pcael

thanks, dont they have a reference book? thanks

Of course you can. Kolmogorov complexity never says anything about finding lower bounds for specific elements. The lower bound is a statament about one string. The upper bound is statement about infinite strings, so you need to prove for infinite strings. In that sense you cant compress all strings and pointing a specific one without representing the index to it with a complexity a least as large as the string itself it represents. Read the part of pointing and telling things apart.

Lol, its funny how people think they know about others peoples lives... and speaking of wasting time...

Thats really interesting.. Do you recommend any books on ergodic theory that are accessible? I have undergrad in math, but it was a while ago. Thanks!

Let me give you an idea, just dont read it then. Im not monetizing anything btw.

Im fully aware. But since you came here to criticize only, thanks.

Its one of the simple forms of lossy compression, so you could have just point out that constructively, but hey this is internet.

Except anyone can use bullets.

And except the section title is basically me resuming what was seeing before:

Taking stock: what we managed to extract

So you want me to use what? Give me a break.

Im not trying anything. I just put as a joke. Im using AI to learn, but I wrote the structure and the references, and remodeled some parts with AI, yes, but I wrote the base input text by hand, in the sense AI would not be needed, but it helps me as English is not my first language.

Does that solve the issue? You can always ask yourself if you can embedd something smaller or not? Kolmogorov is just comparing things.. plus, in order to specifically point to pi in the languages internal table, you will need complexity as large as your representation of pi.

I think that does not hold, Kolmogorov complexity is measured relative to a pre-defined universal machine for everything. The machine is not counted in the description of π, for the same reason a book's length isn't measured by including the size of the reader. You fix one interpreter, then ask "how long is the shortest input that makes something?" The interpreter is a constant — the same constant for π, for the random file, for every string in the post

thats interesting, and maybe beyond my current knowledge, I will certainly look into it. About the entropy being a property of a distribution, thats totally correct and I need to fix the post. Thanks.