User blog comment:Googleaarex/Bashicu Matrix System Analysis (Part 1)/@comment-27516045-20170725132813/@comment-30754445-20170727060400

@Deedlit

"So is there a 'fundamental sequence-less' version of SAN, that could be much simpler both in length and in comprehensibility?"

Even it were possible, what would be the point? When it comes to googology, an ordinal notation with no fundamental sequences is next to useless. I guess that at the level of I or M or K we can still use our intuition to fill in the gaps, but in the long run we really can't do without well-defined fundamental sequences.

At any rate, I don't think the fundamental sequences are the main reason SAN is so complicated. I think the reason is that Hyp Cos didn't invent SAN for pedagogical purposes. His goal was simply to define the strongest recursive notation he could manage, and this was surely challanging enough without the added overhead of "making it as simple and clear as possible".

What we need here is a concentrated effort on that front.

(Ironically, BM itself would be an excellent candidate for such a notation, once we finish analyzing it. Any 12-year old can follow the expansion rules of BM and therefore fetch the fundamental sequences. It really is an amazing piece of work)