User blog comment:Bubby3/Matrix system analysis (new blog post)/@comment-30754445-20181119174959/@comment-30754445-20181119225315

I read your analysis in detail. I do not agree with it. I still stand by my statement that a hydra-based notation cannot get you to Mahlos.

As for the "boost effect", it is worth noting that this effect seems to cancel itself out in the long run.

For example, the fact that (0,0,0)(1,1,1)(2,1,0)(3,2,1) is equivalent to  ψ(Ω_(ω*2)) actually makes perfect sense (it's analogous to the way that (0,0)(1,1)(2,2) is equivalent to ψ(ψ2(0))). Yet this happens after countless of "upgrades" that were made by (1,1,1)'s along the way.

Looking at your other examples, it is clear that these "upgrades" are always quite minor relative the ordinals we've already reached. For example, replacing Ω_(psi_ψ(0)+1)'s with Ω_(psi_ψ(0)+ω)'s is not going to change the end result by much (if at all).

And you still haven't answered our questions regarding:

(1) The actual rule-set of BM4.

(2) Your reasons for believing that this rule-set actually works the way you say it does.

(3) What OCF you're using for your comparisions.