User blog comment:B1mb0w/new Alpha Function/@comment-26428969-20150801143933/@comment-10262436-20150801145001

Hi. The point of the Alpha Function is to provide notation for big numbers and make comparisons simpler. It is not intended to be the fastest growing function itself.

The new version of the function will evaluate some very precise real numbers (> 15 decimal places) to create a unique D function string. Therefore each real number references a the big number (result of the D function string).

I think this gives a more intuitive feel when comparing very big numbers.