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Why? 1. Basically because physical laws obviously allow more than algorithmic cognition and problem solving. (And also: I am bound by thermodynamics as my mot

Why? 1. Basically because physical laws obviously allow more than algorithmic cognition and problem solving. (And also: I am bound by thermodynamics as my mother in Law is, still i get disarranged by her mere presence while I always have to put laxatives in her wine to counter that) 2. human rationality is equally limited as algorithms. Neither an algorithm nor human logic can find itself a path from Newton to Einsteins SR. Because it doesn't exist. 3. Physical laws - where do they really come from? From nature? From logic? Or from that strange thing we do: experience, generate, pattern, abstract, express — and try to make it communicable? I honestly don’t know. In a nutshell: there obviously is no law that forbids us to innovate - we do this, quite often. There only is a logical boundary, that says that there is no way to derive something out of a something that is not part of itself - no way for thinking to point beyond what is thinkable. Imagine little Albert asking his physics teacher in 1880: "Sir - for how long do I have to stay at high speed in order to look as grown up as my elder brother?" ... i guess "interesting thought" would not have been the probable answer... rather something like "have you been drinking? Stop doing that mental crap - go away, you little moron!"

like_any_other 1y ago
> Why? 1. Basically because physical laws obviously allow more than algorithmic cognition and problem solving. You seem to be laboring under the mistaken idea that "algorithmic" does not encompass everything allowed by physics. But, humoring this idea, then if physical laws allow it, why can this "more than algorithmic" cognition not be done artificially? As you say - we can obviously do it. What magical line is preventing an artificial system from doing the same?
nialv7 1y ago
If by algorithmic you just mean anything that a Turing machine can do, then your theorem is asserting that the Church-Turing thesis isn't true. Why not use that as the title of your paper? That a more fundamental claim.
- vidarh 1y ago
  The lack of mention of the Church-Turing thesis in both papers suggest he hasn't even considered that angle. But it is the fundamental objection he would need to overcome. There is no reasonable way to write papers claiming to provide proofs in this space without mentioning Church even once, and to me it's a red flag that suggests a lack of understanding of the field.
catoc 1y ago
“Imagine little Albert asking his physics teacher in 1880: "Sir - for how long do I have to stay at high speed in order to look as grown up as my elder brother?"” Is that not the other way around? “…how long do I have to stay at high speed in order for my younger brother to look as grown up as myself?”
- ben_w 1y ago
  Indeed. One of my other thoughts here on the Relativity example was "That sets the bar high given most humans can't figure out special relativity even with all the explainers for Einstein's work". But I'm so used to AGI being conflated with ASI that it didn't seem worth it compared to the more fundamental errors.
  - catoc 1y ago
    Given rcxdude’s reply it appears I am one of those humans who can’t figure out special relativity (let alone general) Wrt ‘AGI/ASI’, while they’re not the same, after reading Nick Bostrom (and more recently https://ai-2027.com https://ai-2027.com) I hang towards AGI being a blib on the timeline towards ASI. Who knows.
- rcxdude 1y ago
  Staying at high speed is symmetric! You'd both appear to age slower from the other's POV. It's only if one brother turns around and comes back, therefore accelerating, that you get an asymmetry.
vidarh 1y ago
> Basically because physical laws obviously allow more than algorithmic cognition and problem solving. This is not obvious at all. Unless you can prove that humans can compute functions beyond the Turing computable, there is no basis for thinking that humans embody and physics that "allow more than algorithmic cognition". Your claim here also goes against the physical interpretation of the Church-Turing thesis. Without rigorously addressing this, there is no point taking your papers seriously.
- ICBTheory 1y ago
  No problem here is you proof - although a bit long: 1. THEOREM: Let a semantic frame be defined as Ω = (Σ, R), where Σ is a finite symbol set and R is a finite set of inference rules. Let Ω′ = (Σ′, R′) be a candidate successor frame. Define a frame jump as: Frame Jump Condition: Ω′ extends Ω if Σ′\Σ ≠ ∅ or R′\R ≠ ∅ Let P be a deterministic Turing machine (TM) operating entirely within Ω. Then: Lemma 1 (Symbol Containment): For any output L(P) ⊆ Σ, P cannot emit any σ ∉ Σ. (Whereas Σ = the set of all finite symbol strings in the frame; derivable outputs are formed from Σ under the inference rules R.) Proof Sketch: P’s tape alphabet is fixed to Σ and symbols derived from Σ. By induction, no computation step can introduce a symbol not already in Σ. ∎ 2. APPLICATION: Newton → Special Relativity Let Σᴺ = { t, x, y, z, v, F, m, +, · } (Newtonian Frame) Let Σᴿ = Σᴺ ∪ { c, γ, η(·,·) } (SR Frame) Let φ = “The speed of light is invariant in all inertial frames.” Let Tᴿ be the theory of special relativity. Let Pᴺ be a TM constrained to Σᴺ. By Lemma 1, Pᴺ cannot emit any σ ∉ Σᴺ. But φ ∈ Tᴿ requires σ ∈ Σᴿ \ Σᴺ → Therefore Pᴺ ⊬ φ → Tᴿ ⊈ L(Pᴺ) Thus: Special Relativity cannot be derived from Newtonian physics within its original formal frame. 3. EMPIRICAL CONFLICT Let: Axiom N₁: Galilean transformation (x′ = x − vt, t′ = t) Axiom N₂: Ether model for light speed Data D: Michelson–Morley ⇒ c = const In Ωᴺ, combining N₁ and N₂ with D leads to contradiction. Resolving D requires introducing {c, γ, η(·,·)}, i.e., Σᴿ \ Σᴺ But by Lemma 1: impossible within Pᴺ. -> Frame must be exited to resolve data. 4. FRAME JUMP OBSERVATION Einstein introduced Σᴿ — a new frame with new symbols and transformation rules. He did so without derivation from within Ωᴺ. That constitutes a frame jump. 5. FINALLY A: Einstein created Tᴿ with Σᴿ, where Σᴿ \ Σᴺ ≠ ∅ B: Einstein was human C: Therefore, humans can initiate frame jumps (i.e., generate formal systems containing symbols/rules not computable within the original system). Algorithmic systems (defined by fixed Σ and R) cannot perform frame jumps. But human cognition demonstrably can. QED. BUT: Can Humans COMPUTE those functions? (As you asked) -> Answer: a) No - because frame-jumping is not a computation. It’s a generative act that lies outside the scope of computational derivation. Any attempt to perform frame-jumping by computation would either a) enter a Goedelian paradox (truth unprovable in frame),b) trigger the halting problem , or c) collapse into semantic overload , where symbols become unstable, and inference breaks down. In each case, the cognitive system fails not from error, but from structural constraint. AND: The same constraint exists for human rationality.
aoeusnth1 1y ago
The standard model is computable, so no. Physical law does not allow for non-computable behavior.

like_any_other 1y ago

> Why? 1. Basically because physical laws obviously allow more than algorithmic cognition and problem solving. You seem to be laboring under the mistaken idea that "algorithmic" does not encompass everything allowed by physics. But, humoring this idea, then if physical laws allow it, why can this "more than algorithmic" cognition not be done artificially? As you say - we can obviously do it. What magical line is preventing an artificial system from doing the same?

nialv7 1y ago

If by algorithmic you just mean anything that a Turing machine can do, then your theorem is asserting that the Church-Turing thesis isn't true. Why not use that as the title of your paper? That a more fundamental claim.

vidarh 1y ago
The lack of mention of the Church-Turing thesis in both papers suggest he hasn't even considered that angle. But it is the fundamental objection he would need to overcome. There is no reasonable way to write papers claiming to provide proofs in this space without mentioning Church even once, and to me it's a red flag that suggests a lack of understanding of the field.

catoc 1y ago

“Imagine little Albert asking his physics teacher in 1880: "Sir - for how long do I have to stay at high speed in order to look as grown up as my elder brother?"” Is that not the other way around? “…how long do I have to stay at high speed in order for my younger brother to look as grown up as myself?”

ben_w 1y ago
Indeed. One of my other thoughts here on the Relativity example was "That sets the bar high given most humans can't figure out special relativity even with all the explainers for Einstein's work". But I'm so used to AGI being conflated with ASI that it didn't seem worth it compared to the more fundamental errors.
- catoc 1y ago
  Given rcxdude’s reply it appears I am one of those humans who can’t figure out special relativity (let alone general) Wrt ‘AGI/ASI’, while they’re not the same, after reading Nick Bostrom (and more recently https://ai-2027.com https://ai-2027.com) I hang towards AGI being a blib on the timeline towards ASI. Who knows.
rcxdude 1y ago
Staying at high speed is symmetric! You'd both appear to age slower from the other's POV. It's only if one brother turns around and comes back, therefore accelerating, that you get an asymmetry.

vidarh 1y ago

> Basically because physical laws obviously allow more than algorithmic cognition and problem solving. This is not obvious at all. Unless you can prove that humans can compute functions beyond the Turing computable, there is no basis for thinking that humans embody and physics that "allow more than algorithmic cognition". Your claim here also goes against the physical interpretation of the Church-Turing thesis. Without rigorously addressing this, there is no point taking your papers seriously.

ICBTheory 1y ago
No problem here is you proof - although a bit long: 1. THEOREM: Let a semantic frame be defined as Ω = (Σ, R), where Σ is a finite symbol set and R is a finite set of inference rules. Let Ω′ = (Σ′, R′) be a candidate successor frame. Define a frame jump as: Frame Jump Condition: Ω′ extends Ω if Σ′\Σ ≠ ∅ or R′\R ≠ ∅ Let P be a deterministic Turing machine (TM) operating entirely within Ω. Then: Lemma 1 (Symbol Containment): For any output L(P) ⊆ Σ, P cannot emit any σ ∉ Σ. (Whereas Σ = the set of all finite symbol strings in the frame; derivable outputs are formed from Σ under the inference rules R.) Proof Sketch: P’s tape alphabet is fixed to Σ and symbols derived from Σ. By induction, no computation step can introduce a symbol not already in Σ. ∎ 2. APPLICATION: Newton → Special Relativity Let Σᴺ = { t, x, y, z, v, F, m, +, · } (Newtonian Frame) Let Σᴿ = Σᴺ ∪ { c, γ, η(·,·) } (SR Frame) Let φ = “The speed of light is invariant in all inertial frames.” Let Tᴿ be the theory of special relativity. Let Pᴺ be a TM constrained to Σᴺ. By Lemma 1, Pᴺ cannot emit any σ ∉ Σᴺ. But φ ∈ Tᴿ requires σ ∈ Σᴿ \ Σᴺ → Therefore Pᴺ ⊬ φ → Tᴿ ⊈ L(Pᴺ) Thus: Special Relativity cannot be derived from Newtonian physics within its original formal frame. 3. EMPIRICAL CONFLICT Let: Axiom N₁: Galilean transformation (x′ = x − vt, t′ = t) Axiom N₂: Ether model for light speed Data D: Michelson–Morley ⇒ c = const In Ωᴺ, combining N₁ and N₂ with D leads to contradiction. Resolving D requires introducing {c, γ, η(·,·)}, i.e., Σᴿ \ Σᴺ But by Lemma 1: impossible within Pᴺ. -> Frame must be exited to resolve data. 4. FRAME JUMP OBSERVATION Einstein introduced Σᴿ — a new frame with new symbols and transformation rules. He did so without derivation from within Ωᴺ. That constitutes a frame jump. 5. FINALLY A: Einstein created Tᴿ with Σᴿ, where Σᴿ \ Σᴺ ≠ ∅ B: Einstein was human C: Therefore, humans can initiate frame jumps (i.e., generate formal systems containing symbols/rules not computable within the original system). Algorithmic systems (defined by fixed Σ and R) cannot perform frame jumps. But human cognition demonstrably can. QED. BUT: Can Humans COMPUTE those functions? (As you asked) -> Answer: a) No - because frame-jumping is not a computation. It’s a generative act that lies outside the scope of computational derivation. Any attempt to perform frame-jumping by computation would either a) enter a Goedelian paradox (truth unprovable in frame),b) trigger the halting problem , or c) collapse into semantic overload , where symbols become unstable, and inference breaks down. In each case, the cognitive system fails not from error, but from structural constraint. AND: The same constraint exists for human rationality.

aoeusnth1 1y ago

The standard model is computable, so no. Physical law does not allow for non-computable behavior.