A model compresses a state space by capturing a set of invariances that predict the variance in the states. Its free parameters define the latent space of the model and should ideally fully correspond to the variability, the not-invariant (= unexplained) remainder of the state.
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The proper representation of invariances (which include allowed set of values of the free parameters) is conditional on the reason for an invariance. The relationship to this reason is itself an invariance that needs to be made conditional on the foundations of its semantics.
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Most of our models are perceptual. Proofs in perceptual models are conducted by creating global coherence between all perceived features via propagating the state of the free parameters along their relationship functions to each other until a stable configuration is reached.
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Reasoning is not just an alternative to perception. It is a tool that combines a toolbox of algorithms that are being used to repair perceptual models that don't achieve full coherence.
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Replying to @Plinz
I am fascinated by attempts “to reproduce the world” by its perception and fine tuning using our brain, but at the same time, I am fascinated by the possibility that consciousness is a physical (and mathematical) product of the same world. Continued...
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Paradoxically, perception cannot figure out true foundations, and you need reason for that. But reason is much more impoverished than perception when it comes to integrating large amounts of data, so you have to use perception for navigation.
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