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The fundamental result of Gödel's theorem is that logical completeness and logical consistency are complimentary; if a logical system has consistent rules then

The fundamental result of Gödel's theorem is that logical completeness and logical consistency are complimentary; if a logical system has consistent rules then it will contain statements that are unprovable by the rules but true nonetheless, so it is incomplete. Alternately, if there is a proof available for all true statements via the rules then the rules used are inconsistent. I think this means that "AGI" is limited as we are. If we build a machine that proves all true statements then it must use inconsistent rules, implying it is not a machine we can understand in the usual sense. OTOH, if it is using consistent rules (that do not contain contradiction) then it cannot prove all true statements so it ia not generally intelligent, but we can understand how it works. I agree with Dr. Penrose about the misnomer of "artificial Intelligence". We ought to be calling the current batch of intelligence technologies "algabreic intelligence" and admiting that we seek "geometric intelligence" and have no idea how to get there.

neom 2y ago
The issue isn't the mere existence of two thinking modes (algebraic vs. geometric), but that we’ve culturally prioritized and trained mostly algebraic modes (linear language, math, symbolic logic). This has obscured our natural geometric capacity, especially the neurological pathways specialized in visually processing and intuitively understanding phenomena, particularly light itself (photons, vision, direct visual intuition of physics). Historically, algebraic thinking was elevated culturally around the Gnostic period (200 BCE forward), pushing aside the brain's default "geometric mode". Heck, during that period of history, people actively and forcefully campaigned against overly developing the analytical use of the mind. We should be actively mapping neurological pathways specialized for direct intuitive visual-physical cognition (understanding light intuitively at a neurological level, not symbolically or algebraically) for that to happen. Also: Understanding or explainability is not directly linked to consistency in the logical sense. A system can be consistent yet difficult to fully understand, or even inconsistent yet still partially understandable. We are talking right now here because we were put here through a series of historical events. Go back to 200 BCE and play out the Gnostic or Valentinus path to 2025.
- d4rkn0d3z 2y ago
  Thanks for the reply. When I think about understanding, in principle I require consistency not completeness. In fact, understandability is predicated on consistency in my view. If I liken the quest for AGI to the quest for human flight, wherein we learned that the shape of the wing provides nearly effortless lift, while wing flapping only provides a small portion of the lift for comparatively massive energy input, then I suspect we are only doing the AGI equivalent of wing flapping at this point.
  - neom 2y ago
    the human mind itself isn't fully consistent...or at least, consistency isn't necessarily how we operate internally (lots of contradictions, ambiguities, simultaneous beliefs that don't neatly align). Yet we still manage to "understand" things deeply. Complete logical consistency isn't strictly required for understanding in a practical, real world sense. We are totally "flapping" right now with AI, brute forcing algebraic intelligence and missing that elegant "geometric" insight. My point is simply that our brains already have that built in "wing shape" neurologically, we just haven't mapped it out or leveraged it fully yet. The real leap isn't discovering a new wing design, it's understanding we already have one, we just have to leverage it. :) :)
    - d4rkn0d3z 2y ago
      Now I think you come to thw crux of it.
dcreater 2y ago
What does geometric thinking mean?
- d4rkn0d3z 2y ago
  Good question, perhaps its best to start with what I mean by algabreic intelligence, then the contrast will be more clear. Algabreic intelligence uses the simple idea of equality to produce numerical unknowns from the known via standard mechanistic operations. So algabreic intelligence is mechanistic, operational, deductive, and quntitative. In contrast, geometric intelligence is concerned with the higher level abstract concepts of congruity, scale. To return to my previous analogy, algabreic intelligence is wing flapping while geometric intelligence is the shape of the wing. The former is arduous time consuming and energy inefficient while the latter is effortless, and unreasonably effective.
  - dcreater 2y ago
    I agree with where you're going. I've struggled to find the words to describe this correctly - especially that the current brute force approach of bazillion matmul operations being a mock up of intelligence but not intelligence itself perhaps. At least not a good form of intelligence. I haven't found any thing in the web about the term geometric intelligence. I recommend you write about this

neom 2y ago

The issue isn't the mere existence of two thinking modes (algebraic vs. geometric), but that we’ve culturally prioritized and trained mostly algebraic modes (linear language, math, symbolic logic). This has obscured our natural geometric capacity, especially the neurological pathways specialized in visually processing and intuitively understanding phenomena, particularly light itself (photons, vision, direct visual intuition of physics). Historically, algebraic thinking was elevated culturally around the Gnostic period (200 BCE forward), pushing aside the brain's default "geometric mode". Heck, during that period of history, people actively and forcefully campaigned against overly developing the analytical use of the mind. We should be actively mapping neurological pathways specialized for direct intuitive visual-physical cognition (understanding light intuitively at a neurological level, not symbolically or algebraically) for that to happen. Also: Understanding or explainability is not directly linked to consistency in the logical sense. A system can be consistent yet difficult to fully understand, or even inconsistent yet still partially understandable. We are talking right now here because we were put here through a series of historical events. Go back to 200 BCE and play out the Gnostic or Valentinus path to 2025.

d4rkn0d3z 2y ago
Thanks for the reply. When I think about understanding, in principle I require consistency not completeness. In fact, understandability is predicated on consistency in my view. If I liken the quest for AGI to the quest for human flight, wherein we learned that the shape of the wing provides nearly effortless lift, while wing flapping only provides a small portion of the lift for comparatively massive energy input, then I suspect we are only doing the AGI equivalent of wing flapping at this point.
- neom 2y ago
  the human mind itself isn't fully consistent...or at least, consistency isn't necessarily how we operate internally (lots of contradictions, ambiguities, simultaneous beliefs that don't neatly align). Yet we still manage to "understand" things deeply. Complete logical consistency isn't strictly required for understanding in a practical, real world sense. We are totally "flapping" right now with AI, brute forcing algebraic intelligence and missing that elegant "geometric" insight. My point is simply that our brains already have that built in "wing shape" neurologically, we just haven't mapped it out or leveraged it fully yet. The real leap isn't discovering a new wing design, it's understanding we already have one, we just have to leverage it. :) :)
  - d4rkn0d3z 2y ago
    Now I think you come to thw crux of it.

dcreater 2y ago

What does geometric thinking mean?

d4rkn0d3z 2y ago
Good question, perhaps its best to start with what I mean by algabreic intelligence, then the contrast will be more clear. Algabreic intelligence uses the simple idea of equality to produce numerical unknowns from the known via standard mechanistic operations. So algabreic intelligence is mechanistic, operational, deductive, and quntitative. In contrast, geometric intelligence is concerned with the higher level abstract concepts of congruity, scale. To return to my previous analogy, algabreic intelligence is wing flapping while geometric intelligence is the shape of the wing. The former is arduous time consuming and energy inefficient while the latter is effortless, and unreasonably effective.
- dcreater 2y ago
  I agree with where you're going. I've struggled to find the words to describe this correctly - especially that the current brute force approach of bazillion matmul operations being a mock up of intelligence but not intelligence itself perhaps. At least not a good form of intelligence. I haven't found any thing in the web about the term geometric intelligence. I recommend you write about this