[yters]

Hmm, but you could compress text to an equally random sequence. I.e. all minimal programs are by definition Kolmogorov random.

Also, what about crystalline forms, which are very orderly and require minimal computation to reproduce, but are equally insignificant for the average receiver?

[princeofwands]

> you could compress text to an equally random sequence

More or less correct. The key difference is that you could not compress a random coin flip sequence (and that a compressed text is meaningless until decompressed to original).

> all minimal programs are by definition Kolmogorov random

Compression provides an upper bound to K. Kolmogorov Randomness itself is not computable. AKA: You can't ever know if you have a minimal program.

> Crystalline forms

It is possible to both have low significance and low information content. Crystalline forms were very significant to Turing though: https://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphoge...

[yters]

The best approach that I've seen is a combination of Shannon information and Kolmogorov complexity. If an object has high Shannon information, then it is not crystalline. If it also has low Kolmogorov complexity then it is not random. This seems to characterize the sweet spot where meaningful information occurs. Kolmogorov called this quantity "randomness deficiency".

[princeofwands]

Really cool concept. Thanks!