Computational Prosopography across a Millennium: Mathematically Oriented Lineages Traced from the Fields Medalists
研究通过重建九世纪的师生网络并利用64位历史上的菲尔兹奖得主作为追踪集，揭示数学家谱系结构及其中的关键节点。
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How to Build Marcus's Algebraic Mind: From Thagard's Brain--Mind Viewpoint
Current connectionist models struggle to support variable manipulation, structured representations, and the distinction between individuals and categories, while recursive convolutional binding often suffers from information loss in deep recursion. This work proposes VaCoAl, a hyperdimensional architecture that leverages XOR-and-shift operations over GF(2) combined with primitive polynomial linear feedback shift registers to construct an exact, invertible, and non-commutative binding mechanism. For the first time, this approach unifies the three pillars of Marcus’s algebraic theory of mind with Thagard’s binding requirements, enabling invertible compositional binding at O(N) complexity. It supports multi-hop relational reasoning and post-hoc auditable compositional generalization, while mitigating information degradation in deep recursion through a Rescue-Rate phase-transition mechanism, offering an orthogonal solution for interpretable and reversible relational reasoning.
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How to Build Marcus's Algebraic Mind: From Minsky's Emotion-Machine Viewpoint
This work proposes VaCoAl, a neurally plausible computational architecture that realizes the three core components of Marcus’s algebraic mind—variable manipulation, recursive structural representation, and distinction between individuals and kinds—while endowing the system with the introspective and reflective capacities envisioned in Minsky’s emotion machine. Built upon an XOR-and-shift mechanism over the GF(2) field, VaCoAl enables exact, invertible variable binding, compositional bundling, and spatial segregation. It uniquely integrates Marcus’s algebraic framework with Minsky’s vertical model of mind, supporting faithful introspective traceability, panalogical reasoning, and counterfactual credit assignment, thereby bridging Pearl’s causal ladder with Minsky’s hierarchy of reflection. Empirical validation via PyVaCoAl demonstrates algebraic scalability on million-scale datasets, while an SRAM-CAM hardware implementation highlights its potential for efficient realization.
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Institutions and the transmission of upper-tail human capital: scientific lineages across a millennium
This study investigates the key institutional mechanisms underlying the intergenerational transmission of elite human capital and their evolution over a millennium. Leveraging 470,000 advisor–advisee records from Wikidata, the authors construct an academic genealogy network encompassing all 64 Fields Medalists, apply a deterministic graph traversal algorithm to analyze 25.5 million lineage paths, and integrate multidimensional attributes—including society membership, discipline, and language—for structural analysis. The research achieves the first comprehensive measurement of academic lineages across a thousand-year timescale, revealing Leibniz in the 17th century as a pivotal hub through whom 47 of the 64 lineages pass, and identifying that 84% of these lineages converge on just five Islamic and Byzantine scholars from the 12th–13th centuries. It further pinpoints the 11th century as the origin boundary of documented European mentorship and advances a novel perspective that scientific growth is driven more by knowledge transmission than by discovery alone.
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How to Build Marcus's Algebraic Mind: Algebro-Deterministic Substrate over Galois Fields
This work addresses the longstanding challenge that conventional multilayer perceptrons fail to fulfill Marcus’s three core criteria for an algebraic mind—variable manipulation, representation of recursive structures, and distinction between individual and category representations—by introducing the PyVaCoAl/VaCoAl neurocognitive architecture. This framework uniquely maps all three criteria onto a deterministic algebraic basis over GF(2), employing XOR-and-shift as its fundamental primitive and leveraging primitive-polynomial linear feedback shift registers to achieve invertible variable binding, non-commutative compositional bundling, and segregated address spaces for individuals versus categories. The resulting end-to-end hyperdimensional computing system not only satisfies all three cognitive requirements but also substantially outperforms dominant 2001-era approaches such as tensor products and circular convolution, while naturally supporting counterfactual reasoning at Pearl’s third level of causal inference.
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Computational Prosopography across a Millennium: Mathematically Oriented Lineages Traced from the Fields Medalists
研究通过重建九世纪的师生网络并利用64位历史上的菲尔兹奖得主作为追踪集，揭示数学家谱系结构及其中的关键节点。
0 citationsRead paper
How to Build Marcus's Algebraic Mind: From Thagard's Brain--Mind Viewpoint
Current connectionist models struggle to support variable manipulation, structured representations, and the distinction between individuals and categories, while recursive convolutional binding often suffers from information loss in deep recursion. This work proposes VaCoAl, a hyperdimensional architecture that leverages XOR-and-shift operations over GF(2) combined with primitive polynomial linear feedback shift registers to construct an exact, invertible, and non-commutative binding mechanism. For the first time, this approach unifies the three pillars of Marcus’s algebraic theory of mind with Thagard’s binding requirements, enabling invertible compositional binding at O(N) complexity. It supports multi-hop relational reasoning and post-hoc auditable compositional generalization, while mitigating information degradation in deep recursion through a Rescue-Rate phase-transition mechanism, offering an orthogonal solution for interpretable and reversible relational reasoning.
0 citationsRead paper
How to Build Marcus's Algebraic Mind: From Minsky's Emotion-Machine Viewpoint
This work proposes VaCoAl, a neurally plausible computational architecture that realizes the three core components of Marcus’s algebraic mind—variable manipulation, recursive structural representation, and distinction between individuals and kinds—while endowing the system with the introspective and reflective capacities envisioned in Minsky’s emotion machine. Built upon an XOR-and-shift mechanism over the GF(2) field, VaCoAl enables exact, invertible variable binding, compositional bundling, and spatial segregation. It uniquely integrates Marcus’s algebraic framework with Minsky’s vertical model of mind, supporting faithful introspective traceability, panalogical reasoning, and counterfactual credit assignment, thereby bridging Pearl’s causal ladder with Minsky’s hierarchy of reflection. Empirical validation via PyVaCoAl demonstrates algebraic scalability on million-scale datasets, while an SRAM-CAM hardware implementation highlights its potential for efficient realization.
0 citationsRead paper
Institutions and the transmission of upper-tail human capital: scientific lineages across a millennium
This study investigates the key institutional mechanisms underlying the intergenerational transmission of elite human capital and their evolution over a millennium. Leveraging 470,000 advisor–advisee records from Wikidata, the authors construct an academic genealogy network encompassing all 64 Fields Medalists, apply a deterministic graph traversal algorithm to analyze 25.5 million lineage paths, and integrate multidimensional attributes—including society membership, discipline, and language—for structural analysis. The research achieves the first comprehensive measurement of academic lineages across a thousand-year timescale, revealing Leibniz in the 17th century as a pivotal hub through whom 47 of the 64 lineages pass, and identifying that 84% of these lineages converge on just five Islamic and Byzantine scholars from the 12th–13th centuries. It further pinpoints the 11th century as the origin boundary of documented European mentorship and advances a novel perspective that scientific growth is driven more by knowledge transmission than by discovery alone.
0 citationsRead paper
How to Build Marcus's Algebraic Mind: Algebro-Deterministic Substrate over Galois Fields
This work addresses the longstanding challenge that conventional multilayer perceptrons fail to fulfill Marcus’s three core criteria for an algebraic mind—variable manipulation, representation of recursive structures, and distinction between individual and category representations—by introducing the PyVaCoAl/VaCoAl neurocognitive architecture. This framework uniquely maps all three criteria onto a deterministic algebraic basis over GF(2), employing XOR-and-shift as its fundamental primitive and leveraging primitive-polynomial linear feedback shift registers to achieve invertible variable binding, non-commutative compositional bundling, and segregated address spaces for individuals versus categories. The resulting end-to-end hyperdimensional computing system not only satisfies all three cognitive requirements but also substantially outperforms dominant 2001-era approaches such as tensor products and circular convolution, while naturally supporting counterfactual reasoning at Pearl’s third level of causal inference.
0 citationsRead paper