02/03/2008, 10:41 AM

Hello,

This has a fascinating intutive appeal, especially the appearance of even negative integers-just like trivial 0 of Riemann zeta function.

What are the few next values on other axis (- 3, ..., - 5, ... ) and how accurate they seem to be? Meaning is e.g. -1,85.. really close to asymptotic value or it can be - 1,9..

I am asking because of this sum:

=1/1,85035452902718^8-1/(2*1,8503545290271^7+1/(3*1,8503545290271^6-1/(4*1,8503545290271^5+1/(5*1,8503545290271^4=0,007297583=1/137,0316766

which makes sense to me as long as we include only (operations up to) pentation in its approximation.

So long as pentation is faster than tetration, it means that processes (phase transitions) described by tetration need pentation to run processes inside them, - and so on. Infinitely nested phase transitions and not only phase transitions- nested time scales in general.

Ivars Fabriciuss

This has a fascinating intutive appeal, especially the appearance of even negative integers-just like trivial 0 of Riemann zeta function.

What are the few next values on other axis (- 3, ..., - 5, ... ) and how accurate they seem to be? Meaning is e.g. -1,85.. really close to asymptotic value or it can be - 1,9..

I am asking because of this sum:

=1/1,85035452902718^8-1/(2*1,8503545290271^7+1/(3*1,8503545290271^6-1/(4*1,8503545290271^5+1/(5*1,8503545290271^4=0,007297583=1/137,0316766

which makes sense to me as long as we include only (operations up to) pentation in its approximation.

So long as pentation is faster than tetration, it means that processes (phase transitions) described by tetration need pentation to run processes inside them, - and so on. Infinitely nested phase transitions and not only phase transitions- nested time scales in general.

Ivars Fabriciuss