User blog comment:Vel!/Yudkowsky on googology/@comment-5982810-20140326024707/@comment-5982810-20140327041405

@65.26.80.144

I'm reserving Thus/Also Sprach Zarathustra for a significant jump in order-type. Yet  none of the numbers you've described even reaches a  ''grand grand Sprach Zarathustra. '' You can't beat a recursive system by using delimiters defined within that system. The  Sprach Zarathustra Sequence grows faster than the notation used to describe it. That's why by the 2nd-member of the sequence (grand Sprach Zarathustra) is already a number which couldn't be expressed in that notation within the known universe (the use of the ' w/ ' operator is sort of cheating).

As for your numbers we have a similar problem as before. Just like adding the larger numeric arguments didn't do much to boost the value of the expression, using delimiters such as ' # ', ' #^n ' , and ' #^^#># ' won't do much to boost the value of the expressions at this level. Whenever you are tempted to use a large number as either an argument or within a delimiter ... don't, because that functionality is already pre-built into ExE. You can get the same result or better by observing the following...

Replace @N, for googologically large N with @100#k for small k (Assuming N is only a few iterations of @(n) say @(@(@(100))), k will not even need to be as big as 10)

Replace @100&[N]100, for googologically large N with @100&100#k for small k.

In short, you never need to place a value larger than 100 in any argument or delimiter because you can always append a hyperion (#k) to iterate whatever it is your trying to iterate.

Keep in mind however that for any subsystem ExE_&, if $(#) is a delimiter < & then for any googolism, @100 , within the system @100$(#)100 is a trivial extension of it, especially if $(#) is smaller than the largest delimiter contained in @.

Hence, you can't beat the Sprach Zarathustra Sequence using notation that Sprach Zarathustra is already diagonalizing over.

(Sbiis.ExE)