User blog comment:Bubby3/Matrix system analysis (new blog post)/@comment-30754445-20181119125930/@comment-30754445-20181119160052

"For the answer to your first question, BM2.3 and BM4 alawys evaulate the same, so it doesn't matter which one I'm using, and it says that here."

Then why are they given different names?

"The blog post I linked to also provides the expansion rules for them."

There are no expansion rules in your link. There's a link to a source code, but that's not the same thing. If the algorithm is so convoluted that no human being can convert it into a simple set of rules in english, then the system cannot be analyzed at all.

"For your fourth question, it has to do with the process of "upgrading" the level of (n,x,0) terms with (n,x,1) ...This pattern continues with all expressions ending in an (n,1,0) term, replacing the W in the ordinal with a W_w. Similar things happen with (1,1,1)(2,1,1), (1,1,1)(2,1,1)(2,1,1), etc."

I fail to see how this gives hydras the kind of boost you're claiming.

What this does achieve (if defined optimally) is that your hydras can be nested. So (0,0,0)(1,1,1)(2,1,1) gets you to hydras with elements that are - themselves - hydras of ordinary numbers. And (0,0,0)(1,1,1)(2,1,1)(3,1,1) will get you to hydras whose elements are "hydras of hydras of ordinary numbers".

This is still within the scope of inaccessibles. In fact, repeating this an arbitrary number times gets you to exactly ψ(ψi(0)). "You can fill in the gaps with intuition if the analysis is detailed enough and provides all possible scenerioshe for what could happen."

Yeah, you can fill in the gaps in a way that sorta makes sense. But there's absolutely no reason to assume that the end result would be correct.

Also, the structure of the ordinals in question is so complex, that "listing all possible scenarios" is simply not possible. "I am going to fill in the gaps and make it more detailed" A longer list won't do us any good.

What is needed is a detailed explanation for how that list was derived. And by that I mean two things:

(1) What your assumptions were whem making each portion of the list.

(2) Your mathematical reasons for thinking that these assumptions are actually true.

Otherwise, it just looks like you've pulled a bunch of ordinals out of a hat.