God's algorithm as undecidable?

[TimeSkip]

TL;DR Summary

God's algorithm and assessing completeness of its proof.

I posted in the same sub-forum about complexity in mathematics and whether it is determinate. Seemingly, the consensus is that there's no definitive way in assessing a proofs complexity in a manner that is rigorous in regards to any other theorems or otherwise stated in a systematic way other than perhaps informationally.

However, some of the reasons why I post this thread is closely related to the logic of a finite alphabet in two parts. Namely, when a growing alphabet produces an algorithm that (by definition of God's algorithm) is least exhaustive in computability. However isn't it true that this necessitate that it (God's theorem) is likewise the least complex in determination of measurement?

I'd like to call this logic a form of complexity theorem or subject to measurement theory, where μ is provable and exact (as this is what God's algorithm demands by definition).

However, if we cannot determine the complexity of God's algorithm, then isn't this some form of Incompleteness in it due to the above?

Furthermore, it seems that God's theorem is subject on another issue to Incompleteness in for each and every domain application, (the range doesn't matter since the above was stated, and even if we had such an algorithm, the issue still pertains to the proofs assertion in a rigorous manner that it is least complex, even information wise.

 

[suremarc]

Sorry, but I’m going to be straight and say that this post is really frustrating to read. How does a “growing alphabet” produce an algorithm? What does “exhaustive in terms of computability” mean? What is $\mu$ and what is God’s theorem? You cannot simply assume that we know what you mean. None of these things have been precisely defined or explained, and as long as that remains true there is no coherent discussion to be had here.

 

[pinball1970]

Sorry, but I’m going to be straight and say that this post is really frustrating to read. How does a “growing alphabet” produce an algorithm? What does “exhaustive in terms of computability” mean? What is $\mu$ and what is God’s theorem? You cannot simply assume that we know what you mean. None of these things have been precisely defined or explained, and as long as that remains true there is no coherent discussion to be had here.

I was intrigued by the title and google search gave this

https://en.wikipedia.org/wiki/God's_algorithm

Never heard of it, sounds like the quickest way of solving a puzzle or a means to to do that?

μ I am not sure is on there - just a quick glance

 

[TimeSkip]

Sorry, but I’m going to be straight and say that this post is really frustrating to read. How does a “growing alphabet” produce an algorithm? What does “exhaustive in terms of computability” mean? What is $\mu$ and what is God’s theorem? You cannot simply assume that we know what you mean. None of these things have been precisely defined or explained, and as long as that remains true there is no coherent discussion to be had here.

I'm sorry for my inadequate communication skills. I'm basically trying to say that when you have a least complex way of ascertaining the complexity of a proof or say God's algorithm, then what is left is testing it computationally, (this is what I mean by a growing alphabet up to a point). Yet, as per that previous thread, it seems that we have no measure for this task quantitatively, and hence the problem (in my mind) with God's theorem arises, doesn't it? Because by definition God's algorithm states that it takes the least amount of steps to solve a combinatorial problem.

You know, but this is really a bad topic, because God's algorithm only applies to finite tasks, so the Kolmogorov complexity is not indeterminate, I think.