Comment by BlackFly
6 months ago
Yes, I understood what the parent suggested. I am pointing out that such a number may have strange properties like the fact that a number larger than it can have a smaller Kolmogorov complexity, then I am questioning whether there is a number such that every number larger than it has such a large Kolmogorov complexity that it cannot be encoded. The question therefore becomes, is there a limit to the size of physically describable numbers? Or is there always going to be some number larger with some trivial kolmogorov complexity?
Beyond BBλ2(10^100), there is no larger number with complexity under 10^100.
I absolutely love this question.
Postulate: You cannot define a largest physically describable number.
My assumption is that due to the very nature of Kolmogorov complexity (and other Godel related / halting problem related / self referential descriptions), this is not an answerable or sensible question.
It falls under the same language-enabled recursion problems as:
- The least number that cannot be described in less than twenty syllables. - The least number that cannot be uniquely described by an expression of first-order set theory that contains no more than a googol (10^100) symbols.