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They are talking about ML, which is statistical pattern matching and finding. Gödel ruined the fun of automated theorem testing a century ago unless we make si

They are talking about ML, which is statistical pattern matching and finding. Gödel ruined the fun of automated theorem testing a century ago unless we make significant discoveries in math. Type inference is an accessable example of SOTA automated reasoning if you want a more realistic idea of what our current constraints are. We will be restricted to Human assisted Turing machines for the foreseeable future unless there is a major development in pure math. Remember we can't even build a logically consistent model of arithmetic due to Gödel.

uncletaco 4y ago
Nitpicky and probably universalist or whatever but the fact that we can't build a logically consistent model was always the case, Gödel just discovered it.
- nyrikki 4y ago
  No, you are most likely correct, I personally haven't found anything that even gives a reason to hope. But as reductionism and Laplacian Determinism are taught as cannon and not as the best option I sugar coated it. The Wada property arising in simple models like predator/prey models with simple added factors like fear/cover probably also suggests that even simple models may be indeterminate at least with binary operations like modern algebra is based on. Three attractors or exit basins can make this unintuitive topological feature pop up. Note that that fractal behavior is topological and not scale invariant noise like is typically studied with topics like fractal scattering. Indecomposable continua like the Wada property aren't solvable with probabilistic models using automata like in the standard model, which is lucky enough to have less than three exit basins. Here is one fairly accessable paper on the Wada property. Hopefully some n-ary algebras may come forward to deal with restricted problems, but even if we could create a logically consistent model of arithmetic, binary operations will still be indeterminate with feature like the Wada property even with perfect knowledge of initial conditions. https://www.researchgate.net/publication/365233050_Organized_periodic_structures_and_coexistence_of_triple_attractors_in_a_predator-prey_model_with_fear_and_refuge https://www.researchgate.net/publication/365233050_Organized...
gowld 4y ago
There is nothing human can do that Turing proved a computer can't do. Gödel ruined the fun of manual theorem testing the same way.
- nyrikki 4y ago
  A human with a piece of paper and a pen could do. AKA writing down an algorithm. Human reason isn't limited to written algorithms. The missing text problem from NLU is an example of a problem that is thought to be impossible for Turing machines/algorithms but is trivial in most cases for humans.
  - drdeca 4y ago
    > The missing text problem from NLU is an example of a problem that is thought to be impossible for Turing machines/algorithms but is trivial in most cases for humans. Not thought to be impossible by people who believe in scientific materialism, and current mainstream ideas in theoretical physics (like the Bekenstein bound and such), and who have thought carefully about the issue. The laws of physics are believed to be computable, and the information content in a bounded region of space, finite. Therefore, it is believed that, in principle, a Turing machine could run an accurate physical simulation of a person, and could therefore do any cognitive task (as far as input/output correspondence goes) that a human can. If you’d like to explicitly reject scientific materialism though, I’d have no complaints about you doing so.
    - nyrikki 4y ago
      Physics models are models. All models are wrong, some are useful. I am not claiming that useful models need to be computable, in fact the problem with the MTP is that it induces cycles into something that needs to be recursively enumerable to be decidable. "The trophy wouldn't fit in the suitcase because it was too [large,small]" is a nice toy case to consider how NLP can deal with that easily but NLP would have issues. It all relates to VC dimensionality and decidablity in the end. But the math is hard to demonstrate without actually using math.
    - 4y ago

uncletaco 4y ago

Nitpicky and probably universalist or whatever but the fact that we can't build a logically consistent model was always the case, Gödel just discovered it.

nyrikki 4y ago
No, you are most likely correct, I personally haven't found anything that even gives a reason to hope. But as reductionism and Laplacian Determinism are taught as cannon and not as the best option I sugar coated it. The Wada property arising in simple models like predator/prey models with simple added factors like fear/cover probably also suggests that even simple models may be indeterminate at least with binary operations like modern algebra is based on. Three attractors or exit basins can make this unintuitive topological feature pop up. Note that that fractal behavior is topological and not scale invariant noise like is typically studied with topics like fractal scattering. Indecomposable continua like the Wada property aren't solvable with probabilistic models using automata like in the standard model, which is lucky enough to have less than three exit basins. Here is one fairly accessable paper on the Wada property. Hopefully some n-ary algebras may come forward to deal with restricted problems, but even if we could create a logically consistent model of arithmetic, binary operations will still be indeterminate with feature like the Wada property even with perfect knowledge of initial conditions. https://www.researchgate.net/publication/365233050_Organized_periodic_structures_and_coexistence_of_triple_attractors_in_a_predator-prey_model_with_fear_and_refuge https://www.researchgate.net/publication/365233050_Organized...

gowld 4y ago

There is nothing human can do that Turing proved a computer can't do. Gödel ruined the fun of manual theorem testing the same way.

nyrikki 4y ago
A human with a piece of paper and a pen could do. AKA writing down an algorithm. Human reason isn't limited to written algorithms. The missing text problem from NLU is an example of a problem that is thought to be impossible for Turing machines/algorithms but is trivial in most cases for humans.
- drdeca 4y ago
  > The missing text problem from NLU is an example of a problem that is thought to be impossible for Turing machines/algorithms but is trivial in most cases for humans. Not thought to be impossible by people who believe in scientific materialism, and current mainstream ideas in theoretical physics (like the Bekenstein bound and such), and who have thought carefully about the issue. The laws of physics are believed to be computable, and the information content in a bounded region of space, finite. Therefore, it is believed that, in principle, a Turing machine could run an accurate physical simulation of a person, and could therefore do any cognitive task (as far as input/output correspondence goes) that a human can. If you’d like to explicitly reject scientific materialism though, I’d have no complaints about you doing so.
  - nyrikki 4y ago
    Physics models are models. All models are wrong, some are useful. I am not claiming that useful models need to be computable, in fact the problem with the MTP is that it induces cycles into something that needs to be recursively enumerable to be decidable. "The trophy wouldn't fit in the suitcase because it was too [large,small]" is a nice toy case to consider how NLP can deal with that easily but NLP would have issues. It all relates to VC dimensionality and decidablity in the end. But the math is hard to demonstrate without actually using math.
  - 4y ago