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    Mathematical structures capture deep nomological regulari... — Carmelics
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    Challenges→The success and plausibility of purely formal (Pythagorean) analogies in physics should evoke puzzlement.

    Mathematical structures capture deep nomological regularities in nature, so formal analogies track real physical relationships rather than being mysterious coincidences.

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    Reasons For

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    Reason for
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    • 1.Mathematics has predictive power across diverse physical domains, suggesting it captures genuine structure rather than being human-imposed.
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    • 2.Formal analogies (e.g., wave equations in quantum and classical mechanics) yield novel predictions later confirmed experimentally.
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    • 3.The unreasonable effectiveness of mathematics suggests our formal frameworks align with nature's deep organization, not mere coincidence.
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    Reasons Against

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    Reason against
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    • 1.Humans select and emphasize analogies that work while ignoring thousands that fail, creating illusion of deep connection via confirmation bias.
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    • 2.Mathematical isomorphism between domains may reflect only shared structural features we've imposed, not nomological reality itself.
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    • 3.Predictive success could stem from mathematics being a flexible language humans tailor to observations, rather than capturing nature's laws.
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    Related

    Formal analogies (e.g., wave equations in quantum and classical mechanics) yield...Humans select and emphasize analogies that work while ignoring thousands that fa...Mathematical isomorphism between domains may reflect only shared structural feat...Mathematics has predictive power across diverse physical domains, suggesting it ...
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    Predictive success could stem from mathematics being a flexible language humans ...The success and plausibility of purely formal (Pythagorean) analogies in physics...The unreasonable effectiveness of mathematics suggests our formal frameworks ali...

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