Re: Physical Applications of Tetration

Am 29.03.2007 21:30 schrieb Ioannis:
Greetings everyone,

have any of you come across any references which link tetration to any
physical processes?

I have checked out Knoebel's article "Exponentials Reiterated", but the
applications he cites in biology are sort of lukewarm and are only indirectly
related to tetration.

I tried to look into nuclear fission but it looks as though such processes are
mainly growing as simple exponentials. Tetration seems to be too "fast" (or
too powerful if you wish) to describe anything physical in this universe.

I was thinking that perhaps this was a good reason why the hierarchy of
operators {+,*,^,^^,...} has a discrepancy at "^^". Maybe tetration is too
powerful a process to describe anything physical.

If any of you have come across any actual physical applications, (such as
something "growing" tetrationally, for example), I would appreciate the

Many thanks,

I found a text called "WexZal" , which deals with the x^^2 term.
Don't know about the relevance regarding your question. It was some
years ago, so I don't know, whether this document was continued,
or whether it is still online at all.

cite from Preface of WexZal:

This book is about the solution to and properties of the Coupled
Exponent equation (y=x^x). The solution to this equation is called the
"Coupled Root function". This work details our research efforts since
1975. Included are computers/calculators used, evolution of ideas,
history of our efforts and still outstanding problems. We have organized
the work into different topics such as "Applications", "Solving logarithmic
Equations", "Integration", etc. to make it easier for the reader to find
a topic. This is a work where the appendices and tables are (in some ways)
more important then the text itself. The text is to explain the theory;
the tables have the actual items of interest.
Our goal in writing this book is to show the (in our opinion) interesting
things we found and to encourage research into this topic as we feel this
is one area that has been mostly overlooked. We feel that the Coupled
Root function has many hidden properties that have the potential to be
useful. Two such applications have been found so far: Ballistics (internal
& external) and automobile acceleration. There is no doubt other areas where
the Coupled Root could be used.


Gottfried Helms