If a human brain works why can't AGI?
I think the problem with "AGI" is that people don't want "AGI," they want Einstein as their butler. A merely generally intelligent AI might be only as intelligent as the average human.
AGI is Mathematically Impossible 2: When Entropy Returns
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Re: AGI is Mathematically Impossible 2: When Entropy Returns
#262[flagged]
It's just a typical crackpot paper like those math enthusiasts who self-claimed to prove Goldbach's conjecture or disprove special relativity. If it's not obvious enough, see the author's comment here: https://news.ycombinator.com/item?id=44350876 This post proves an interesting theory though: even the most random thing can get traction on HN as long as it mentions AI.
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Re: AGI is Mathematically Impossible 2: When Entropy Returns
#263Earlier quoted context omitted.
> 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. Witho…
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 Contain…
None of this is relevant to what I wrote. If anything, they sugget that you don't understand the argument.
If anything, your argument is begging the question - it's a logical fallacy - because your argument rests on humans exceeding the Turing computable, to use human abilities as evidence. But if humans do not exceed the Turing computable, then everything humans can do is evidence that something is Turing computable, and so you can not use human abilities as evidence something isn't Turing computable.
And so your reasoning is trivially circular.
EDIT:
To go into more specific errors, this is fasle:
> 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.
P can do so by simulating a TM P' whose alphabet includes σ. This is fundamental to the theory of computability, and holds for any two sets of symbols: You can always handle the larger alphabet by simulating one machine on the other.
When your "proof" contains elementary errors like this, it's impossible to take this seriously.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#264If a human brain works why can't AGI? I think the problem with "AGI" is that people don't want "AGI," they want Einstein as their butler. A merely generally intelligent AI might be only as intelligent as the average human.
One problem with the paper is that it defines AGI in such a way that if it fails to solve a problem that is inherently unsolvable, AGI can be written off as impossible. It tries to synthesise a definition from different sources whose own definitions don't have any particular reason to overlap in any meaningful way.
I'm just not sure "AGI" is a useful term at this point. It's either something trivially reachable from what we can see today or something totally impossible, depending entirely on the preference of the speaker.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#265What a cope
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#266I'm pretty sure the central permise is flawed because human computation over infinite problem spaces is subject to the halting problem too.
Skimmed and saw this, decided it was just a crank at that moment. The problem is not well defined enough and you could easily apply the same argument to humans. It's just abusing mathematical notation to make subjective arguments:
A.3.1. Example: The Weight Question as an Irreducibly Infinite Space
Let us demonstrate that the well-known example of the “weight question” (see Sectin 2.1) meets the formal criteria of an irreducibly infinite decision space as defined above.
We define the decision space X as the set of all contextually valid responses (verbal and nonverbal) to the utterance: “Darling, please be honest: have I gained weight?”
Let Σ be the symbol space available to the AI system (e.g., predefined vocabulary, intonation classes, gesture tags). Let R be the transformation rules the system uses to generate candidate outputs.
Then:
1. Non-Enumerability: There exists no total computable function such that every socially acceptable response is eventually enumerated. Reason: The meaning and acceptability of any response depend on unbounded, semantically unstable factors (facial expressions, past relationship dynamics, momentary tone, cultural norms), which cannot be finitely encoded.
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Just want to add that I don't mean to be an asshole here, in case this stays the top reply. I'm quite interested in quantifiable measures of intelligence myself, and it takes guts to put something like this out there with your name on it.
What I think what might help the author is to think of his attempts to disprove AGI as a more adversarial mini-max. Whatever theory or example you have regarding an example that is not possible under AGI, why could a better designed intelligence not achieve it, and why does it not also apply to humans?
For example, instead of assuming that an AI will search infinitely without giving up, consider whether the AI might put a limit on the time it expends solving a problem, or decide to think about something besides aether if it's taking too long to solve that problem that way, or give up because the problem isn't important enough to keep going, or whether humans suffer from epistemic uncertainty too.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#267Earlier quoted context omitted.
I'm not sure if this will help, but happy to elaborate further: The set of Turing computable functions is computationally equivalent to the lambda calculus, is computationally equivalent to the generally recursive functions. You don't need to understand those terms, only to know that these functions define the set of functions we believe to include all computable functions . (There are functions that we know to not b…
Compute functions != Intelligence though. For example learning from experience (which LLMs cannot do because they cannot experience anything and they cannot learn) is clearly an attribute of an intelligent machine. LLMs can tell you about the taste of a beer, but we know that they have never tasted a beer. Flight simulators can't take you to Australia, no matter how well they simulate the experience.
> Compute functions != Intelligence though.
If that is true, you have a proof that the Church-Turing thesis is false.
> LLMs can tell you about the taste of a beer, but we know that they have never tasted a beer. Flight simulators can't take you to Australia, no matter how well they simulate the experience.
For this to be relevant, you'd need to show that there are possible sensory inputs that can't be simulated to a point where the "brain" in question - be it natural or artificial - can't tell the difference.
Which again, would boil down to proving the Church-Turing thesis wrong.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#268Earlier quoted context omitted.
could you explain for a layman
I'm not sure if this will help, but happy to elaborate further: The set of Turing computable functions is computationally equivalent to the lambda calculus, is computationally equivalent to the generally recursive functions. You don't need to understand those terms, only to know that these functions define the set of functions we believe to include all computable functions . (There are functions that we know to not b…
> then the only way of showing that an artificial intelligence can not theoretically be constructed to at least meet the same bar is by showing that humans can compute more than the Turing computable.
I would reframe: the only way of showing that artificial intelligence can be constructed is by showing that humans cannot compute more than the Turing computable.
Given that Turing computable functions are a vanishingly small subset of all functions, I would posit that that is a rather large hurdle to meet. Turing machines (and equivalents) are predicated on a finite alphabet / state space, which seems woefully inadequate to fully describe our clearly infinitary reality.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#269Earlier quoted context omitted.
> 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. Witho…
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 Contain…
Whoa there boss, extremely tough for you to casually assume that there is a consistent or complete metascience / metaphysics / metamathematics happening in human realm, but then model it with these impoverished machines that have no metatheoretic access.
This is really sloppy work, I'd encourage you to look deeper into how (eg) HOL models "theories" (roughly corresponding to your idea of "frame") and how they can evolve. There is a HOL-in-HOL autoformalization. This provides a sound basis for considering models of science.
Noncomputability is available in the form of Hilbert's choice, or you can add axioms yourself to capture what notion you think is incomputable.
Basically I don't accept that humans _do_ in fact do a frame jump as loosely gestured at, and I think a more careful modeling of what the hell you mean by that will dissolve the confusion.
Of course I accept that humans are subject to the Goedelian curse, and we are often incoherent, and we're never quite surely when we can stop collecting evidence or updating models based on observation. We are computational.
Re: AGI is Mathematically Impossible 2: When Entropy Returns
#270FTA: > Strange, isn't it? The AI hasn’t crashed. It’s still running. As a human I answer a question because my time to do so is finite. Why can't we just ask an AI to give its best answer in due time ? As a human I can do that easily. Will my answer be optimal ? No of course, but every manager on earth do that all the time. We're all happy with approximate answers. (and I would add: approximation are sometimes based…
G. E. Moore (in his Principia Ethica, 1903) makes a very similar case to this relation to consequentialist ethics: "The first difficulty in the way of establishing a probability that one course of action will give a better total result than another, lies in the fact that we have to take account of the effects of both throughout an infinite future. We have no certainty but that, if we do one action now, the Universe w…
tldr: it's impossible to know for sure which choice is the absolute best.
In a sense, I get why they write verbosely, but...
The first and most important task of our lives is to determine what our goal is.