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JohnSidles comments on Quotes and Notes on Scott Aaronson’s "The Ghost in the Quantum Turing Machine" - Less Wrong
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The entanglement(s) of hot-noisy-evolved biological cognition with abstract ideals of cognition that Eliezer Yudkowsky vividly describes in Harry Potter and the Methods of Rationality, and the quantum entanglement(s) of dynamical flow with the physical processes of cognition that Scott Aaronson vividly describes in Ghost in the Quantum Turing Machine, both find further mathematical/social/philosophical echoes in Joshua Landsberg's Tensors: Geometry and Applications (2012), specifically in Landsberg's thought-provoking introductory section Section 0.3: Clash of Cultures (this introduction is available as PDF on-line).
E.g., the above discussions above relating to "map versus object" distinctions can be summarized by:
as contrasted with the opposing assertion
As Landsberg remarks
The Yudkowsky/Aaronson philosophical divide is vividly mirrored in the various divides that Landsberg describes between geometers and algebraists, and mathematicians and engineers.
Question Has it happened before, that philosophical conundrums have arisen in the course of STEM investigation, then been largely or even entirely resolved by further STEM progress?
Answer Yes of course (beginning for example with Isaac Newton's obvious-yet-wrong notion that "absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external").
Conclusion It may be that, in coming decades, the philosophical debate(s) between Yudkowsky and Aaronson will be largely or even entirely resolved by mathematical discourse following the roadmap laid down by Landsberg's outstanding text.
An elaboration of the above argument now appears on Shtetl Optimized, essentially as a meditation on the question: What strictly mathematical proposition would comprise rationally convincing evidence that the key linear-quantum postulates of "One Ghost in the Quantum Turing Machine* amount to “an unredeemed claim [that has] become a roadblock rather than an inspiration” (to borrow an apt phrase from Jaffe and Quinn's arXiv:math/9307227).
Readers of Not Even Wrong seeking further (strictly mathematical) mathematical illumination in regard to these issues may wish to consult Arnold Neumaier and Dennis Westra's textbook-in-progress Classical and Quantum Mechanics via Lie Algebras (arXiv:0810.1019, 2011), whose Introduction states:
That the Neumaier/Westra textbook is an unfinished work-in-progress constitutes proof prima facie that the final tractatus upon these much-discussed logico-physico-philosophicus issues has yet to be written! :)