Develop AI systems to efficiently learn new skills and solve open-ended problems, rather than depend exclusively on AI systems trained with extensive datasets
A rough set of ideas grounding the reasoning behind my initial approach to the ARC.
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Sharing the angle I'm going after to start! It's a physics inspired angle, where the grids we are given are "universes" that have matter in them which can be interacted with via other matter and forces.
Why physics-based?
My theory is that reasoning is a strictly three-dimensional phenomenon. I'm not actually sure about strictly, but fairly confident that it's less prevalent in 2D and 4D universes.
In a 2D world, a being with senses needs no reasoning. There is a best next move given their sense information. Without another dimension, there are no problems to work through, just a local min or max to choose to go towards. Limiting factor: information.
In a 4D world, perhaps it's the same problem but for the opposite reason. There's so much information that the solution is just known. No reasoning needed. Just as you could see something in front of you, you could see the solution as a concrete "object" in 4D space.
Ancient mystics and New Age thinkers alike have taught about a certain new mode of being that goes beyond thought and reasoning. This comes about by "raising awareness" or raising your "level of consciousness". Some even straight up call it 5th-dimensional awareness (4 + 1?).
So, back to the task of formalizing reasoning.
I'm inclined to lean on physics, but also more exotic (esoteric) parts of physics like quantum, alchemy, string theory, etc.
Wait, how did Alchemy get in there? Well, part of my hypothesis is that reasoning follows some kind of symbolic framework. Alchemy was and still is this area of study. It's not about turning lead into gold, though that may well come in handy as a real transformation we'd learn for these challenges.
Instead, I see alchemy as symbolic and meaningful beyond the physics of our world, such that it is more fundamental than even quantum physics.
We could speculate that:
Our everyday reasoning is heavily influenced by our experience in three-dimensional space and linear time.
Language, which is crucial for most of our reasoning, might be inherently limited to describing 3D reality (maybe why visions and mystical experiences defy explanation).
Some physicists propose higher-dimensional models of reality (e.g., string theory). If true, our 3D-based reasoning might be just a limited subset of possible cognition.
While it might look like it's 2D because we have a NxM matrix, the color of each square is our third dimension. We could also convert color into depth and I think you could solve these in the same way. Although, the separation of materials (color) is probably more helpful than a separation in depth.
Why not just imagine them as they are: 2D matrices with filled points? Because you may learn something as you give the space some depth.
Like this classic, giving depth reveals areas that can viably hold a "liquid".
Why else is it important? Depth means we can give the algorithm a birds-eye view of the proble. Somehow, I'm confident we need let the algorithm "see" the full example set all at once. It can't be scanning a 2D representation of points and colors. It's not what we do, and it's not how reasoning is done.
How we encode this? I am not sure. Thinking about Cymatics and converting this 3D world into a 2D representation better for computers. This conversion introduces uncertainty (Heisenburg's uncertainty, Fourier transforms), but that may be necessary and it's certainly not uncommon in quantum processes and large search space problems like this one.