goedel's Record Player

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Here is an analogy to Goedel's Theorem (any sufficiently strong arithmetical theory contains true theorems which have no proofs in the theory). It is

due to ouglas Hofstadter.

The better a record player is, the higher the fidelity with which it can reproduce recorded sound. It is known that for any mechanical apparatus, there is a particular pitch which will vibrate the apparatus destructively, so that (if the sound is loud enough) it will fall apart. It is therefore possible to create a record which will destroy the record player on which it is being played. As a result, there is no such thing as a record player which can play every record whatsoever.

There are only two escapes from this paradox. One is to have a poor record player which cannot play some records. The other is to try to change the record player so that it will not fall apart, or if it does fall apart, will reassemble itself. Nevertheless, there is always some part which is critical to it, and which the creator of the malicious record will target with his noises.

The analogy:

  • record -> true theorem
  • record player -> theory of arithmetic
  • playing of a record by a player -> proof of a theorem under a theory
  • poor record player -> weak theory of arithmetic
  • malicious record -> Goedel sentence