User blog comment:Simplicityaboveall/Extremely Large Numbers 2/@comment-5529393-20160801203256/@comment-28633611-20160804053508

Here's an analogy that will make things clearer.

Imagine a computer language which allows us the following:

(1) Accepting input.

(2) Write arithemtic expressions using addition and multplication and exponentiation.

(3) Storing intermediate results in variables.

(4) Outputing a result.

Note that in this (very limited) language, we're not allowed to use conditionals or create loops, so any form of recursion is impossible. And since the strongest available operator is exponentiation, this means that any function stronger than 10^^x would be "uncomputable" by this language.

So here's a question: is it possible to create a function F with this language, such that F(10^^^100)>10^^^101? Sure. We can simply write a program with 10^^^101 lines, each stating N←N+1.

But can it be done in a googolplex characters or less? It isn't too difficult to see that the answer to this question is no. The best we could do is write something like N←N^N^N a bunch of times,and we'll still need more than 10^^^100 repetitions to reach our goal.

Exactly the same situation (on a vastly grander scale) occurs when trying to beat Rayo's number with a computable function. The only difference is that my example toy language can be made more powerful by adding features, while the term "computable function" already encompasses everything that can computed.