Mirroring, Rotation and the Boundary of Cognition: On the Ontological Limitations of Mathematics and Physics and the Necessary Postulation of the Unknown X

Starting from the meta-question of why i^2=-1 can be interpreted as rotation, this paper constructs the Four-Tier Theory of Cognitive Mirroring, demonstrating that rotation in mathematics is essentially a composite of mirror reflections rather than an ontological counterpart of physical rotation. Physical circles exist inherently, independent of mathematical recognition. Addressing the "unreasonable effectiveness of mathematics," this paper proposes a Homology Explanation: as products of human consciousness, mathematics shares a common origin with humans themselves, who in turn emerge from cosmic evolution. Hence mathematics bears an intrinsic structural affinity with the observable universe. Further, via the principle of infinite regress, this paper proves the logical necessity of a more fundamental entity (denoted X) permanently inaccessible to human cognition. Following Occam’s Razor, we advocate explicitly postulating X as the absolute boundary of cognition, rather than attempting to eliminate or define it. Science functions as scaffolding erected over an abyss of the unknown; its mission lies not in erasing cognitive boundaries, but in upholding rigorous humility at those limits.

本文从“ i^2 = -1 何以解释为旋转”这一元问题出发,构建“认知镜像四层论”,论证数学中的旋转本质是“镜像反射的复合”,而非物理旋转的本体。物理圆天然独立,不依赖数学认可。针对数学“不可思议的有效性”,本文提出“同源性解释”:数学作为人类意识的产物,与人类本身同源,而人类又是宇宙演化的产物,故数学与可观测宇宙具有结构上的内在亲近性。进一步地,利用无限回溯原理,本文证明必然存在人类尚未认知的更根本性存在(X)。基于奥卡姆剃刀原则,本文主张将X明确假设为认知的绝对边界,而非妄图消解或定义它。科学是搭建在未知深渊上的脚手架,其使命不在于消除边界,而在于在边界处保持严谨的谦卑。