How do you differentiate a tetration function?

“Indeed, one could define science as reason’s attempt to compensate for our inability to perceive big numbers.”
Scott Aaronson

A wonderful quote, eh? Well, I think it is.

Anyway, for some odd reason, today I was thinking about the mathematical operation of tetration. Many people have heard about addition, multiplication (which is interated addition) and exponentiation (which is iterated multiplication) but tetration is the obscure forth operation in this sequence–interated exponentiation. There are others that follow in this sequence of operations–repeated tetration, and so on–but let’s just wrap our brains around this first.

Anyway, again, I was searching the Web for information about tetration and I came across Aaronson’s interesting collection of essays on computer science, mathematics, AI and other matters. This kid’s existance reassures me that universities are still turning out smart people.

Anyway, still again, if anyone knows the rule for differentiating tetration functions, let me know in the comments. Or mail me.

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