Space/Science — HabitableZone

Space/Science » in reply to Kolmogorov Complexity, String Information, Panspermia and the Fermi Paradox

re: Kolmogorov Complexity and Goedel Numbers? Big deal....

I'm a little befuddled by these posts on KC. Okay, granted, we can encode any arbitrarily complex procedure or set of variable values into a string- that we can and how we can do it goes all the way back to the turn of the century when Goedel created (over-simplifying, yada yada:) a fully self-reflecting system to encode mathematics. But how do you extract it again meaningfully once the encoding algorithm is lost. Sure, of course you can encode the encoding algo and send that along to, but where do you get the key for that? The point that I am trying to make is that the K string for any system will be extractable to an uncountably infinite number of systems without a key. In fact, the encoded function and the encoded data may be indescipherable from eachother in an infinite number of cases.

What you are essentially talking about, if I understand you, boils down to data-compression or encryption, with a bit of Goedel numbering thrown in.

Even if we could detect the transmission of a K-sequence like you describe, the binary stream would almost certainly be indescipherable from noise (ie, it will mimic the complexity of the system it describes, which if is a genome would be enormous!) without the encoding algorithm at our hands.

These K-sequences, whatever they are (I'm not going to say I know much about them beyond whats been posted here), seem to be nothing more than a function over, essentially, goedel numbers- a way of analyzing the complexity of the underlying procedure or variable set encoded by a numbering. I don't see them as anything particularily interesting or new, and I certainly don't see them as a viable method of transmitting 'universally decodable' data from point to point accross the universe. They are most certainly not 'traveling life streams'- its just encoded data like any other encoded data.

Furthermore, being smack-dab in 'goedel land' means that you have all sorts of problems and fundamental limitations. Infinities are going to pop up too.

DL

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