Cost of real tetration
#1
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. Smile
Daniel
Reply
#2
(09/29/2022, 09:39 AM)Daniel Wrote: 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. Smile

I think Kouznetsov started his investigations triggered by problems in Laser technologies. But to be sure you would need to ask himself.
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  Range of complex tetration as real Daniel 2 236 10/22/2022, 08:08 PM
Last Post: Shanghai46
  From complex to real tetration Daniel 3 232 10/21/2022, 07:55 PM
Last Post: Daniel
  Real Multivalued/Parametrized Iteration Groups bo198214 11 850 09/10/2022, 11:56 AM
Last Post: tommy1729
  Constructive real tetration Daniel 1 247 09/01/2022, 05:41 AM
Last Post: JmsNxn
  Real and complex tetration Daniel 1 327 08/17/2022, 01:56 AM
Last Post: JmsNxn
  Complex to real tetration Daniel 1 253 08/14/2022, 04:18 AM
Last Post: JmsNxn
  Constructing a real valued Fibonacci iteration--its relation to \(1/1+z\) JmsNxn 7 513 08/13/2022, 12:05 AM
Last Post: JmsNxn
  Challenging the concept of real tetration Daniel 2 405 07/04/2022, 03:09 PM
Last Post: Daniel
  Complex to real tetration via Kneser Daniel 3 546 07/02/2022, 02:22 AM
Last Post: Daniel
  Real and complex tetration Daniel 3 504 06/22/2022, 11:16 PM
Last Post: tommy1729



Users browsing this thread: 2 Guest(s)