On randomness and a complete description of the universe

[Rudolph Mondal]

Is there an intrinsic randomness to the universe? I understand that to completely compress something, that thing would appear totally random to us. If so, let's say we totally compress our theories regarding how the universe operates. The resultant theories then would be completely random. If that's the case, does this say something about our inability to completely know a system? I'd also appreciate anyone pointing out the misconceptions I have in my understanding of all of this.

 

[nexion]

It would be a foolish mistake to assume that our inability to properly conceive the inner workings of the universe is synonymous with the universe being inherently chaotic, but I doubt humanity will ever know either way.

Concerning the notion that to "completely" compress something means that that thing would appear totally random, I have a few questions:

I. What does it mean to "completely" compress something, and how would you even begin to apply that compression to a body of propositions, many of which are contradictory in some way?
II. How does a "completely" compressed entity appear random?
III. What does it even mean for something to "appear" random?

Your post is short but loaded, there are giant logical leaps which may or may not have any relevancy. It is regardless impossible to determine since these leaps make no sense whatsoever. You would do well to at least explain the logical connections behind these thoughts, perhaps then it would be much easier to evaluate their truth value.

 

[Rudolph Mondal]

It would be a foolish mistake to assume that our inability to properly conceive the inner workings of the universe is synonymous with the universe being inherently chaotic, but I doubt humanity will ever know either way.

I first thought I agreed with you and then later on not so much and right now I'm as I'm writing this I realize that I'm fine with it being either way.

 

[Rudolph Mondal]

Concerning the notion that to "completely" compress something means that that thing would appear totally random, I have a few questions:

I. What does it mean to "completely" compress something, and how would you even begin to apply that compression to a body of propositions, many of which are contradictory in some way?
II. How does a "completely" compressed entity appear random?
III. What does it even mean for something to "appear" random?

Your post is short but loaded, there are giant logical leaps which may or may not have any relevancy. It is regardless impossible to determine since these leaps make no sense whatsoever. You would do well to at least explain the logical connections behind these thoughts, perhaps then it would be much easier to evaluate their truth value.

I didn't notice you edited your post. Anyway, so that was an idea from information theory. An object with zero entropy contains no information and an object with maximum entropy contains highest information.

Also, there's the idea of Kolgomorov complexity whereby the complexity of a string is determined by the input plus the simplest algorithm which can process that string to produce that string when given that input. So, if a string is maximally compressed, no algorithm and its input can be simpler (as in take up less number of bits) than its output. A completely random string is one which no algorithm can process and so a completely random string is maximally compressed.

What does it mean for something to be random? Well, by Kolmogorov complexity, it would mean that there is no algorithm when given a certain input is simpler than the output (the random string). So every bit in that string is maximally unknowable and has to be taken as an axiom. I.e., there's no finite set of axioms that would give you all the information of that maximally random string. Some mathematician proved (I forgot who but it was in a book I read authored by Gregory Chaitin titled Metamath!) that all yes/no questions can be contained in that random string and if every bit has to be taken as an axiom, it means we can't get all the answers to all of the yes/no questions we can pose with a particular language. So in other words, we can never get a complete description of the universe.

 

[Symmetricon]

Im not familiar with complexity theory, so please pardon any errors.

'A completely random string is one which no algorithm can process and so a completely random string is maximally compressed.'

Why does a completely random string have to be maximally compressed, does there not exist other algorithmically unprocessable strings? For example some infinity string (or finite but algorithmically/computationally infeasable) ?


The idea here then that if one was to formulate all yes/no questions of the universe into this random bit within the kolomogrov framework above, that some information would be lost whilst processing the set of all questions. Hence leading to a lack of answers on output.

This assumes that all relevant yes/no questions can be presented within this framework, a rather significant assumption. Have you the mathematical proof ?

I think it depends on the observer as to whether one percieves randomness in the universe or not. I do not think the universie can be considered as absolutely random/ordered (disregarding the degree of randomness/chaoticity), it's entirely dependent on ones perspective/point of view, similar to fractal/hausdorff dimension and quantum theory.
Hence there may exist inherent randomness from some perspectives, but not from others.