揭示强自修改如何动摇超级智能的自我同一性
Deconstructing Superintelligence: Identity, Self-Modification and Différance
- 用代数框架建模自修改，关键在更新与差分算子不交换
- 不交换性会传递到自我表征，导致系统内部矛盾
- 揭示超智能依赖的自我持续性可能被自修改破坏
自修改常被视为人工超级智能（SI）的核心特征，但修改是相对动作，需依赖外部补充。本文在关联算子代数 $\mathcal{A}$ 中形式化这一机制，引入更新算子 $\hat U$、差分算子 $\hat D$ 与自我表征算子 $\hat R$，将补充识别为 $\operatorname{Comm}(\hat U)$。传播定理表明 $[\hat U,\hat R]$ 可通过 $[\hat U,\hat D]$ 分解，即不交换性会传递至自我表征。当 $[\hat T,Π_L]=0$ 时，谎言悖论为一阶情形；在类 $\mathbf{A}$ 系统中，$\hat U$ 作用于 $\hat D$，可复现该结构，其整体形式与 Priest 的封闭模式及德里达的「différance」一致。研究显示，被视作定义超智能的强自修改，可能瓦解其赖以成立的持续自我同一性。
原文摘要 · Abstract (English)
Self-modification is routinely treated as constitutive of artificial superintelligence (\textbf{SI}), yet modification is a relative action requiring a \emph{supplement} outside the operation. We formalise this on an associative operator algebra $\mathcal{A}$ with update operator $\hat U$, difference operator $\hat D$, and self-representation operator $\hat R$, identifying the supplement with $\operatorname{Comm}(\hat U)$. A propagation theorem shows $[\hat U,\hat R]$ decomposes through $[\hat U,\hat D]$, so non-commutation propagates to self-representation. The liar paradox is the rank-one case $[\hat T,Π_L]=0$, and \emph{class $\mathbf{A}$} systems, in which $\hat U$ acts on $\hat D$, reproduce it at system scale, yielding a structure coinciding with Priest's inclosure schema and Derrida's \emph{différance}. Our results show that the strong self-modification taken to define superintelligence may undermine the persistent identity upon which such systems are premised.
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