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Comment on Bizarre Systems Thinking

BenRayfield Sat, Sep 11, 2010
You think that's bizarre? I'll show you bizarre...

A fact of math is http://en.wikipedia.org/wiki/Incompleteness_theorem  which proves things like this:
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (essentially, a computer program) is capable of proving all facts about the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem shows that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself.

...and...
Gödel's theorem shows that, in theories that include a small portion of number theory, a complete and consistent finite list of axioms can never be created, nor even an infinite list that can be enumerated by a computer program. Each time a new statement is added as an axiom, there are other true statements that still cannot be proved, even with the new axiom. If an axiom is ever added that makes the system complete, it does so at the cost of making the system inconsistent.


That appears to be more technical than is relevant to this thread, but its the core subject which all bizarreness comes from, usually indirectly.

Everything can be divided into 3 groups. We don't know which things go in which of the 3 groups, but there is some true grouping of them that way. Such uncertainty is predicted byhttp://en.wikipedia.org/wiki/Incompleteness_theorem

The 3 groups are:
(1) Things that are completely random. They are not influenced or changed by anything. They are the definition of everything thats not logic.
(2) Things that are completely logical. Everything that can be completely known based on the things it depends on.
(3) Combinations of (1) and (2) that are not completely (1) and are not completely (2).

(3) is a subset of the combination of (1) and (2).

At any 1 observation, (1) is a subset of (2), but (1) is a different subset of (2) each time its observed.

Therefore all possible things are a subset of (2) in 1 way or another.

Therefore the entire universe (including everything that was, is, and will be) is a subset of (2) in 1 way or another.

(2) is proven to be accurately described byhttp://en.wikipedia.org/wiki/Incompleteness_theorem

Therefore, whatever subset of (2) the universe is (subset of all possible things), the universe is accurately described byhttp://en.wikipedia.org/wiki/Incompleteness_theorem

Therefore those things I quoted above apply to the universe.

Therefore, as Douglas Adams wrote, and I mean this in the most abstract and indirect way...

There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened.


Douglas Adams was obviously writing about http://en.wikipedia.org/wiki/Incompleteness_theorem  because of this quote:

He attempts to discover The Ultimate Question by extracting it from his brainwave patterns, as abusively[2] suggested by Marvin the Paranoid Android, when a Scrabble-playing caveman spells out forty two. Arthur pulls random letters from a bag, but only gets the sentence "What do you get if you multiply six by nine"?
“ "Six by nine. Forty two."

"That's it. That's all there is."

"I always thought something was fundamentally wrong with the universe"

Six times nine is, of course, fifty-four. The program on the "Earth computer" should have run correctly, but the unexpected arrival of the Golgafrinchans on prehistoric Earth caused input errors into the system—computing (because of the garbage in, garbage out rule) the wrong question—the question in Arthur's subconscious being invalid all along.


Its a fictional book, but theres parts of it that he meant as real philosophy questions. If you really want bizarre... Figure out why Douglas Adams wrote as fiction what Max Tegmark more recently wrote as serious physics research papers.

Language is bizarre, but so is everything else, because logically it has to be.