is obviously a far way off, what we’ve tried to do here is to outline a clear mathematical and conceptual direction for moving toward it.
10.6 Conclusion
The Mind-World Correspondence Principle presented here — if in the vicinity of correctness — constitutes a non-trivial step toward fleshing out the concept of a general theory of general intelligence. But obviously the theory is still rather abstract, and also not completely rigorous. There’s a lot more work to be done.
The Mind-World Correspondence Principle as articulated above is not quite a formal math- ematical statement. It would take a little work to put in all the needed quantifiers to formulate it as one, and it’s not clear the best way to do so the details would perhaps become clear in the course of trying to prove a version of it rigorously. One could interpret the ideas presented in this chapter as a philosophical theory that hopes to be turned into a mathematical theory and to play a key role in a scientific theory.
For the time being, the main role to be served by these ideas is qualitative: to help us think about concrete AGI designs like CogPrime in a sensible way. It’s important to understand what the goal of a real-world AGI system needs to be: to achieve the ability to broadly learn and generalize, yes, but not with infinite capability rather with biases and patterns that are implicitly and/or explicitly tuned to certain broad classes of goals and environments. The Mind-World
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