Kolmogorov complexity is definitely meaningful, but it's not (Shannon) entropy, just conceptually similar. Many people think of something like Kolmogorov-complex sequences when they think of "random" sequences, which is (IMO) why they have trouble thinking of entropy as being about a probability distribution.
The one case where they coincide (sort of) is if you believe your random sequence is generated by a randomly chosen Turing machine, which I've only really seen in philosophical settings.
A uniformly chosen 64-bit integer still has exactly 64 bits of entropy, regardless of how much Kolmogorov complexity the actual bits you generate have.
The one case where they coincide (sort of) is if you believe your random sequence is generated by a randomly chosen Turing machine, which I've only really seen in philosophical settings.
A uniformly chosen 64-bit integer still has exactly 64 bits of entropy, regardless of how much Kolmogorov complexity the actual bits you generate have.