## Church's beginning ### Or: Let there be calls ### Or: Numbers are calls ### Or: Booleans are calls ### Or: No names allowed ### Or: Names are tricky --- 0: Once upon a time, there was a guy named Sam. 1: Ooh I love story time. 0: Sam had an unusual family tree. As a child, during that earliest stage of life when we're looking around the world for the first time and learning what things are called, Sam learned the following: 1. Your Name: Sam 2. Your Father: Alonzo Church 3. Your Brother: Alonzo Church 4. Your Grandfather: Alonzo Church 1: That's a lot of Alonzo Church. 0: For real. And Sam wasn't Alonzo Church. He was the only one who wasn't. 1: Must be rough to get excluded from being Alonzo Church when everyone you know gets to be that. 0: Exactly. So when it came time for Sam to have a son, he pulled a fast one on his brother -- the first born -- and added an item of his own to the family's family tree. So now, thanks to Sam, the family tree looked like this. 1. Your Name: Sam 2. Your Father: Alonzo Church 3. Your Brother: Alonzo Church 4. Your Grandfather: Alonzo Church 5. Your Son: Alonzo Church 1: Damn Sam. That's cold. 0: "Take that, Alonzo Church," I imagine him saying to his brother Alonzo Church, when he named his son Alonzo Church. 1: Did he actually say that? 0: No idea. But eventually Sam's son would have a son of his own. And he called--- 1: I wonder what he's gonna call it. 0: Drumroll. 1. Your Name: Sam 2. Your Father: Alonzo Church 3. Your Brother: Alonzo Church 4. Your Grandfather: Alonzo Church 5. Your Son: Alonzo Church 6. Your Grandson: Alonzo Church 1: Why are we talking about this? 0: Because trinities are known to be full of mysteries. And Alonzo Church is the first member of our trinity. 1: All five Alonzo Churches are members of the trinity? 0: No. Just one. 1: Which one? 0: Sam's son. The one who wasn't supposed to be Alonzo Church. 1: I'm glad it was that one. He seemed like the underdog. 0: Alonzo Church would go on to do a lot of things, but he's most well known for one thing. 1: What one thing? 0: For inventing the first programming language. 1: Woah seriously? 0: Before computers. Before the field even had an agreed upon definition of "computation." 1: What did it run on? 0: Paper. 1: Woah. 0: It was a strange programming language with only one type. 1: Only one type? 0: Only one type. In terms of built-in types, the language has no numbers. 1: No numbers?! 0: No booleans. 1: No booleans?!?! 0: No `if` or `for` or `while`. 1: This language sounds insane. 0: There's only one built-in type. 1: Is it Alonzo Church? 0: Nope. But Alonzo Church had a lot of experience with systems where everything is one type. 1: Like his family? 0: Yep. So when he grew up and went into the foundations of mathematics, and even more deep into the foundations of logic itself, he came up with a system where everything is functions. 1: Numbers are functions?! 0: Numbers are functions. 1: Booleans are functions?!?! 0: Booleans are functions. 1: Such an Alonzo Church thing to do. 0: Weird idea right? 1: Can we see some more details? 0: Sure, let's go take a tour. ## Alonzo Church ### Or: Call me anonymous ### Or: Church of λambda ### Or: On the λamb ### Or: Son of Sam --- > _I never had any mathematical conversations with anybody,_ > _because there was nobody else in my field._ > -Alonzo Church (Son of Sam) --- ![[church-01.png]] 1: Woah you weren't just making that up? 0: Of course not. I would never lie to you. ![[church-03.png|400]] 1: Hey there's another one! 0: Told ya. They're all over the place. ![[church-02.png]] 1: Damn look at that handsome guy. 0: For real. Could have gone into Hollywood. 1: Why didn't he? 0: Well he's a foundational person. So naturally, he went into foundations. 1: What did he do? 0: Well he started with standard foundations. 1: I don't think I even know what "standard foundations" is. 0: Ok, to appreciate the rest of where we're heading, we should probably do at least a drive by. 1: A drive by of what? 0: The other Church's Thesis. 1: The other Church's Thesis? 0: Yep, follow me. goto: [[2 - Church's Thesis (Not that one)]]