3 ms·

There was a religious apologetics claim, widely presented and debated in the 1990s, that there were statistical anomalies in the Torah to show that it was reall

by schoen 6y ago

There was a religious apologetics claim, widely presented and debated in the 1990s, that there were statistical anomalies in the Torah to show that it was really written by God: https://en.wikipedia.org/wiki/Bible_code https://en.wikipedia.org/wiki/Bible_code However, the measurement technique was somewhat underdetermined, which is a problem akin to p-hacking (as you could look for many possible anomalies and only publish the ones that you successfully find). > anyone could verify that it was authored by someone with more computing power than the universe I never thought of this that way, but that's an excellent way to put it! (Although you also need to assume that the hash is extremely strongly preimage-resistant, which we don't have good mathematical techniques to prove today.) One challenge for this: what is the canonical text encoding and canonicalization, and what is the canonical hash function?

p1mrx 6y ago
Well, if I were God, I would just define a canonical encoding and hash function as part of the message. Mathematicians would study the algorithm over the years, but never find any flaws.
- readyplayeremma 6y ago
  Isn't that cheating though? By controlling the hash function you can alter the function itself until your message will meet the requirements, even though someone later on would find it impossible to compute a new message that meets the same?
  - p1mrx 6y ago
    Presumably, God could foresee the cryptographic flaws of any algorithm, and could therefore design a simpler secure hash function than any human. In this case, "secure" means that there exists no algorithm to compute a preimage faster than brute force. This would be a "nothing up my sleeve" function, in contrast to something like https://en.wikipedia.org/wiki/Dual_EC_DRBG https://en.wikipedia.org/wiki/Dual_EC_DRBG that cryptographers would identify as sketchy. Hypothetical question: What is the Kolmogorov complexity of a secure 256-bit hash function?
    - Y_Y 6y ago
      Hence God must have computational power greater than a Turing machine, at least if he wants to prove His hash function minimises Kolmogorov complexity. For a rough upper bound, there are some examples at [0], which could be less than 100 characters of C (once golfed). [0] https://stackoverflow.com/a/14409947/5327391 https://stackoverflow.com/a/14409947/5327391

by schoen 6y ago

p1mrx 6y ago

Well, if I were God, I would just define a canonical encoding and hash function as part of the message. Mathematicians would study the algorithm over the years, but never find any flaws.

readyplayeremma 6y ago
Isn't that cheating though? By controlling the hash function you can alter the function itself until your message will meet the requirements, even though someone later on would find it impossible to compute a new message that meets the same?
- p1mrx 6y ago
  Presumably, God could foresee the cryptographic flaws of any algorithm, and could therefore design a simpler secure hash function than any human. In this case, "secure" means that there exists no algorithm to compute a preimage faster than brute force. This would be a "nothing up my sleeve" function, in contrast to something like https://en.wikipedia.org/wiki/Dual_EC_DRBG https://en.wikipedia.org/wiki/Dual_EC_DRBG that cryptographers would identify as sketchy. Hypothetical question: What is the Kolmogorov complexity of a secure 256-bit hash function?
  - Y_Y 6y ago
    Hence God must have computational power greater than a Turing machine, at least if he wants to prove His hash function minimises Kolmogorov complexity. For a rough upper bound, there are some examples at [0], which could be less than 100 characters of C (once golfed). [0] https://stackoverflow.com/a/14409947/5327391 https://stackoverflow.com/a/14409947/5327391