05/06/2021, 06:23 AM
Very damn impressive, Leo.
I'll need sometime to think about this more. I like your examples, though; you're explaining yourself very well. And, again, what I mean is; you as a human are choosing how to perform the black box. Which is to say,
\(
\zeta\{f|h\}
\)
Doesn't have one, single clean formula. I was wondering how you were classifying the choices for \( \zeta\{f|h\} \); and yes, we can perform abel iterations; it's making it reductive to a single algorithm that's the real trouble.
For example, on the real-line. Let's assume we have an analytic super function \( F(z) \) for \( z \) in a neighborhood of the real-line; where here \( f(F(x)) = F(x+1) \). There always exists a perturbation; which is a 1-periodic function \( \theta(z+1) = \theta(z) \) and \( \theta(x) \in \mathbb{R}^+ \) ; where \( F_\theta(x) = F(x + \theta(x)) \). Where now \( F_\theta \) is also a real valued super-function. Furthermore, it's pretty much indistinguishable from any other iteration.
So, as you've introduced it, is a set of functions. The really hard part, is distinguishing between each member of the set.
But again, I'll read over more carefully what you've written tomorrow.
I'll need sometime to think about this more. I like your examples, though; you're explaining yourself very well. And, again, what I mean is; you as a human are choosing how to perform the black box. Which is to say,
\(
\zeta\{f|h\}
\)
Doesn't have one, single clean formula. I was wondering how you were classifying the choices for \( \zeta\{f|h\} \); and yes, we can perform abel iterations; it's making it reductive to a single algorithm that's the real trouble.
For example, on the real-line. Let's assume we have an analytic super function \( F(z) \) for \( z \) in a neighborhood of the real-line; where here \( f(F(x)) = F(x+1) \). There always exists a perturbation; which is a 1-periodic function \( \theta(z+1) = \theta(z) \) and \( \theta(x) \in \mathbb{R}^+ \) ; where \( F_\theta(x) = F(x + \theta(x)) \). Where now \( F_\theta \) is also a real valued super-function. Furthermore, it's pretty much indistinguishable from any other iteration.
So, as you've introduced it, is a set of functions. The really hard part, is distinguishing between each member of the set.
But again, I'll read over more carefully what you've written tomorrow.