The growth of BB is certainly mind-boggling; however, I personally find its growth rate so untouchable as obviate any attempt at understanding. There's nothing to gain purchase on.
The fast growing hierarchy, on the other hand, provides oodles of structure for us to explore, and we can construct numbers that are vastly larger than anything BB(6) is likely to hit. In fact, this is why we use the fast growing hierarchy to approximate really big numbers all the time!
When we take something like f_Γ_0 and try to unpack even just the barest surface of its size, I get a feeling of vastness similar to those videos of diving endlessly into fractals.
The fast growing hierarchy, on the other hand, provides oodles of structure for us to explore, and we can construct numbers that are vastly larger than anything BB(6) is likely to hit. In fact, this is why we use the fast growing hierarchy to approximate really big numbers all the time!
When we take something like f_Γ_0 and try to unpack even just the barest surface of its size, I get a feeling of vastness similar to those videos of diving endlessly into fractals.