All mathematics is produced by physical objects (brains, computers). Therefore the laws of physics determine what theorems are possible, and mathematics has no existence independent of our universe.
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Agree, what Penrose is proposing must be falsifiable. Perhaps you could use an alternative example to illustrate the point from another angle: Real numbers with infinite digits cannot be physically relevant because they imply the existence of infinite information.
Real numbers exist in our minds. They're constructs of our brains, and as such they're physical entities.
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I disagree. Infinite information requires an infinite volume of space or surface to be encoded according to holography. There is a dependency between the variables, that is what entropy tells us at a fundamental level.https://twitter.com/Crappyfork/status/1447842074011836420 …
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Not every real number with infinite digits requires an infinite amount of information to encode though - for example, "the unique positive solution to the equation X**2 = 2".
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