# Re: Physical Applications of Tetration

*From*: Gottfried Helms <helms@xxxxxxxxxxxxx>*Date*: Fri, 30 Mar 2007 14:00:20 +0000 (UTC)

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

reference.

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.

HTH -

Gottfried Helms

.

**References**:**Physical Applications of Tetration***From:*Ioannis

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