## Callmy Name
### Or: Kleene Kleene Kleene
### Or: IM is what IM is
### Or: Kleeneliness is next to Gödeliness
0: Ok this is from Church's 1935 paper "An Unsolvable Problem of Elementary Number Theory." This came out about 7 months before Turing's famous paper that showed the same thing.
1: No way!
![[church-says-kleene-kleene-kleene-00.png]]
0: Turing's paper broke new ground in different ways, but Church got there first.
1: Never heard that before.
0: And if we read this paper, it's pretty clear that "Church" getting there first is like 80-90% Kleene.
1: Kleene's not even a co-author though.
0: Not sure why. Church generally seemed like a generous dude. But just drag your eyes lazily over the pictures below this. This is all from the same paper.
![[church-says-kleene-kleene-kleene-01.png]]
![[church-says-kleene-kleene-kleene-02.png]]
![[church-says-kleene-kleene-kleene-03.png]]
![[church-says-kleene-kleene-kleene-04.png]]
![[church-says-kleene-kleene-kleene-05.png]]
![[church-says-kleene-kleene-kleene-06.png]]
![[church-says-kleene-kleene-kleene-08.png]]
![[church-says-kleene-kleene-kleene-09.png]]
![[church-says-kleene-kleene-kleene-10.png]]
![[church-says-kleene-kleene-kleene-11.png]]
![[church-says-kleene-kleene-kleene-12.png]]
![[church-says-kleene-kleene-kleene-13.png]]
1: Damn that's a lot of Kleene.
0: Church is like "Our integers are different.
![[church-says-kleene-kleene-kleene-14.png]]
0: But this proof is Kleene.
![[church-says-kleene-kleene-kleene-15.png]]
![[church-says-kleene-kleene-kleene-16.png]]
1: Why is he citing him so much?
0: Kleene implemented everything.
1: Definite first programmer vibes.
![[church-says-kleene-kleene-kleene-19.png]]
![[church-says-kleene-kleene-kleene-20.png]]
1: This is an impressive git blame.
0: Seriously. Church is acting more like a faithful `git blame` implementation than a normal human writing an academic paper.
1: The more I learn about these logic folks the more I like them.
0: How so?
1: I dunno. They're nerds. It feels familiar.
![[church-says-kleene-kleene-kleene-21.png]]
1: Church is like "I'm still here guys, I'm gonna say Kleene some more."
![[church-says-kleene-kleene-kleene-22.png]]
1: Good lord man.
![[church-says-kleene-kleene-kleene-23.png]]
1: It keeps going.
![[church-says-kleene-kleene-kleene-24.png]]
1: This is getting ridiculous.
![[church-says-kleene-kleene-kleene-26.png]]
1: I don't even know what he's talking about but this makes me want to read Kleene.
0: We will. That's why I'm showing you this.
1: Why?
0: So you don't get sad when we get to the frighteningly technical book.
1: Uh oh. Is it bad?
0: Nah it's easy. You'll enjoy it.
![[church-says-kleene-kleene-kleene-27.png]]
![[church-says-kleene-kleene-kleene-28.png]]
1: I've got to say, I thought you exaggerating but that was intense.
0: That's from _one_ paper.
1: Damn, Church.
0: Ok but I was unfair to Church earlier. When Kleene said "I have to give the credit to Church, I can't take it myself," he wasn't talking about all the programming, he was talking about Church's thesis.
1: What's Church's thesis.
0: "That's everything."
1: What's everything?
0: Church's thesis is "Hey Kleene, I think maybe we got everything?"
1: _What's everything?_
0: All the computable functions. Or effectively calculable as they called them back then.
1: That's Church's thesis. "We're done."
0: That's it.
1: Why "thesis" and not "theorem"?
0: Because it's saying "I think this informal concept equals this formal concept." Can't exactly prove that in the usual mathematical sense. It's pre-mathematics. The hypothesis is that lambda definability captures what we intuitively mean by "computable." Way more powerful than just a theorem.
1: What on earth made him thing "We got ALL computation"?
0: Kleene.
1: Kleene?
0: I mean Kleene's programming. Church was convinced before Kleene was. Then Kleene tried to disprove Church, failed, and got converted.
> Someone: Was Church's thesis just an offhand remark?
>
> Steve Kleene: Well he spent some months sweating over it. And saying "Don't you think it's so?" And I was a skeptic! When he came out and asserted the thesis I said "He can't be right." So I went home and I thought I would diagonalize myself out. Out of the class of the lambda definable functions and get another effectively calculable function that wasn't lambda definable. Well just in one night I realized you couldn't do that, and from that point on I was a convert.
>
> Steve Kleene: Then Gödel arrived on the scene and---
0: Ooh perfect. [[1 - Gödel Numbers|1 - Gödel Numbers]] time. Follow me.
1: What abou---