User blog comment:Alejandro Magno/Extended Arrow Notation/@comment-10429372-20140919073818/@comment-5150073-20140919093830

I'd agree with that. How strong ^(^(n)^(n)^(n)^(n)^)^ might be? I guess it should be e(1) or z(0), but since definition becomes informal, it's impossible to analyze further.