User blog comment:Vel!/Ordinal BEAF/@comment-5150073-20130315133136/@comment-5150073-20130315140417

Since pentational arrays in the form X => X^X^X...X^X^X => ... => X^X^X...X^X^X (where => indicates the number X's in the following tower), then we can increase the structural level of array if we repeatedly apply addition and multiplication on the rightmost power tower until the number of X's increases by one. It adds 1 to the next power tower, but in googology, if such thing can be done once, then it can be done twice, thrice, fource, X-ce. Eventually 2nd power tower will added to itself and it adds 2* to it. We can climb to the 2nd tower like 1st, and eventually add one to the 3rd power tower, and so on. Where I wrong?