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There is an undeniable thread of invariance running through any coherent process, a thread that linear algebra, with its basis-independent operators and change-of-basis theorems, captures beautifully. It is precisely this invariance under transformation that endows deep learning and other ML models with their robustness and generalization: the same underlying relations persist even as their representations shift. Were there no stable, ordered links binding successive “time-slices” of reality, no consistent symmetries or conserved structures, our experience of a lawful world would collapse into chaos. To deny such universals, as nominalism does, is to cast aside the very framework through which proofs remain valid regardless of one’s choice of symbols and to mistake arbitrary labels for the bedrock of intelligibility.
