The only way a discrete basis might be used to overcome the AGI
complexity problem without a solution to p=np would be if
incommensurate references could be used to overcome the elementary
problems of understanding. Discrete methods can retain the elementary
and intermediate forms of the components of reasoning. Yes, you can
retain the elementary references using weighted methods but if you did
then you would tend to lose the efficiencies that those methods can
provide. The value of having the elementary and intermediate
references is that they can be used both to explore ideas and to build
more insightful knowledge about the methods used.

One of the ways that research towards p=np might help would in the
efficient derivation of multiple references which were based on
complicated conditionals. You can often find multiple solutions to a
logical problem. Conceptual resolution through the integration of
incommensurate references would not –in itself- help with this
particular quality of logic except that it might be used to bridge
multiple discrete systems of ideas (or idea like particles used in
knowledge).

Jim Bromer


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AGI
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