Tor Nerretranders, "The User Illusion"에서: Infinite Algorithms

''Tor Nerretranders, The User Illusion 에서" 의 계속

 

Chapter 3: "Infinite Algorithms" 에서:

 

Gödel had shown that in any closed system, questions will arise that cannot be answered -- true statements that cannot be deduced. (p 54)

 

The further development of Gödel's theorem in the 1960s were given several names -- the theory of Algorithmic information, algorithmic complexity, algorithmic randomness -- whichever name we choose, it had three fathers: Ray Solomonoff, Andrei Kolgomorov, and Gregory Chaitin. (p 58)

 

So we can differentiate between random numbers and ordered numbers: random ones are the ones that cannot be described more concisely, while ordered one are the ones that can. (p 59)

 

We cannot propose a general rule that can tell us how to figure out whether a number is random or not -- whether it can be expressed more concisely or not. This is a direct consequence of Gödel's realization. it is Gödel's theorem; it is what he proved. (p 60)

 

Information is a measure of randomness because randomness is a measure of disorder: something that is difficult to describe.... Gödel's theorem tells us that we can never know whether there is order in something random. (p 61)

 

"Gödel's theorem may be demonstrated using arguments having an information-theoretic flavor," Chaitin writes. "In such an approach it's possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms." (p 62)

 

Kolgomorov had equated complexity with randomness, and thereby complexity with information. (p 76)