/sci/ - Science & Math

He doesn't even claim to have quantized his field theory

>>12163730
I'd think

>>12163730
[math] f^{\sf MAXSTEPS}({\sf startPose}) [/math]

where
[math] f^k({\sf pos}) := {\sf pos} + {\sf dir}\cdot {\sf sdfSphere}\left(f^{k-1}({\sf pos}) \right) [/math]
and
[math] f^0({\sf pos}) := {\sf pos} [/math]

but do a quick implementation like that to confirm

>>12124605
What if ZF proves that for some particular Turing machine [math]t[/math] there exists ("exists") an [math]n\in {\mathbb N}[/math], such that [math]t[/math] halts at execution step [math]n[/math], while [math]PA[/math] can't decide it and it actually not ever happening in reality (i.e. in reality the Turing machine can never actually halt, i.e. what if ZF is self-consistent but wrong)?

>>11810425
>we can check every algorithm which produces the result and that is less steps than the trivial one, there is a finite amount of them, thus a minimum exists.
I'm not certain if I interpret the sentence correct, but to rule one reading out let me point out that every computable function [math] \phi [/math] with a program implementation [math] P [/math] , there's infinitely many definite programs [math] P', P'',\dots [/math] that do the job. (E.g., if [math] P(n) [/math] is the result that [math] P [/math] gives, then [math] P'(n) [/math] defined as factoring [math] 14 [/math] and then computing [math] P [/math] also implements [math] \phi [/math] . And factoring [math] 14 [/math] twice and trice gives new programs that also correspond to the same computable function.)

>>11810418
>Let [math]Υ[/math] be a finite set such that [math]Υ\subset {\mathbb N} [/math]. We can write an algorithm F(n) that either accepts n if n∈Υ or rejects otherwise.
Tiresome remark, but possible worth it: This language, which is class classical math language in a computability theory context, is a bit sloppy.

Take at face value, here the counter example:
Let [math] Y = \{4,6,9\} [/math] if Goldbach's conjecture is true and [math] Y = \{0, 2, 5, 6, 11\} [/math] if Goldbach's conjecture is false.
Questions such as [math] 2\in Y [/math] are extremely hard to answer and could in fact be undecidable.
In any case, making the assumption that [math] Y = \{4,6,9\} [/math] or [math] Y = \{0, 2, 5, 6, 11\} [/math], we have that [math]Υ\subset {\mathbb N} [/math], but there may be no slow algorithm that decides whether [math] 2 [/math] should be accepted.

But okay, say your friend writes down [math] \{0, 2, 5, 6, 11\} [/math] on a paper and asks you for fastest program.
I think you want to look at:
https://en.wikipedia.org/wiki/Kolmogorov_complexity

Possibly relevant also:
https://en.wikipedia.org/wiki/Rice%27s_theorem

Do you have some online PDF's, preferably some with a lot of math/theory?

>>11625700
>Papa flammy did his master's thesis on the fractional derivatives of ζ
Ah, I remember heaving heard that.
Just looked it up.
https://www.researchgate.net/publication/339627752_The_Fractional_Derivatives_of_the_Riemann_Zeta_and_Dirichlet_Eta_Function

Impressions:
70 pages. Fractional derivative is only introduced on page 42. I see he doesn't really choose a formally explicit theorem-proof declaration style. I notice he switching between "I" and "we" and "paper" and "thesis".
p. shows it's about
https://en.wikipedia.org/wiki/Gr%C3%BCnwald%E2%80%93Letnikov_derivative
(only 1 edit in 2019, sad)
Seems to work out ideas presented in a paper one can also find online.
He bashes the author, lel
Looks like the [math] \alpha [/math]'th derivative of the zeta function has a shifted critical strip and a functional equation/reflection formula (that is quite complex, in fact it's a tripple sum).
It's mostly looking at the series you get if you apply that fractional derivative operation to Hurwitz-type functions.

tl;dr It has not too much about the theory of fractional derivatives in general, but aims at parametrizing zeta-function results with a parameter [math] \alpha [/math] in the way implies by that operation.