I'm looking at Paulsen's website and tetration calculator as I review his publications. The calculator is way cool. While Paulsen asserts that real tetration is the most natural form of tetration, it appears to me that the cost might be the of allowing significant discontinuities (maybe just branch cuts?).
I believe that the different forms of tetration are like the Lie groups, there is no "best" group so important that it invalidates the study of the other groups. Also I expect tetration education will improve in the future - our arguments will be polished and reduced to the essence. That said, in considering the different approaches to tetration I wonder which if any versions could have a physical implementation. Here simpler would be better. Of course the it is possible that the multiple approaches to tetration actually manifest in the physical Universe. Maybe tetration doesn't exist in physics because the Universe doesn't know which one to use.
I believe that the different forms of tetration are like the Lie groups, there is no "best" group so important that it invalidates the study of the other groups. Also I expect tetration education will improve in the future - our arguments will be polished and reduced to the essence. That said, in considering the different approaches to tetration I wonder which if any versions could have a physical implementation. Here simpler would be better. Of course the it is possible that the multiple approaches to tetration actually manifest in the physical Universe. Maybe tetration doesn't exist in physics because the Universe doesn't know which one to use.
Daniel
