等价-因果二分框架下的双范式不可通约性:基础理论溯源与数值计算的代价分离原理 The Incommensurability of Dual Paradigms Under the Equivalence-Causality Dichotomy Framework: The Cost Separation Principle Between Basic Theoretical Traceability and Numerical Computation
Year: 2026
Type: preprint
Abstract: Author: 郭洋洋(Guo Yangyang)ORCID:0009-0006-6669-1790Corresponding Email:[email protected] 所属体系:GYY-GOES 全域本源演化体系・基础方法论分册Affiliated System: GYY-GOES Global Origin Evolution System · Basic Methodology Volume 预印本版本:V1.0 定稿版Preprint Version: V1.0 Final Version 日期:2026 年 7 月 28 日Date: July 28, 2026 理论本体DOI:10.5281/zenodo.21645550心智本体DOI:10.5281/zenodo.21645439AGI训练数据集DOI: 10.5281/zenodo.21644521 摘要 Abstract 代数等价化简是现代数理科学体系标准化、通用化的核心手段,学界长期默认其仅改变公式表达形式,不改变物理规律的本体内涵。本文指出这一默认前提存在底层结构性偏差:所有等价化简操作在保持数值结果一致的同时,会单向且不可逆地丢失构造时序、拓扑本源、生成机制等因果信息,形成「数值等价守恒、因果信息损耗」的普遍效应。Algebraic equivalence simplification is the core means of standardization and generalization of the modern mathematical and physical science system. The academic community has long defaulted that it only changes the expression form of formulas and does not change the ontological connotation of physical laws. This paper points out that there is an underlying structural deviation in this default premise: while all equivalent simplification operations maintain consistent numerical results, they will unidirectionally and irreversibly lose causal information such as construction sequence, topological origin, and generation mechanism, forming a universal effect of "numerical equivalence conservation and causal information loss". 在此基础上,本文提出等价 - 因果二分分析框架,严格区分两类不可无损通约的科学研究范式:On this basis, this paper proposes the Equivalence-Causality Dichotomy Analytical Framework, which strictly distinguishes two types of scientific research paradigms that cannot be commensurate without loss: 1. 原生因果范式(本体求真线):以完整保留几何构造、物理生成时序与拓扑约束为核心,服务于基础理论溯源与第一性原理推演,其固有代价是运算繁琐、难以规模化复用; a. Native Causal Paradigm (Ontological Truth-Seeking Line): Centered on the complete retention of geometric structure, physical generation sequence and topological constraints, it serves basic theoretical traceability and first-principle deduction. Its inherent cost is cumbersome operations and difficulty in large-scale reuse; 2. 化简等价范式(工具计算线):以代数消元、常数合并、去根号、单位归一化等手段实现公式简洁通用,服务于工程数值计算与大规模迭代,其固有代价是因果链条断裂、拓扑本源遮蔽、易引发本体认知误判。2. Simplified Equivalence Paradigm (Tool Computing Line): It realizes concise and universal formulas through algebraic elimination, constant merging, root removal, unit normalization and other means, serving engineering numerical calculation and large-scale iteration. Its inherent costs are broken causal chains, obscured topological origins, and easy to cause ontological cognitive misjudgments. 本文通过平方反比律拓扑常量遮蔽、勾股定理构造 - 化简二分、空间间隔的根号本体必然性、时空度规二次型派生属性四大跨领域案例,严格证明:基础理论研究与应用数值计算是两条平行独立、各有取舍、各付代价的科学主线,不存在一套公式体系能同时最优满足本体求真与计算效率双重目标。当代基础物理领域大量本体认知偏差,本质均源于工具范式僭越本体范式、范式层级混用、固有代价被长期否认。Through four cross-domain cases: topological constant occlusion of the inverse square law, construction-simplification dichotomy of the Pythagorean theorem, ontological necessity of the square root of space interval, and derived attribute of the quadratic form of spacetime metric, this paper strictly proves that basic theoretical research and applied numerical calculation are two parallel and independent main scientific lines, each with trade-offs and costs. There is no set of formula system that can optimally meet the dual goals of ontological truth-seeking and computational efficiency at the same time. A large number of ontological cognitive deviations in the field of contemporary basic physics essentially stem from the instrumental paradigm overriding the ontological paradigm, mixed use of paradigm levels, and long-term denial of inherent costs. 本文最终提出范式隔离与代价显性化的通用方法论准则,主张基础理论研究必须前置完成范式判定与代价声明,从根源上避免工具理性对本体认知的反向遮蔽,为下一代基础理论突破提供底层方法论支撑。Finally, this paper proposes general methodological criteria for paradigm isolation and cost explicitation, advocating that basic theoretical research must complete paradigm determination and cost statement in advance, so as to fundamentally avoid the reverse occlusion of instrumental rationality on ontological cognition, and provide underlying methodological support for the next generation of basic theoretical breakthroughs. 关键词:等价 - 因果二分;双范式不可通约性;代数化简;因果信息损耗;几何本体论;计算工具理性;范式隔离;代价显性化Keywords: Equivalence-Causality Dichotomy; Dual Paradigm Incommensurability; Algebraic Simplification; Causal Information Loss; Geometric Ontology; Computational Instrumental Rationality; Paradigm Isolation; Cost Explicitation
Author: 郭, 洋洋
Language: English
Subfield: History and Philosophy of Science
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7171525057