Collatz_problem [comrade/them]

  • 0 Posts
  • 98 Comments
Joined 5 years ago
cake
Cake day: November 13th, 2020

help-circle



  • This means that you could write a syntactically valid statement which cannot be proven from the axioms of that system even if you were to add more axioms.

    You can actually add the statement itself as an axiom. The point of the theorem is that no finite number of additional axioms will completely eliminate all unprovable true statements from the theory.

    Also, it relies on consistency of the formal system, because inconsistent system can prove anything. In fact, you can prove consistency of a formal system if and only if it is inconsistent.

    Information-theoretic incompleteness is new to me, but seems to be similar to Gödel’s theorem but with a focus on computation saying that if you have a complex enough system there are functions that won’t be recursively definable. As in you can’t just break it down into smaller parts that can be computed and work upwards to it.

    In fact, any function, growing fast enough, will be non-recursive. And the same applies to various similar definitions, resulting in fast-growing hierarchy.

    All in all this means that no algorithmic theory could actually describe everything. This means you cannot break all of physics down into a finite set of rules that can be used to compute reality. Ergo, we can’t be in a simulation because there are physical phenomena that exist which are impossible to compute.

    It should be noted that it doesn’t rule out analog simulations.











  • Step forward: we hear
    That you are a good man.
    You cannot be bought, but the lightning
    Which strikes the house, also
    Cannot be bought.
    You hold to what you said.
    But what did you say?
    You are honest, you say your opinion.
    Which opinion?
    You are brave.
    Against whom?
    You are wise.
    For whom?
    You do not consider your personal advantages.
    Whose advantages do you consider then?
    You are a good friend.
    Are you also a good friend of the good people?

    Hear us then: we know.
    You are our enemy. This is why we shall
    Now put you in front of a wall. But in consideration of your merits and good qualities
    We shall put you in front of a good wall and shoot you
    With a good bullet from a good gun and bury you
    With a good shovel in the good earth.

    Also, why don’t we have Brecht emojis?