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Comment by at_a_remove | Hacker News Reader

What about the trivial case of the AGI simply self-replicating? Then you have a child, it is identical, and is therefore of identical intelligence (however you measure that), and therefore it is not necessarily less intelligent.

What if the AGI is intelligent enough to randomly mutate offspring here and there? Then one might be more intelligent, and again it is not necessarily less intelligent.

What if the AGI is intelligent enough to look at its own code, identify some kind of bias in its programming (not unlike human introspection), and produce a child without that bias? That child would then be better able to model reality -- a core element of intelligence -- and again you've got a smarter child.

I have a difficult time buying the "necessarily" part.

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I have a difficult time buying the "necessarily" part.

Yes. That's borrowed from an old theological argument.

Especially since much of the progress in machine learning is just putting more hardware and data on the same algorithms.

Could you clarify what you mean when you say "That's borrowed from an old theological argument"?

I think a variation of the argument is: You couldn't simulate the universe in the universe because you would need at least as many resources as the universe has but are limited to resources within the universe (unless you want to get hacky).

I assume they are implying that this thought process may not apply.

One of the neat things about the argument in my paper is that it doesn't involve the parent AGI actually running the child AGI. It merely involves the parent writing source-code and knowing that IF it had enough resources to run the source-code, then the result would be a truthful AGI child.

Sigh. Here, from a creationist site.[1] There's an argument that the second law of thermodynamics prevents evolution, because evolution decreases entropy.

Having a star around to power things helps beat that problem.

[1] https://christiananswers.net/q-eden/edn-thermodynamics.html

The only similarity between that and my argument is that both involve a measure decreasing. Are you saying that one fallacious argument involving a decreasing measure invalidates all arguments ever that involve (completely unrelated) decreasing measures?

As is so often the case in academia, the basic idea is hidden by all the academic jargon. The basic idea is quite simple. Suppose you roll up your sleeves, get to work, and announce to the world: "Turing machine #57835 is an AGI with truthful knowledge". Then, without even needing to run Turing machine #57835 (which might be prohibitively expensive), just as a purely logical consequence of your announcement, you can conclude that the following ordinal number A is a computable ordinal: "The supremum of all ordinals B such that B has some code k such that Turing machine #57835 knows that k is a code of a computable ordinal". By construction, this ordinal A, for which you concretely know a code, is larger than any ordinal for which Turing machine #57835 knows a code. So in at least one extremely specific technical sense (the sense of knowing codes for large ordinals), you are more intelligent than Turing machine #57835.

Which part of this argument is unclear?

You answer the question, but why the sigh? Shouldn't relevant clarifications be encouraged?

Right, I should have clarified that I meant: create a child in such a way as to know the child's truthfulness and source-code. Of course, without that requirement, a monkey could blindly type up an AGI source-code on a typewrite by sheer dumb luck. As for an AGI simply self-replicating, that is possible but then the AGI would not know the child's truthfulness and source-code, since an AGI cannot know its own truthfulness and source-code.

Still, if it is identical, then it could not necessarily be less than.

I may not know what value is in the box (my own truthfulness and source-code), but if it is replicated, then the value ought to be identical, and therefore not less than.

Right, but the machine which prints its own source-code does not do so in such a way as to know the child's truthfulness (because the machine cannot know its own truthfulness and source-code, assuming the machine itself is truthful and satisfies basic assumptions about how it can reason).

I could design a program that systematically prints out all possible source-codes, and then try to claim credit for designing the first AGI (because, at least if AGI is possible at all, my brute-force source-code-printer will eventually print it). But that would be silly because I wouldn't actually know which of the many many outputs from my printer is the actual AGI source-code :)

I think the "knowing" is irrelevant.

If I have two boxes, and you tell me that the contents, the value of box one is identical to box two, then I do not need to know the value of the box to know that box two is not less than box one. Here is a pointer to a section of memory; copy it.

As long as the copy operation is successful, you do not need to know the value of what you have copied to know that it is identical, and therefore not "less than."

Hence, if you self-replicate, then it is not "less than;" and if you cannot know that two things are identical, then you cannot self-replicate.

I think you are stuck saying that your AGI cannot self-replicate if you want to hold onto "necessarily less than." It's just a basic principle of equality, you cannot get around it.

I think we're talking past each other. My claim is that if an AGI single-handedly creates a child AGI, in such a way as to know the child's source-code and truthfulness, then the parent is more intelligent than the child (in a certain technical sense).

You rightly point out that an AGI can duplicate itself (if it knows its own source-code). This doesn't contradict my claim, because it doesn't satisfy the premise. It's like if I give you a box of candies and I say, "Every blue candy in this box is round", and you pull out a red candy which is square, you can't say my statement was false because that red candy isn't round. To falsify the statement you'd have to produce a blue candy that isn't round.

The AGI which self-duplicates would only falsify my claim if it self-duplicates in such a way as to know the duplicate's source-code and truthfulness. Assuming said AGI is truthful and satisfies certain assumptions about how it can reason and know, then it can't know its own source-code and truthfulness, so it doesn't falsify my claim.

I don't think we are talking past each other, I think we're having a debate as to whether or not methods of replication have some impact on whether or not two things are identical, and therefore have the same value.

Imagine a simple single-celled organism. It is well-suited for its environment and so forth. It reproduces asexually without error. Now, it isn't terribly bright, it hasn't developed PCR or anything, it hasn't had a Watson or a Crick, so it doesn't "know" its source code, but it has definitely replicated and done so to produce an identical copy. I'm not even sure what truthfulness means in this context, but I can confidently say that identical things have the same value, and therefore the offspring organism not not less than the original.

The "in such a way" has an impact in the way you're viewing it, and to me, I do not understand that. Identical is identical. I don't have any other way of looking at that. If the "in such a way" does have some kind of effect, then they are not identical and you can hardly say that the AGI has self-replicated.

Can your AGI "quine out" a copy of itself or not? Can I look at the two programs on disc and perform a binary comparison to prove that they are byte-per-byte identical?

I'm not debating about whether an AGI can duplicate itself or not. If an AGI knows its own source-code, it can duplicate itself. I literally acknowledge this in the paper itself (section 5.2).

Rather, what I am saying is that it doesn't have any bearing on the thesis, "If an AGI single-handedly creates a child AGI, in such a way as to know the child's truth and source-code, then the child is less intelligent than the parent". And the reason it has no bearing is because, since an AGI cannot know its own truthfulness and source-code, AGI self-duplication does not satisfy the hypotheses of the claim.

Again, this is like if I claim "If x>2 then x²>4". The fact that 1² is not >4 has no bearing on the truth of the claim, because 1 is not >2. To make the analogy crystal clear, the "x>2" part corresponds to "the AGI single-handedly creates a child AGI in such a way as to know its truthfulness and source-code", and the "x²>4" part corresponds to "the child AGI is less intelligent than the parent".

Then true clarity would be to say "The AGI has no access to its own source or even compiled code, and therefore cannot self-replicate an identical copy." That's much clearer. These abstract terms like "truthfulness" and "know" are not obvious, and your scenario is a little baffling. Most people concerned about AGIs self-improving consider access to their own source code or even the ability to copy a directory as a given.

I keep using extremely concrete terms here, with specific examples, and you keep returning to this one sentence where a lot of work is being performed by words like "know." The idea that an AGI somehow "cannot" (is it forbidden by a directive? has the information been hidden away? is this a physical principle of the universe emerging from conservation of baryon number?) "know" (what does this word do?) its source-code just seems very far away from scenarios most people would consider.

I never said an AGI cannot know its own code, I said it cannot know both its own code AND its own truthfulness (while being truthful and satisfying certain other idealized assumptions). As for why this is the case: it's not an assumption, but rather, a theorem, one which has been known for a long time.

Here's an extremely oversimplified proof: suppose Turing machine #500 encodes an AGI X and that AGI X knows "My knowledge is truthful" and "I am encoded by Turing machine #500". Using Goedel's diagonal lemma, there is a sentence phi, in the language of Peano arithmetic, which expresses "Turing machine #500 knows the negation of phi". Since X knows himself to be Turing machine #500 and X knows himself to be truthful, X should be able to infer that phi is false (because if phi were true, then Turing machine #500 would know the negation of phi, so (since Turing machine #500 is truthful), phi would be false, a contradiction). So X knows that that phi is false. But phi is synonymous with the assertion that X knows phi is false---so, since we have shown "X knows phi is false", we have in fact shown phi is true. Absurd. Our only escape from the paradox is to acknowledge that X cannot know "I am truthful" and "I am Turing machine #500" simultaneously (and also really be truthful and satisfy idealizing assumptions that allow X to make the above inferences).

You're right that I keep using words informally, because this is hacker news and not a logic journal. If you want to see things spelled out in gruesome detail (warning: math), you can read here: https://philpapers.org/archive/ALEMTI-2.pdf

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