Hello,

I am still around, but have been looking for physical models of tetration just to have SOME intuitive understanding what it may represent.

Here is how far I have got:

I truly think that Nature has more than logarithms to give us for improving computation speed,since it ITSELF somputes much faster.

If we take a truly continuous medium based system which has e.g infinite number of nested phase transitions and within all these phase transition between them the decay time behaves exponentially, if we take them all together, as a whole, we get infinitely iterated exponential, or infinite tetration which will characterize the system. Well, infinite tetration ( and its inverse, self root) exibits enormous speeds and very peculiar properties, like returning purely imaginary or complex results for iteration of purely real arguments ( as analytical continuation).

As long as Complex math is true, this means existance of such systems is possible (e.g turbulence of an infinitely continuous dissipationless fluid , or , one which dissipates from real value of parameter into imaginary ( e.g. spinor)).

I think turbulence in general would be the right place to use also finite tetration (when number of scales is limited due to existance of quanta/discreteness in the system) and other hyperfast functions, since it involves multiple nested time/space scales.

Ivars

I am still around, but have been looking for physical models of tetration just to have SOME intuitive understanding what it may represent.

Here is how far I have got:

I truly think that Nature has more than logarithms to give us for improving computation speed,since it ITSELF somputes much faster.

If we take a truly continuous medium based system which has e.g infinite number of nested phase transitions and within all these phase transition between them the decay time behaves exponentially, if we take them all together, as a whole, we get infinitely iterated exponential, or infinite tetration which will characterize the system. Well, infinite tetration ( and its inverse, self root) exibits enormous speeds and very peculiar properties, like returning purely imaginary or complex results for iteration of purely real arguments ( as analytical continuation).

As long as Complex math is true, this means existance of such systems is possible (e.g turbulence of an infinitely continuous dissipationless fluid , or , one which dissipates from real value of parameter into imaginary ( e.g. spinor)).

I think turbulence in general would be the right place to use also finite tetration (when number of scales is limited due to existance of quanta/discreteness in the system) and other hyperfast functions, since it involves multiple nested time/space scales.

Ivars