User blog comment:Edwin Shade/A Complete Analysis of Taranovsky's Notation/@comment-30118230-20180201150715/@comment-34434829-20180201155939

Because such a result would be completely useless without calibartion.

You can calculate a fundamental sequence of any TON expression immediately (there are easy rules for doing so), but this doesn't tell you squat about how large the actual ordinal is.

How will you know if and when you reach 2nd order arithmetic, for example? Imagine a person who doesn't know any OCF-level notations trying to figure out when TON reaches Psi(Psi_I(0)). Even if he'll manage to get the TON expressions correctly (which would be a miracle without prior knowledge of how the ordinals at these levels work), how would he know when he reached his goal?

Using Bashicu-Matrices won't solve this problem either. It just shifts the problem from estimating the TON's directly to estimating the BM expressions. Same difference.