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2020 | OriginalPaper | Chapter

AGI and the Knight-Darwin Law: Why Idealized AGI Reproduction Requires Collaboration

Author : Samuel Allen Alexander

Published in: Artificial General Intelligence

Publisher: Springer International Publishing

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Abstract

Can an AGI create a more intelligent AGI? Under idealized assumptions, for a certain theoretical type of intelligence, our answer is: “Not without outside help”. This is a paper on the mathematical structure of AGI populations when parent AGIs create child AGIs. We argue that such populations satisfy a certain biological law. Motivated by observations of sexual reproduction in seemingly-asexual species, the Knight-Darwin Law states that it is impossible for one organism to asexually produce another, which asexually produces another, and so on forever: that any sequence of organisms (each one a child of the previous) must contain occasional multi-parent organisms, or must terminate. By proving that a certain measure (arguably an intelligence measure) decreases when an idealized parent AGI single-handedly creates a child AGI, we argue that a similar Law holds for AGIs.

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Footnotes
1
Our approach to AGI is what Goertzel [11] describes as the Universalist Approach: we consider “...an idealized case of AGI, similar to assumptions like the frictionless plane in physics”, with the hope that by understanding this “simplified special case, we can use the understanding we’ve gained to address more realistic cases.”
 
2
Knowledge and truth are formally treated in [4] but here we aim at a more general audience. For the purposes of this paper, an AGI can be thought of as knowing a fact if and only if the AGI would list that fact if commanded to spend eternity listing all the facts that it knows. We assume such knowledge is closed under deduction, an assumption which is ubiquitous in modal logic, where it often appears in a form like \(K(\phi \rightarrow \psi )\rightarrow (K(\phi )\rightarrow K(\psi ))\). Of course, it is only in the idealized context of this paper that one should assume AGIs satisfy such closure.
 
3
This may initially seem to contradict some mathematical constructions [18, 22] of infinite descending chains of theories. But those constructions only work for weaker languages, making them inapplicable to AGIs which comprehend linguistically strong second-order predicates.
 
4
Even prokaryotes can be considered to occasionally have multiple parents, if lateral gene transfer is taken into account.
 
5
This argument appeared in a fully rigorous form in [4], but in this paper we attempt to make it more approachable.
 
6
Possibly formalizing a relationship implied offhandedly by Chaitin, who suggests ordinal computation as a mathematical challenge intended to encourage evolution, “and the larger the ordinal, the fitter the organism” [7].
 
7
For example, X could write a general program Sim(c) that simulates an input AGI c waking up in an empty room and being commanded to spend eternity enumerating Intuitive Ordinal Notations. This program Sim(c) would then output whatever outputs AGI c outputs under those circumstances. Having written Sim(c), X could then obtain P by pasting Y’s code into Sim (a string operation—not actually running Sim on Y’s code). Nowhere in this process do we require X to actually execute Sim (which might be computationally infeasible).
 
8
This is essentially true by definition, unfortunately the formal definition of ordinal numbers is outside the scope of this paper.
 
9
This suggests possible generalizations of the Knight-Darwin Law such as “There cannot be an infinite sequence \(x_1, x_2,\ldots \) of biological organisms such that each \(x_i\) is the lone grandparent of \(x_{i+1}\),” and AGI versions of same. This also raises questions about the relationship between the set of AGIs initially created by humans and how intelligent the offspring of those initial AGIs can be. These questions go beyond the scope of this paper but perhaps they could be a fruitful area for future research.
 
10
That is, an AGI which believes itself to be the only entity in the universe.
 
11
Or to perfectly isolate different AGIs away from one another—see [25].
 
12
Wang has correctly pointed out [23] that an AGI consists of much more than merely a knowledge-set of mathematical facts. Still, we feel mathematical knowledge is at least one important aspect of an AGI’s intelligence.
 
13
Hibbard’s intelligence measure [13] is an infinite ladder which is nevertheless short enough that many AGIs can scale the whole ladder—the AGIs which do not “have finite intelligence” in Hibbard’s words (see Hibbard’s Proposition 3). It should be possible to use a fast-growing hierarchy [24] to transfinitely extend Hibbard’s ladder and reduce the set of whole-ladder-scalers. This would make Hibbard’s measurement ordinal-valued (perhaps Hibbard intuited this; his abstract uses the word “ordinal” in its everyday sense as synonym for “natural number”).
 
14
Thus, this ladder avoids a common problem that arises when trying to measure machine intelligence using IQ tests, namely, that for any IQ test, an algorithm can be designed to dominate that test, despite being otherwise unintelligent [5].
 
15
Namely, because if the set of Intuitive Ordinal Notations were computably enumerable, the program p which enumerates them would itself be an Intuitive Ordinal Notation, which would force \(|p|>|p|\).
 
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Metadata
Title
AGI and the Knight-Darwin Law: Why Idealized AGI Reproduction Requires Collaboration
Author
Samuel Allen Alexander
Copyright Year
2020
Book
Artificial General Intelligence

Print ISBN: 978-3-030-52151-6

Electronic ISBN: 978-3-030-52152-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-52152-3_1

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