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Algorithmically Coding the Universe

1993, Developments in Language Theory

Abstract

All science is founded on the assumption that the physical universe is ordered. Our aim is to challenge this hypothesis using arguments,from the algorithmic information theory.

Key takeaways

  • The secret number Ω is introduced in Section 3 in connection with the coding of the halting problem.
  • (here Ω n is the number consisting of the first n bits of Ω) one can solve the halting problem for all n-bit programs as follows:
  • Of course, Ω isn't the only possibility to encode the halting problem.
  • In view of the above discussion we may consider Ω as a crude model for the Universe.
  • , X m if and only if the ith bit of Ω equals 1.