>>12548626You'd need very very good rational approximations of pi for this approach to work and I don't think even wolfram can actually do the fourth tetration accurately enough. 22/7 - 223/72 is only about 0.04, small enough that in the second tetration the difference is about 0.15, but in the fourth tetration the difference is more than 10^(10^17) by wolfram.
We probably need something more clever, especially for taller towers; unfortunately hyperexponentiation is not well studied so there isn't a unified continuous extension to all rationals. here's one person's approach: ingalidakis . com/math/exponents4 . html
>>12548669Error grows really really quickly. pi^pi^pi^pi > 3^7625597484987> 10^(10^12.5), a number with a trillion digits before the decimal.
